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finance 4e

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finance 4e

Marcia Millon CornettBentley University

Troy A. Adair Jr.Harvard Business School

John NofsingerUniversity of Alaska Anchorage

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M: FINANCE, FOURTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2019 by McGraw-Hill Education. All rights reserved. Printed inthe United States of America. Previous editions © 2016, 2014 and 2012. No part of this publication may be reproduced or distributed in any form or by anymeans, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in anynetwork or other electronic storage or transmission, or broadcast for distance learning.

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a note from the authors“There is a lot to cover in this course so I focus on the core concepts, theories, and problems.”

“I like to teach the course by using examples from their own individual lives.”

“My students come into this course with varying levels of math skills.”

How many of these quotes might you have said while teaching the undergraduate corporate finance course? Ourmany years of teaching certainly reflect such sentiments, and as we prepared to write this book, we conducted manymarket research studies that confirm just how much these statements—or ones similar—are common across thecountry. This critical course covers so many crucial topics that instructors need to focus on core ideas to ensure thatstudents are getting the preparation they need for future classes—and for their lives beyond college.

We did not set out to write this book to change the way finance is taught, but rather to parallel and support theway that instructors from across the country currently teach finance. Well over 600 instructors teaching this coursehave shared their class experiences and ideas via a variety of research methods that we used to develop theframework for this text. We are excited to have authored a book that we think you will find fits your classroom styleperfectly.

KEY THEMESThis book’s framework emphasizes three themes. See the next section in this preface for a description of features inour book that support these themes.

Finance is about connecting core concepts. We all struggle with fitting so many topics into this course, so thistext strives to make it easier for you by getting back to the core concepts, key research, and current topics. Werealize that today’s students expect to learn more in class from lectures than in closely studying their textbooks, sowe’ve created brief chapters that clearly lead students to crucial material that they need to review if they are tounderstand how to approach core financial concepts. The text is also organized around learning goals, making iteasier for you to prep your course and for students to study the right topics.Finance can be taught using a personal perspective. Most long-term finance instructors have often heardstudents ask “How is this course relevant to me?” on the first day of class. We no longer teach classes dedicatedsolely to finance majors; many of us now must teach the first finance course to a mix of business majors. We needto give finance majors the rigor they need while not overwhelming class members from other majors. Foryears, instructors have used individual examples to help teach these concepts, but this is the first text tointegrate this personal way of teaching into the chapters.Finance focuses on solving problems and decision making. This isn’t to say that concepts and theories aren’timportant, but students will typically need to solve some kind of mathematical problem—or at least understand theimpact of different numerical scenarios—to make the right decision on common finance issues. If you, as aninstructor, either assign problems for homework or create exams made up almost entirely of mathematical material,you understand the need for good problems (and plenty of them). You also understand from experience the numberof office hours you spend tutoring students and grading homework. Students have different learning styles, and thistext aims to address that challenge to allow you more time in class to get through the critical topics.

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changes in the fourth editionBased on feedback from users and reviewers, we undertook an ambitious revision in order to make the book followyour teaching strategy even more closely. Below are the changes we made for this fourth edition, broken out bychapter.

OVERALLSimplified figures where appropriate and added captions to emphasize the main “takeaways”Updated data, company names, and scenarios to reflect latest available data and real-world changesCross-referenced numbered examples with similar end-of-chapter problems and self-test problems so students caneasily model their homeworkUpdated the numbers in the end-of-chapter problems to provide variety and limit the transfer of answers fromprevious classes

chapter oneINTRODUCTION TO FINANCIAL MANAGEMENT

Updated the Personal Application with information on firms that have filed for bankruptcy more recentlyChanged Learning Goal 1-9 to address the ramifications of China’s slowdown and the drop in the price of oilRevised the Finance at Work—Markets box to discuss quantitative easing in the United States and around theworldRevised the Finance at Work—Corporate box to cover the proposed merger of AB InBev and SABMillerUpdated the data in Example 1-2 on executive compensationReplaced Section 1.7 on the financial crisis with a new Section 1.7: Big Picture Environment, including discussionsof the ramifications of plummeting oil prices and China’s economic slowdown

chapter twoREVIEWING FINANCIAL STATEMENTS

Added a discussion of difference between EBIT and operating incomeIncluded extended definitions of net sales, cost of goods sold, and operating expensesAdded a discussion of the interpretation of a cash-based income statementAdded a new Finance at Work box

chapter threeANALYZING FINANCIAL STATEMENTS

Added more discussion of debt ratios

chapter fourTIME VALUE OF MONEY 1: ANALYZING SINGLE CASH FLOWS

Updated the data in Figure 4.5 on gold pricesAdded equation functions to Table 4.2 and Table 4.4Revised the data for the end-of-chapter Excel problem

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Added a new end-of-chapter Excel problem

chapter fiveTIME VALUE OF MONEY 2: ANALYZING ANNUITY CASH FLOWS

Revised the chapter introduction to discuss BoeingAdded equation functions to Tables 5.1, 5.2, 5.5, and 5.6Updated the present value of multiple annuities example to discuss the new David Price contract with the BostonRed SoxChanged the Finance at Work—Behavioral box to address the record Powerball jackpot of $1.5 billion on January12, 2016Added a new end-of-chapter Excel problem

chapter sixUNDERSTANDING FINANCIAL MARKETS AND INSTITUTIONS

Updated all figures, tables, and values in the body of the chapterAdded a section on the loanable funds theory/determination of equilibrium interest ratesAdded new end-of-chapter problemsDecreased the coverage of the financial crisis (detailed information is available in the Web Appendix for Chapter 6available in Connect or at mhhe.com/Cornett4e)

chapter sevenVALUING BONDS

Updated the Personal Application with new dataUpdated Figures 7.1–7.5 on bond issuance, interest rate path, yield to maturities, new bond quotes, and a summaryof the bond marketAdded equation functions to Tables 7.3 and 7.5Revised the data for the end-of-chapter Excel problemAdded a new end-of-chapter Excel problem

chapter eightVALUING STOCKS

Updated all table and figure values in the body of the chapterUpdated the coverage of the stock market exchange in Section 8.2 to discuss the changes that have occurred in theNYSE and elsewhereRevised Example 8-1 to include new Coca-Cola dataUpdated Example 8-4 with new P/E data for CaterpillarAdded a new end-of-chapter Excel problem

chapter nineCHARACTERIZING RISK AND RETURN

Revised the example that runs throughout the chapter to discuss StaplesUpdated all table and figure values in the body of the chapterAdded equation functions to Table 9.3 and Table 9.5

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Updated Example 9-2 to include new Mattel dataUpdated the data in the Finance at Work—Markets boxRevised the data for the end-of-chapter Excel problemAdded a new end-of-chapter Excel problem

chapter tenESTIMATING RISK AND RETURN

Updated values and data in Tables 10.1–10.4Added a new end-of-chapter Excel problem

chapter elevenCALCULATING THE COST OF CAPITAL

Clarified and expanded the discussion of use of market values versus book values in the calculation of WACCExpanded the discussion of when to use CAPM versus the constant-growth model when estimating the cost ofequityExpanded the discussion of computation of marginal tax rate for WACCEnhanced the discussion of use of firm versus project WACCsEnhanced the discussion of appropriateness of divisional WACCs

chapter twelveESTIMATING CASH FLOWS ON CAPITAL BUDGETING PROJECTS

Clarified the definition of salvage valueExpanded the discussion of substitutionary and complementary effectsEnhanced the discussion of income tax shield from a project having taxable lossesEnhanced the discussion of NWC changes “leading” changes in salesExpanded the discussion of the half-year convention in depreciation

chapter thirteenWEIGHING NET PRESENT VALUE AND OTHER CAPITAL BUDGETING CRITERIA

Clarified the discussion of the goal of capital budgeting decision rules and the differing environments ofinvestment and capital budgeting decisionsExpanded the discussion of why using rate-based and time-based decision statistics to choose across projects canbe misleading with regards to NPV

chapter fourteenWORKING CAPITAL MANAGEMENT AND POLICIES

Expanded the discussion of the rationale for NWC and the tradeoffs inherent in having too little or too muchRefined discussion of cash flows vs. the cash account

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brief contents

part oneINTRODUCTION 3chapter 1 Introduction to Financial Management 3

part twoFINANCIAL STATEMENTS 27chapter 2 Reviewing Financial Statements 27

chapter 3 Analyzing Financial Statements 59

part threeVALUING OF FUTURE CASH FLOWS 89chapter 4 Time Value of Money 1: Analyzing Single Cash Flows 89

chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows 115

part fourVALUING OF BONDS AND STOCKS 147

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chapter 6 Understanding Financial Markets and Institutions 147

Appendix 6A: The Financial Crisis: The Failure of Financial Institution Specialness (located atwww.mhhe.com/Cornett4e) 186

chapter 7 Valuing Bonds 199

chapter 8 Valuing Stocks 233

part fiveRISK AND RETURN 261chapter 9 Characterizing Risk and Return 261

chapter 10 Estimating Risk and Return 289

part sixCAPITAL BUDGETING 315chapter 11 Calculating the Cost of Capital 315

chapter 12 Estimating Cash Flows on Capital Budgeting Projects 339

Appendix 12A: MACRS Depreciation Tables 362

chapter 13 Weighing Net Present Value and Other Capital Budgeting Criteria 369

part sevenWORKING CAPITAL MANAGEMENT AND FINANCIAL PLANNING 399chapter 14 Working Capital Management and Policies 399

Appendix 14A: The Cash Budget 422

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contentsCHAPTER 1 INTRODUCTION TO FINANCIAL MANAGEMENT 31.1 • FINANCE IN BUSINESS AND IN LIFE 4

What Is Finance? 5Subareas of Finance 8

Application and Theory for Financial Decisions 9Finance versus Accounting 10

1.2 • THE FINANCIAL FUNCTION 11The Financial Manager 11

Finance in Other Business Functions 11Finance in Your Personal Life 12

1.3 • BUSINESS ORGANIZATION 12Sole Proprietorships 12

Partnerships 13Corporations 14

Hybrid Organizations 151.4 • FIRM GOALS 151.5 • AGENCY THEORY 17

Agency Problem 17

Corporate Governance 18The Role of Ethics 19

1.6 • FINANCIAL MARKETS, INTERMEDIARIES, AND THE FIRM 211.7 • BIG PICTURE ENVIRONMENT 21

Oil Prices Plummet 21

China Slows Down 22

CHAPTER 2 REVIEWING FINANCIAL STATEMENTS 272.1 • BALANCE SHEET 28

Assets 29

Liabilities and Stockholders’ Equity 29

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Managing the Balance Sheet 30

2.2 • INCOME STATEMENT 33Debt versus Equity Financing 35

Corporate Income Taxes 362.3 • STATEMENT OF CASH FLOWS 38

GAAP Accounting Principles 39Noncash Income Statement Entries 39

Sources and Uses of Cash 402.4 • FREE CASH FLOW 422.5 • STATEMENT OF RETAINED EARNINGS 442.6 • CAUTIONS IN INTERPRETING FINANCIAL STATEMENTS 44

CHAPTER 3 ANALYZING FINANCIAL STATEMENTS 593.1 • LIQUIDITY RATIOS 603.2 • ASSET MANAGEMENT RATIOS 62

Inventory Management 62

Accounts Receivable Management 63Accounts Payable Management 63

Fixed Asset and Working Capital Management 64Total Asset Management 64

3.3 • DEBT MANAGEMENT RATIOS 66Debt versus Equity Financing 66

Coverage Ratios 673.4 • PROFITABILITY RATIOS 683.5 • MARKET VALUE RATIOS 703.6 • DUPONT ANALYSIS 71

3.7 • OTHER RATIOS 75Spreading the Financial Statements 75Internal and Sustainable Growth Rates 76

3.8 • TIME SERIES AND CROSS-SECTIONAL ANALYSES 773.9 • CAUTIONS IN USING RATIOS TO EVALUATE FIRM PERFORMANCE 78

CHAPTER 4 TIME VALUE OF MONEY 1: ANALYZING SINGLE CASH FLOWS 894.1 • ORGANIZING CASH FLOWS 904.2 • FUTURE VALUE 91

Single-Period Future Value 91

Compounding and Future Value 924.3 • PRESENT VALUE 98

Discounting 984.4 • USING PRESENT VALUE AND FUTURE VALUE 101

Moving Cash Flows 1014.5 • COMPUTING INTEREST RATES 103

Return Asymmetries 1054.6 • SOLVING FOR TIME 105

CHAPTER 5 TIME VALUE OF MONEY 2: ANALYZING ANNUITY CASH FLOWS 1155.1 • FUTURE VALUE OF MULTIPLE CASH FLOWS 116

Finding the Future Value of Several Cash Flows 116Future Value of Level Cash Flows 118

Future Value of Multiple Annuities 1195.2 • PRESENT VALUE OF MULTIPLE CASH FLOWS 122

Finding the Present Value of Several Cash Flows 122

Present Value of Level Cash Flows 123Present Value of Multiple Annuities 124

Perpetuity—A Special Annuity 1275.3 • ORDINARY ANNUITIES VERSUS ANNUITIES DUE 1275.4 • COMPOUNDING FREQUENCY 129

Effect of Compounding Frequency 129

5.5 • ANNUITY LOANS 133What Is the Interest Rate? 133

Finding Payments on an Amortized Loan 134

CHAPTER 6 UNDERSTANDING FINANCIAL MARKETS AND INSTITUTIONS 1476.1 • FINANCIAL MARKETS 148

Primary Markets versus Secondary Markets 148

Money Markets versus Capital Markets 151Other Markets 153

6.2 • FINANCIAL INSTITUTIONS 155Unique Economic Functions Performed by Financial Institutions 156

6.3 • INTEREST RATES AND THE LOANABLE FUNDS THEORY 159Supply of Loanable Funds 161

Demand for Loanable Funds 162Equilibrium Interest Rate 163

Factors That Cause the Supply and Demand Curves for Loanable Funds to Shift 163Movement of Interest Rates over Time 167

6.4 • FACTORS THAT INFLUENCE INTEREST RATES FOR INDIVIDUAL SECURITIES 167Inflation 168

Real Risk-Free Rate 168Default or Credit Risk 169

Liquidity Risk 170Special Provisions or Covenants 171

Term to Maturity 1716.5 • THEORIES EXPLAINING THE SHAPE OF THE TERM STRUCTURE OF INTEREST RATES 174

Unbiased Expectations Theory 174Liquidity Premium Theory 176

Market Segmentation Theory 1776.6 • FORECASTING INTEREST RATES 179Appendix 6A The financial Crisis: The Failure of Financial Institution Specialness 186

CHAPTER 7 VALUING BONDS 1997.1 • BOND MARKET OVERVIEW 200

Bond Characteristics 200

Bond Issuers 202Other Bonds and Bond-Based Securities 204

Reading Bond Quotes 2077.2 • BOND VALUATION 209

Present Value of Bond Cash Flows 209Bond Prices and Interest Rate Risk 211

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7.3 • BOND YIELDS 213Current Yield 213Yield to Maturity 214

Yield to Call 215Municipal Bonds and Yield 217

Summarizing Yields 2187.4 • CREDIT RISK 219

Bond Ratings 219Credit Risk and Yield 221

7.5 • BOND MARKETS 222Following the Bond Market 223

CHAPTER 8 VALUING STOCKS 2338.1 • COMMON STOCK 2348.2 • STOCK MARKETS 235

Tracking the Stock Market 238

Trading Stocks 2408.3 • BASIC STOCK VALUATION 241

Cash Flows 241Dividend Discount Models 243

Preferred Stock 245Expected Return 246

8.4 • ADDITIONAL VALUATION METHODS 248Variable-Growth Techniques 248

The P/E Model 251Estimating Future Stock Prices 254

CHAPTER 9 CHARACTERIZING RISK AND RETURN 2619.1 • HISTORICAL RETURNS 262

Computing Returns 262Performance of Asset Classes 265

9.2 • HISTORICAL RISKS 266Computing Volatility 266

Risk of Asset Classes 269

Risk versus Return 270

9.3 • FORMING PORTFOLIOS 271Diversifying to Reduce Risk 271

Modern Portfolio Theory 274

CHAPTER 10 ESTIMATING RISK AND RETURN 28910.1 • EXPECTED RETURNS 290

Expected Return and Risk 290

Risk Premiums 29210.2 • MARKET RISK 294

The Market Portfolio 294Beta, a Measure of Market Risk 295

The Security Market Line 296Finding Beta 298

Concerns about Beta 30010.3 • CAPITAL MARKET EFFICIENCY 301

Efficient Market Hypothesis 302Behavioral Finance 303

10.4 • IMPLICATIONS FOR FINANCIAL MANAGERS 304Using the Constant-Growth Model for Required Return 304

CHAPTER 11 CALCULATING THE COST OF CAPITAL 31511.1 • THE WACC FORMULA 316

Calculating the Component Cost of Equity 317Calculating the Component Cost of Preferred Stock 318

Calculating the Component Cost of Debt 318Choosing Tax Rates 319

Calculating the Weights 32111.2 • FIRM WACC VERSUS PROJECT WACC 322

Project Cost Numbers to Take from the Firm 323Project Cost Numbers to Find Elsewhere: The Pure-Play Approach 324

11.3 • DIVISIONAL WACC 326Pros and Cons of a Divisional WACC 326

Subjective versus Objective Approaches 32811.4 • FLOTATION COSTS 330

Adjusting the WACC 331

CHAPTER 12 ESTIMATING CASH FLOWS ON CAPITAL BUDGETING PROJECTS339

12.1 • SAMPLE PROJECT DESCRIPTION 34012.2 • GUIDING PRINCIPLES FOR CASH FLOW ESTIMATION 341

Opportunity Costs 342Sunk Costs 342

Substitutionary and Complementary Effects 342Stock Dividends and Bond Interest 343

12.3 • TOTAL PROJECT CASH FLOW 343Calculating Depreciation 343

Calculating Operating Cash Flow 344Calculating Changes in Gross Fixed Assets 345

Calculating Changes in Net Working Capital 346Bringing It All Together 348

12.4 • ACCELERATED DEPRECIATION AND THE HALF-YEAR CONVENTION 349MACRS Depreciation Calculation 349

Section 179 Deductions 350

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Impact of Accelerated Depreciation 351

12.5 • “SPECIAL” CASES AREN’T REALLY THAT SPECIAL 35212.6 • CHOOSING BETWEEN ALTERNATIVE ASSETS WITH DIFFERING LIVES: EAC 35412.7 • FLOTATION COSTS REVISITED 356APPENDIX 12A: MACRS DEPRECIATION TABLES 362

CHAPTER 13 WEIGHING NET PRESENT VALUE AND OTHER CAPITALBUDGETING CRITERIA 369

13.1 • THE SET OF CAPITAL BUDGETING TECHNIQUES 37113.2 • THE CHOICE OF DECISION STATISTIC FORMAT 37213.3 • PROCESSING CAPITAL BUDGETING DECISIONS 37313.4 • PAYBACK AND DISCOUNTED PAYBACK 374

Payback Statistic 374

Payback Benchmark 375Discounted Payback Statistic 375

Discounted Payback Benchmark 376Payback and Discounted Payback Strengths and Weaknesses 378

13.5 • NET PRESENT VALUE 378NPV Statistic 378

NPV Benchmark 378NPV Strengths and Weaknesses 380

13.6 • INTERNAL RATE OF RETURN AND MODIFIED INTERNAL RATE OF RETURN 381Internal Rate of Return Statistic 382

Internal Rate of Return Benchmark 382Problems with Internal Rate of Return 383

IRR and NPV Profiles with Non-Normal Cash Flows 384Differing Reinvestment Rate Assumptions of NPV and IRR 385

Modified Internal Rate of Return Statistic 385IRRs, MIRRs, and NPV Profiles with Mutually Exclusive Projects 385

MIRR Strengths and Weaknesses 38913.7 • PROFITABILITY INDEX 390

Profitability Index Statistic 390Profitability Index Benchmark 390

CHAPTER 14 WORKING CAPITAL MANAGEMENT AND POLICIES 39914.1 • REVISITING THE BALANCE-SHEET MODEL OF THE FIRM 40014.2 • TRACING CASH AND NET WORKING CAPITAL 401

The Operating Cycle 402

The Cash Cycle 40214.3 • SOME ASPECTS OF SHORT-TERM FINANCIAL POLICY 403

The Size of the Current Assets Investment 403Alternative Financing Policies for Current Assets 404

14.4 • THE SHORT-TERM FINANCIAL PLAN 407Unsecured Loans 407

Secured Loans 408Other Sources 408

14.5 • CASH MANAGEMENT 409Reasons for Holding Cash 409

Determining the Target Cash Balance: The Baumol Model 409Determining the Target Cash Balance: The Miller-Orr Model 410

Other Factors Influencing the Target Cash Balance 41114.6 • FLOAT CONTROL: MANAGING THE COLLECTION AND DISBURSEMENT OF CASH 413

Accelerating Collections 414

Delaying Disbursements 414Ethical and Legal Questions 415

14.7 • INVESTING IDLE CASH 415Why Firms Have Surplus Cash 416

What to Do with Surplus Cash 41614.8 • CREDIT MANAGEMENT 416

Credit Policy: Terms of the Sale 416Credit Analysis 416

Collection Policy 417APPENDIX 14A THE CASH BUDGET 422VIEWPOINTS REVISITED 426CHAPTER EQUATIONS 434INDEX 439

D

chapter oneintroduction tofinancial management

© John Lamb/Getty Images/Photodisc

o you know: What finance entails? How financial management functions within the business world?Why you might benefit from studying financial principles? This chapter is the ideal place to getanswers to those questions. Finance is the study of applying specific value to things we own, services

we use, and decisions we make. Examples are as varied as shares of stock in a company, payments on ahome mortgage, the purchase of an entire firm, and the personal decision to retire early. In this text, wefocus primarily on one area of finance, financial management, which concentrates on valuing things from theperspective of a company, or firm.

finance The study of applying specific value to things we own, services we use, and decisions we make.

financial management The process for and the analysis of making financial decisions in the business context.

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LEARNING GOALS

LG1-1 Define the major areas of finance as they apply to corporate financial management.LG1-2 Show how finance is at the heart of sound business decisions.LG1-3 Learn the financial principles that govern your personal decisions.LG1-4 Examine the three most common forms of business organization in the United States today.LG1-5 Distinguish among appropriate and inappropriate goals for financial managers.LG1-6 Identify a firm’s primary agency relationship and discuss the possible conflicts that may arise.LG1-7 Discuss how ethical decision making is part of the study of financial management.LG1-8 Describe the complex, necessary relationships among firms, financial institutions, and financial markets.LG1-9 Explain the business ramifications of the decline in the price of oil and China’s economic slowdown.

viewpointsbusiness APPLICATIONCaleb has worked very hard to create and expand his juice stand at the mall. He has finally perfected his products and feels that he isoffering the right combination of juice and food. As a result, the stand is making a nice profit. Caleb would like to open more stands atmalls all over his state and eventually all over the country.

Caleb knows he needs more money to expand. He needs money to buy more equipment, buy more inventory, and hire and trainmore people. How can Caleb get the capital he needs to expand? (See the solution at the end of the book.)

Financial management is critically important to the success of any business organization, andthroughout the text we concentrate on describing the key financial concepts in corporate finance. As abonus, you will find that many tools and techniques for handling the financial management of a firm alsoapply to broader types of financial problems, such as personal finance decisions.

In finance, cash flow is the term that describes the process of paying and receiving money. It makessense to start our discussion of finance with an illustration of various financial cash flows. We use simplegraphics to help explain the nature of finance and to demonstrate the different subareas of the field offinance.

After we have an overall picture of finance, we will discuss three important variables in the businessenvironment that can and do have significant impact on the firm’s financial decisions. These are (1) theorganizational form of the business, (2) the agency relationship between the managers and owners of afirm, and (3) ethical considerations as finance is applied in the real world.

1.1 • FINANCE IN BUSINESS AND IN LIFE LG1-1If your career leads you to making financial decisions, then this book will be indispensable. If not, it is likely thatyour activities in a business will involve interacting with the finance functions. After all, the important investmentsof a firm involve capital and, therefore, finance. Expanding marketing channels, developing new products, andupgrading a factory all cost money. A firm spends its capital on these projects to foster growth. Understanding howfinance professionals evaluate those projects will help you be successful in your business focus. In addition,everyone will benefit in their personal life from learning finance and understanding financial decisions.

And what exactly makes up this engine of financial decision making? Successful application of financial theorieshelps money flow from individuals who want to improve their financial future to businesses that want to expand thescale or scope of their operations. These exchanges lead to a growing economy and more employment opportunitiesfor people at all income levels. So, two important things result from this simple exchange: The economy will bemore productive, and individuals’ wealth will grow into the future.

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personal APPLICATIONDagmar is becoming interested in investing some of her money. However, she has heard about several corporations in which theinvestors lost all of their money. Recently, Dagmar has heard that RadioShack (2015), Wet Seal (2015), and THQ (2013) have all filedfor bankruptcy. These firms’ stockholders lost their entire investments in these firms.

Many of the stockholders who lost money were employees of these companies who had invested some of their retirement money inthe company stock. Dagmar wonders what guarantee she has as an investor against losing her money. (See the solution at the endof the book.)

What is the best way for Dagmar to ensure a happy retirement?

In this first section, we develop a comprehensive description of finance and its subareas, and we look at the specificdecisions that professionals in each subarea must make. As you will see, all areas of finance share a common set ofideas and application tools.

What Is Finance?To get the clearest possible picture of how finance works, let’s begin by grouping all of an economy’s participantsalong two dimensions. The first dimension is made up of those who may have “extra” money (i.e., money above andbeyond their current spending needs) for investment. The second dimension is made up of those who have an abilityto develop viable business ideas, a sense of business creativity. Both money and ideas are fuel for the financialengine. In our simple model, these two dimensions result in four groups representing economic roles in society, asshown in Figure 1.1. Of course, people can move from one group to another over time.

Type 1 people in our model do not lend significant sums of money (capital) or spend much money in a businesscontext, so they play no direct role in financial markets, the mechanisms by which capital is exchanged. Althoughthese people probably play indirect roles by providing labor to economic enterprises or by consuming their products,for simplicity we focus on those who play direct roles. Therefore, type 1 participants will be asked to step aside.

financial markets The arenas through which funds flow.

Type 4 people use financial tools to evaluate their own business concepts and then choose the ideas with the mostpotential. From there, they create their own enterprises to implement their best ideas efficiently and effectively.Type 4 individuals, however, are self-funded and do not need financial markets. The financial tools they use and thetypes of decisions they make are narrowly focused or specific to their own purposes. For our discussion,then, type 4 individuals also are asked to move to the sidelines.

FIGURE 1-1 Participants in Our Hypothetical Economy

No Extra Money Extra MoneyNo Economically Viable Business Ideas Type 1: No money and no ideas Type 2: Money but no ideasEconomically Viable Business Ideas Type 3: No money but ideas Type 4: Both money and ideas

Four groups form according to the availability of money and ideas.

Now for our financial role players, the type 2 and type 3 people. Financial markets and financial institutions allowthese people to participate in a mutually advantageous exchange. Type 2 people temporarily lend their money totype 3 people, who put that money to use with their good business ideas.

In most developed economies, type 2 participants are usually individual investors. You will likely be an individualinvestor for most of your life. Each of us separately may not have a lot of extra money at any one time, but byaggregating our available funds, we can provide sizable amounts for investment.

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investors Those who buy securities or other assets in hopes of earning a return and getting more money back in the future.

Type 3 participants, the idea generators, may be individuals, but they are more commonly corporations or othertypes of companies with research and development (R&D) departments dedicated to developing innovative ideas.It’s easy to see that investors and companies can help one another. If investors lend their “extra” capital tocompanies, as shown in Figure 1.2, then companies can use this capital to fund expansion projects. Economicallysuccessful projects will eventually be able to repay the money (plus profit) to investors, as Figure 1.3 shows.

FIGURE 1-2 Capital flow from Investors to Companies

Investors are people or groups who need ideas to make more money, and companies are groups who need money to develop the ideasthey do have.

FIGURE 1-3 Return of Capital to Investors

In this basic process, the company can expand its business, hire more employees, and create a promising future for its own growth.Meanwhile, the investor can increase wealth for the future.

finance at work //: marketsQuantitative Easing in the United States and around the World

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©DAJ/Getty Images

The Financial Crisis of 2007 to 2008 led to a global recession that ended in the United States in 2009. The severe recession is oftenreferred to as the “Great Recession” to give it a Great Depression flavor. However, the ensuing economic recovery was slow. It did nothave the typical bounce-back that often occurs after an acute recession.

To foster economic growth and give the financial sector time to recover, the U.S. Federal Reserve embarked on a grand experimentcalled quantitative easing (QE). QE is a monetary policy designed to increase the money supply in the economy through buyingsecurities in the market and lowering short-term interest rates. The first round of QE involved the Fed buying potentially toxic mortgage-backed securities (see Chapter 7), primarily from banks. This removed the suspect securities from the banks’ balance sheets andallowed them time to get financially stronger. Also, short-term interest rates were cut to zero.

This initial round of QE ended in early 2010 after the Fed had purchased $1.25 trillion of mortgage-backed securities. Chapter 6discusses QE’s impact on the financial system. By the end of 2010, the economy was still not as strong as desired. The Fed’s missionhas been to foster maximum employment in an environment of 2 percent inflation. But the employment market was still lackluster andinflation was near zero in 2010.

In the fourth quarter of 2010 the Fed began QE 2, in which it bought $600 billion of long-term U.S. Treasury securities over theensuing nine months. This was an attempt to lower long-term interest rates. It did not have the desired impact on long-term rates, so QE3 was implemented in late 2012 and continued through 2013. For QE 3, the Fed sold short-term bonds in order to purchase more long-term securities. Short-term interest rates were kept near zero. The low interest rates had profound impacts on the bond market (seeChapter 7) and companies’ cost of capital (see Chapter 11).

Instead of ending QE 3, the Fed decided to reduce its purchases each month through most of 2014. This QE taper was an attempt towean the economy from the constant Fed influence. QE 3 finally tapered out at the end of 2014. Speculation then grew about when theFed would start raising interest rates. The Fed finally raised its key interest rate to 0.25% on December 16, 2015. It was the first rate hikein nearly 10 years.

One ramification of declining interest rates, or near zero rates, is that a country’s currency weakens against foreign currencies (seeChapter 19). This is likely to increase exports and decrease imports.

The economies of other countries and regions have also struggled to grow since the Financial Crisis, and many of them have alsoimplemented quantitative easing programs—two notable examples are the European Central Bank and Japan. With the U.S. ending itsQE programs and raising interest rates while these other countries are continuing their monetary expansion, the U.S. dollar is likely tostrengthen. That would make exports more expensive and imports cheaper.

Want to know more?Key Words to Search for Updates: quantitative easing, zero rate environment, QE taper, currency exchange rates

Of course, not all of the cash will return to the investors. In reality, sources of friction arise in this system, and theamount of capital returned to investors is reduced. Two primary sources of friction are retained earnings, which arebasically funds the firm keeps for its ongoing operations, and taxes, which the government imposes on the companyand individuals to help fund public services. Figure 1.4 shows an analysis of cash flows with the associated retainedearnings and tax payments. In a very simple way, this figure provides an intuitive overall explanation of finance andof its major subareas. For example, individuals must assess which investment opportunities are right for theirneeds and risk tolerance; financial institutions and markets must efficiently distribute the capital; and

companies must evaluate their potential projects and wisely decide which projects to fund, what kind of capital touse, and how much capital to return to investors. All of these types of decisions deal with the basic cash flows offinance shown in Figure 1.4, but from different perspectives.

retained earnings The portion of company profits that are kept by the company rather than distributed to the stockholders as cashdividends.

Subareas of FinanceInvestments is the subarea of finance that involves methods and techniques for making decisions about what kinds ofsecurities to own (e.g., bonds or stocks), which firms’ securities to buy, and how to pay the investor back in the formthat the investor wishes (e.g., the timing and certainty of the promised cash flows). Figure 1.5 models cash flowsfrom the investor’s perspective. The concerns of the investments subarea of finance are shown (with the movementof red arrows) from the investor’s viewpoint (seen as the blue box).

investment The analysis and process of choosing securities and other assets to purchase.

Financial management is the subarea that deals with a firm’s decisions in acquiring and using the cash that isreceived from investors or from retained earnings. Figure 1.6 depicts the financial management process very simply.As we know, this text focuses primarily on financial management. We’ll see that this critical area of financeinvolves decisions about

How to organize the firm in a manner that will attract capital.How to raise capital (e.g., bonds versus stocks).

Which projects to fund.How much capital to retain for ongoing operations and new projects.

How to minimize taxation.How to pay back capital providers.

All of these decisions are quite involved, and we will discuss them throughout later chapters.

FIGURE 1-4 The Complete Cash Flows of Finance

All the subareas of the financial system interact, with retained earnings and taxes playing a role in the flows.

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FIGURE 1-5 Investments

Investors mark the start and end of the financial process; they put money in and reap the rewards (or take the risk).

Financial institutions and markets make up another major subarea of finance. These two dynamic entities work indifferent ways to facilitate capital flows between investors and companies. Figure 1.7 illustrates the process in whichthe firm acquires capital and investors take part in ongoing securities trading to increase that capital. Financialinstitutions, such as banks and pension administrators, are vital players that contribute to the dynamics of interestrates.

financial institutions and markets The organizations that facilitate the flow of capital between investors and companies.

International finance is the final major subarea of finance we will study. As the world has transformed into a globaleconomy, finance has had to become much more innovative and sensitive to changes in other countries. Investors,companies, business operations, and capital markets may all be located in different countries. Adapting to thisenvironment requires understanding of international dynamics, as Figure 1.8 shows. In the past, internationalfinancial decisions were considered to be a straightforward application of the other three financial subareas. Butexperience has shown that the uncertainty about future exchange rates, political risk, and changing business lawsacross the globe adds enough complexity to these decisions to classify international finance as a subarea of financein its own right.

international finance The use of finance theory in a global business environment.

Application and Theory for Financial DecisionsCash flows are neither instantaneous nor guaranteed. We need to keep this in mind as we begin to apply financetheory to real decisions. Future cash flows are uncertain in terms of both timing and size, and we refer to thisuncertainty as risk. Investors experience risk about the return of their capital. Companies experience risk in fundingand operating their business projects. Most financial decisions involve comparing the rewards of a decision to therisks that decision may generate.

risk A potential future negative impact to value and/or cash flows. It is often discussed in terms of the probability of loss and theexpected magnitude of the loss.

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Comparing rewards with risks frequently involves assessing the value today of cash flows that we expect to receivein the future. For example, the price of a financial asset, something worth money, such as a stock or a bond, shoulddepend on the cash flows you expect to receive from that asset in the future. A stock that’s expected to deliver highcash flows in the future will be more valuable today than a stock with low expected future cash flows. Ofcourse, investors would like to buy stocks whose market prices are currently lower than their actual values.They want to get stocks on sale! Similarly, a firm’s goal is to fund projects that will give them more value than theircosts.

financial asset A general term for securities like stocks, bonds, and other assets that represent ownership in a cash flow.

FIGURE 1-6 Financial Management

Financial managers make decisions that should benefit both the company and the investor.

FIGURE 1-7 Financial Institutions and Markets

Financial institutions and markets facilitate the flows of money between investors and companies.

Financial assets are normally grouped into asset classes according to their risk and return characteristics. The mostcommonly accepted groups of asset classes are stocks, bonds, money market instruments, real estate, and derivativesecurities, all of which we will discuss in more detail later in the book. As the risk and return profiles of each ofthese asset classes differ widely between classes, the mathematical models, terminology, and expertise of each classtend to be very specialized and trading tends to happen in distinct, separate financial markets for each asset class.

asset classes A group of securities that exhibit similar characteristics, behave similarly in the marketplace, and are subject to the samelaws and regulations.

Despite the large number of stories about investors who’ve struck it rich in the stock market, it’s actually morelikely that a firm will find “bargain” projects, projects that may yield profit for a reasonable investment, thaninvestors will find underpriced stocks. Firms can find bargains because business projects involve real assets tradingin real markets (markets in tangible assets). In the real environment, some level of monopoly power, specialknowledge, and expertise possibly can make such projects worth more than they cost. Investors, however, aretrading financial assets in financial markets, where the assets are more likely to be worth, on average, exactly whatthey cost.

real assets Physical property like gold, machinery, equipment, or real estate.

real markets The places and processes that facilitate the trading of real assets.

The method for relating expected or future cash flows to today’s value, called present value, is known as time value ofmoney (TVM). Chapters 4 and 5 cover this critical financial concept in detail and apply it to the financial world (aswell as daily life). Since the expected cash flows of either a business project or an investment are likely to beuncertain, any TVM analysis must account for both the timing and the risk level of the cash flows.

time value of money (TVM) The theory and application of valuing cash flows at various points in time.

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Risk tolerance varies among individuals.©Purestock/Superstock

Finance versus AccountingIn most companies, the financial function is usually closely associated with the accounting function. In a very roughsense, the accountant’s job is to keep track of what happened in the past to the firm’s money, while the finance jobuses these historical figures with current information to determine what should happen now and in thefuture with the firm’s money. The results of financial decisions will eventually appear in accountingstatements, so this close association makes sense. Nevertheless, accounting tends to focus on and characterize thepast, while finance focuses on the present and future.

FIGURE 1-8 International Finance

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Laws, risks, and business relationships are variable across different countries but can interact profitably.

time out!1-1 What are the main subareas of finance and how do they interact?

1.2 • THE FINANCIAL FUNCTION LG1-2As we said previously, this text focuses primarily on financial management, so we will discuss the particularfunctions and responsibilities of the firm’s financial manager. We will also explain how the financial function fits inand interacts with the other areas of the firm. Finally, to make this study as interesting and as relevant as possible,we will make the connections that allow you to see how the concepts covered in this book are important in your ownpersonal finances.

The Financial ManagerThe firm’s highest-level financial manager is usually the chief financial officer, or CFO. Both the company treasurerand the controller report to the CFO. The treasurer is typically responsible for

Managing cash and credit.Issuing and repurchasing financial securities such as stocks and bonds.

Deciding how and when to spend capital for new and existing projects.Hedging (reducing the firm’s potential risk) against changes in foreign exchange and interest rates.

In larger corporations, the treasurer may also oversee other areas, such as purchasing insurance or managing thefirm’s pension fund investments. The controller oversees the accounting function, usually managing the tax, costaccounting, financial accounting, and data processing functions.

Finance in Other Business FunctionsAlthough the CFO and treasurer positions tend to be the firm’s most visible finance-related positions, finance affectsthe firm in many ways and throughout all levels of a company’s organizational chart. Finance permeates theentire business organization, providing guidance for both strategic and day-to-day decisions of the firm andcollecting information for control and feedback about the firm’s financial decisions.

EXAMPLE1-1 Finance Applications LG1-3

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

Chloe realizes how important finance will be for her future business career.However, some of the ways that she will see financial applications seem wayoff in the future. She is curious about how the theory applies to her personallife, both in the near term and in the long term.

SOLUTION:

Chloe will quickly find that her financial health now and in the future willdepend upon many decisions she makes as she goes through life—startingnow! For example, she will learn that the same tools that she applies to abusiness loan analysis can be applied to her own personal debt. After thiscourse, Chloe will be able to evaluate credit card offers and select one thatcould save her hundreds of dollars per year. When she buys a new car andthe dealership offers her a low-interest-rate loan or a higher-rate loan withcash back, she will be able to pick the option that will truly cost her the least.Also, when Chloe gets her first professional job, she will know how to directher retirement account so that she can earn millions of dollars for her future.(Of course, inflation between now and when she retires will imply that Chloe’smillions won’t be worth as much as they would today.)

Operational managers use finance daily to determine how much overtime labor to use, or to perform cost/benefitanalysis when they consider new production lines or methods. Marketing managers use finance to assess the costeffectiveness of doing follow-up marketing surveys. Human resource managers use finance to evaluate thecompany’s cost for various employee benefit packages. No matter where you work in business, finance can help youdo your job better.

Finance in Your Personal Life LG1-3Finance can help you make good financial decisions in your personal life. Consider these common activities youwill probably face in your life:

Borrowing money to buy a new car.

Refinancing your home mortgage at a lower rate.Making credit card or student loan payments.

Saving for retirement.

You will be able to perform all of these tasks better after learning about finance. Recent changes throughout oureconomy and the U.S. business environment make knowledge of finance even more valuable to you than before. Forexample, most companies have switched from providing defined benefit retirement plans to employees to offeringdefined contribution plans (such as 401k plans) and self-funded plans like Individual Retirement Accounts (IRAs). Taxchanges in the early 1980s made this switch more or less inevitable. It appears that each of us will have to ensureadequate funds for our own retirement—much more so than previous generations.

defined benefit plan A retirement plan in which the employer funds a pension generally based on each employee’s years of service andsalary.

defined contribution plan A retirement plan in which the employee contributes money and directs its investment. The amount ofretirement benefits are directly related to the amount of money contributed and the success of its investment.

401k plan A defined contribution plan that is sponsored by corporate employers.

Individual Retirement Account (IRA) A self-sponsored retirement program.

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time out!1-2 How might the application of finance improve your professional and personal decisions?

1.3 • BUSINESS ORGANIZATION LG1-4In the United States, people can structure businesses in any of several ways; the number of owners is the key to howbusiness structures are classified. Traditionally, single owners, partners, and corporations operate businesses. Wecan express the advantages and disadvantages of each organizational form through several dimensions:

Who controls the firm.

Who owns the firm.What are the owners’ risks.

What access to capital exists.What are the tax ramifications.

Recently, small businesses have adopted hybrid structures that capture the benefits from multiple organizationalforms. We’ll discuss those hybrid structures after we cover the more common, traditional types of businessorganizations.

Sole ProprietorshipsThe sole proprietorship represents, by far, the most common type of business in the United States.1 A soleproprietorship is defined as any unincorporated business owned by a single individual.2 Perhaps these businesses areso popular because they are relatively easy to start, and they’re subject to a much lighter regulatory and paperworkburden than other business forms. The owner, or sole proprietor, of the business has complete control of the firm’sactivities. The owner also receives all of the firm’s profits and is solely responsible for all losses.

sole proprietorship A business entity that is not legally separate from its owner.

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Venture capital helped Starbucks become a success story.

©McGraw-Hill Education/Jon Flournoy, photographer

The biggest disadvantage that sole proprietorships carry relative to other organizational forms is that they haveunlimited liability for their companies’ debts and actions. The owner’s personal assets may be confiscated if thebusiness fails. The law recognizes no distinction between the owner’s business assets and personal assets. Theincome of the business is also added to the owner’s personal income and taxed by the government at the appropriatepersonal tax rate. Finally, sole proprietors have a difficult time obtaining capital to expand their business operations.Banks and other lenders are not typically interested in lending much money to sole proprietors because small firmshave only one person liable for paying back the debt. A sole proprietor could raise capital by issuing equity toanother investor. Angel investors and venture capitalists exchange capital for ownership in a business. But this requiresre-forming the business as a partnership and the sole proprietor must give up some of the ownership (and thuscontrol) of the firm. Table 1.1 summarizes sole proprietorships’ characteristics, along with those of the three otherbusiness organizations we will study.

unlimited liability A situation in which a person’s personal assets are at risk from a business liability.

equity An ownership interest in a business enterprise.

angel investors Individuals who provide small amounts of capital and expert business advice to small firms in exchange for anownership stake in the firm.

venture capitalists Similar to angel investors except that they are organized as groups of investors and can provide larger amounts ofcapital.

PartnershipsA general partnership, or as it is more commonly known, a partnership, is an organizational form that featuresmultiple individual owners. Each partner can own a different percentage of the firm. Firm control is typicallydetermined by the size of partners’ ownership stakes. Business profits are split among the partners according to aprearranged agreement, usually by the percentage of firm ownership. Received profits are added to eachpartner’s personal income and taxed at personal income tax rates.

general partnership A form of business organization where the partners own the business together and are personally liable for legalactions and debts of the firm.

▼ TABLE 1.1 Characteristics of Business Organization

Ownership Control Ownership Risk

Accessto

Capital Taxes

SoleProprietor Single individual Proprietor Unlimited liability Very limited Paid by owner

Partnership Multiple people Shared bypartners

Unlimited liability Limited Paid by partners

CorporationPublic investorswho own thestock

Companymanagers

Stockholders can onlylose their investment inthe firm

Easy accessCorporation pays income tax andstockholders pay taxes ondividends

Hybrids: S-corp, LLP,LLC, LP

Partners orshareholders Shared Mostly limited

Limited byfirm sizerestrictions

Paid by partners or shareholders

finance at work //: corporateMore Beer

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©Steven Cukrov/123RF

In November 2015, Anheuser-Busch InBev NV agreed to buy SABMiller for $107 billion. AB InBev produces the popular beer brandsBudweiser, Corona, Stella Artois, Beck’s, Hoegaarden, and Leffe. SABMiller is known for Miller, Foster’s, and Grolsch, among others.These are the two largest brewing companies in the world. The combined firm would produce nearly a third of the beer worldwide.

InBev will pay 44 pounds sterling (nearly $63) in cash per share for a majority of SABMiller shares. This is a 50 percent increase, orpremium, over the market price of SABMiller stock. This proposed merger raises many interesting finance questions. For example, whydoes InBev believe that SABMiller should be valued at least 50 percent more than the market does? Why are they paying cash for theshares instead of exchanging their stock for SABMiller stock? What are the business opportunities and cost-cutting cash flows of thecombined firm that are not available as separate firms?

This book describes the theories and tools needed to make these judgments. The practice of finance isn’t just about numbers, it’sabout real valuation and cash flow—the results of the financial analysis are very dynamic and exciting!

This proposed merger will have significant hurdles to overcome in order to be completed. Governments regulate mergers to ensurecompetition in consumer markets. For example, in many regions of the United States, Budweiser and Miller together make up a highpercentage of the market. Thus, if one firm owned both brands, a near monopoly would occur. The U.S. regulatory system would notallow that. So to prevent this objection, SABMiller is selling its stake in this brand to Molson Coors Brewing for $12 billion. Othercountries may have similar concerns. This proposed mega merger may take an entire year to gain the needed regulatory approvalaround the world.

Want to know more?Key Words to Search for Updates: InBev, SABMiller, beer

The partners jointly share unlimited personal liability for the debts of the firm and all are obligated for contractsagreed to by any one of the partners. Banks are more willing to lend to partnerships than to sole proprietorships,because all partners are liable for repaying the debt. Partners would have to give up some ownership and control inthe firm to raise more equity capital. In order to raise enough capital for substantial growth, a partnership oftenchanges into a public corporation.

CorporationsA public corporation is a legally independent entity entirely separate from its owners. This independence dramaticallyalters the firm’s characteristics. Corporations hold many rights and obligations of individual persons, such as theability to own property, sign binding contracts, and pay taxes. Federal and state governments tax corporateincome once at the corporate level. Then shareholders pay taxes again at the personal level when corporate

profits are paid out as dividends. This practice is generally known as double taxation.

public corporation A company owned by a large number of stockholders from the general public.

double taxation A situation in which two taxes must be paid on the same income.

Corporate owners are stockholders, also called shareholders. Public corporations typically have thousands ofstockholders. The firm must hire managers to direct the firm, since thousands of individual shareholders could notdirect day-to-day operations under any sort of consensus. As a result, managers control the company. Strongpossibilities of conflicts of interests arise when one group of people owns the business, but another group controls it.We’ll discuss conflicts of interest and their resolution later in the chapter.

As individual legal entities, corporations assume liability for their own debts, so the shareholders have only limitedliability. That is, corporate shareholders cannot lose more money than they originally paid for their shares of stock.This limited liability is one reason that many people feel comfortable owning stock. Corporations are thus able toraise incredible amounts of money by selling stock (equity) and borrowing money. The largest businesses in theworld are organized as corporations.

limited liability Limitation of a person’s financial liability to a fixed sum or investment.

Hybrid OrganizationsTo promote the growth of small businesses, the U.S. government allows for several types of business organizationsthat simultaneously offer limited personal liability for the owners and provide a pass-through of all firm earnings tothe owners, so that the earnings are subject only to single taxation.

Hybrid organizations offer single taxation and limited liability to all owners. Examples are S corporations, limitedliability partnerships (LLPs), and limited liability companies (LLCs). Others, called limited partnerships (LPs), offersingle taxation and limited liability to the limited partners, but also have general partners, who benefit from singletaxation but also must bear personal liability for the firm’s debts.

hybrid organizations Business forms that have some attributes of corporations and some of proprietorships/partnerships.

The U.S. government typically restricts hybrid organization status to relatively small firms. The government limitsthe maximum number of shareholders or partners involved,3 the maximum amount of investment capital allowed,and the lines of business permitted. These restrictions are consistent with the government’s stated reason forallowing the formation of these forms of business organization—to encourage the formation and growth of smallbusinesses.

time out!1-3 Why must an entrepreneur give up some control of the business as it grows into a public corporation?1-4 What advantages does the corporate form of organization hold over a partnership?

1.4 • FIRM GOALS LG1-5Tens of thousands of public corporations operate in the United States. Many of them are the largest businessorganizations in the world. Because U.S. corporations are so large and because there are so many of them,corporations have a tremendous impact on society. Given the power that these huge firms wield, many peoplequestion what the corporate goals should be. Two different, well-developed viewpoints have arisen concerning whatthe goal of the firm should be. The owners’ perspective holds that the only appropriate goal is to maximize shareholderwealth. The competing viewpoint is from the stakeholders’ perspective, which emphasizes social responsibility over

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profitability. This view maintains that managers must maximize the total satisfaction of all stakeholders in abusiness. These stakeholders include the owners and shareholders, but also include the business’s customers,employees, and local communities.

maximization of shareholder wealth A view that management should first and foremost consider the interests of shareholders in itsbusiness decisions.

stakeholder A person or organization that has a legitimate interest in a corporation.

While strong arguments speak in favor of both perspectives, financial practitioners and academics now tend tobelieve that the manager’s primary responsibility should be to maximize shareholder wealth and give only secondaryconsideration to other stakeholders’ welfare. One of the first, and most well known, proponents of thisviewpoint was Adam Smith, an 18th-century economist who argued that, in capitalism, an individualpursuing his own interests tends also to promote the good of his community.4

Smith argued that the invisible hand of the market, acting through competition and the free price system, wouldensure that only those activities most efficient and beneficial to society as a whole would survive in the long run.Thus, those same activities would also profit the individual most. When companies try to implement a goal otherthan profit maximization, their efforts tend to backfire. Consider the firm that tries to maximize employment. Thehigh number of employees raises costs. Soon the firm will find that its costs are too high to allow it to competeagainst more efficient firms, especially in a global business environment. When the firm fails, all employees are letgo and employment ends up being minimized, not maximized.

invisible hand A metaphor used to illustrate how an individual pursuing his own interests also tends to promote the good of thecommunity.

Regardless of whether you believe Smith’s assertion or not, a more pragmatic reason supports the argument thatmaximizing owners’ wealth is an admirable goal. As we will discuss, the owners of the firm hire managers to workon their behalf, so the manager is morally, ethically, and legally required to act in the owners’ best interests. Anyrelationships between the manager and other firm stakeholders are necessarily secondary to the goal thatshareholders give to their hired managers.

Maximizing owners’ equity value means carefully consideringHow best to bring additional funds into the firm.Which projects to invest in.

How best to return the profits from those projects to the owners over time.

For corporations, maximizing the value of owners’ equity can also be stated as maximizing the current value pershare, or stock price, of existing shares. To the extent that the current stock price can be expected to include thepresent value of any future expected cash flows accruing to the owners, the goal of maximizing stock price providesus with a single, concrete, measurable gauge of value. You may be tempted to choose several other potential goalsover maximizing the value of owners’ equity. Common alternatives are

Maximizing net income or profit.Minimizing costs.

Maximizing market share.

Although these may look appealing, each of these goals has some potentially serious shortcomings. For example, netincome is measured on a year-by-year or quarter-by-quarter basis. When we say that we want to maximize profits, towhich net income figure are we referring? We can maximize this year’s net income in several legitimate ways, butmany of these ways impose costs that will reduce future income. Or, current net income can be pushed into futureyears. Neither of these two extremes will likely encourage the firm’s short-term and long-term stability. One morelikely goal would be to maximize today’s value of all future years of net income. Of course, this possible goal isvery close to maximizing the current stock price, without the convenient market-oriented measure of the stock price.Another problem with considering maximizing all future profits as the goal is that net income (for reasons we’ll gointo later) does not really measure how much money the firm is actually earning.

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time out!1-5 Describe why the primary objective of maximizing shareholder value may actually be the most beneficial for society in the

long run.

Minimizing costs and maximizing market share also have fundamental problems as potential goals. Certainlyminimizing costs would not make some stakeholders, such as employees, very happy. In addition, without spendingthe money on R&D and new product development, many companies would not survive long in the ever-evolvingeconomy without improving their products. A firm can always increase market share by lowering price. But if a firmloses money on every product sold, then selling more products will simply drive the firm into fiscal distress.

1.5 • AGENCY THEORY LG1-6Whenever one party (the principal) hires someone else (the agent) to work for him or her, their interaction is calledan agency relationship. The agent is always supposed to act in the principal’s best interests. For example, anapartment complex manager should ensure that tenants aren’t doing willful damage to the property, that fire codesare enforced, and that the vacancy rate is kept as low as possible, because these are best for the apartment owner.

Agency ProblemIn the context of a public corporation, we have already noted that stockholders hire managers to run the firm.Ideally, managers will operate the firm so that the shareholders realize maximum value for their equity. Butmanagers may be tempted to operate the firm to serve their own best interests. Managers could spend companymoney to improve their own lifestyle instead of earning more profits for shareholders. Sometimes the manager’sbest interest does not necessarily align with shareholder goals. This creates a situation that we refer to as the agencyproblem.

Perks can range from extra vacation to private transportation.©Digital Vision/Getty Images

agency problem The difficulties that arise when a principal hires an agent and cannot fully monitor the agent’s actions.

For example, suppose it is time to buy a new corporate car for the firm’s chief executive officer (CEO). Assuming thatthe CEO has no extraordinary driving requirements, shareholders might wish for the CEO to buy a nice,conservative domestic sedan. But suppose that the CEO demands the newest, biggest luxury car available. It’s

page 18

tempting to say that the shareholders could just tell the CEO which car to buy. But remember, the CEO has most ofthe control in a public corporation. Organizational behavior specialists have identified three basic approaches tominimize this conflict of interest. First, ignore it. If the amount of money involved is small enough relative to thefirm’s cash flows, or if the suitability of the purchase in question is ambiguous enough, shareholders might be bestserved to simply overlook the problem. A good deal of research literature suggests that allowing the manager acertain amount of such perks (perquisites) might actually enhance owner value, in that such items may boostmanagers’ productivity.5

chief executive officer (CEO) The highest-ranking corporate manager.

perks/perquisites Nonwage compensation, often in the form of company car, golf club membership, etc.

The second approach to mitigating this conflict is to monitor managers’ actions. Monitoring at too fine a level ofdetail is probably counterproductive and prohibitively expensive. However, major firm decisions are usuallymonitored at least roughly through the accounting auditing process.

In addition, concentrated ownership in the firm by large stakeholders such as financial institutions, investmentcompanies, individual block holders, or debt holders give those large stakeholders increased incentives to monitorthe activities of management. These incentives are often driven by both economies of scale in monitoring and by theclaim of the stakeholder having a different risk/return profile than the claim of other stakeholders.

economies of scale Cost advantages when fixed costs are spread over a large number of units.

To see the impact of economies of scale in monitoring costs, consider a simple example: Suppose that it costs $3each way (i.e., $6 round-trip) for a shareholder in a firm to hop on the subway and ride down to the firm’s offices inorder to go through the firm’s financial statements, and that the most savings to shareholders that could possiblyresult from this monitoring would be $5 per share. Would anyone owning a single share ever take the ride to checkup on the firm? No, because it would cost a certain $6 in order to save a possible $5. However, someone owning 100shares in the firm would find it worthwhile to pay for the subway ride, assuming that the chance of saving $5 × 100= $500 is large enough.

To envision the effect of one stakeholder having a different claim than others, consider the position of a bondholderin a firm where there isn’t much free cash flow in the firm above and beyond that which is needed to make theinterest payments on her bond. If the manager of the firm is going to spend an extra $20,000 to buy anunnecessarily luxurious company car, that $20,000 is very likely to come out of the bondholder’s pocket, soshe will definitely have a heightened incentive to monitor the manager’s company car purchase. On the other hand,if the firm had so much free cash flow available that the expenditure of the extra $20,000 is unlikely to affect thepayment of the bond interest, then the bondholder would have much less incentive to monitor.6

The final approach for aligning managers’ personal interests with those of owners is to make the managers owners—that is, to offer managers an equity stake in the firm so that management participates in any equity value increase.Many corporations take this approach, either through explicitly granting shares to managers, by awarding themoptions on the firm’s stock, or by allowing them to purchase shares at a subsidized price through an employee stockoption plan (ESOP). When firm managers are also firm owners, their incentives are more likely to align withstockholders’ best interests.

option The opportunity to buy stock at a fixed price over a specific period of time.

employee stock option plan (ESOP) An incentive program that grants options to employees (typically managers) as compensation.

Corporate GovernanceWe refer to the process of monitoring managers and aligning their incentives with shareholder goals as corporategovernance. Theoretically, managers work for shareholders. In reality, because shareholders are usually inactive, thefirm actually seems to belong to management. Generally speaking, the investing public does not know what goes onat the firm’s operational level. Managers handle day-to-day operations, and they know that their work is mostlyunknown to investors. This lack of supervision demonstrates the need for monitors. Figure 1.9 shows the people andorganizations that help monitor corporate activities.

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corporate governance The set of laws, policies, incentives, and monitors designed to handle the issues arising from the separation ofownership and control.

FIGURE 1-9 Corporate Governance Monitors

Corporate governance balances the needs of stockholders and managers. Inside the public firm, the members of the board of directorsmonitor how the firm is run. Outside the firm, auditors, analysts, investment banks, and credit rating agencies act as monitors.

EXAMPLE1-2 Executive Compensation LG1-6

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

In 2014, the largest 350 firms in terms of sales paid their CEOs, on average,$16.3 million—a 3.9 percent increase over the previous year and a 54.3percent increase since the end of the financial crisis in 2009. The averageCEO compensation was 303 times the average employee’s compensation.Every year, the controversy over CEO pay arises again. What argumentscould be made for each side?

SOLUTION:

Many people believe that CEOs are paid too much for the services theyprovide. They receive compensation that is far higher than workers’ pay withintheir firms. Over the years, executive compensation has also increased at afaster rate than has the value of the stockholders’ wealth. For example, the

Economic Policy Institute reports that after adjusting for inflation, CEO payincreased nearly 1,000% between 1978 and 2014. As a comparison, thetypical worker’s inflation adjusted pay increased less than 11 percent duringthe same period. Each firm’s board of directors sets CEO compensation.However, CEOs may have undue influence over director selection, tenure,and committee assignments—even over selecting the compensation advisors.This practice creates an unhealthy conflict of interest.

Others believe that a skilled CEO can positively affect company performanceand that, therefore, the firm needs to offer high compensation and a bundle ofperquisites to attract the best talent. To overcome agency problems,managers must be given incentives that pay very well when the companyperforms very well. If CEOs create a substantial amount of shareholderwealth, then who is to say that they are overpaid?

The monitors inside a public firm are the board of directors, who are appointed to represent shareholders’ interests.The board hires the CEO, evaluates management, and can also design compensation contracts to tie management’ssalaries to firm performance.

board of directors The group of directors elected by stockholders to oversee management in a corporation.

The monitors outside the firm include auditors, analysts, investment banks, and credit rating agencies. Auditorsexamine the firm’s accounting systems and comment on whether financial statements fairly represent the firm’sfinancial position. Investment analysts follow a firm, conduct their own evaluations of the company’s businessactivities, and report to the investment community. Investment banks, which help firms access capital markets andadvise managers about how to interact with those capital markets, also monitor firm performance. Credit analystsexamine a firm’s financial strength for its debt holders. The government also monitors business activities throughthe Securities and Exchange Commission (SEC) and the Internal Revenue Service (IRS).

auditor A person who performs an independent assessment of the fairness of a firm’s financial statements.

investment analyst A person who analyzes a company’s business prospects and gives opinions about its future success.

investment banks Banks that help companies and governments raise capital.

credit analyst A person who analyzes a company’s ability to repay its debts and reports the findings as a grade.

The Role of Ethics LG1-7Ethics must play a strong role in any practice of finance. Finance professionals commonly manage other people’smoney. For example, corporate managers control the stockholder’s firm, bank employees manage deposits, andinvestment advisors manage people’s investment portfolios. These fiduciary relationships create temptingopportunities for finance professionals to make decisions that either benefit the client or benefit the advisorsthemselves. Professional associations (such as for treasurers, bank executives, investment professionals, etc.) place astrong emphasis on ethical behavior and provide ethics training and standards. Nevertheless, as with any professionwith millions of practitioners, a few are bound to act unethically.

ethics The study of values, morals, and morality.

fiduciary A legal duty between two parties where one party must act in the interest of the other party.

The agency relationship between corporate managers and stockholders can create ethical dilemmas. Sometimes thecorporate governance system has failed to prevent unethical managers from stealing from firms, which ultimatelymeans stealing from shareholders. Governments all over the world have passed laws and regulations meant to ensurecompliance with ethical codes of behavior.7 And if professionals don’t act appropriately, governments have set upstrong punishments for financial malfeasance. In the end, financial managers must realize that they not only owetheir shareholders the very best decisions to further shareholder interests, but they also have a broader obligation tosociety as a whole.

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finance at work //: corporateThe Amazing Story of Apple Inc. and Steve Jobs

©McGraw-Hill Education/Christopher Kerrigan, photographer

Steven Jobs and Stephen Wozniak started Apple Computer in 1976 as an equal partnership. Together, they built 50 computers in agarage using money borrowed from family, the proceeds from the sale of a VW bus, and credit from the parts distributor.

Jobs and Wozniak then designed the Apple II computer. But a higher production level to make more than 50 computers requiredmore space and employees. They needed much more capital. They could not get a loan until angel investor Mike Markkula (an Intelexecutive) became a partner in the firm. He invested $92,000 and his personal guarantee induced a bank to loan Apple $250,000. Asproduction ramped up in 1977, Apple Computer incorporated. Most shares were owned by Jobs, Wozniak, and Markkula, but theprincipals made some shares available to employees. They also hired an experienced manager (Mike Scott) to be the CEO and run thefirm. Note that as the firm expanded, Jobs’s ownership level and control got diluted. By 1980, Apple Computer had sold a total of121,000 computers—against a potential demand of millions more. Apple needed even more capital.

At the end of 1980, Apple became a public corporation and sold $65 million worth of stock to public investors. Steve Jobs, cofounderof Apple, still owned more shares than anyone else (7.5 million), but he owned less than half of the firm. He gave up a great deal ofownership to new investors in exchange for the capital to expand the firm. Unhappy with Mike Scott’s leadership, Steve Jobs alsobecame CEO of Apple.

After a couple of years, Apple’s board of directors felt that Jobs was not experienced enough to steer the firm through its rapidexpansion. They hired John Sculley as CEO in 1983. In 1985, a power struggle ensued for control of the firm, and the board backedSculley over Jobs. Jobs was forced out of Apple and no longer had a say in business operations, even though he was the largestshareholder and an original cofounder of the firm.

So, Steve Jobs bought Pixar in 1986 for $5 million and founded NeXT Computer. Over the next 10 years, Jobs’s Pixar producedmega hit movies like Toy Story, A Bug’s Life, and Monsters, Inc. This time, he kept 53 percent ownership of Pixar to ensure keeping fullcontrol. In the meantime, Apple Computer began to struggle, with losses of $800 million in 1996 and $1 billion in 1997. To get SteveJobs back into the firm, Apple bought NeXT for $400 million and hired him as Apple’s CEO. Over the next few years, Jobs introduced theiMac, iPod, and iTunes, and Apple became very profitable again! Jobs was given the use of a $90 million Gulfstream jet as a perk. Torealign his incentives, he became an Apple owner again via compensation that included options on 10 million shares of stock and 30million shares of restricted stock. Then in 2006, Disney bought Pixar by swapping $7.4 billion worth of Disney stock for Pixar stock.When the deal closed, Steve Jobs became the largest owner of Disney stock (7 percent) and joined Disney’s board of directors.

Wow! What a story of accessing capital, business organizational form, company control, and corporate governance.

Want to know more?Key Words to Search for Updates: Steve Jobs, Apple Computer, Pixar

restricted stock A special type of stock that is not transferable from the current holder to others until specific conditions are satisfied.

1.6 • FINANCIAL MARKETS, INTERMEDIARIES, AND THEFIRM LG1-8Astute readers will note that our emphasis on the role of financial markets and intermediaries grew throughout thischapter. This emphasis is intentional, as we feel that you must understand the role and impact of these institutions onthe firm if you are to grasp the context in which professionals make financial management decisions.

time out!1-6 What unethical activities might managers engage in because of the agency problem?1-7 Explain how the corporate governance system reduces the agency problem.

We want to emphasize one other important point about these financial institutions (FI). Very astute readers maywonder how, if financial markets are competitive, investment banks and other financial institutions are able to makesuch impressive profits. Although FIs assist others with transactions involving financial assets in the financialmarkets, they do so as paid services. Successful execution of those services takes unique assets and expertise. Asshown in Figure 1.10, it’s the use of those unique assets and expertise that provides financial institutions with theirhigh profit margins.

1.7 • BIG PICTURE ENVIRONMENT LG1-9The business world is constantly changing. Companies must constantly adapt in order to succeed. These changesand adaptations include the field of finance. For example, when interest rates increase in an economy, then the costof capital increases for companies. This could make some projects that were worthy of corporate investment becometoo costly. In other words, changes in interest rates directly lead to changes in the amount of expansion projectstaken on by companies. Similarly, changes in currency exchange rates between countries directly impact theattractiveness of expansion into foreign markets. Therefore, while managers often direct most of their focus to theirown firms, it is useful to keep an eye on the big picture.

time out!1-8 What is the role of financial institutions in a capitalist economy?

Oil Prices PlummetIn early 2009, the price of oil was around $40 per barrel. During the next two years, that price more than doubled toover $100. It then hovered near $100 into 2014. The steady high price of oil caused much investment in oilexploration and production in the United States and around the world. The oil that is easy and cheap to pump out ofthe ground has already been found. New wells are expensive due to their location (under the Arctic Ocean) or thestatus of the oil (trapped in shale deposits).

FIGURE 1-10 Financial Institutions’ Cash Flows

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The unique services and products that financial institutions provide allow them to make money.

Because of these high oil prices, new technologies were created to find and develop new oil wells. One example isthe procedure to extract oil from shale formations, called fracking. A company might estimate that the cost offinding and drilling a new oil well using fracking is $60 per barrel. This is significantly lower than the manyyears of oil priced at $100 per barrel and has therefore caused much activity in the oil industry. Between2010 and 2015, U.S. oil production increased from 5.6 million barrels a day to 9.3 million barrels in 2015. This wasa huge boon for the economy and added jobs in states from North Dakota to Texas. This characterizes one of the keyfinancial concepts presented in this book—capital budgeting. Specifically, how firms define different new projects,decide which ones are worthy of investment, and determine how to finance them.

Similarly, increases in production occurred all over the world. Simple supply and demand economics forecasts thatlarge increases in supply cause prices to fall. And boy did they! Starting in mid-2014, oil prices fell to $50 in onlysix months. By the end of 2015, oil prices were below $30. There is a saying that “a decline in oil prices is like a taxcut.” This comes from the idea that consumers pay much less on gas for their cars and can spend that moneyelsewhere. It is meant to describe a positive event for the overall U.S. economy. But times have changed.

The U.S. no longer imports most of its oil. It was nice when foreign oil producers paid for U.S. consumer savings.But now, the U.S. produces most of its own oil demand needs. Any savings by consumers at the pump are lostincome to the U.S. oil industry. Oil producing areas of the U.S. are experiencing slowing economies and job losses.So oil price changes may no longer have net impacts on the U.S. economy overall. But oil companies are affected.The stock prices of oil companies are way down. Some small oil companies have declared bankruptcy and defaultedon their bonds and other debts. This will, in turn, impact the banks, mutual funds, pension funds, and other investorsthat own these securities.

China Slows DownFor the last two decades, China was the growth engine for the global economy. It went from a minor player ininternational trade to the second largest economy in the world, largely through exporting goods to the moredeveloped markets like the United States and Europe. Chinese production included economic interaction withnearby countries like Vietnam and Laos. This development included hundreds of millions of rural Chinese movingto the economic city centers. An enormous amount of infrastructure was built: roads, trains, housing, hydroelectricdams, and so on. This required massive quantities of basic materials and energy, which China imported from places

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like Australia, Russia, and several African countries. A new Chinese middle class was created. These newly affluentpeople want the same material luxuries and services as others around the world. China is trying to increase itsservice-based industries to satisfy this new demand. However, this aspect of China’s growth will not create manyinternational trade opportunities.Although China’s economy is expected to grow, that growth seems to be slowing down. This will have manyimplications throughout the global economy. For example, those companies that produce basic materials such assteel, iron ore, and copper will see a lower demand than expected. Indeed, we have already seen falling commodityprices. Of course, this lower commodity cost is good for companies that use these basic materials in their ownproducts.

The more interesting impacts of the slowdown occur in the second order dynamics. For example, the real estatemarket in Sydney, Australia, has declined as a result of China needing less of the basic materials that Australiaproduces. However, some capital is leaving China in search of better investment opportunities. Some of the moneyis going to Manhattan, New York, which has seen a spike in real estate prices. This shifting global environment willcreate new winners and losers all over the world. How companies react and plan for these changes will determinetheir level of success or failure.

Get Online

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Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…

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Questions1. Describe the type of people who use the financial markets. (LG1-1)

2. What is the purpose of financial management? Describe the kinds of activities that financial managementinvolves. (LG1-1)

3. What is the difference in perspective between finance and accounting? (LG1-2)

4. What personal decisions can you think of that will benefit from your learning finance? (LG1-3)

5. What are the three basic forms of business ownership? What are the advantages and disadvantages to each?(LG1-4)

6. Among the three basic forms of business ownership, describe the ability of each form to access capital. (LG1-4)

7. Explain how the founder of a business can eventually lose control of the firm. How can the founder ensure thiswill not happen? (LG1-4)

8. Explain the shareholder wealth maximization goal of the firm and how it can be measured. Make an argumentfor why it is a better goal than maximizing profit. (LG1-5)

9. Name and describe as many corporate stakeholders as you can. (LG1-5)

10. What conflicts of interest can arise between managers and stockholders? (LG1-6)

11. Figure 1.9 shows firm monitors. In your opinion, which group is in the best position to monitor thefirm? Explain. Which group has the potential to be the weakest monitor? Explain. (LG1-6)

12. In recent years, governments all over the world have passed laws that increased the penalties for executives’crimes. Do you think this will deter unethical corporate managers? Explain. (LG1-6)

13. Every year, the media report on the vast amounts of money (sometimes hundreds of millions of dollars) thatsome CEOs earn from the companies they manage. Are these CEOs worth it? Give examples. (LG1-6)

14. Why is ethical behavior so important in the field of finance? (LG1-7)

15. Does the goal of shareholder wealth maximization conflict with behaving ethically? Explain. (LG1-7)

16. Describe how financial institutions and markets facilitate the expansion of a company’s business. (LG1-8)

NotesCHAPTER 11. According to the Small Business Administration, over 70 percent of all businesses in the U.S. were sole proprietorships.2. However, if you are the sole member of a domestic limited liability company (LLC, discussed below), you are not a sole proprietor if you

elect to treat the LLC as a corporation.3. For example, current federal regulations limit the number of shareholders in an S corporation to no more than 100.4. See Book IV of his The Wealth of Nations.5. See, for example, Raghuram Rajan and Julie Wulf, “Are Perks Really Managerial Excess?” Journal of Financial Economics 79(1),

2006, 1–33.

6. In case you are wondering why the stockholders—who would be the eventual recipients of such “extra” free cash flow—wouldn’t thenhave increased incentives to monitor, they would. But, considering that the typical bond sells for $1,000 or more while the typical shareof stock sells for much less, and taking into account that bond ownership tends to be much more concentrated than stock ownership inmany firms, ask yourself whether bondholders or stockholders are more likely to enjoy economies of scale in monitoring.

7. The Sarbanes-Oxley Act of 2002 was passed in response to a number of recent major corporate accounting scandals including thoseaffecting Enron, Tyco International, and WorldCom. The goal of the act was to make the accounting and auditing procedures moretransparent and trustworthy.

C

chapter tworeviewingfinancial statements

©Photographer’s Choice/ Getty Images

orporate managers must issue many reports to the public. Most stockholders, analysts, governmententities, and other interested parties pay particular attention to annual reports. An annual reportprovides four basic financial statements: the balance sheet, the income statement, the statement of

cash flows, and the statement of retained earnings. A financial statement provides an accounting-basedpicture of a firm’s financial condition.

financial statement Statement that provides an accounting-based picture of a firm’s financial position.

Whereas accountants use reports to present a picture of what happened in the past, financeprofessionals use financial statements to draw inferences about the future. The four statements functionto provide key information to managers, who make financial decisions, and to investors, who will acceptor reject possible future investments in the firm. When you encountered these four financial statements inaccounting classes, you learned how they function to place the right information in the right places. In thischapter, you will see how understanding these statements, which are the “right places” for crucialinformation, creates a solid base for your understanding of decision-making processes in managerialfinance.

Financial statements of publicly traded firms can be found in a number of places. For example, allquarterly and annual financial statements can be found at a firm’s website (often under a section titled“investor relations”). Financial statements of publicly traded companies are reported to the Securities and

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Exchange Commission (SEC), who makes them publicly available at their website (www.sec.gov); annualreports are listed under the term 10-K, and quarterly financial statements are listed as 10-Qs. Finally, anumber of websites exist (e.g., finance.yahoo.com) where one can view and download financialstatements of publicly traded companies. Nonpublic firms are not required to submit financial statementsto the SEC. Thus, it can be quite difficult to find detailed financial information about thesefirms. This is one reason why some large firms (Cargill, Toys “R” Us, Fidelity) hesitate tobecome publicly traded; they prefer to keep their financial statement information private.

LEARNING GOALS

LG2-1 Recall the major financial statements that firms must prepare and provide.LG2-2 Differentiate between book (or accounting) value and market value.LG2-3 Explain how taxes influence corporate managers’ and investors’ decisions.LG2-4 Differentiate between accounting income and cash flows.LG2-5 Demonstrate how to use a firm’s financial statements to calculate its cash flows.LG2-6 Observe cautions that should be taken when examining financial statements.

viewpointsbusiness APPLICATIONThe managers of DPH Tree Farm, Inc., believe the firm could double its sales if it had additional factory space and acreage. If DPHpurchased the factory space and acreage in 2019, these new assets would cost $27 million to build and would require an additional$1 million in cash, $5 million in accounts receivable, $6 million in inventory, and $4 million in accounts payable. In addition to accountspayable, DPH Tree Farm would finance the new assets with the sale of a combination of long-term debt (40 percent of the total) andcommon stock (60 percent of the total). Assuming all else stays constant, what will these changes do to DPH Tree Farm’s 2019balance sheet assets, liabilities, and equity? (See 2018 balance sheet in Table 2.1.) (See the solution at the end of the book.)

It should also be noted that this chapter presents a basic set of financial statements; enough so that,from a financial manager’s viewpoint, we can identify the basic categories on each statement andrelationships across statements. Individual firms’ financial statements may look different from thosepresented in the chapter, depending on the level of detail and accounting methods used. Further, financialstatements may be presented in various formats, e.g., in a pdf file or in an Excel spreadsheet.Appendix 2A to the chapter (available online in Connect) presents the 2015 financial statements forColgate-Palmolive Company as listed in its Annual Report, in its 10-K statement, and in an Excelspreadsheet. While the numbers are the same in all formats, the presentation of the numbers can varygreatly.

This chapter examines each statement to clarify its major features and uses. We highlight thedifferences between the accounting-based (book) value of a firm (reflected in these statements) and thetrue market value of a firm, which we will come to understand more fully. We also make a clear distinctionbetween accounting-based income and actual cash flows, a topic further explored in Chapter 3, where wesee how important cash flows are to the study of finance.

We also open a discussion in this chapter about how firms choose to represent their earnings. We’llsee that managers have substantial discretion in preparing their firms’ financial statements, depending onstrategic plans for the organization’s future. This is worth looking into as we keep the discipline of financegrounded in a real-world context. Finally, leading into Chapter 3, we discuss some cautions to bear inmind when reviewing and analyzing financial statements. ■

*See Appendix 2A: Various Formats for Financial Statements in Connect or online at mhhe.com/Cornett4e.

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2.1 • BALANCE SHEET LG2-1The balance sheet reports a firm’s assets, liabilities, and equity at a particular point in time. It is a picture of the assetsthe firm owns and who has claims on these assets as of a given date, for example, December 31, 2018. A firm’sassets must equal (balance) the liabilities and equity used to purchase the assets (hence the term balance sheet):

balance sheet The financial statement that reports a firm’s assets, liabilities, and equity at a particular point in time.

(2-1)

personal APPLICATIONChris Ryan is looking to invest in DPH Tree Farm, Inc. Chris has the most recent set of financial statements from DPH Tree Farm’sannual report but is not sure how to read them or what they mean. What are the four financial statements that Chris should pay mostattention to? What information will these key financial statements contain? (See the solution at the end of the book.)

Thinking of starting your own business?

Figure 2.1 illustrates a basic balance sheet and Table 2.1 presents a simple balance sheet for DPH Tree Farm, Inc., asof December 31, 2018 and 2017. The left side of the balance sheet lists assets of the firm and the right side listsliabilities and equity. Both assets and liabilities are listed in descending order of liquidity, that is, the time and effortneeded to convert the accounts to cash. The most liquid assets—called current assets —appear first on the asset sideof the balance sheet. The least liquid, called fixed assets, appear last. Similarly, current liabilities—those obligationsthat the firm must pay within a year—appear first on the right side of the balance sheet. Stockholders’ equity, whichnever matures, appears last on the balance sheet.

liquidity The ease with which an asset can be converted into cash.

AssetsFigure 2.1 shows that assets fall into two major categories: current assets and fixed assets. Current assets willnormally convert to cash within one year. They include cash and marketable securities (short-term, low-rateinvestment securities held by the firm for liquidity purposes), accounts receivable, and inventory. Fixed assets have auseful life exceeding one year. This class of assets includes physical (tangible) assets, such as net plant andequipment, and other, less tangible, long-term assets, such as patents and trademarks. We find the value of net plantand equipment by taking the difference between gross plant and equipment (or the fixed assets’ original value) andthe depreciation accumulated against the fixed assets since their purchase.

current assets Assets that will normally convert to cash within one year.

marketable securities Short-term, low-rate investment securities held by the firm for liquidity purposes.

fixed assets Assets with a useful life exceeding one year.

Liabilities and Stockholders’ EquityLenders provide funds, which become liabilities, to the firm. Liabilities fall into two categories as well: current orlong-term. Current liabilities constitute the firm’s obligations due within one year, including accrued wages and taxes,accounts payable, and notes payable. Long-term debt includes long-term loans and bonds with maturities of more thanone year.

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liabilities Funds provided by lenders to the firm.

current liabilities Obligations of the firm that are due within one year.

long-term debt Obligations of the firm that are due in more than one year.

The difference between total assets and total liabilities of a firm is the stockholders’ (or owners’) equity. The firm’spreferred and common stock owners provide the funds known as stockholders’ equity. Preferred stock is a hybridsecurity that has characteristics of both long-term debt and common stock. Preferred stock is similar to commonstock in that it represents an ownership interest in the issuing firm but, like long-term debt, it pays a fixedperiodic (dividend) payment. Preferred stock appears on the balance sheet as the cash proceeds when thefirm sells preferred stock in a public offering. Common stock and paid-in surplus is the fundamental ownership claim ina public or private company. The proceeds from common stock and paid-in surplus appear as the other componentof stockholders’ equity. If the firm’s managers decide to reinvest cumulative earnings (recorded on the firm’sincome statement) rather than pay the dividends to stockholders, the balance sheet will record these funds as retainedearnings.

stockholders’ equity Funds provided by the firm’s preferred and common stock owners.

preferred stock A hybrid security that has characteristics of both long-term debt and common stock.

common stock and paid-in surplus The fundamental ownership claim in a public or private company.

retained earnings The portion of company profits that are kept by the company rather than distributed to the stockholders as cashdividends.

FIGURE 2-1 The Basic Balance Sheet

Total Assets Total Liabilities and EquityCurrent assets Current liabilities

Cash and marketable securities Accrued wages and taxes

Accounts receivable Accounts payable

Inventory Notes payable

Fixed assets Long-term debtGross plant and equipment Stockholders’ equity

Less: Accumulated depreciation Preferred stock

Net plant and equipment Common stock and paid-in surplus

Other long-term assets Retained earnings

Managing the Balance SheetManagers must monitor a number of issues underlying items reported on their firms’ balance sheets. We examinethese issues in detail throughout the text. In this chapter, we briefly introduce them. These issues include the

Accounting method for fixed asset depreciation.Level of net working capital.

Liquidity position of the firm.Method for financing the firm’s assets—equity or debt.

Difference between the book value reported on the balance sheet and the true market value of the firm.

Accounting Method for Fixed Asset Depreciation Managers can choose the accounting method they use torecord depreciation against their fixed assets. Recall from accounting that depreciation is the charge against incomethat reflects the estimated dollar cost of the firm’s fixed assets. The straight-line method and the MACRS (modifiedaccelerated cost recovery system) are two choices. Companies commonly choose MACRS when computing thefirm’s taxes and the straight-line method when reporting income to the firm’s stockholders. The MACRS methodaccelerates depreciation, which results in higher depreciation expenses and lower taxable income, thus lower taxes,in the early years of a project’s life. Regardless of the depreciation method used, over time both the straight-line andMACRS methods result in the same amount of depreciation and therefore tax (cash) outflows. However, because theMACRS method defers the payment of taxes to later periods, firms often favor it over the straight-line method of

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depreciation. We discuss this choice further in Chapter 12.

Net Working Capital We arrive at a net working capital figure by taking the difference between a firm’s currentassets and current liabilities.

(2-2)

net working capital The difference between a firm’s current assets and current liabilities.

So, clearly, net working capital is positive when the firm has more current assets than current liabilities. Table 2.1shows the 2018 and 2017 year-end balance sheets for DPH Tree Farm, Inc. At year-end 2018, the firm had $205million of current assets and $123 million of current liabilities. So the firm’s net working capital was $82 million. Afirm needs cash and other liquid assets to pay its bills as expenses come due. As described in more detail in Chapter14, liability holders monitor net working capital as a measure of a firm’s ability to pay its obligations. Positive networking capital values are usually a sign of a healthy firm.

Liquidity As we noted previously, any firm needs cash and other liquid assets to pay its bills as debts come due.Liquidity actually refers to two dimensions: the ease with which the firm can convert an asset to cash, and the degreeto which such a conversion takes place at a fair market value. You can convert any asset to cash quickly if you pricethe asset low enough. But clearly, you will wish to convert the asset without giving up a great portion of its value.So a highly liquid asset can be sold quickly at its fair market value. An illiquid asset, on the other hand, cannot besold quickly unless you reduce the price far below fair value.

Current assets, by definition, remain relatively liquid, including cash and assets that will convert to cashwithin the next year. Inventory is the least liquid of the current assets. Fixed assets, then, remain relativelyilliquid. In the normal course of business, the firm would have no plans to liquefy or convert these tangible assetssuch as buildings and equipment into cash.

Liquidity presents a double-edged sword on a balance sheet. The more liquid assets a firm holds, the less likely thefirm will be to experience financial distress. However, liquid assets generate little or no profits for a firm. Forexample, cash is the most liquid of all assets, but it earns little, if any, for the firm. In contrast, fixed assets areilliquid, but provide the means to generate revenue. Thus, managers must consider the trade-off between theadvantages of liquidity on the balance sheet and the disadvantages of having money sitting idle rather thangenerating profits.

Debt versus Equity Financing You learned in your high school physics class that levers are very useful andpowerful machines—given a long enough lever, you can move almost anything. Financial leverage is likewise verypowerful. Leverage in the financial sense refers to the extent to which a firm chooses to finance its ventures or assetsby issuing debt securities. The more debt a firm issues as a percentage of its total assets, the greater its financialleverage. We discuss in later chapters why financial leverage can greatly magnify the firm’s gains and losses for thefirm’s stockholders.

financial leverage The extent to which debt securities are used by a firm.

When a firm issues debt securities—usually bonds—to finance its activities and assets, debt holders usually demandfirst claim to a fixed amount of the firm’s cash flows. Their claims are fixed because the firm must only pay theinterest owed to bondholders and any principal repayments that come due within any given period. Stockholders—who buy equity securities or stocks—claim any cash flows left after debt holders are paid. When a firm does well,financial leverage increases shareholders’ rewards, since the share of the firm’s profits promised to debt holders isset and predictable.

▼ TABLE 2.1 Balance Sheet for DPH Tree Farm, Inc.

DPH TREE FARM, INC.Balance Sheet as of December 31, 2018 and 2017

(in millions of dollars)

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2018 2017 2018 2017

Assets Liabilities and Equity

Current assets Current liabilities

Cash and marketablesecurities

$ 24 $ 25 Accrued wages and taxes $ 20 $ 15

Accounts receivable 70 65 Accounts payable 55 50

Inventory 111 100 Notes payable  48  45

Total $205 $190 Total $123 $110

Fixed assets Long-term debt 192 190

Gross plant and equipment $368 $300 Total debt 315 300

Less: Accumulateddepreciation

 53  40 Stockholders’ equity

Net plant and equipment $315 $260 Preferred stock (5 million shares) $ 5 $ 5

Other long-term assets 50 50 Common stock and paid-in surplus (20million shares)

40 40

      Retained earnings 210 155

Total $365 $310 Total $255 $200

Total assets $570 $500 Total liabilities and equity $570 $500

However, financial leverage also increases risk. Leverage can create the potential for the firm to experiencefinancial distress and even bankruptcy. If the firm has a bad year and cannot make its scheduled debtpayments, debt holders can force the firm into bankruptcy. As described in more detail in Chapter 16, managersoften walk a fine line as they decide upon the firm’s capital structure—the amount of debt versus equity financingheld on the balance sheet—because it can determine whether the firm stays in business or goes bankrupt.

capital structure The amount of debt versus equity financing held on the balance sheet.

Book Value versus Market Value LG2-2 Beginning finance students usually have already taken accounting,so they are familiar with the accounting point of view. For example, a firm’s balance sheet shows its book (orhistorical cost) value based on generally accepted accounting principles (GAAP). Under GAAP, assets appear on thebalance sheet at what the firm paid for them, regardless of what those assets might be worth today if the firm were tosell them. Inflation and market forces make many assets worth more now than they were worth when the firmbought them. So in many cases, book values differ widely from market values for the same assets—the amount thatthe assets would fetch if the firm actually sold them. For the firm’s current assets—those that mature within a year—the book value and market value of any particular asset will remain very close. For example, the balance sheet listscash and marketable securities at their market value. Similarly, firms acquire accounts receivable and inventory andthen convert these short-term assets into cash fairly quickly, so the book value of these assets is generally close totheir market value.

book (or historical cost) value The amount the firm paid for the assets.

market value The amount the firm would get if it sold the assets.

The “book value versus market value” issue really arises when we try to determine how much a firm’s fixed assetsare worth. In this case, book value is often very different from market value. For example, if a firm owns land for100 years, this asset appears on the balance sheet at its historical cost (of 100 years ago). Most likely, the firm wouldreap a much higher price on the land upon its sale than the historical price would indicate.

EXAMPLE Calculating Book versus Market

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2-1 Value LG2-2

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example, log in toConnect or go tomhhe.com/CornettM4e.

EZ Toy, Inc., lists fixed assets of $25 million on its balance sheet. The firm’sfixed assets were recently appraised at $32 million. EZ Toy, Inc.’s, balancesheet also lists current assets at $10 million. Current assets were appraised at$11 million. Current liabilities’ book and market values stand at $6 million andthe book and market value of the firm’s long-term debt is $15 million.Calculate the book and market values of the firm’s stockholders’ equity.Construct the book value and market value balance sheets for EZ Toy, Inc.

SOLUTION:

Recall the balance sheet identity in equation 2-1: Assets = Liabilities + Equity.Rearranging this equation: Equity = Assets – Liabilities. Thus, the balancesheets would appear as follows:

BookValue

MarketValue

BookValue

MarketValue

Assets Liabilities andEquity

Currentassets

$10m $11m Current liabilities $ 6m $ 6m

Fixedassets

25m 32m Accrued wages andtaxes

15m 15m

Stockholders’ equity 14m 14m

Total $35m $43m Total $35m $43m

Similar to Problems 2-17, 2-18, Self-Test Problem 2

Again, accounting tools reflect the past: Balance sheet assets are listed at historical cost. Managers wouldthus see little relation between the total asset value listed on the balance sheet and the current market valueof the firm’s assets. Similarly, the stockholders’ equity listed on the balance sheet generally differs from the truemarket value of the equity. In this case, the market value may be higher or lower than the value listed on the firm’saccounting books. So financial managers and investors often find that balance sheet values are not always the mostrelevant numbers. The following example illustrates the difference between the book value and the market value of afirm’s assets.

The book value and market value of a classic car can be very different.©Sreedhar Yedlapati/Getty Images

time out!2-1 What is a balance sheet?2-2 Which are the most liquid assets and liabilities on a balance sheet?

2.2 • INCOME STATEMENT LG2-1You will recall that income statements show the total revenues that a firm earns and the total expenses the firm incursto generate those revenues over a specific period of time, for example, the year 2018. Remember that while thebalance sheet reports a firm’s position at a point in time, the income statement reports performance over a period oftime, for example, over the last year. Figure 2.2 illustrates a basic income statement and Table 2.2 shows a simpleincome statement for DPH Tree Farm, Inc., for the years ended December 31, 2018 and 2017. DPH’s revenues (ornet sales) appear at the top of the income statement. Net sales are defined as gross sales minus any discounts and/orreturns. The income statement then shows various expenses (cost of goods sold [e.g., raw material costs], otheroperating expenses [e.g., utilities], depreciation, interest, and taxes) subtracted from revenues to arrive at profit orincome measures.

income statement Financial statement that reports the total revenues and expenses over a specific period of time.

FIGURE 2-2 The Basic Income Statement

Net salesLess: Cost of goods soldGross profitsLess: Other operating expensesEarnings before interest, taxes, depreciation, and amortization (EBITDA)Less: Depreciation and amortizationEarnings before interest and taxes (EBIT)

Operating income

Less: InterestEarnings before taxes (EBT)

Financing and tax considerations

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Less: TaxesNet income before preferred dividends

Less: Preferred stock dividendsNet income available to common stockholders

The top part of the income statement reports the firm’s operating income. First, we subtract the cost of goods sold(the direct costs of producing the firm’s product) from net sales to get gross profit (so, DPH Tree Farm enjoyed grossprofits of $155 million in 2017 and $182 million in 2018). Next, we deduct other operating expenses from grossprofits to get earnings before interest, taxes, depreciation, and amortization (EBITDA); DPH Tree Farm’s EBITDAwas $140 million in 2017 and $165 million in 2018. Other operating expenses include marketing and sellingexpenses as well as general and administrative expenses. Finally, we subtract depreciation and amortization fromEBITDA to get operating income or earnings before interest and taxes (EBIT)1 (so DPH Tree Farm’s EBITwas $128 million in 2017 and $152 million in 2018). The EBIT figure represents the profit earned from the sale ofthe product without any financing cost or tax considerations.

gross profit Net sales minus cost of goods sold.

EBITDA Earnings before interest, taxes, depreciation, and amortization.

EBIT Earnings before interest and taxes.

The bottom part of the income statement summarizes the firm’s financial and tax structure. First, we subtract interestexpense (the cost to service the firm’s debt) from EBIT to get earnings before taxes (EBT). So, as we follow oursample income statement, DPH Tree Farm had EBT of $110 million in 2017 and $136 million in 2018. Of course,firms differ in their financial structures and tax situations. These differences can cause two firms with identicaloperating income to report differing levels of net income. For example, one firm may finance its assets with onlydebt, while another finances with only common equity. The company with no debt would have no interest expense.Thus, even though EBIT for the two firms is identical, the firm with all-equity financing and no debt would reporthigher net income. We subtract taxes from EBT to get the last item on the income statement (the “bottom line”), ornet income. DPH Tree Farm, Inc., reported net income of $70 million in 2017 and $90 million in 2018.

EBT Earnings before taxes.

net income The bottom line on the income statement.

Below the net income, or bottom line, on the income statement, firms often report additional informationsummarizing income and firm value. For example, with its $90 million of net income in 2018, DPH Tree Farm, Inc.,paid its preferred stockholders cash dividends of $10 million and its common stockholders cash dividends of $25million, and added the remaining $55 million to retained earnings. Table 2.1 shows that retained earnings on thebalance sheet increased from $155 million in 2017 to $210 million in 2018. Other items reported below thebottom line include:

▼ TABLE 2.2 Income Statement for DPH Tree Farm, Inc.

DPH TREE FARM, INC.Balance Sheet as of December 31, 2018 and 2017

(in millions of dollars)

2018 2017

Net sales (all credit) $ 315 $ 275

Less: Cost of goods sold   133   120

Gross profits $ 182 $ 155

Less: Other operating expenses   17   15

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Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 165 $ 140

Less: Depreciation and amortization   13   12

Earnings before interest and taxes (EBIT) $ 152 $ 128

Less: Interest   16   18

Earnings before taxes (EBT) $ 136 $ 110

Less: Taxes   46   40

Net income $  90 $  70

Less: Preferred stock dividends $  10 $  10

Net income available to common stockholders $  80 $  60

Less: Common stock dividends   25   25

Addition to retained earnings $  55 $  35

Per (common) share data:

Earnings per share (EPS) $ 4.00 $ 3.00

Dividends per share (DPS) 1.25 1.25

Book value per share (BVPS) 12.50 9.75

Market value (price) per share (MVPS) 17.25 15.60

(2-3)

(2-4)

(2-5)

(2-6)

We discuss these items further in Chapter 3.

Debt versus Equity FinancingAs mentioned earlier, when a firm issues debt to finance its assets, it gives the debt holders first claim to a fixedamount of its cash flows. Stockholders are entitled to any residual cash flows, or net income. Thus, when a firmalters its capital structure to include more or less debt (and, in turn, less or more equity), it impacts the residual cashflows available for the stockholders, i.e., the numerator of the EPS equation. Further, as the firm alters its capitalstructure, it will issue more shares of stock when it increases equity to reduce debt, or it will buy back shares ofstock when it decreases equity to increase debt, i.e., the denominator of the EPS equation. Thus, a change in capitalstructure will cause a firm’s stockholders’ EPS to change. The question is: Will the reduction (increase) in financialdistress and bankruptcy risk from the reduction (increase) in financial leverage appease the stockholderswho have lost (gained) earnings per share, and ultimately, how will the change affect stockholder wealth?

EXAMPLE2-2

Impact of Capital Structure on aFirm’s EPS LG2-1

For interactiveversions of this

Consider a firm with an EBIT of $750,000. The firm finances its assets with

example, log in toConnect or go tomhhe.com/CornettM4e.

$1,600,000 debt (costing 5 percent) and 200,000 shares of stock selling at$6.00 per share. To reduce the firm’s risk associated with this financialleverage, the firm is considering reducing its debt by $600,000 by selling anadditional 100,000 shares of stock. The firm is in the 40 percent tax bracket.The change in capital structure will have no effect on the operations of thefirm. Thus, EBIT will remain at $750,000. Calculate the dilution in the firm’sEPS from this change in capital structure.

SOLUTION:

The EPS before and after this change in capital structure is illustrated below:

ChangeBefore Capital

Structure ChangeAfter Capital

Structure Change

EBIT $750,000 $750,000

Less: Interest ($1,600,000× 0.05)

 80,000 ($1,000,000× 0.05)

 50,000

EBT $670,000 $700,000

Less: Taxes(40%)

268,000 280,000

Net income $402,000 $420,000

Divided by # ofshares

200,000 300,000

EPS $  2.01 $  1.40

The change in capital structure would dilute the stockholders’ EPS by $0.61.

Similar to Problems 2-5, 2-6, 2-23, 2-24

Corporate Income Taxes LG2-3Firms pay out a large portion of their earnings in taxes. For example, in 2015, Walmart had EBT of $24.80 billion.Of this amount, Walmart paid $8.50 billion (over 34 percent of EBT) in taxes. Firms may also defer taxes, e.g., in2015, Walmart listed a provision for deferred taxes of $0.52 billion. Deferred taxes occur when a companypostpones paying taxes on profits earned in a particular period. For example, some expenses, such as thoseassociated with research and development or incurred in mergers, may be written off over a fixed number of years.In these cases, the firm’s current year profits for tax purposes would be lower than the profits computed foraccounting purposes. Thus, the company ends up postponing part of its tax liability on this year’s profits to futureyears.

Congress oversees the U.S. tax code, which determines corporate tax obligations. Corporate taxes can thus changewith changes of administration or other changes in the business or public environment. As you might expect, theU.S. tax system is extremely complicated, so we do not attempt to cover it in detail here. However, firms recognizetaxes as a major expense item and many financial decisions arise from tax considerations. In this section we provide

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a general overview of the U.S. corporate tax system.

▼ TABLE 2.3 Corporate Tax Rates as of 2018

Taxable Income Pay This Amount on Base Income Plus This Percentage on Anything over the Base

$0–$50,000 $  0 15%

$50,001–$75,000 7,500 25

$75,001–$100,000 13,750 34

$100,001–$335,000 22,250 39

$335,001–$10,000,000 113,900 34

$10,000,001–$15,000,000 3,400,000 35

$15,000,001–$18,333,333 5,150,000 38

Over $18,333,333 $6,416,667 35

The 2018 corporate tax schedule appears in Table 2.3. Note from this table that the U.S. tax structure is progressive,meaning that the larger the income, the higher the taxes assessed and the higher the taxes paid per dollar ofincome. However, corporate tax rates do not increase in any kind of linear way based on this progressivenature: They rise from a low of 15 percent to a high of 39 percent, then drop to 34 percent, rise to 38 percent, andfinally drop to 35 percent.

EXAMPLE2-3

Calculation of Corporate Taxes LG2-3

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example, log in toConnect or go tomhhe.com/CornettM4e.

Indian Point Kennels, Inc., earned $16.5 million taxable income (EBT) in2018. Use the tax schedule in Table 2.3 to determine the firm’s 2018 taxliability, its average tax rate, and its marginal tax rate.

SOLUTION:

From Table 2.3, the $16.5 million of taxable income puts Indian Point Kennelsin the 38 percent marginal tax bracket. Thus,

Note that the base amount is the maximum dollar value listed in the previoustax bracket. In this example, we take the highest dollar value ($15,000,000) inthe preceding tax bracket (35 percent). The additional percentage owedresults from multiplying the income above and beyond the $15,000,000 (or$1,500,000) by the marginal tax rate (38 percent). The average tax rate forIndian Point Kennels, Inc., comes to:

If Indian Point Kennels earned $1 more of taxable income, it would pay 38cents (its tax rate of 38 percent) more in taxes. Thus, the firm’s marginal tax

rate is 38 percent.

Similar to Problems 2-7, 2-8, 2-25, 2-26, Self-Test Problem 3

In addition to calculating their tax liability, firms also want to know their average tax rate and marginal tax rate. Youcan figure the average tax rate as the percentage of each dollar of taxable income that the firm pays in taxes.

average tax rate The percentage of each dollar of taxable income that the firm pays in taxes.

marginal tax rate The amount of additional taxes a firm must pay out for every additional dollar of taxable income it earns.

(2-7)

From your economics classes, you can probably guess that the firm’s marginal tax rate is the amount of additionaltaxes a firm must pay out for every additional dollar of taxable income it earns.

Interest and Dividends Received by Corporations Any interest that corporations receive is taxable, althougha notable exception arises: Interest on state and local government bonds is exempt from federal taxes. The U.S. taxcode allows this exception to encourage corporations to be better community citizens by supporting localgovernments. Another exception of sorts arises when one corporation owns stock in another corporation. Seventypercent of any dividends received from other corporations is tax exempt. Only the remaining 30 percent is taxed atthe receiving corporation’s tax rate.2

EXAMPLE2-4

Corporate Taxes with Interest andDividend Income LG2-3

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example, log in toConnect or go tomhhe.com/CornettM4e.

In the previous example, suppose that in addition to the $16.5 million oftaxable income, Indian Point Kennels, Inc., received $250,000 of interest onstate-issued bonds and $500,000 of dividends on common stock it owns inDPH Tree Farm, Inc. How do these items affect Indian Point Kennel’s taxliability, average tax rate, and marginal tax rate?

SOLUTION:

In this case, interest on the state-issued bonds is not taxable and should notbe included in taxable income. Further, the first 70 percent of the dividendsreceived from DPH Tree Farm is not taxable. Thus, only 30 percent of thedividends received are taxed, so:

Taxable income = $16,500,000 + (0.3)$500,000 = $16,650,000

Now Indian Point Kennel’s tax liability will be:

Tax liability = $5,150,000 + 0.38($16,650,000 − $15,000,000) = $5,777,000

The $500,000 of dividend income increased Indian Point Kennel’s tax liabilityby $57,000. Indian Point Kennels, Inc.’s, resulting average tax rate is now:

Average tax rate = $5,777,000 / $16,650,000 = 34.70%

Finally, if Indian Point Kennels earned $1 more of taxable income, it would stillpay 38 cents (based upon its marginal tax rate of 38 percent) more in taxes.

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Similar to Problems 2-8, 2-25, 2-26

Interest and Dividends Paid by Corporations Corporate interest payments appear on the income statement asan expense item, so we deduct interest payments from operating income when the firm calculates taxable income.But any dividends paid by corporations to their shareholders are not tax deductible. This is one factor thatencourages managers to finance projects with debt financing rather than to sell more stock. Suppose one firm usesmainly debt financing and another firm, with identical operations, uses mainly equity financing. The equity-financed firm will have very little interest expense to deduct for tax purposes. Thus, it will have highertaxable income and pay more taxes than the debt-financed firm. The debt-financed firm will pay fewer taxes and beable to pay more of its operating income to asset funders, that is, its bondholders and stockholders. So, all elseconstant, even stockholders prefer that firms finance assets primarily with debt rather than with stock. However, asmentioned earlier, increasing the amount of debt financing of the firm’s assets also increases risks. So these affectsmust be balanced when selecting the optimal capital structure for a firm. The debt-versus-equity financing issue iscalled capital structure.

time out!2-3 What is an income statement?2-4 When a corporation owns stock in another corporation, what percentage of dividends received on the stock is taxed?

2.3 • STATEMENT OF CASH FLOWS LG2-4Income statements and balance sheets are the most common financial documents available to the public. However,managers who make financial decisions need more than these two statements—reports of past performance—onwhich to base their decisions for today and into the future. A very important distinction between the accountingpoint of view and the finance point of view is that financial managers and investors are far more interested in actualcash flows than in the backward-looking profit listed on the income statement.

The statement of cash flows is a financial statement that shows the firm’s cash flows over a given period of time. Thisstatement reports the amounts of cash the firm has generated and distributed during a particular time period.The bottom line on the statement of cash flows—the difference between cash sources and uses—equals thechange in cash and marketable securities on the firm’s balance sheet over a period of time. That is, the statement ofcash flows reconciles noncash balance sheet items and income statement items to show changes in the cash andmarketable securities account on the balance sheet over the particular analysis period.

statement of cash flows Financial statement that shows the firm’s cash flows over a period of time.

EXAMPLE2-5

Effect of Debt-versus-EquityFinancing on Funders’ Returns LG2-1

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example, log in toConnect or go tomhhe.com/CornettM4e.

Suppose that you are considering a stock investment in one of two firms(AllDebt, Inc., and AllEquity, Inc.), both of which operate in the same industryand have identical operating incomes of $5 million. AllDebt, Inc., finances its$12 million in assets with $11 million in debt (on which it pays 10 percent

interest) and $1 million in equity. AllEquity, Inc., finances its $12 million inassets with no debt and $12 million in equity. Both firms pay 30 percent tax ontheir taxable income. Calculate the income that each firm has available to payits debt and stockholders (the firms’ asset funders) and the resulting returns tothese asset funders for the two firms.

SOLUTION:

AllDebt AllEquity

Operating income $5.00m $5.00m

Less: Interest 1.10m 0.00m

Taxable income $3.90m $5.00m

Less: Taxes (30%) 1.17m 1.50m

Net income $2.73m $3.50m

Income available for assetfunders(= Operating income −Taxes)

$3.83m $3.50m

Return on asset-funders’investment

$3.83m/$12.00m =31.92%

$3.50m/$12.00m =29.17%

By financing most of its assets with debt and receiving the associated taxbenefits from the interest paid on this debt, All Debt, Inc., is able to pay moreof its operating income to the funders of its assets, i.e., its debt holders andstockholders, than All Equity, Inc.

Similar to Problems 2-19, 2-20

To clarify why this statement is so crucial, it helps to understand that figures on an income statement may notrepresent the actual cash inflows and outflows for a firm during a given period of time. There are two main issues,GAAP accounting principles and noncash income statement entries.

GAAP Accounting PrinciplesCompany accountants must prepare firm income statements following GAAP principles. GAAP procedures requirethat the firm recognize revenue at the time of sale. But sometimes the company receives the cash before or after thetime of sale. Likewise, GAAP counsels the firm to show production and other expenses on the income statement asthe sales of those goods take place. So production and other expenses associated with a particular product’s saleappear on the income statement (for example, cost of goods sold and depreciation) only when that product sells. Ofcourse, just as with revenue recognition, actual cash outflows incurred with production may occur at a very differentpoint in time—usually much earlier than GAAP principles allow the firm to formally recognize the expenses.

Noncash Income Statement EntriesFurther, income statements contain several noncash entries, the largest of which is depreciation. Depreciation

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attempts to capture the noncash expense incurred as fixed assets deteriorate from the time of purchase to the pointwhen those assets must be replaced.

Let’s illustrate the effect of depreciation: Suppose a firm purchases a machine for $100,000. The machine has anexpected life of five years and at the end of those five years, the machine will have no expected salvage value. Thefirm incurs a $100,000 cash outflow at the time of purchase. But the entire $100,000 does not appear on the incomestatement in the year that the firm purchases the machine—in accounting terms, the machine is not expensed in theyear of purchase. Rather, if the firm’s accounting department uses the straight-line depreciation method, it deductsonly $100,000/5, or $20,000, each year as an expense. This $20,000 equipment expense is not a cash outflow for thefirm. The person in charge of buying the machine knows that the cash flow occurred at the time of purchase—and ittotaled $100,000 rather than $20,000.

In conclusion, even though a company may report a large amount of net income on its income statement during ayear, the firm may actually receive a positive, negative, or zero amount of cash. For example, DPH Tree Farm, Inc.,reported net income of $90 million on its income statement (in Table 2.2), yet reported a net change in cash andmarketable securities of −$1 million on its balance sheet (in Table 2.1). Accounting rules under GAAP create thissense of discord: Net income is the result of accounting rules, or GAAP, that do not necessarily reflect the firm’scash flows. Finance professionals know that the firm needs cash, not accounting profits, to pay the firm’s obligationsas they come due, to fund the firm’s operations and growth, and to compensate the firm’s ultimate owners: itsshareholders. While the income statement shows a firm’s accounting-based income, the statement of cash flowsmore often reflects reality today and is thus more important to managers and investors as they seek to answer suchimportant questions as

Does the firm generate sufficient cash to pay its obligations, thus avoiding financial distress?

Does the firm generate sufficient cash to purchase assets needed for sustained growth?Does the firm generate sufficient cash to pay down its outstanding debt obligations?

Sources and Uses of Cash LG2-5In general, some activities increase cash (cash sources) and some decrease cash (cash uses). Figure 2.3 classifies thefirm’s basic cash sources and uses. Cash sources include decreasing noncash assets or increasing liabilities (orequity). For example, a drop in accounts receivable means that the firm has collected cash from its credit sales—acash source. Likewise, if a firm sells new common stock, the firm has used primary markets to raise cash. Incontrast, a firm uses cash when it increases noncash assets (buying inventory) or decreases a liability (paying off abank loan). The statement of cash flows separates these cash flows into four categories or sections:

1. Cash flows from operating activities.2. Cash flows from investing activities.

3. Cash flows from financing activities.4. Net change in cash and marketable securities.

The basic setup of a statement of cash flows is shown in Figure 2.4, and a more detailed statement of cash flows forDPH Tree Farm for the year ending December 31, 2018, appears as Table 2.4.

Cash flows from operations (Section A in Figure 2.4 and Table 2.4) are those cash inflows and outflows that resultdirectly from producing and selling the firm’s products over a period of time. These cash flows include

cash flows from operations Cash flows that are the direct result of the production and sale of the firm’s products.

Net income (adding back depreciation,3 a noncash expense item that is included in net income).Change in working capital accounts other than cash and operations-related short-term debt.

Most finance professionals consider this top section of the statement of cash flows to be the most important. Itshows quickly and compactly the firm’s cash flows generated by and used for the production process. For example,DPH Tree Farm, Inc., generated $97 million in cash flows from its 2018 production. That is, producing and sellingthe firm’s product resulted in a net cash inflow for the firm. Managers and investors look for positive cash flowsfrom operations as a sign of a successful firm—positive cash flows from the firm’s operations is precisely whatgives the firm value. Unless the firm has a stable, healthy pattern in its cash flows from operations, it is not

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financially healthy no matter what its level of cash flow from investing activities or cash flows from financingactivities.

FIGURE 2-3 Sources and uses of Cash

Sources of Cash Uses of CashNet income Net lossesDepreciation Increase a noncash current assetDecrease a noncash current assetIncrease a fixed assetDecrease a fixed asset Decrease a current liabilityIncrease a current liability Decrease long-term debtIncrease long-term debt Repurchase common or preferred stockSell common or preferred stock Pay dividends

Cash flows from investing activities (Section B in Figure 2.4 and Table 2.4) are cash flows associated with the buying orselling of fixed or other long-term assets. This section of the statement of cash flows shows cash inflows andoutflows from changes in long-term investing activities—most significantly the firm’s investment in fixed assets.For example, DPH Tree Farm, Inc., used $68 million in cash to purchase fixed and other long-term assets in 2018.DPH funded this $68 million cash outflow with the $97 million cash surplus DPH Tree Farm produced from itsoperations.

cash flows from investing activities Cash flows associated with the purchase or sale of fixed or other long-term assets.

Cash flows from financing activities (Section C in Figure 2.4 and Table 2.4) are cash flows that result from changes indebt and equity financing. These include raising cash by

cash flows from financing activities Cash flows that result from debt and equity financing transactions.

Issuing short-term debtIssuing long-term debt

Issuing stock

or using cash toPay dividendsPay off debt

Buy back stock

In 2018, DPH Tree Farm, Inc.’s, financing activities produced a net cash outflow of $30 million. As we saw withcash flows from financing activities, this $30 million cash outflow was funded (at least partially) with the $97million cash surplus DPH Tree Farm produced from its operations. Managers, investors, and analysts normallyexpect the cash flows from financing activities to include small amounts of net borrowing along with dividendpayments. If, however, a firm is going through a major period of expansion, net borrowing could reasonably bemuch higher.

Net change in cash and marketable securities (Section D in Figure 2.4 and Table 2.4), the bottom line of the statement ofcash flows, shows the sum of cash flows from operations, investing activities, and financing activities. This sum willreconcile to the net change in cash and marketable securities account on the balance sheet over the period ofanalysis. For example, the bottom line of the statement of cash flows for DPH Tree Farm is −$1 million.This is also the change in the cash and marketable securities account on the balance sheet (in Table 2.1) between2017 and 2018 ($24 million – $25 million = −$1 million). In this case, the firm’s operating, investing, and financingactivities combined to produce a net drain on the firm’s cash during 2018—cash outflows were greater than cashinflows, largely because of the $68 million investment in long-term and fixed assets. Of course, when the bottomline is positive, a firm’s cash inflows exceed cash outflows for the period.

net change in cash and marketable securities The sum of the cash flows from operations, investing activities, and financing activities.

▼FIGURE 2-4 The Statement of Cash Flows

Section A. Cash flows from operating activitiesNet incomeAdditions:

Depreciation

Decrease in noncash current assets (e.g., decrease in accounts receivable)

Increase in accrued wages and taxes

Increase in accounts payable

Subtractions:

Increase in noncash current assets (e.g., increase in inventory)

Decrease in accrued wages and taxes

Decrease in accounts payable

Section B. Cash flows from investing activitiesAdditions:

Decrease in fixed assets

Decrease in other long-term assets

Subtractions:

Increase in fixed assets

Increase in other long-term assets

Section C. Cash flows from financing activitiesAdditions:

Increase in notes payable

Increase in long-term debt

Increase in common and preferred stock

Subtractions:

Decrease in notes payable

Decrease in long-term debt

Decrease in common and preferred stock

Dividends paid

Section D. Net change in cash and marketable securities

▼ TABLE 2.4 Characteristics of Business Organization

DPH TREE FARM, INC. Statement of Cash Flows for Year Ending December 31, 2018

(in millions of dollars)

2018

Section A. Cash flows from operating activities

Net income $90

Additions:

Depreciation 13

Increase in accrued wages and taxes ($20 − $15) 5

Increase in accounts payable ($55 − $50) 5

Subtractions:

Increase in accounts receivable ($65 − $70) −5

Increase in inventory ($100 − $111) −11

Net cash flow from operating activities $97

Section B. Cash flows from investing activities

Subtractions:

Increase in fixed assets ($300 − $368) −$68

Increase in other long-term assets ($50 − $50)   ;0

Net cash flow from investing activities −$68

Section C. Cash flows from financing activities

Additions:

Increase in notes payable ($48 − $45) $ 3

Increase in long-term debt ($192 − $190) 2

Increase in common and preferred stock ($40 − $40) + ($5 − $5) 0

Subtractions:

Preferred stock dividends paid − 10

Common stock dividends paid − 25

Net cash flow from financing activities −$30

Section D. Net change in cash and marketable securities −$ 1

When evaluating the statement of cash flows, the overall change in the cash account should be evaluated with care.For example, a negative cash flow could be the result when a growing firm invests in new fixed assets, inventory,and so on. Cash expenditures used to expand firm capacity would drain cash during the expansion period. However,if utilized efficiently, would result in increases in cash flows through time. Thus, the cash flow statement assistsfinancial professionals to identify where cash is generated and where cash is dispersed over a time period. Thesecash inflows and outflows should then be evaluated based on how they added to the value of the firm to itsstockholders.

time out!2-5 What is a statement of cash flows?2-6 What are the main sections on the statement of cash flows?

2.4 • FREE CASH FLOW LG2-5The statement of cash flows measures net cash flow as net income plus noncash adjustments. However, to maintaincash flows over time, firms must continually replace working capital and fixed assets and develop new products.Thus, firm managers cannot use the available cash flows any way they please. Specifically, the value of a firm’soperations depends on the future expected free cash flows, defined as after-tax operating profit minus the amount ofnew investment in working capital, fixed assets, and the development of new products. Thus, free cash flowrepresents the cash that is actually available for distribution to the investors in the firm—the firm’s debt holders and

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stockholders—after the investments that are necessary to sustain the firm’s ongoing operations are made.

free cash flows The cash that is actually available for distribution to the investors in the firm after the investments that are necessary tosustain the firm’s ongoing operations are made.

DPH Tree Farm reported net income of $90 million yet reported a net change in cash and marketable securities of −$1 million on itsstatement of cash flows.Source: USDA Natural Resources Conservation Service

To calculate free cash flow (FCF), we use the mathematical equation that appears below:

(2-8)

Notice from this equation that free cash flow merges information from the income statement (performance) withinformation from the balance sheet (resources used to produce performance).

To calculate free cash flow, we start with operating cash flow. Firms generate operating cash flow (OCF) after theyhave paid necessary operating expenses and taxes. This net operating profit after taxes (NOPAT) is the net profita firm earns after taxes, but before any financing costs. It is the profit available for debt holders andstockholders if the firm does not replace existing or invest in new working capital or fixed assets. Depreciation, anoncash charge, is added back to NOPAT to determine total OCF. We add other relevant noncash charges, such asamortization and depletion, back as well. Firms either buy physical assets or earmark funds for eventual equipmentreplacement to sustain firm operations; this is called investment in operating capital (IOC). In accounting terms,IOC includes the firm’s gross investments (or changes) in fixed assets, current assets, and spontaneous currentliabilities (such as accounts payable and accrued wages). Thus, free cash flow measures how well managers utilizethe resources of the company to increase firm performance and, thus, enhance shareholder wealth.

net operating profit after taxes (NOPAT) Net profit a firm earns after taxes but before any financing costs.

Like the bottom line shown on the statement of cash flows, the level of free cash flow can be positive, zero, ornegative. A positive free cash flow value means that the firm may distribute funds to its investors (debt holders andstockholders). When the firm’s free cash flows come in as zero or negative, however, the firm’s operations produceno cash flows available for investors. Of course, if free cash flow is negative because operating cash flow isnegative, investors are likely to take up the issue with the firm’s management. Negative free cash flows as a result ofnegative operating cash flows generally indicate that the firm is experiencing operating or managerial problems. A

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firm with positive operating cash flows, but negative free cash flows, however, is not necessarily a poorly managedfirm. Firms that invest heavily in operating capital to support growth often have positive operating cash flows butnegative free cash flows. But in this case, the negative free cash flow will likely result in growing future profits.

EXAMPLE2-6

Calculating Free Cash Flow LG2-5

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

From Tables 2.1 and 2.2, in 2018, DPH Tree Farm, Inc., had EBIT of $152million, a tax rate of 33.82 percent ($46m/$136m), and depreciation expenseof $13 million. Therefore, DPH Tree Farm’s operating cash flow was:

DPH Tree Farm’s gross fixed assets increased by $68 million between 2017and 2018. The firm’s current assets increased by $15 million andspontaneous current liabilities increased by $10 million ($5 million in accruedwages and taxes and $5 million in accounts payable). Therefore, DPH’sinvestment in operating capital for 2018 was:

Accordingly, what was DPH Tree Farm’s free cash flow for 2018?

SOLUTION:

In other words, in 2018, DPH Tree Farm, Inc., had cash flows of $41 millionavailable to pay its stockholders and debt holders.

Similar to Problems 2-11, 2-12, Self-Test Problem 4

2.5 • STATEMENT OF RETAINED EARNINGS LG2-1The statement of retained earnings provides additional details about changes in retained earnings during a reportingperiod. This financial statement reconciles net income earned during a given period and any cash dividends paidwithin that period on one side with the change in retained earnings between the beginning and ending of the periodon the other. Table 2.5 presents DPH Tree Farm, Inc.’s, statement of retained earnings as of December 31, 2018.The statement shows that DPH Tree Farms brought in a net income of $90 million during 2018. The firm paid out$10 million in dividends to preferred stockholders and another $25 million to common stockholders. The firm thenhad $55 million to reinvest back into the firm, which shows as an increase in retained earnings. Thus, the retainedearnings account on the balance sheet (Table 2.1) increased from $155 million at year-end 2017 to $210 million atyear-end 2018.

statement of retained earnings Financial statement that reconciles net income earned during a given period and any cash dividendspaid with the change in retained earnings over the period.

time out!2-7 What is a statement of retained earnings?2-8 If, during a given period, a firm pays out more in dividends than it has net income, what happens to the firm’s retained

earnings?

Increases in retained earnings occur not just because a firm has net income, but also because the firm’s commonstockholders agree to let management reinvest net income back into the firm rather than pay it out as dividends. Ifthe shareholders disagreed with the firm’s policy, they would simply sell their shares. Reinvesting earnings is lessexpensive than raising capital from outside sources (equity markets). Further, reinvesting net income into retainedearnings allows the firm to grow by providing additional funds that can be spent on plant and equipment, inventory,and other assets needed to generate even more profit. So, retained earnings represent a claim against all of the firm’sassets and not against a particular asset.

EXAMPLE2-7

Statement of RetainedEarnings LG2-1

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

Indian Point Kennels, Inc., earned net income in 2018 of $10.78 million. Thefirm paid out $1 million in cash dividends to its preferred stockholders and$2.5 million in cash dividends to its common stockholders. The firm ended2017 with $135.75 million in retained earnings. Construct a statement ofretained earnings to calculate the year-end 2018 balance of retainedearnings.

SOLUTION:

The statement of retained earnings for 2018 is as follows:

INDIAN POINT KENNELS, INC.Statement of Retained Earnings as of December 31, 2018

(in millions of dollars)

Balance of retained earnings, December 31, 2017 $135.75

Plus: Net income for 2018 10.78

Less: Cash dividends paid

Preferred stock $1.0

Common stock  2.5

Total cash dividends paid   3.50

Balance of retained earnings, December 31, 2018 $143.03

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Similar to Problems 2-13, 2-14, Self-Test Problem 1

2.6 • CAUTIONS IN INTERPRETING FINANCIALSTATEMENTS LG2-6As we mentioned earlier in the chapter, firms must prepare their financial statements according to GAAP. GAAPprovides a common set of standards intended to produce objective and precise financial statements. But recall alsothat managers have significant discretion over their reported earnings. Managers and financial analysts haverecognized for years that firms use considerable latitude in using accounting rules to manage their reported earningsin a wide variety of contexts. Indeed, within the GAAP framework, firms can “smooth” earnings. That is, firmsoften take steps to over- or understate earnings at various times. Managers may choose to smooth earnings to showinvestors that firm assets are growing steadily. Similarly, one firm may be using straight-line depreciation for itsfixed assets, while another is using a modified accelerated cost recovery method (MACRS), which causesdepreciation to accrue quickly. If the firm uses MACRS accounting methods, its managers write fixed asset valuesdown quickly; assets will thus have lower book values than if the firm used straight-line depreciation methods.Managers’ choices in these areas make comparisons of such measures as EPS and BVPS across firms difficult.

time out!2-9 What is earnings management?

This process of controlling a firm’s earnings is called earnings management. At the extreme, earnings management hasresulted in some widely reported accounting scandals involving Enron, Merck, WorldCom, and other major U.S.corporations that tried to artificially influence their earnings by manipulating accounting rules. Congress respondedto the spate of corporate scandals that emerged after 2001 with the Sarbanes-Oxley Act, passed in June 2002.Sarbanes-Oxley requires public companies to ensure that their corporate boards’ audit committees have considerableexperience applying generally accepted accounting principles (GAAP) for financial statements. The act also requiresthat a firm’s senior management must sign off on the financial statements of the firm, certifying the statements asaccurate and representative of the firm’s financial condition during the period covered. If a firm’s board of directorsor senior managers fail to comply with Sarbanes-Oxley (SOX), the firm may be delisted from stock exchanges.

earnings management The process of controlling a firm’s earnings.

Sarbanes-Oxley Act of 2002 Requires that a firm’s senior management must sign off on the financial statements of the firm, certifyingthe statements as accurate and representative of the firm’s financial condition during the period covered.

American Spectrum Realty failed to file quarterly and annual reports in 2013 and 2014 in a timely manner. As aresult, as discussed in the nearby Finance at Work box, the firm’s common stock became subject to delisting.Congress’s goal in passing SOX was to prevent deceptive accounting and management practices and to bringstability to jittery stock markets battered in 2002 by accounting and managerial scandals that cost employees theirlife savings and harmed many innocent shareholders as well. See also the discussion of the role of ethics in financein Chapter 1.

▼ TABLE 2.5 Statement of Retained Earnings for DPH Tree Farm, Inc.

DPH TREE FARM, INC.Statement of Retained Earnings as of December 31, 2018

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(in millions of dollars)

Balance of retained earnings, December 31, 2017 $155

Plus: Net income for 2018 90

Less: Cash dividends paid

Preferred stock $10

Common stock 25

Total cash dividends paid  35

Balance of retained earnings, December 31, 2018 $210

finance at work //: marketsAmerican Spectrum Realty Receives Letter from the NYSE MKT That It Has Determined toInitiate Delisting Proceedings

©jmks/Getty Images

American Spectrum Realty, Inc.–a real estate investment management and leasing company–announced that it has received a letterindicating that the staff of NYSE Regulation, Inc. has determined to commence proceedings to delist the Company’s common stock fromthe NYSE MKT LLC. Trading in the Company’s common stock was halted on a continuous basis since NYSE Regulation initiated atrading halt on April 15, 2014. Trading in the Company’s common stock was immediately suspended intraday on February 19, 2015. Asdetermined by NYSE Regulation, the suspension is the result of

the Company’s inability to complete its outstanding SEC filings, per Sections 134 and 1101 of the NYSE MKT Company Guide;the financial condition of the Company, which is so impaired that it appears questionable, in the opinion of the NYSE MKT, as towhether the Company will be able to continue operations and/or meet its obligations as they mature, per Section 1003(a)(iv) of theCompany Guide; and

the Company’s failure to timely disclose corporate events per Section 1003(d) of the Company Guide.

As disclosed on November 14, 2014, and January 8, 2015, the Company had submitted plans to the NYSE MKT outlining steps toregain compliance with the requirements of the Company Guide, and the NYSE MKT had granted the Company a period throughFebruary 19, 2016, for the Company to regain compliance as outlined in its plans of compliance, so long as the Company made progressconsistent with such plans. However, due to the financial condition of the Company, the Company was unable to make progressconsistent with such plans, and accordingly, the Board determined it to be in the best interest of the Company and its shareholders to notappeal NYSE Regulation’s delisting determination.American Spectrum Realty, Inc., is a real estate investment company that owns, through an operating partnership, interests in office,industrial/commercial, retail, self-storage, retail, multi-family properties and undeveloped land throughout the United States. AmericanSpectrum Management Group, Inc., a wholly owned subsidiary of the Company, manages and leases all properties owned by AmericanSpectrum Realty, Inc. as well as for third-party clients, totaling 7 million square feet in multiple states.

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Source: “American Spectrum Realty Receives Letter from the NYSE MKT That It Has Determined to Initiate Delisting Proceedings,”Business Wire, February 25, 2015. Reprinted with permission from Business Wire.

Want to know more?Key Words to Search For Updates: Sarbanes-Oxley Act of 2002, stock delistings, 10Q filing, 10K filing

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Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. List and describe the four major financial statements. (LG2-1)

2. On which of the four major financial statements (balance sheet, income statement, statement of cash flows, orstatement of retained earnings) would you find the following items? (LG2-1)

a. Earnings before taxes.b. Net plant and equipment.c. Increase in fixed assets.

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d. Gross profits.e. Balance of retained earnings, December 31, 20xx.f. Common stock and paid-in surplus.g. Net cash flow from investing activities.h. Accrued wages and taxes.i. Increase in inventory.

3. What is the difference between current liabilities and long-term debt? (LG2-1)

4. How does the choice of accounting method used to record fixed asset depreciation affect management of thebalance sheet? (LG2-1)

5. What are the costs and benefits of holding liquid securities on a firm’s balance sheet? (LG2-1)

6. Why can the book value and market value of a firm differ? (LG2-1)

7. From a firm manager’s or investor’s point of view, which is more important—the book value of a firm or themarket value of the firm? (LG2-2)

8. What do we mean by a progressive tax structure? (LG2-3)

9. What is the difference between an average tax rate and a marginal tax rate? (LG2-3)

10. How does the payment of interest on debt affect the amount of taxes the firm must pay? (LG2-4)

11. The income statement is prepared using GAAP. How does this affect the reported revenue and expensemeasures listed on the balance sheet? (LG2-4)

12. Why do financial managers and investors find cash flows to be more important than accounting profit? (LG2-4)

13. Which of the following activities result in an increase (decrease) in a firm’s cash? (LG2-5)

a. Decrease fixed assets.b. Decrease accounts payable.c. Pay dividends.d. Sell common stock.e. Decrease accounts receivable.f. Increase notes payable.

14. What is the difference between cash flows from operating activities, cash flows from investing activities, andcash flows from financing activities? (LG2-5)

15. What are free cash flows for a firm? What does it mean when a firm’s free cash flow is negative? (LG2-5)

16. What is earnings management? (LG2-6)

17. What does the Sarbanes-Oxley Act require of firm managers? (LG2-6)

ProblemsBASIC PROBLEMS

2-1 Balance Sheet You are evaluating the balance sheet for Goodman Bees Corporation. From the balancesheet you find the following balances: cash and marketable securities = $400,000, accounts receivable =$1,200,000, inventory = $2,100,000, accrued wages and taxes = $500,000, accounts payable = $800,000,and notes payable = $600,000. Calculate Goodman Bees’ net working capital. (LG2-1)

2-2 Balance Sheet Casello Mowing & Landscaping’s year-end 2018 balance sheet lists current assets of$435,200, fixed assets of $550,800, current liabilities of $416,600, and long-term debt of $314,500.Calculate Casello’s total stockholders’ equity. (LG2-1)

2-3 Income Statement The Fitness Studio, Inc.’s, 2018 income statement lists the following income and

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expenses: EBIT = $538,000, interest expense = $63,000, and net income = $435,000. Calculate the 2018taxes reported on the income statement. (LG2-1)

2-4 Income Statement The Fitness Studio, Inc.’s, 2018 income statement lists the following income and

expenses: EBIT = $773,500, interest expense = $100,000, and taxes = $234,500. The firm has no preferredstock outstanding and 100,000 shares of common stock outstanding. Calculate the 2018 earnings per share.(LG2-1)

2-5 Income Statement Consider a firm with an EBIT of $850,000. The firm finances its assets with$2,500,000 debt (costing 7.5 percent) and 400,000 shares of stock selling at $5.00 per share. To reduce thefirm’s risk associated with this financial leverage, the firm is considering reducing its debt by $1,000,000by selling an additional 200,000 shares of stock. The firm is in the 40 percent tax bracket. The change incapital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $850,000.Calculate the change in the firm’s EPS from this change in capital structure. (LG2-1)

2-6 Income Statement Consider a firm with an EBIT of $550,000. The firm finances its assets with$1,000,000 debt (costing 5.5 percent) and 200,000 shares of stock selling at $12.00 per share. The firm isconsidering increasing its debt by $900,000, using the proceeds to buy back 75,000 shares of stock. Thefirm is in the 40 percent tax bracket. The change in capital structure will have no effect on the operations ofthe firm. Thus, EBIT will remain at $550,000. Calculate the change in the firm’s EPS from this change incapital structure. (LG2-1)

2-7 Corporate Taxes Oakdale Fashions, Inc., had $245,000 in 2018 taxable income. Using the tax schedule inTable 2.3, calculate the company’s 2018 income taxes. What is the average tax rate? What is the marginaltax rate? (LG2-3)

2-8 Corporate Taxes Hunt Taxidermy, Inc., is concerned about the taxes paid by the company in 2018. Inaddition to $42.4 million of taxable income, the firm received $2,975,000 of interest on state-issued bondsand $1,000,000 of dividends on common stock it owns in Oakdale Fashions, Inc. Calculate HuntTaxidermy’s tax liability, average tax rate, and marginal tax rate. (LG2-3)

2-9 Statement of Cash Flows Ramakrishnan, Inc., reported 2018 net income of $15 million and depreciationof $2,650,000. The top part of Ramakrishnan, Inc.’s, 2018 and 2017 balance sheets is reproduced below (inmillions of dollars):

Calculate the 2018 net cash flow from operating activities for Ramakrishnan, Inc. (LG2-4)

2018 2017 2018 2017

Current assets: Current liabilities:

Cash and marketablesecurities

$ 20 $ 15 Accrued wages andtaxes

$ 19 $ 18

Accounts receivable 84 75 Accounts payable 51 45

Inventory 121 110 Notes payable  45  40

  Total $225 $200   Total $115 $103

2-10 Statement of Cash Flows In 2018, Usher Sports Shop had cash flows from investing activities of -$4,364,000 and cash flows from financing activities of −5,880,000. The balance in the firm’s cashaccount was $1,615,000 at the beginning of 2018 and $1,742,000 at year-end. Calculate Usher SportsShop’s cash flow from operations for 2018. (LG2-4)

2-11 Free Cash Flow You are considering an investment in Fields and Struthers, Inc., and want to evaluate

the firm’s free cash flow. From the income statement, you see that Fields and Struthers earned anEBIT of $62 million, had a tax rate of 30 percent, and its depreciation expense was $5 million. Fieldsand Struthers’s NOPAT gross fixed assets increased by $32 million from 2017 and 2018. The firm’scurrent assets increased by $20 million and spontaneous current liabilities increased by $12 million.

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Calculate Fields and Struthers’s NOPAT operating cash flow, investment in operating capital, and freecash flow for 2018. (LG2-5)

2-12 Free Cash Flow Tater and Pepper Corp. reported free cash flows for 2018 of $39.1 million andinvestment in operating capital of $22.1 million. Tater and Pepper incurred $13.6 million indepreciation expense and paid $28.9 million in taxes on EBIT in 2018. Calculate Tater and Pepper’s2018 EBIT. (LG2-5)

2-13 Statement of Retained Earnings Mr. Husker’s Tuxedos Corp. began the year 2018 with $256 millionin retained earnings. The firm earned net income of $33 million in 2018 and paid dividends of $5million to its preferred stockholders and $10 million to its common stockholders. What is the year-end2018 balance in retained earnings for Mr. Husker’s Tuxedos? (LG2-1)

2-14 Statement of Retained Earnings Use the following information to find dividends paid to commonstockholders during 2018. (LG2-1)

Balance of retained earnings, December 31, 2017 $ 462m

Plus: Net income for 2018 15m

Less: Cash dividends paid

Preferred stock $ 1m

Common stock

Total cash dividends paid $

Balance of retained earnings, December 31, 2018 $ 470m

INTERMEDIATE PROBLEMS

2-15 Balance Sheet Brenda’s Bar and Grill has total assets of $15 million, of which $5 million are currentassets. Cash makes up 10 percent of the current assets and accounts receivable makes up another 40percent of current assets. Brenda’s gross plant and equipment has a book value of $11.5 million, andother long-term assets have a book value of $500,000. Using this information, what is the balance ofinventory and the balance of depreciation on Brenda’s Bar and Grill’s balance sheet? (LG2-1)

2-16 Balance Sheet Glen’s Tobacco Shop has total assets of $91.8 million. Fifty percent of these assets arefinanced with debt of which $28.9 million is current liabilities. The firm has no preferred stock but thebalance in common stock and paid-in surplus is $20.4 million. Using this information, what is thebalance for long-term debt and retained earnings on Glen’s Tobacco Shop’s balance sheet? (LG2-1)

2-17 Market Value versus Book Value Muffin’s Masonry, Inc.’s, balance sheet lists net fixed assets as$14 million. The fixed assets could currently be sold for $19 million. Muffin’s current balance sheetshows current liabilities of $5.5 million and net working capital of $4.5 million. If all the currentaccounts were liquidated today, the company would receive $7.25 million cash after paying the $5.5million in current liabilities. What is the book value of Muffin’s Masonry’s assets today? What is themarket value of these assets? (LG2-2)

2-18 Market Value versus Book Value Ava’s SpinBall Corp. lists fixed assets of $12 million on its

balance sheet. The firm’s fixed assets have recently been appraised at $16 million. Ava’s SpinBallCorp.’s balance sheet also lists current assets at $5 million. Current assets were appraised at $6million. Current liabilities’ book and market values stand at $3 million, and the firm’s book andmarket values of long-term debt are $7 million. Calculate the book and market values of the firm’sstockholders’ equity. Construct the book value and market value balance sheets for Ava’s SpinBallCorp. (LG2-2)

2-19 Debt versus Equity Financing You are considering a stock investment in one of two firms(NoEquity, Inc., and NoDebt, Inc.), both of which operate in the same industry and have identicaloperating income of $32.5 million. NoEquity, Inc., finances its $65 million in assets with $64 millionin debt (on which it pays 10 percent interest annually) and $1 million in equity. NoDebt, Inc., financesits $65 million in assets with no debt and $65 million in equity. Both firms pay a tax rate of 30 percenton their taxable income. Calculate the net income and return on assets for the two firms. (LG2-1)

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2-20 Debt versus Equity Financing You are considering a stock investment in one of two firms (AllDebt,Inc., and AllEquity, Inc.), both of which operate in the same industry and have identical operatingincome of $12.5 million. AllDebt, Inc., finances its $25 million in assets with $24 million in debt (onwhich it pays 10 percent interest annually) and $1 million in equity. AllEquity, Inc., finances its $25million in assets with no debt and $25 million in equity. Both firms pay a tax rate of 30 percent ontheir taxable income. Calculate the income available to pay the asset funders (the debt holders andstockholders) and resulting return on assets for the two firms. (LG2-1)

2-21 Income Statement You have been given the following information for Corky’s Bedding Corp.:a. Net sales = $11,250,000.b. Cost of goods sold = $7,500,000.c. Other operating expenses = $250,000.d. Addition to retained earnings = $1,000,000.e. Dividends paid to preferred and common stockholders = $495,000.f. Interest expense = $850,000.

2-22 Income Statement You have been given the following information for Moore’s HoneyBee Corp.:a. Net sales = $32,000,000.b. Gross profit = $18,700,000.c. Other operating expenses = $2,500,000.d. Addition to retained earnings = $4,700,000.e. Dividends paid to preferred and common stockholders = $2,900,000.f. Depreciation expense = $2,800,000.

The firm’s tax rate is 35 percent. Calculate the cost of goods sold and the interest expense forMoore’s HoneyBee Corp. (LG2-1)

2-23 Income Statement Consider a firm with an EBIT of $1,000,000. The firm finances its assets with$4,500,000 debt (costing 8 percent) and 200,000 shares of stock selling at $16.00 per share. To reducerisk associated with this financial leverage, the firm is considering reducing its debt by $2,500,000 byselling additional shares of stock. The firm is in the 40 percent tax bracket. The change in capitalstructure will have no effect on the operations of the firm. Thus, EBIT will remain at $1,000,000.Calculate the change in the firm’s EPS from this change in capital structure. (LG2-1)

2-24 Income Statement Consider a firm with an EBIT of $10,500,000. The firm finances its assets with

$50,000,000 debt (costing 6.5 percent) and 10,000,000 shares of stock selling at $10.00 per share. Thefirm is considering increasing its debt by $25,000,000, using the proceeds to buy back shares of stock.The firm is in the 40 percent tax bracket. The change in capital structure will have no effect on theoperations of the firm. Thus, EBIT will remain at $10,500,000. Calculate the change in the firm’s EPSfrom this change in capital structure. (LG2-1)

2-25 Corporate Taxes The Dakota Corporation had a 2018 taxable income of $33,365,000 from operationsafter all operating costs but before (1) interest charges of $8,500,000; (2) dividends received of$750,000; (3) dividends paid of $5,250,000; and (4) income taxes. (LG2-3)

a. Use the tax schedule in Table 2.3 to calculate Dakota’s income tax liabilityb. What are Dakota’s average and marginal tax rates on taxable income?

2-26 Corporate Taxes Suppose that in addition to $17.85 million of taxable income, Texas Taco, Inc.,received $1,105,000 of interest on state-issued bonds and $760,000 of dividends on common stock itowns in Arizona Taco, Inc. (LG2-3)

a. Use the tax schedule in Table 2.3 to calculate Texas Taco’s income tax liability.b. What are Texas Taco’s average and marginal tax rates on taxable income?

2-27 Statement of Cash Flows Use the balance sheet and income statement below to construct a statementof cash flows for Clancy’s Dog Biscuit Corporation. (LG2-5)

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CLANCY’S DOG BISCUIT CORPORATIONBalance Sheet as of December 31, 2018 and 2017

(in millions of dollars)

2018 2017 2018 2017

Assets Liabilities and Equity

Current assets: Current liabilities:

Cash and marketablesecurities

$ 5 $ 5 Accrued wages and taxes $ 10 $ 6

Accounts receivable 20 19 Accounts payable 16 15

Inventory  36  29 Notes payable  14  13

Total $ 61 $ 53 Total $ 40 $ 34

Fixed assets: Long-term debt: $ 57 $ 53

Gross plant andequipment

$106 $ 88

Less: Accumulateddepreciation

 15  11 Stockholders’ equity:

$ 91 $ 77 Preferred stock (2 million shares) $ 2 $ 2

Net plant andequipment

Common stock and paid-insurplus (5 million shares)

11 11

Other long-termassets

  15   15 Retained earnings  57  45

Total $106 $ 92 Total $ 70 $ 58

Total assets $167 $145 Total liabilities and equity $167 $145

CLANCY’S DOG BISCUIT CORPORATIONIncome Statement for Years Ending December 31, 2018 and 2017

(in millions of dollars)

2018 2017

Net sales $ 76 $ 80

Less: Cost of goods sold   38   34

Gross profits $ 38 $ 46

Less: Other operating expenses    6    5

Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 32 $ 41

Less: Depreciation    4    4

Earnings before interest and taxes (EBIT) $  28 $ 37

Less: Interest    5    5

Earnings before taxes (EBT) $  23 $ 32

Less: Taxes    7   10

Net income $  16 $  22

Less: Preferred stock dividends $  1 $  1

Net income available to common stockholders $  15 $ 21

Less: Common stock dividends    3    3

Addition to retained earnings $  12 $ 18

Per (common) share data:

Earnings per share (EPS) $ 3.00 $ 4.20

Dividends per share (DPS) $ 0.60 $ 0.60

Book value per share (BVPS) $13.60 $11.20

Market value (price) per share (MVPS) $14.25 $14.60

2-28 Statement of Cash Flows Use the balance sheet and income statement below to construct a statementof cash flows for Valium’s Medical Supply Corporation. (LG2-5)

VALIUM’S MEDICAL SUPPLY CORPORATION Balance Sheet as of December 31, 2018 and 2017(in millions of dollars)

2018 2017 2018 2017

Assets Liabilities and Equity

Current assets Current liabilities

Cash andmarketablesecurities

$ 74 $ 73 Accrued wages and taxes $ 58 $  45

Accountsreceivable

199 189 Accounts payable 159 145

Inventory  322  291 Notes payable  131  131

Total $ 595 $ 553 Total $ 348 $ 321

Fixed assets Long-term debt $ 565 $ 549

Gross plant andequipment

$1,084 $ 886

Less:Accumulateddepreciation

 153  116 Stockholders’ equity

Net plant andequipment

$ 931 770 Preferred stock (6 thousandshares)

$  6 $  6

Common stock and paid-insurplus (100 thousandshares)

120 120

Other long-termassets

  130  130 Retained earnings   617   457

Total $1,061 $ 900 Total $ 743 $ 583

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Total assets $1,656 $1,453 Total liabilities and equity $1,656 $1,453

VALIUM’S MEDICAL SUPPLY CORPORATIONIncome Statement for Years Ending December 31, 2018 and 2017

(in thousands of dollars)

2018 2017

Net sales $ 888 $ 798

Less: Cost of goods sold  387  350

Gross profits $ 501 $ 448

Less: Other operating expenses   48   42

Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 453 $ 406

Less: Depreciation   37   35

Earnings before interest and taxes (EBIT) $ 416 $ 371

Less: Interest   46   40

Earnings before taxes (EBT) $ 370 $ 331

Less: Taxes  129  112

Net income $ 241 $ 219

Less: Preferred stock dividends $  6 $  6

Net income available to common stockholders $ 235 $ 213

Less: Common stock dividends   75   75

Addition to retained earnings $ 160 $ 138

Per (common) share data:

Earnings per share (EPS) $2.35 $2.13

Dividends per share (DPS) $0.75 $0.75

Book value per share (BVPS) $7.37 $5.77

Market value (price) per share (MVPS) $8.40 $6.25

2-29 Statement of Cash Flows Chris’s Outdoor Furniture, Inc., has net cash flows from operatingactivities for the last year of $340 million. The income statement shows that net income is $315million and depreciation expense is $46 million. During the year, the change in inventory on thebalance sheet was $38 million, change in accrued wages and taxes was $15 million, and change inaccounts payable was $20 million. At the beginning of the year, the balance of accounts receivablewas $50 million. Calculate the end-of-year balance for accounts receivable. (LG2-5)

2-30 Statement of Cash Flows Dogs 4 U Corporation has net cash flow from financing activities for thelast year of $34 million. The company paid $178 million in dividends last year. During the year, thechange in notes payable on the balance sheet was $39 million and change in common and preferredstock was $0. The end-of-year balance for long-term debt was $315 million. Calculate the beginning-of-year balance for long-term debt. (LG2-5)

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2-31 Free Cash Flow The 2018 income statement for Duffy’s Pest Control shows that depreciationexpense was $197 million, EBIT was $494 million, and the tax rate was 30 percent. At the beginningof the year, the balance of gross fixed assets was $1,562 million and net operating working capital was$417 million. At the end of the year, gross fixed assets was $1,803 million. Duffy’s free cash flow forthe year was $424 million. Calculate the end-of-year balance for net operating working capital. (LG2-5)

2-32 Free Cash Flow The 2018 income statement for Egyptian Noise Blasters shows that depreciationexpense is $85 million, NOPAT is $246 million. At the end of the year, the balance of gross fixedassets was $655 million. The change in net operating working capital during the year was $73 million.Egyptian’s free cash flow for the year was $190 million. Calculate the beginning-of-year balance forgross fixed assets. (LG2-5)

2-33 Statement of Retained Earnings Thelma and Louie, Inc., started the year with a balance of retained

earnings of $543 million and ended the year with retained earnings of $589 million. The company paiddividends of $35 million to the preferred stockholders and $88 million to common stockholders.Calculate Thelma and Louie’s net income for the year. (LG2-1)

2-34 Statement of Retained Earnings Jamaica Tours, Inc., started the year with a balance of retainedearnings of $1,780 million. The company reported net income for the year of $284 million and paiddividends of $17 million to the preferred stockholders and $59 million to common stockholders.Calculate Jamaica Tour’s end-of-year balance in retained earnings. (LG2-1)

ADVANCED PROBLEMS

2-35 Income Statement Listed below is the 2018 income statement for Tom and Sue Travels, Inc. (LG2-5)

TOM AND SUE TRAVELS, INC.Income Statement for Year Ending December 31, 2018

(in millions of dollars)

Net sales $16.500

Less: Cost of goods sold  7.100

Gross profits $ 9.400

Less: Other operating expenses  3.200

Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 6.200

Less: Depreciation  2.900

Earnings before interest and taxes (EBIT) $ 3.300

Less: Interest  0.950

Earnings before taxes (EBT) $ 2.350

Less: Taxes  0.705

Net income $ 1.645

The CEO of Tom and Sue’s wants the company to earn a net income of $2.250 million in 2019. Cost ofgoods sold is expected to be 60 percent of net sales, depreciation and other operating expenses are notexpected to change, interest expense is expected to increase to $1.050 million, and the firm’s tax rate willbe 30 percent. Calculate the net sales needed to produce net income of $2.250 million. (LG2-1)

2-36 Income Statement You have been given the following information for PattyCake’s Athletic WearCorp. for the year 2018:

a. Net sales = $38,250,000.

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b. Cost of goods sold = $22,070,000.c. Other operating expenses = $5,300,000.d. Addition to retained earnings = $1,195,500.e. Dividends paid to preferred and common stockholders = $1,912,000.f. Interest expense = $1,785,000.g. The firm’s tax rate is 30 percent.

In 2019:h. Net sales are expected to increase by $9.75 million.i. Cost of goods sold is expected to be 60 percent of net sales.j. Depreciation and other operating expenses are expected to be the same as in 2018.k. Interest expense is expected to be $2,004,286.l. The tax rate is expected to be 30 percent of EBT.

m. Dividends paid to preferred and common stockholders will not change.Calculate the addition to retained earnings expected in 2019. (LG2-1)

2-37 Free Cash Flow Rebecky’s Flowers 4U, Inc., had free cash flows during 2018 of $43 million,NOPAT of $85 million, and depreciation of $14 million. Using this information, fill in the blanks onRebecky’s balance sheet below. (LG2-5)

REBECKY’S FLOWERS 4U, INC.Balance Sheet as of December 31, 2018 and 2017

(in millions of dollars)

2018 2017 2018 2017

Assets Liabilities and Equity

Current assets: Current liabilities:

Cash andmarketablesecurities

$ 28 $ 25 Accrued wages and taxes $ 17 $ 15

Accounts receivable 75 65 Accounts payable 50

Inventory  118 100 Notes payable  45 45

Total $221 $190 Total $ $110

Fixed assets: Long-term debt: $ $190

Gross plant andequipment

$333 $300

Less: Accumulateddepreciation

54 40 Stockholders’ equity:

Net plant andequipment

$279 $260 Preferred stock (5 millionshares)

$ 5 $ 5

Common stock and paid-insurplus (20 million shares)

40 40

Other long-termassets

50 50 Retained earnings  192  155

Total $329 $310 Total $237 $200

Total assets $550 $500 Total liabilities and equity $550 $500

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2-38 Free Cash Flow Vinny’s Overhead Construction had free cash flow during 2018 of $25.4 million.The change in gross fixed assets on Vinny’s balance sheet during 2018 was $7.0 million and thechange in net operating working capital was $8.4 million. Using this information, fill in the blanks onVinny’s income statement below. (LG2-5)

VINNY’S OVERHEAD CONSTRUCTION CORP.Income Statement for Year Ending December 31, 2018

(in millions of dollars)

Net sales $

Less: Cost of goods sold 116.10

Gross profits $66.00

Less: Other operating expenses 12.40

Earnings before interest, taxes, depreciation, and amortization (EBITDA) $53.60

Less: Depreciation 10.20

Earnings before interest and taxes (EBIT)

Less: Interest

Earnings before taxes (EBT) $

Less: Taxes

Net income $27.64

NotesCHAPTER 21. Technically operating income and EBIT are different. Specifically, operating income is considered an official financial measure under

GAAP, while EBIT is a non-GAAP measure. EBIT makes adjustment for items that are not accounted for in operating income. In amajority of cases, these differences are minimal and not crucially important to individual investors who are reviewing financialstatements. As a result, operating income and EBIT are used interchangeably across much of the accounting and finance world.

2. This tax code provision prevents or reduces any triple taxation that could occur: Income could be taxed at three levels: (1) on theincome from the dividend-paying firm, (2) as income for the dividend-receiving firm, and (3) finally, on the personal income ofstockholders who receive dividends.

3. Any other noncash expense (e.g., amortization) would also be added back to net income and any noncash revenue would besubtracted.

chapter threeanalyzingfinancial statements

©Zigzag Mountain Art/Shutterstock

W

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e reviewed the major financial statements in Chapter 2. These financial statements provideinformation on a firm’s financial position at a point in time or its operations over some past periodof time. But the real value of these financial statements lies in the fact that managers, investors,

and analysts can use the information the statements contain to analyze the current financial performanceor condition of the firm. More importantly, managers can use this information to plan changes that willimprove the firm’s future performance and, ultimately, its market value. Managers, investors, and analystsuniversally use ratios to evaluate financial statements. Ratio analysis involves calculating and analyzingfinancial ratios to assess a firm’s performance and to identify actions that could improve firm performance.The most frequently used ratios fall into five groups: (1) liquidity ratios, (2) asset management ratios, (3)debt management ratios, (4) profitability ratios, and (5) market value ratios. Each of the five groupsfocuses on a specific area of the financial statements that managers, investors, and analysts assess.

ratio analysis The process of calculating and analyzing financial ratios to assess the firm’s performance and to identify actions neededto improve firm performance.

LEARNING GOALS

LG3-1 Calculate and interpret major liquidity ratios.LG3-2 Calculate and interpret major asset management ratios.LG3-3 Calculate and interpret major debt management ratios.LG3-4 Calculate and interpret major profitability ratios.LG3-5 Calculate and interpret major market value ratios.LG3-6 Appreciate how various ratios relate to one another.LG3-7 Understand the differences between time series and cross-sectional ratio analyses.LG3-8 Explain cautions that should be taken when examining financial ratios.

viewpointsbusiness APPLICATIONThe managers of DPH Tree Farm, Inc., have released public statements that the firm’s performance surpasses that of other firms inthe industry. They cite the firm’s liquidity and asset management positions as particularly strong. DPH’s superior performance in theseareas has resulted in superior overall returns for their stockholders. What are the key financial ratios that DPH Tree Farm, Inc., needsto calculate and evaluate in order to justify these statements? (See the solution at the end of the book.)

In this chapter, we review these ratios, describe what each ratio means, and identify the general trend(higher or lower) that managers and investment analysts look for in each ratio. Note as we review theratios that the number calculated for a ratio is not always good or bad and that extreme values (eitherhigh or low) can be a bad sign for a firm. We will discuss how a ratio that seems too good can actually bebad for a company. We will also see how ratios interrelate—how a change in one ratio may affect thevalue of several ratios. It is often hard to make sense of a set of performance ratios. Thus, whenmanagers or investors review a firm’s financial position through ratio analysis, they often start byevaluating trends in the firm’s financial ratios over time and by comparing their firm’s ratios with that ofother firms in the same industry. Finally, we discuss cautions that you should take when using ratioanalysis to evaluate firm performance. As we go through the chapter, we show sample ratio analysisusing the financial statements for DPH Tree Farm, Inc., listed in Tables 2.1 and 2.2.

3.1 • LIQUIDITY RATIOS LG3-1

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As we stated in Chapter 2, firms need cash and other liquid assets (or current assets) to pay their bills (or currentliabilities) as they come due. Liquidity ratios measure the relationship between a firm’s liquid (or current) assets andits current liabilities. The three most commonly used liquidity ratios are the current ratio, the quick (or acid-test)ratio, and the cash ratio.

liquidity ratios Measure the relationship between a firm’s liquid (or current) assets and its current liabilities.

(3-1)

The broadest liquidity measure, the current ratio, measures the dollars of current assets available to pay each dollarof current liabilities.

(3-2)

Inventories are generally the least liquid of a firm’s current assets. Further, inventory is the current asset for whichbook values are the least reliable measures of market value. In practical terms, what this means is that if the firmmust sell inventory to pay upcoming bills, the firm will most likely have to discount inventory items in order toliquidate them, and thus they are the current assets on which losses are most likely to occur. Therefore, thequick (or acid-test) ratio measures a firm’s ability to pay off short-term obligations without relying oninventory sales. The quick ratio measures the dollars of more liquid assets (cash and marketable securities andaccounts receivable) available to pay each dollar of current liabilities.

personal APPLICATIONChris Ryan is looking to invest in DPH Tree Farm, Inc. Chris has the most recent set of financial statements from DPH Tree Farm’sannual report but is not sure how to evaluate them or measure the firm’s performance relative to other firms in the industry. What arethe financial ratios with which Chris should measure the performance of DPH Tree Farm, Inc.? How can Chris use these ratios toevaluate the firm’s performance? (See the solution at the end of the book.)

So how can these financial ratios work in your life?

(3-3)

If the firm sells accounts receivable to pay upcoming bills, the firm must often discount the accounts receivable tosell them—the assets once again bring less than their book value. Therefore, the cash ratio measures a firm’s abilityto pay short-term obligations with its available cash and marketable securities.

Of course, liquidity on the balance sheet is important. The more liquid assets a firm holds, the less likely the firm isto experience financial distress. Thus, the higher the liquidity ratios, the less liquidity risk a firm has. But aswith everything else in business, high liquidity represents a painful trade-off for the firm. Liquid assetsgenerate little, if any, profits for the firm. In contrast, fixed assets are illiquid, but generate revenue for the firm.Thus, extremely high levels of liquidity guard against liquidity crises, but at the cost of lower returns on assets. Highliquidity levels may actually show bad or indecisive firm management. Thus, in deciding the appropriate level ofcurrent assets to hold on the balance sheet, managers must consider the trade-off between the advantages of beingliquid versus the disadvantages of reduced profits. Note that a company with very predictable cash flows canmaintain low levels of liquidity without incurring much liquidity risk.

EXAMPLE 3-1 Calculating Liquidity Ratios LG3-1

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for theasset management ratios.

SOLUTION:

The liquidity ratios for DPH Tree Farm, Inc., are calculated as follows.The industry average is reported alongside each ratio.

Industry average =1.50 times

Industry average =0.50 times

Industry average =0.15 times

All three liquidity ratios show that DPH Tree Farm, Inc., has moreliquidity on its balance sheet than the industry average (we discuss theprocess used to develop an industry average in section 3.8). Thus,DPH Tree Farm has more cash and other liquid assets (or currentassets) available to pay its bills (or current liabilities) as they come duethan does the average firm in the tree farm industry.

Similar to Problems 3-1, 3-2, Self-Test Problem 1

3.2 • ASSET MANAGEMENT RATIOS LG3-2Asset management ratios measure how efficiently a firm uses its assets (inventory, accounts receivable, and fixedassets), as well as how efficiently the firm manages its accounts payable. The specific ratios allow managers andinvestors to evaluate whether a firm is holding a reasonable amount of each type of asset and whether managementuses each type of asset to effectively generate sales. The most frequently used asset management ratios are listed inthe following sections, grouped by type of asset.

asset management ratios Measure how efficiently a firm uses its assets (inventory, accounts receivable, and fixed assets), as well asits accounts payable.

The inventory turnover ratio measures the number of dollars of sales produced per dollar of inventory.

©Ryan McVay/Getty Images

time out!3-1 What are the three major liquidity ratios used in evaluating financial statements?3-2 How do the three major liquidity ratios used in evaluating financial statements differ?3-3 Does a firm generally want to have high or low liquidity ratios? Why?

Inventory ManagementAs they decide the optimal inventory level to hold on the balance sheet, managers must consider the trade-offbetween the advantages of holding sufficient levels of inventory to keep the production process going versus thecosts of holding large amounts of inventory. Two frequently used ratios are the inventory turnover and days’ sales ininventory.

(3-4)

The inventory turnover ratio measures the number of dollars of sales produced per dollar of inventory. Cost of goodssold is used in the numerator when managers want to emphasize that inventory is listed on the balance sheet at cost,that is, the cost of sales generated per dollar of inventory.

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(3-5)

The days’ sales in inventory ratio measures the number of days that inventory is held before the final product is sold.

In general, a firm wants to produce a high level of sales per dollar of inventory; that is, it wants to turn inventoryover (from raw materials to finished goods to sold goods) as quickly as possible. A high level of sales per dollar ofinventory implies reduced warehousing, monitoring, insurance, and any other costs of servicing the inventory. So, ahigh inventory turnover ratio or a low days’ sales in inventory is generally a sign of good management.

However, if the inventory turnover ratio is extremely high and the days’ sales in inventory is extremely low, the firmmay not be holding sufficient inventory to prevent running out (or stocking out) of the raw materials needed to keepthe production process going. Thus, production and sales stop, which wastes the firm’s fixed resources. So,extremely high levels for the inventory turnover ratio and low levels for the days’ sales in inventory ratio mayactually be a sign of bad firm or production management. Note that companies with very good supply chainrelations can maintain lower levels of inventory without incurring as much risk of stockouts.

Accounts Receivable ManagementAs they decide the level of accounts receivable to hold on the firm’s balance sheet, managers must consider thetrade-off between the advantages of increased sales by offering customers better terms versus the disadvantages offinancing large amounts of accounts receivable. Two ratios used here are the accounts receivable turnover andaverage collection period.

(3-6)

The accounts receivable turnover measures the number of dollars of sales produced per dollar of accountsreceivable.

(3-7)

The average collection period (ACP) measures the number of days accounts receivable are held before the firmcollects cash from the sale. This ratio is also sometimes termed the days’ sales outstanding (DSO).

In general, a firm wants to produce a high level of sales per dollar of accounts receivable; that is, it wants to collectits accounts receivable as quickly as possible to reduce any cost of financing accounts receivable, including interestexpense on liabilities used to finance accounts receivable and defaults associated with accounts receivable. Ingeneral, a high accounts receivable turnover or a low ACP is a sign of good management, which is well aware offinancing costs and customer remittance habits.

However, if the accounts receivable turnover is extremely high and the ACP is extremely low, the firm’s accountsreceivable policy may be so strict that customers prefer to do business with competing firms. Firms offer accountsreceivable terms as an incentive to get customers to buy products from their firm rather than a competing firm. Byoffering customers the accounts receivable privilege, management allows them to buy (more) now and pay later.Without this incentive, customers may choose to buy the goods from the firm’s competitors who offer better creditterms. So extremely high accounts receivable turnover levels and low ACP levels may be a sign of bad firmmanagement.

Accounts Payable ManagementAs they decide the accounts payable level to hold on the balance sheet, managers must consider the trade-offbetween maximizing the use of free financing that raw material suppliers offer versus the risk of losing theopportunity to buy on account. Two ratios commonly used are the accounts payable turnover and average paymentperiod.

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(3-8)

The accounts payable turnover ratio measures the dollar cost of goods sold per dollar of accounts payable.

(3-9)

The average payment period (APP) measures the number of days that the firm holds accounts payable before it hasto extend cash to pay for its purchases.

In general, a firm wants to pay for its purchases as slowly as possible. The slower the firm pays for its supplypurchases, the longer it can avoid obtaining other costly sources of financing such as notes payable or long-termdebt. Thus, a low accounts payable turnover or a high APP is generally a sign of good management.

However, if the accounts payable turnover is extremely low and the APP is extremely high, the firm may be abusingthe credit terms that its raw materials suppliers offer. At some point, the firm’s suppliers may revoke its ability tobuy raw materials on account and the firm will lose this source of free financing. If this situation is developing,extremely low levels for the accounts receivable turnover and high levels for the APP may point to bad firmmanagement.

Fixed Asset and Working Capital ManagementTwo ratios that summarize the efficiency in a firm’s overall asset management are the fixed asset turnover and salesto working capital ratios.

(3-10)

The fixed asset turnover ratio measures the number of dollars of sales produced per dollar of net fixed assets.

(3-11)

Similarly, the sales to working capital ratio measures the number of dollars of sales produced per dollar of networking capital (current assets minus current liabilities).

In general, the higher the level of sales per dollar of fixed assets and working capital, the more efficiently the firm isbeing run. Thus, high fixed asset turnover and sales to working capital ratios are generally signs of goodmanagement. However, if either the fixed asset turnover or sales to working capital ratio is extremely high, the firmmay be close to its maximum production capacity. If capacity is hit, the firm cannot increase production or sales.Accordingly, extremely high fixed asset turnover and sales to working capital ratio levels may actually indicate badfirm management if managers have allowed the company to approach maximum capacity without making anyaccommodations for growth.

Note a word of caution here. The age of a firm’s fixed assets will affect the fixed asset turnover ratio level. A firmwith older fixed assets, listed on its balance sheet at historical cost, will tend to have a higher fixed asset turnoverratio than will a firm that has just replaced its fixed assets and lists them on its balance sheet at a (most likely) highervalue. Accordingly, the firm with newer fixed assets would have a lower fixed asset turnover ratio. But this isbecause it has updated its fixed assets, while the other firm has not. It is not correct to conclude that the firm withnew assets is underperforming relative to the firm with older fixed assets listed on its balance sheet. Similarly, forfirms that are in an expansion phase, a lower fixed asset turnover is actually a good sign. It is not correct to concludethat a firm with expanding assets is underperforming relative to a firm with no growth.

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time out!3-4 What are the major asset management ratios?3-5 Does a firm generally want to have high or low values for each of these ratios?3-6 Explain why many of these ratios are mirror images of one another.

Total Asset ManagementThe final two asset management ratios put it all together. They are the total asset turnover and capital intensityratios.

(3-12)

The total asset turnover ratio measures the number of dollars of sales produced per dollar of total assets.

(3-13)

Similarly, the capital intensity ratio measures the dollars of total assets needed to produce a dollar of sales.

In general, a well-managed firm produces many dollars of sales per dollar of total assets, or uses few dollars ofassets per dollar of sales. Thus, in general, the higher the total asset turnover and lower the capital intensityratio, the more efficient the overall asset management of the firm will be. However, if the total assetturnover is extremely high and the capital intensity ratio is extremely low, the firm may actually have an assetmanagement problem. As described above, inventory stockouts, capacity problems, or tight account receivablespolicies can all lead to a high total asset turnover and may actually be signs of poor firm management.

EXAMPLE 3-2Calculating Asset ManagementRatios LG3-2

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for theasset management ratios.

SOLUTION:

We calculate the asset management ratios for DPH Tree Farm, Inc., asfollows. The industry average is reported alongside each ratio.

Industry average =2.15 times

Industry average =170 days

Industry average =3.84 times

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Industry average =95 days

Industry average =3.55 times

Industry average =102 days

Industry average =0.85 times

Industry average =3.20 times

Industry average =0.40 times

Industry average =2.50 times

In all cases, asset management ratios show that DPH Tree Farm, Inc.,is outperforming the industry average. The firm is turning over itsinventory faster than the average firm in the tree farm industry, thusproducing more dollars of sales per dollar of inventory. It is alsocollecting its accounts receivable faster and paying its accountspayable slower than the average firm. Further, DPH Tree Farm isproducing more sales per dollar of fixed assets, working capital, andtotal assets than the average firm in the industry.

Similar to Problems 3-3, 3-4, Self-Test Problem 1

3.3 • DEBT MANAGEMENT RATIOS LG3-3As we discussed in Chapter 2, financial leverage refers to the extent to which the firm uses debt securities in itscapital structure. The more debt a firm uses as a percentage of its total assets, the greater is its financial leverage.Debt management ratios measure the extent to which the firm uses debt (or financial leverage) versus equity to financeits assets as well as how well the firm can pay off its debt. The specific ratios allow managers and investors toevaluate whether a firm is financing its assets with a reasonable amount of debt versus equity financing, as well aswhether the firm is generating sufficient earnings or cash to make the promised payments on its debt. The mostcommonly used debt management ratios are listed in the following sections.

debt management ratios Measure the extent to which the firm uses debt (or financial leverage) versus equity to finance its assets aswell as how well the firm can pay off its debt.

Debt versus Equity Financing

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Managers’ choice of capital structure—the amount of debt versus equity to issue—affects the firm’s viability as along-term entity. In deciding the level of debt versus equity financing to hold on the balance sheet, managers mustconsider the trade-off between maximizing cash flows to the firm’s stockholders versus the risk of being unable tomake promised debt payments. Ratios that are commonly used are the debt ratio, debt-to-equity, and equitymultiplier.

capital structure The amount of debt versus equity financing held on the balance sheet.

(3-14)

The debt ratio measures the percentage of total assets financed with debt.

(3-15)

The debt-to-equity ratio measures the dollars of debt financing used for every dollar of equity financing.

(3-16)

The equity multiplier ratio measures the dollars of assets on the balance sheet for every dollar of equity (or justcommon stockholders’ equity) financing.

As you might suspect, all three measures are related.1 Specifically

Notice in all three ratios, the less debt (and more equity) a firm uses, the lower the value of the ratio. Conversely, thelower the debt, debt-to-equity, or equity multiplier, the less debt and more equity the firm uses to finance its assets(i.e., the bigger the firm’s equity cushion).

When a firm issues debt to finance its assets, it gives the debt holders first claim to a fixed amount of its cash flows.Stockholders are entitled to any residual cash flows—those left after debt holders are paid. When a firm does well,financial leverage increases the reward to shareholders since the amount of cash flows promised to debt holders isconstant and capped. So when firms do well, financial leverage creates more cash flows to share with stockholders—it magnifies the return to the stockholders of the firm (recall Example 2-5). This magnification is one reason thatstockholders encourage the use of debt financing.

However, financial leverage also increases the firm’s potential for financial distress and even failure. If the firm hasa bad year and cannot make promised debt payments, debt holders can force the firm into bankruptcy. Thus,a firm’s current and potential debt holders (and even stockholders) look at equity financing as a safetycushion that can absorb fluctuations in the firm’s earnings and asset values and guarantee debt service payments.Clearly, the larger the fluctuations or variability of a firm’s cash flows, the greater the need for an equity cushion.

Coverage RatiosThree additional debt management ratios are the times interest earned, fixed charge coverage, and cash coverageratios. These ratios are different measures of a firm’s ability to meet its debt obligations.

(3-17)

The times interest earned ratio measures the number of dollars of operating earnings available to meet each dollar ofinterest obligations on the firm’s debt.

(3-18)

EXAMPLE 3-3Calculating Debt ManagementRatios LG3-3

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for theasset management ratios.

SOLUTION:

The debt management ratios for DPH Tree Farm, Inc., are calculatedas follows. The industry average is reported alongside each ratio.

Industry average =68.50%

Industry average =2.17 times

Industry average =4.10 times

              Industry average =4.14 times

Industry average =5.15 times

Industry average =5.70 times

Industry average =7.78 times

In all cases, debt management ratios show that DPH Tree Farm, Inc.,holds less debt on its balance sheet than the average firm in the treefarm industry. Further, the firm has more dollars of operating earningsand cash available to meet each dollar of interest obligations (there areno other fixed charges listed on DPH Tree Farm’s income statement)on the firm’s debt. This lack of financial leverage decreases the firm’spotential for financial distress and even failure, but may also decreaseequity shareholders’ chance for magnified earnings. If the firm has abad year, it has promised relatively few payments to debt holders.Thus, the risk of bankruptcy is small. However, when DPH Tree Farm,Inc., does well, the low level of financial leverage dilutes the return tothe stockholders of the firm. This dilution of profit is likely to upsetcommon stockholders of the firm.

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Similar to Problems 3-5, 3-6, Self-Test Problem 1

The fixed-charge coverage ratio measures the number of dollars of operating earnings available to meet the firm’sinterest obligations and other fixed charges.

(3-19)

The cash coverage ratio measures the number of dollars of operating cash available to meet each dollar of interestand other fixed charges that the firm owes.

With the help of the times interest earned, fixed-charge coverage, and cash coverage ratios, managers, investors, andanalysts can determine whether a firm has taken on a debt burden that is too large. These ratios measure the dollarsavailable to meet debt and other fixed-charge obligations. A value of one for these ratios means that $1 of earningsor cash is available to meet each dollar of interest or fixed-charge obligations. A value of less (greater) than onemeans that the firm has less (more) than $1 of earnings or cash available to pay each dollar of interest or fixed-charge obligations.2 Further, the higher the times interest earned, fixed-charge coverage, and cash coverage ratios,the more equity and less debt the firm uses to finance its assets. Thus, low levels of debt will lead to a dilution of thereturn to stockholders due to increased use of equity as well as to not taking advantage of the tax deductibility ofinterest expense.

time out!3-7 What are the major debt management ratios?3-8 Does a firm generally want to have high or low values for each of these ratios?3-9 What is the trade-off between using too much financial leverage and not using enough leverage? Who is likely to complain

the most in each case?

3.4 • PROFITABILITY RATIOS LG3-4The liquidity, asset management, and debt management ratios examined so far allow for an isolated or narrow lookat a firm’s performance. Profitability ratios show the combined effects of liquidity, asset management, and debtmanagement on the overall operating results of the firm. Profitability ratios are among the most watched and bestknown of the financial ratios. Indeed, firm values (or stock prices) react quickly to unexpected changes in theseratios. The most commonly used profitability ratios are listed below.

profitability ratios Ratios that show the combined effect of liquidity, asset management, and debt management on the firm’s overalloperating results.

(3-20)

The gross profit margin is the percent of sales left after costs of goods sold are deducted.

(3-21)

The operating profit margin is the percent of sales left after all operating expenses are deducted.

(3-22)

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A company’s profit margin is inversely related to its sales.©B.O’Kane/Alamy Stock Photo

The profit margin is the percentage of sales left after all firm expenses are deducted. Thus, this ratio provides the netprofit margin of the firm, as opposed to the gross profit or operating profit margin.

(3-23)

The basic earnings power ratio measures the operating return on the firm’s assets, regardless of financial leverageand taxes. This ratio measures the operating profit (EBIT) earned per dollar of assets on the firm’s balance sheet.

(3-24)

Return on assets (ROA) measures the overall return on the firm’s assets, including financial leverage and taxes. Thisratio is the net income earned per dollar of assets on the firm’s balance sheet.

(3-25)

Return on equity (ROE) measures the return on the common stockholders’ investment in the assets of the firm. ROEis the net income earned per dollar of common stockholders’ equity. The value of a firm’s ROE is affected not onlyby net income, but also by the amount of financial leverage or debt that firm uses. As stated previously, financialleverage magnifies the return to the stockholders of the firm. However, financial leverage also increases thefirm’s potential for financial distress and even failure. Generally, a high ROE is considered to be a positivesign of firm performance. However, if performance comes from a high degree of financial leverage, a high ROE canindicate a firm with an unacceptably high level of bankruptcy risk as well.

EXAMPLE 3-4Calculating ProfitabilityRatios LG3-4

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for theasset management ratios.

SOLUTION:

The profitability ratios for DPH Tree Farm, Inc., are calculated asfollows. The industry average is reported alongside each ratio.

Industry average =56.65%

Industry average =46.88%

Industry average =23.25%

Industry average =22.85%

Industry average =9.30%

Industry average =38.00%

Industry average =30.90%

These ratios show that DPH Tree Farm, Inc., is more profitable thanthe average firm in the tree farm industry. The profit margin, gross profitmargin, operating profit margin, BEP, and ROA are all higher thanindustry figures. Despite this, the ROE for DPH Tree Farm is muchlower than the industry average. DPH’s low debt level and high equitylevel relative to the industry is the main reason for DPH’s strong figuresrelative to the industry. As we mentioned above, DPH’s managerialdecisions about capital structure dilute its returns, which will likely upsetits common stockholders. To counteract common stockholders’discontent, DPH Tree Farm pays out a slightly larger percentage of itsincome to its common stockholders as cash dividends. Of course, thisslightly high dividend payout ratio means that DPH Tree Farm retainsless of its profits to reinvest into the business. A profitable firm thatretains its earnings increases its equity capital level as well as its ownvalue.

Similar to Problems 3-7, 3-8, Self-Test Problem 1

(3-26)

Finally, the dividend payout ratio is the percentage of net income available to common stockholders that the firmactually pays as cash to these investors.

For all but the dividend payout, the higher the value of the ratio, the higher the profitability of the firm. But just ashas been the case previously in this chapter, high profitability ratio levels may result from poor management in otherareas of the firm as much as superior financial management. A high profit (and gross profit or operating profit)margin means that the firm has low expenses relative to sales. The BEP reflects how much the firm’s assets earn

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from operations, regardless of financial leverage and taxes. It follows logically that managers, investors, andanalysts find BEP a useful ratio when they compare firms that differ in financial leverage and taxes. In contrast,ROA measures the firm’s overall performance. It shows how the firm’s assets generate a return that includesfinancial leverage and tax decisions made by management.

ROE measures the return on common stockholders’ investment. Since managers seek to maximize common stockprice, managers, investors, and analysts monitor ROE above all other ratios. The dividend payout ratio measureshow much of the profit the firm retains versus how much it pays out to common stockholders as dividends. Thelower the dividend payout ratio, the more profits the firm retains for future growth or other projects. A profitablefirm that retains its earnings increases its level of equity capital as well as its own value.

time out!3-10 What are the major profitability ratios?3-11 Does a firm generally want to have high or low values for each of these ratios?3-12 What are the trade-offs to having especially high or low values for ROE?

3.5 • MARKET VALUE RATIOS LG3-5As noted, ROE is a most important financial statement ratio for managers and investors to monitor. Generally, ahigh ROE is considered to be a positive sign of firm performance. However, if a high ROE results from a highlyleveraged position, it can signal a firm with a high level of bankruptcy risk. While ROE does not directly incorporatethis risk, for publicly traded firms, market prices of the firm’s stock do. (We look at stock valuation in Chapter 8.)Since the firm’s stockholders earn their returns primarily from the firm’s stock market value, ratios that incorporatestock market values are equally, and arguably more, important than other financial statement ratios.

The final group of ratios is market value ratios. Market value ratios relate a firm’s stock price to its earnings and itsbook value. For publicly traded firms, market value ratios measure what investors think of the company’s futureperformance and risk.

market value ratios Ratios that relate a firm’s stock price to its earnings and book value.

(3-27)

The market-to-book ratio measures the amount that investors will pay for the firm’s stock per dollar of equity usedto finance the firm’s assets. Book value per share is an accounting-based number reflecting the firm’s assets’historical costs, and hence historical value. The market-to-book ratio compares the market (current) value of thefirm’s equity to its historical cost. In general, the higher the market-to-book ratio, the better the firm. If liquidity,asset management, debt management, and accounting profitability are good for a firm, then the market-to-book ratiowill be high. A market-to-book ratio greater than one (or 100 percent) means that stockholders will pay apremium over book value for their equity investment in the firm.

EXAMPLE 3-5Calculating Market ValueRatios LG3-5

For interactive versionsof this example, log in

to Connect or go to

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the

mhhe.com/CornettM4e. asset management ratios.

SOLUTION:

The profitability ratios for DPH Tree Farm, Inc., are calculated asfollows. The industry average is reported alongside each ratio.

Industry average =2.15 times

Industry average =6.25 times

These ratios show that DPH Tree Farm’s investors will not pay asmuch for a share of DPH’s stock per dollar of book value and earningsas the average for the industry. DPH’s low leverage level and highreliance on equity relative to the industry are likely the main reason forinvestors’ disinterest. As mentioned previously, DPH’s seeminglyintentional return dilution will likely upset the firm’s commonstockholders. Accordingly, stockholders lower the amount they arewilling to invest per dollar of book value and EPS.

Similar to Problems 3-9, 3-10, Self-Test Problem 1

(3-28)

One of the best known and most often quoted figures, the price-earnings (or PE) ratio measures how much investorsare willing to pay for each dollar the firm earns per share of its stock. PE ratios are often quoted in multiples—thenumber of dollars per share—that fund managers, investors, and analysts compare within industry classes. Managersand investors often use PE ratios to evaluate the relative financial performance of the firm’s stock. Generally, thehigher the PE ratio, the better the firm’s performance. Analysts and investors, as well as managers, expectcompanies with high PE ratios to experience future growth, to have rapid future dividend increases, or both, becauseretained earnings will support the company’s goals. However, for value-seeking investors, high-PE firms indicateexpensive companies. Further, higher PE ratios carry greater risk because investors are willing to pay higher pricestoday for a stock in anticipation of higher earnings in the future. These earnings may or may not materialize. Low-PE firms are generally companies with little expected growth or low earnings. However, note that earnings dependon many factors (such as financial leverage or taxes) that have nothing to do directly with firm operations.

time out!3-13 What are the major market value ratios?3-14 Does a firm generally want to have high or low values for each of these ratios?3-15 Discuss the price-earnings ratio and explain why it assumes particular importance among all of the other ratios we have

presented.

3.6 • DUPONT ANALYSIS LG3-6Table 3.1 lists the ratios we discuss, their values for DPH Tree Farm, Inc., as of 2018, and the corresponding valuesfor the tree farm industry. The value of each ratio for DPH Tree Farm is highlighted in green if it is generallystronger than the industry and is highlighted in red if it is generally a negative sign for the firm. As we noted in this

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chapter’s introduction, many of the ratios we have discussed thus far are interrelated. So a change in one ratio maywell affect the value of several ratios. Often these interrelations can help evaluate firm performance. Managers andinvestors often perform a detailed analysis of ROA (return on assets) and ROE (return on equity) using the DuPontsystem of analysis. Popularized by the DuPont Corporation, the DuPont system of analysis uses the balance sheet andincome statement to break the ROA and ROE ratios into component pieces.

DuPont system of analysis An analytical method that uses the balance sheet and income statement to break the ROA and ROE ratiosinto component pieces.

▼ TABLE 3.1 Summary of Ratios and their values for DPH Tree Farm, Inc., and the Tree Farm Industry

Ratio Value for DPH TreeFarm, Inc.Value for the Tree

Farm Industry

Liquidity ratios:

1.67 times 1.50 times

0.76 times 0.50 times

0.20 times 0.15 times

Asset management ratios:

2.84 times 2.15 times

129 days 170 days

4.50 times 3.84 times

81 days 95 days

2.42 times 3.55 times

151 days 102 days

1.00 times 0.85 times

3.71 times 3.20 times

0.55 times 0.40 times

1.81 times 2.50 times

Debt management ratios:

55.26% 68.50%

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1.24 times 2.17 times

2.24 times 4.10 times

2.28 times 4.14 times

9.50 times 5.15 times

9.50 times 5.70 times

10.31 times7.78 times

Profitability ratios:

57.78% 56.65%

48.25% 46.88%

25.40% 23.25%

26.67% 22.85%

14.04% 9.30%

32.00% 38.00%

31.25% 30.90%

Market value ratios:

1.38 times 2.15 times

4.31 times 6.25 times

The basic DuPont equation looks at ROA as the product of the profit margin and the total asset turnover ratios:

(3-29)

The basic DuPont equation looks at the firm’s overall profitability as a function of the profit the firm earns per dollarof sales (operating efficiency) and the dollar of sales produced per dollar of assets on the balance sheet (efficiency in

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asset use). With this tool, managers can see the reason for any changes in ROA in more detail. For example, if ROAincreases, the DuPont equation may show that the net profit margin was constant, but the total asset turnover(efficiency in using assets) increased, or that total asset turnover remained constant, but profit margins (operatingefficiency) increased. Managers can identify the reasons for an ROA change more specifically by using the ratiosdescribed above to further break down operating efficiency and efficiency in asset use.

FIGURE 3-1 DuPont System Analysis Breakdown of ROA and ROE

Next, the DuPont system looks at ROE as the product of ROA and the equity multiplier.

(3-30)

Notice that this version of the equity multiplier uses the return to common stockholders (the firm’s owners) only. Sothe DuPont equity multiplier uses common stockholders’ equity only, rather than total equity (which includespreferred stock).

Taking this breakdown one step further, the DuPont system breaks ROE into the product of the profit margin, thetotal asset turnover, and the equity multiplier.

(3-31)

This presentation of ROE allows managers, analysts, and investors to look at the return on equity as a function of thenet profit margin (profit per dollar of sales from the income statement), the total asset turnover (efficiency in the useof assets from the balance sheet), and the equity multiplier (financial leverage from the balance sheet). Again, we

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can break these components down to identify possible causes for an ROE change more specifically. Figure 3.1illustrates the DuPont system of analysis breakdown of ROA and ROE. The figure highlights how many of the ratiosdiscussed in this chapter are linked.

time out!3-16 What are the DuPont ROA and ROE equations?3-17 How do each of these equations help to explain firm performance and pinpoint areas for improvement?

EXAMPLE 3-6Application of DuPontAnalysis LG3-6

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for theasset management ratios.

SOLUTION:

The ROA and ROE DuPont equations for DPH Tree Farm, Inc., arecalculated as follows. The industry average is reported below eachratio.

As we saw with profitability ratios, DPH Tree Farm, Inc., is moreprofitable than the average firm in the tree farm industry when it comesto overall efficiency expressed as return on assets, or ROA. TheDuPont equation highlights that this superior performance comes fromboth profit margin (operating efficiency) and total asset turnover(efficiency in asset use). Despite this, the ROE for DPH Tree Farm lagsthe average industry ROE. The DuPont equation highlights that this

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inferior performance is due solely to the low level of debt and high levelof equity used by DPH Tree Farm relative to the industry.

Similar to Problems 3-11, 3-12

3.7 • OTHER RATIOSSpreading the Financial Statements LG3-6In addition to the many ratios listed, managers, analysts, and investors can also compute additional ratios bydividing all balance sheet amounts by total assets and all income statement amounts by net sales. These calculations,sometimes called spreading the financial statements, yield what we call common-size financial statements that correctfor sizes. Year-to-year growth rates in common-size balance sheets and income statement balances provide usefulratios for identifying trends. They also allow for an easy comparison of balance sheets and income statements acrossfirms in the industry. Common-size financial statements may provide quantitative clues about the direction that thefirm (and perhaps the industry) is moving. They may thus provide roadmaps for managers’ next moves.

common-size financial statements Dividing all balance sheet amounts by total assets and all income statement amounts by net sales.

Internal and Sustainable Growth RatesRemember again that any firm manager’s job is to maximize the firm’s market value. The firm’s ROA and ROE canbe used to evaluate the firm’s ability to grow and its market value to be maximized. Specifically, managers, analysts,and investors use these ratios to calculate two growth measures: the internal growth rate and the sustainable growthrate.

The internal growth rate is the growth rate a firm can sustain if it uses only internal financing—that is, retainedearnings—to finance future growth. Mathematically, the internal growth rate is

internal growth rate The growth rate a firm can sustain if it finances growth using only internal financing, that is, retained earningsgrowth.

(3-32)

where RR is the firm’s earnings retention ratio. The retention ratio represents the portion of net income that the firmreinvests as retained earnings:

(3-33)

Since a firm either pays its net income as dividends to its stockholders or reinvests those funds as retained earnings,the dividend payout and the retention ratios must always add to one:

(3-34)

EXAMPLE 3-7Calculating Internal andSustainable Growth Rates LG3-6

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For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Use the balance sheet (Table 2.1) and income statement (Table 2.2)for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for theasset management ratios.

SOLUTION:

The internal and sustainable growth rates for DPH Tree Farm, Inc., arecalculated as follows. The industry average is reported alongside eachratio.

These ratios show that DPH Tree Farm, Inc., can grow faster than theindustry if the firm uses only retained earnings to finance the growth.However, if DPH grows while keeping the debt ratio constant (e.g., bothdebt and retained earnings are used to finance the growth), industryfirms can grow much faster than DPH Tree Farm. Once again, DPH’slow debt level and high equity level relative to the industry creates thisdisparity. Therefore, DPH Tree Farm limits its growth as a result of itsmanagerial decisions.

Similar to Problems 3-13, 3-14, Self-Test Problem 2

the Math Coach on…

“When putting values into the equation, enter them in decimal format,not percentage format:CORRECT: 1 – (0.1404 X 0.6875)NOT CORRECT: 1 – (14.04 X 68.75)„

A problem arises when a firm relies only on internal financing to support asset growth: Through time, its debt ratiowill fall because as asset values grow, total debt stays constant—only retained earnings finance asset growth. If totaldebt remains constant as assets grow, the debt ratio decreases. As we noted above, shareholders often becomedisgruntled if, as the firm grows, a decreasing debt ratio (increasing equity financing) dilutes their return. So as firmsgrow, managers must often try to maintain a debt ratio that they view as optimal. In this case, managers finance asset

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growth with new debt and retained earnings. The maximum growth rate that can be achieved this way is thesustainable growth rate. Mathematically, the sustainable growth rate is

sustainable growth rate The growth rate a firm can sustain if it finances growth using both debt and internal financing such that thedebt ratio remains constant.

(3-35)

Maximizing the sustainable growth rate helps firm managers maximize firm value. When applying the DuPont ROEequation (3-31) here (i.e., ROE = Profit margin × Total asset turnover × Equity multiplier), notice that a firm’ssustainable growth depends on four factors:

1. The profit margin (operating efficiency).2. The total asset turnover (efficiency in asset use).

3. Financial leverage (the use of debt versus equity to finance assets).4. Profit retention (reinvestment of net income into the firm rather than paying it out as dividends).

Increasing any of these factors increases the firm’s sustainable growth rate and hence helps to maximize firm value.Managers, analysts, and investors will want to focus on these areas as they evaluate firm performance and marketvalue.

time out!3-18 What does “spreading the financial statements” mean?3-19 What are retention rates and internal and sustainable growth rates?3-20 What factors enter into sustainable growth rates?

3.8 • TIME SERIES AND CROSS-SECTIONALANALYSES LG3-7We have explored many ratios that allow managers and investors to examine firm performance. But to really analyzeperformance in a meaningful way, we must interpret our ratio results against some kind of standard or benchmark.To interpret financial ratios, managers, analysts, and investors use two major types of benchmarks: (1) performanceof the firm over time (time series analysis) and (2) performance of the firm against one or more companies in the sameindustry (cross-sectional analysis).

time series analysis Analyzing firm performance by monitoring ratio trends.

cross-sectional analysis Analyzing the performance of a firm against one or more companies in the same industry.

Analyzing ratio trends over time, along with absolute ratio levels, gives managers, analysts, and investorsinformation about whether a firm’s financial condition is improving or deteriorating. For example, ratio analysismay reveal that the days’ sales in inventory is increasing. This suggests that inventories, relative to the sales theysupport, are not being used as well as they were in the past. If this increase is the result of a deliberate policy toincrease inventories to offer customers a wider choice and if it results in higher future sales volumes or increasedmargins that more than compensate for increased capital tied up in inventory, the increased relative size of theinventories is good for the firm. Managers and investors should be concerned, on the other hand, if increasedinventories result from declining sales but steady purchases of supplies and production.

Looking at one firm’s financial ratios, even through time, gives managers, analysts, and investors only a limited

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picture of firm performance. Ratio analysis almost always includes a comparison of one firm’s ratios relative to theratios of other firms in the industry, or cross-sectional analysis. The key to cross-sectional analysis is identifyingsimilar firms that compete in the same markets, have similar asset sizes, and operate in a similar manner to the firmbeing analyzed. Since no two firms are identical, obtaining such a comparison group is no easy task. Thus, thechoice of which companies to use in a cross-sectional analysis is at best subjective. Note that as we calculated thefinancial ratios for DPH Tree Farm, Inc., throughout the chapter, we compared them to the industry average.Comparative ratios that can be used in cross-sectional analysis are available from many sources. For example, ValueLine Investment Surveys, Robert Morris Associates, Hoover’s Online (at www.hoovers.com), and MSN Moneywebsite (at moneycentral.msn.com) are examples of four major sources of financial ratios for numerous industriesthat operate within the United States and worldwide.

time out!3-21 What is time series analysis of a firm’s operations?3-22 What is cross-sectional analysis of a firm’s operations?3-23 How do time series and cross-sectional analyses differ, and what information would you expect to gain from each?

3.9 • CAUTIONS IN USING RATIOS TO EVALUATE FIRMPERFORMANCE LG3-8Financial statement analysis allows managers, analysts, and investors to better understand a firm’s performance.However, data from financial statements should not be received without certain cautions. These include

1. Financial statement data are historical. Historical data may not reflect future performance. While we can make projections usinghistorical data, we must also remember that projections may be inaccurate if historical performance does not persist.

2. As we discussed in Chapter 2, firms use different accounting procedures. For example, inventory methods can vary. One firm may useFIFO (first-in, first-out), transferring inventory at the first purchase price, while another uses LIFO (last-in, first-out), transferringinventory at the last purchase price. Likewise, the depreciation method used to value a firm’s fixed assets over time may vary acrossfirms. One firm may use straight-line depreciation, while another may use an accelerated depreciation method (e.g., MACRS).Particularly when reviewing cross-sectional ratios, differences in accounting rules can affect balance sheet values and financial ratios.It is important to know which accounting rules the firms under consideration are using before making any conclusions about theirperformance from ratio analysis.

3. Similarly, a firm’s cross-sectional competitors may often be located around the world. Financial statements for firms based outside theUnited States do not necessarily conform to GAAP. Even beyond inventory pricing and depreciation methods, different accountingstandards and procedures make it hard to compare financial statements and ratios of firms based in different countries.

4. Sales and expenses vary throughout the year. Managers, analysts, and investors need to note the timing of these fund flows whenperforming cross-sectional analysis. Otherwise they may draw conclusions from comparisons that are actually the result of seasonalcash flow differences. Similarly, firms end their fiscal years at different dates. For cross-sectional analysis, this complicatesany comparison of balance sheets during the year. Likewise, one-time events, such as a merger, may affect a firm’sfinancial performance. Cross-sectional analysis involving these events can result in misleading conclusions.

5. Large firms often have multiple divisions or business units engaged in different lines of business. In this case, it is difficult to trulycompare a set of firms with which managers and investors can perform cross-sectional analysis.

6. Firms often window dress their financial statements to make annual results look better. For example, to improve liquidity ratioscalculated with year-end balance sheets, firms often delay payments for raw materials, equipment, loans, and so on to build up theirliquid accounts and thus their liquidity ratios. If possible, it is often more accurate to use something other than year-end financialstatements to conduct ratio analysis.

7. Individual analysts may calculate ratios in modified forms. For example, one analyst may calculate ratios using year-end balance sheetdata, while another may use the average of the beginning- and end-of-year balance sheet data. If the firm’s balance sheet haschanged significantly during the year, this difference in the way the ratio is calculated can cause large variations in ratio values for agiven period of analysis and large variations in any conclusions drawn from these ratios regarding the financial health of the firm.

Financial statement ratio analysis is a major part of evaluating a firm’s performance. If managers, analysts, orinvestors ignore the issues noted here, they may well draw faulty conclusions from their analysis. However, usedintelligently and with good judgment, ratio analysis can provide useful information on a firm’s current position andhint at future performance.

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time out!3-24 What cautions should managers and investors take when using ratio analysis to evaluate a firm?

Get Online

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Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. Classify each of the following ratios according to a ratio category (liquidity ratio, asset management ratio, debtmanagement ratio, profitability ratio, or market value ratio). (LG3-1 through LG3-5)

a. Current ratio

b. Inventory turnover

c. Return on assets

d. Average payment period

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e. Times interest earned

f. Capital intensity

g. Equity multiplier

h. Basic earnings power

2. For each of the following actions, determine what would happen to the current ratio. Assume nothing else onthe balance sheet changes and that net working capital is positive. (LG3-1)

a. Accounts receivable are paid in cash.

b. Notes payable are paid off with cash.

c. Inventory is sold on account.

d. Inventory is purchased on account.

e. Accrued wages and taxes increase.

f. Long-term debt is paid with cash.

g. Cash from a short-term bank loan is received.

3. Explain the meaning and significance of the following ratios. (LG3-1 through LG3-5)

a. Quick ratio

b. Average collection period

c. Return on equity

d. Days’ sales in inventory

e. Debt ratio

f. Profit margin

g. Accounts payable turnover

h. Market-to-book ratio

4. A firm has an average collection period of 10 days. The industry average ACP is 25 days. Is this a good or poorsign about the management of the firm’s accounts receivable? (LG3-2)

5. A firm has a debt ratio of 20 percent. The industry average debt ratio is 65 percent. Is this a good or poor signabout the management of the firm’s financial leverage? (LG3-3)

6. A firm has an ROE of 20 percent. The industry average ROE is 12 percent. Is this a good or poor sign about themanagement of the firm? (LG3-4)

7. Why is the DuPont system of analysis an important tool when evaluating firm performance? (LG3-6)

8. A firm has an ROE of 10 percent. The industry average ROE is 15 percent. How can the DuPont system ofanalysis help the firm’s managers identify the reasons for this difference? (LG3-6)

9. What is the difference between the internal growth rate and the sustainable growth rate? (LG3-6)

10. What is the difference between time series analysis and cross-sectional analysis? (LG3-7)

11. What information do time series and cross-sectional analyses provide for firm managers, analysts, andinvestors? (LG3-7)

12. Why is it important to know a firm’s accounting rules before making any conclusions about its performancefrom ratios analysis? (LG3-8)

13. What does it mean when a firm window dresses its financial statements? (LG3-8)

ProblemsBASIC PROBLEMS

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3-1  Liquidity Ratios You are evaluating the balance sheet for PattyCake’s Corporation. From the balancesheet you find the following balances: cash and marketable securities = $400,000; accounts receivable =$1,200,000; inventory = $2,100,000; accrued wages and taxes = $500,000; accounts payable = $800,000;and notes payable = $600,000. Calculate PattyCake’s current ratio, quick ratio, and cash ratio. (LG3-1)

3-2  Liquidity Ratios The top part of Ramakrishnan, Inc.’s, 2018 and 2017 balance sheets is listed below (inmillions of dollars). Calculate Ramakrishnan, Inc.’s, current ratio, quick ratio, and cash ratio for 2018 and2017. (LG3-1)

2018 2017 2018 2017

Current assets Current liabilities

 Cash and marketable securities $ 34 $ 25  Accrued wages and taxes $ 32 $ 31

 Accounts receivable 143 128  Accounts payable 87 76

 Inventory 206 187  Notes payable 76 68

  Total $383 $340   Total $195 $175

3-3 Asset Management Ratios Tater and Pepper Corp. reported sales for 2018 of $23 million. Tater andPepper listed $5.6 million of inventory on its balance sheet. Using a 365-day year, how many days didTater and Pepper’s inventory stay on the premises? How many times per year did Tater and Pepper’sinventory turn over? (LG3-2)

3-4 Asset Management Ratios Mr. Husker’s Tuxedos Corp. ended the year 2018 with an average collectionperiod of 32 days. The firm’s credit sales for 2018 were $56.1 million. What is the year-end 2018 balancein accounts receivable for Mr. Husker’s Tuxedos? (LG3-2)

3-5 Debt Management Ratios Tiggie’s Dog Toys, Inc., reported a debt-to-equity ratio of 1.75 times at the endof 2018. If the firm’s total debt at year-end was $25 million, how much equity does Tiggie’s have on itsbalance sheet? (LG3-3)

3-6 Debt Management Ratios You are considering a stock investment in one of two firms (LotsofDebt, Inc.,and LotsofEquity, Inc.), both of which operate in the same industry. LotsofDebt, Inc., finances its $30million in assets with $29 million in debt and $1 million in equity. LotsofEquity, Inc., finances its $30million in assets with $1 million in debt and $29 million in equity. Calculate the debt ratio, equitymultiplier, and debt-to-equity ratio for the two firms. (LG3-3)

3-7 Profitability Ratios Maggie’s Skunk Removal Corp.’s 2018 income statement listed net sales of $12.5million, gross profit of $6.9 million, EBIT of $5.6 million, net income available to common stockholdersof $3.2 million, and common stock dividends of $1.2 million. The 2018 year-end balance sheet listed totalassets of $52.5 million and common stockholders’ equity of $21 million with 2 million sharesoutstanding. Calculate the gross profit margin, operating profit margin, profit margin, basic earningspower, ROA, ROE, and dividend payout. (LG3-4)

3-8 Profitability Ratios In 2018, Jake’s Jamming Music, Inc., announced an ROA of 8.56 percent, ROE of14.5 percent, and profit margin of 20.5 percent. The firm had total assets of $9.5 million at year-end 2018.Calculate the 2018 values of net income available to common stockholders, common stockholders’ equity,and net sales for Jake’s Jamming Music, Inc. (LG3-4)

3-9 Market Value Ratios You are considering an investment in Roxie’s Bed & Breakfast Corp. During thelast year, the firm’s income statement listed an addition to retained earnings of $4.8 million and commonstock dividends of $2.2 million. Roxie’s year-end balance sheet shows common stockholders’ equity of$35 million with 10 million shares of common stock outstanding. The common stock’s market price pershare was $9.00. What is Roxie’s Bed & Breakfast’s book value per share and earnings per share?Calculate the market-to-book ratio and PE ratio. (LG3-5)

3-10 Market Value Ratios Dudley Hill Golf Club’s market-to-book ratio is currently 2.5 times and the PEratio is 6.75 times. If Dudley Hill Golf Club’s common stock is currently selling at $22.50 per share,what are the book value per share and earnings per share? (LG3-5)

3-11 DuPont Analysis If Silas 4-Wheeler, Inc., has an ROE of 18 percent, equity multiplier of 2, and aprofit margin of 18.75 percent, what are the total asset turnover and the capital intensity? (LG3-6)

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3-12 DuPont Analysis Last year, Hassan’s Madhatter, Inc., had an ROA of 7.5 percent, a profit margin of12 percent, and sales of $25 million. Calculate Hassan’s Madhatter’s total assets. (LG3-6)

3-13 Internal Growth Rate Last year, Lakesha’s Lounge Furniture Corporation had an ROA of 7.5percent and a dividend payout ratio of 25 percent. What is the internal growth rate? (LG3-6)

3-14 Sustainable Growth Rate Last year Lakesha’s Lounge Furniture Corporation had an ROE of 17.5percent and a dividend payout ratio of 20 percent. What is the sustainable growth rate? (LG3-6)

INTERMEDIATE PROBLEMS

3-15 Liquidity Ratios Brenda’s Bar and Grill has current liabilities of $15 million. Cash makes up 10percent of the current assets and accounts receivable makes up another 40 percent of current assets.Brenda’s current ratio is 2.1 times. Calculate the value of inventory listed on the firm’s balance sheet.(LG3-1)

3-16 Liquidity and Asset Management Ratios Mandesa, Inc., has current liabilities of $8 million, currentratio of 2 times, inventory turnover of 12 times, average collection period of 30 days, and credit salesof $64 million. Calculate the value of cash and marketable securities. (LG3-1, LG3-2)

3-17 Asset Management and Profitability Ratios You have the following information on Els’ Putters,Inc.: Sales to working capital is 4.6 times, profit margin is 20 percent, net income available tocommon stockholders is $5 million, and current liabilities are $6 million. What is the firm’s balance ofcurrent assets? (LG3-2, LG3-4)

3-18 Asset Management and Debt Management Ratios Use the following information to complete thefollowing balance sheet. Sales are $8.8 million, capital intensity ratio is 2.10 times, debt ratio is 55percent, and fixed asset turnover is 1.2 times. (LG3-2, LG3-3)

Assets Liabilities and Equity

Current assets $   Total liabilities $  

Fixed assets    Total equity   

Total assets $   Total liabilities and equity $  

3-19 Debt Management Ratios Tiggie’s Dog Toys, Inc., reported a debt-to-equity ratio of 1.75 times atthe end of 2018. If the firm’s total assets at year-end were $25 million, how much of their assets arefinanced with debt and how much with equity? (LG3-3)

3-20 Debt Management Ratios Calculate the times interest earned ratio for LaTonya’s Flop Shops, Inc.,using the following information. Sales are $1.5 million, cost of goods sold is $600,000, depreciationexpense is $150,000, other operating expenses is $300,000, addition to retained earnings is $146,250,dividends per share is $1, tax rate is 30 percent, and number of shares of common stock outstanding is90,000. LaTonya’s Flop Shops has no preferred stock outstanding. (LG3-3)

3-21 Profitability and Asset Management Ratios You are thinking of investing in Nikki T’s, Inc. Youhave only the following information on the firm at year-end 2018: Net income is $250,000, total debtis $2.5 million, and debt ratio is 55 percent. What is Nikki T’s ROE for 2018? (LG3-2, LG3-4)

3-22 Profitability Ratios Rick’s Travel Service has asked you to help piece together financial informationon the firm for the most current year. Managers give you the following information: Sales are $8.2million, total debt is $2.1 million, debt ratio is 40 percent, and ROE is 18 percent. Using thisinformation, calculate Rick’s ROA. (LG3-4)

3-23 Market Value Ratios Leonatti Labs’ year-end price on its common stock is $35. The firm has totalassets of $50 million, debt ratio of 65 percent, no preferred stock, and 3 million shares of commonstock outstanding. Calculate the market-to-book ratio for Leonatti Labs. (LG3-5)

3-24 Market Value Ratios Leonatti Labs’ year-end price on its common stock is $15. The firm has a profitmargin of 8 percent, total assets of $42 million, a total asset turnover of 0.75, no preferred stock, and 3million shares of common stock outstanding. Calculate the PE ratio for Leonatti Labs. (LG3-5)

3-25 DuPont Analysis Last year, Stumble-on-Inn, Inc., reported an ROE of 18 percent. The firm’s debt

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ratio was 55 percent, sales were $15 million, and the capital intensity was 1.25 times. Calculate the netincome for Stumble-on-Inn last year. (LG3-6)

3-26 DuPont Analysis You are considering investing in Nuran Security Services. You have been able tolocate the following information on the firm: Total assets are $24 million, accounts receivable are $3.3million, ACP is 25 days, net income is $3.5 million, and debt-to-equity is 1.2 times. Calculate theROE for the firm. (LG3-6)

3-27 Internal Growth Rate Dogs R Us reported a profit margin of 10.5 percent, total asset turnover of0.75 times, debt-to-equity of 0.80 times, net income of $500,000, and dividends paid to commonstockholders of $200,000. The firm has no preferred stock outstanding. What is Dogs R Us’s internalgrowth rate? (LG3-6)

3-28 Sustainable Growth Rate You have located the following information on Webb’s Heating & AirConditioning: Debt ratio is 54 percent, capital intensity is 1.10 times, profit margin is 12.5 percent,and the dividend payout is 25 percent. Calculate the sustainable growth rate for Webb. (LG3-6)

Use the following financial statements for Lake of Egypt Marina, Inc., to answer Problems 3-29 through 3-33.

LAKE OF EGYPT MARINA, INC.Balance Sheet as of December 31, 2018 and 2017

(in millions of dollars)

2018 2017 2018 2017

Assets Liabilities and Equity

Current assets Current liabilities

Cash and marketablesecurities

$ 75 $ 65 Accrued wages and taxes $ 40 $ 43

Accounts receivable 115 110 Accounts payable 90 80

Inventory 200 190 Notes payable   80   70

Total $ 390 $ 365 Total $ 210 $ 193

Fixed assets Long-term debt $ 300 $ 280

Gross plant and equipment $ 580 $ 471

Less: Depreciation  110  100 Stockholders’ equity

Net plant and equipment $ 470 $ 371 Preferred stock (5 million shares) $ 5 $ 5

Common stock and paid-in surplus (65million shares)

65 65

Other long-term assets   50   49 Retained earnings  330  242

Total $ 520 $ 420 Total $ 400 $ 312

Total assets $ 910 $ 785 Total liabilities and equity $ 910 $ 785

LAKE OF EGYPT MARINA, INC.Income Statement for Years Ending December 31, 2018 and 2017

(in millions of dollars)

2018 2017

Net sales (all credit) $ 515 $ 432

Less: Cost of goods sold   230   175

Gross profits $ 285 $ 257

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Less: Other operating expenses    30    25

Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 255 $ 232

Less: Depreciation    22    20

Earnings before interest and taxes (EBIT) $ 233 $ 212

Less: Interest    33    30

Earnings before taxes (EBT) $ 200 $ 182

Less: Taxes    57    55

Net income $ 143 $ 127

Less: Preferred stock dividends $ 5 $ 5

Net income available to common stockholders $ 138 $ 122

Less: Common stock dividends 65 65

Addition to retained earnings $ 73 $ 57

Per (common) share data:

 Earnings per share (EPS) $ 2.123 $ 1.877

 Dividends per share (DPS) $ 1.000 $ 1.000

 Book value per share (BVPS) $ 6.077 $ 4.723

 Market value (price) per share (MVPS) $14.750 $12.550

3-29 Spreading the Financial Statements Spread the balance sheets and income statements of Lake ofEgypt Marina, Inc., for 2018 and 2017. (LG3-6)

3-30 Calculating Ratios Calculate the following ratios for Lake of Egypt Marina, Inc., as of year-end2018. (LG3-1 through LG3-5)

Lake of Egypt Marina, Inc. Industry

a. Current ratio 2.00 times

b. Quick ratio 1.20 times

c. Cash ratio 0.25 times

d. Inventory turnover 3.60 times

e. Days’ sales in inventory 101.39 days

f. Average collection period 32.50 days

g. Average payment period 45.00 days

h. Fixed asset turnover 1.25 times

i. Sales to working capital 4.25 times

j. Total asset turnover 0.85 times

k. Capital intensity 1.18 times

l. Debt ratio 62.50%

m. Debt-to-equity 1.67 times

n. Equity multiplier (total equity) 2.67 times

o. Times interest earned 8.50 times

p. Cash coverage 8.75 times

q. Profit margin 28.75%

r. Gross profit margin 56.45%

s. Operating profit margin 46.78%

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t. Basic earnings power 32.50%

u. ROA 19.75%

v. ROE 36.88%

w. Dividend payout 35.00%

x. Market-to-book ratio 2.55 times

y. PE ratio 15.60 times

3-31 DuPont Analysis Construct the DuPont ROA and ROE breakdowns for Lake of Egypt Marina, Inc.(LG3-6)

3-32 Internal and Sustainable Growth Rates Calculate the internal and sustainable growth rate for Lakeof Egypt Marina, Inc. (LG3-6)

3-33 Cross-Sectional Analysis Using the ratios from Problem 3-30 for Lake of Egypt Marina, Inc., and theindustry, what can you conclude about Lake of Egypt Marina’s financial performance for 2018? (LG3-7)

ADVANCED PROBLEMS

3-34 Ratio Analysis Use the following information to complete the balance sheet below. (LG3-1 throughLG3-5)

Current ratio = 2.5 timesProfit margin = 10%Sales = $1,200mROE = 20% Long-term debt to long-term debt and equity = 55%

Current assets $   Current liabilities $ 210

Fixed assets    Long-term debt   

Stockholders’ equity   

Total assets $   Total liabilities and equity $  

3-35 Ratio Analysis Use the following information to complete the balance sheet below. (LG3-1 throughLG3-5)

Current ratio = 2.20 timesCredit sales = $1,200mAverage collection period = 60 daysInventory turnover = 1.50 timesTotal asset turnover = 0.75 timesDebt ratio = 60%

Cash $  

Accounts receivable     Current liabilities $500m

Inventory     Long-term debt    

Current assets $   Total Debt $  

Fixed assets     Stockholders’ equity    

Total assets $    Total liabilities and equity $   

3-36 DuPont Analysis Last year, K9 WebbWear, Inc., reported an ROE of 20 percent. The firm’s debtratio was 55 percent, sales were $20 million, and the capital intensity was 1.25 times. Calculate the netincome and profit margin for K9 WebbWear last year. This year, K9 WebbWear plans to increase itsdebt ratio to 60 percent. The change will not affect sales or total assets; however, it will reduce thefirm’s profit margin to 11 percent. By how much will the change in K9 WebbWear’s debt ratio affectits ROE? (LG3-6)

3-37 DuPont Analysis You are considering investing in Dakota’s Security Services. You have been able to

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locate the following information on the firm: Total assets are $32 million, accounts receivable are $4.4million, ACP is 25 days, net income is $4.66 million, and debt-to-equity is 1.2 times. All sales are oncredit. Dakota’s is considering loosening its credit policy such that ACP will increase to 30 days. Thechange is expected to increase credit sales by 5 percent. Any change in accounts receivable will beoffset with a change in debt. No other balance sheet changes are expected. Dakota’s profit margin willremain unchanged. How will this change in accounts receivable policy affect Dakota’s net income,total asset turnover, equity multiplier, ROA, and ROE? (LG3-6)

3-38 Internal Growth Rate Last year, Marly Brown, Inc., reported an ROE of 20 percent. The firm’s debt-to-equity was 1.50 times, sales were $20 million, the capital intensity was 1.25 times, and dividendspaid to common stockholders were $1,000,000. The firm has no preferred stock outstanding. Thisyear, Marly Brown plans to decrease its debt-to-equity ratio to 1.20 times. The change will not affectsales, total assets, or dividends paid; however, it will reduce the firm’s profit margin to 9.85 percent.Use the DuPont equation to determine how the change in Marly Brown’s debt ratio will affect itsinternal growth rate. (LG3-6)

3-39 Sustainable Growth Rate You are considering investing in Annie’s Eatery. You have been able tolocate the following information on the firm: Total assets are $40 million, accounts receivable are $6.0million, ACP is 30 days, net income is $4.75 million, debt-to-equity is 1.5 times, and dividendpayout ratio is 45 percent. All sales are on credit. Annie’s is considering loosening its creditpolicy such that ACP will increase to 35 days. The change is expected to increase credit sales by 5percent. Any change in accounts receivable will be offset with a change in debt. No other balancesheet changes are expected. Annie’s profit margin and dividend payout ratio will remain unchanged.Use the DuPont equation to determine how this change in accounts receivable policy will affectAnnie’s sustainable growth rate. (LG3-6)

NotesCHAPTER 31 To see this remember the balance sheet identity is Assets (A) = Debt (D) + Equity (E). Dividing each side of this equation by assets, we

get A/A = D/A + E/A. Rearranging this equation, D/A = A/A − E/A = 1 − E/A = 1 − [1/(A/E)]. Also, D/A = (A − E)/A = 1/[A/(A − E)] = 1/[(A− E + E)/(A − E)] = 1/[(E/(A − E) + (A − E)/(A − E)] = 1/[E/D + 1] = 1/[1/(D/E) + 1]. Dividing each side of the balance sheet identityequation by equity, we get A/E = D/E + E/E, or A/E = D/E + 1. Also, rearranging this equation, D/E = A/E − 1.

2 The fixed-charge and cash coverage ratios can be tailored to a particular firm’s situation, depending on what really constitutes fixedcharges that must be paid. One version of it follows: (EBIT + Lease payments)/[Interest + Lease payments + Sinking fund/(1 − t)],where t is the firm’s marginal tax rate. Here, it is assumed that sinking fund payments must be made. They are adjusted by the divisionof (1 − t) into a before-tax cash outflow so they can be added to other before-tax cash outflows.

I

chapter fourtime value of money 1:analyzing single cash flows

©liseykina/Shutterstock

n business and personal life, cash flows of different types are paid and received in the future. Yourcompany can contract to build and ship its product to a foreign buyer for a $10 million single payment intwo years. You may have a car loan and a $300 per month level payment over the next four years. It

may be that you will pay a series of uneven tuition payments over the next couple of years as tuitionchanges. Whether the future entails single, level, or uneven cash flows, we need a method for comparingthem when paid at different points in time.

Both this chapter and the next illustrate time value of money (TVM) calculations, which we will usethroughout the rest of this book. We hope you will see what powerful tools they are for making financialdecisions. Whether you’re managing the financial or other functional area of a business or makingdecisions in your personal life, being able to make TVM calculations will help you make financially sounddecisions.

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This background will also allow you to understand why CEOs, CFOs, and other professionals makethe decisions that they do. Together, this chapter and the next will present all aspects of TVM. Sincesome students find this topic intimidating, we split the topic into two chapters as a way of providing moreexamples and practice opportunities. As you see the examples and work the practice problems, webelieve that you will find that TVM is not difficult.

Factors to consider when making time value of money decisions includeSize of the cash flows.

Time between the cash flows.Rate of return we can earn.

LEARNING GOALS

LG4-1 Create a cash flow time line.LG4-2 Compute the future value of money.LG4-3 Show how the power of compound interest increases wealth.LG4-4 Calculate the present value of a payment made in the future.LG4-5 Move cash flows from one year to another.LG4-6 Apply the Rule of 72.LG4-7 Compute the rate of return realized on selling an investment.LG4-8 Calculate the number of years needed to grow an investment.

viewpointsbusiness APPLICATIONAs the production manager of Head Phone Gear, Inc., you have received an offer from the supplier who provides the wires used inheadsets. Due to poor planning, the supplier has an excess amount of wire and is willing to sell $500,000 worth for only $450,000.You already have one year’s supply on hand. It would cost you $2,000 to store the wire until Head Phone Gear needs it next year.What implied interest rate would you be earning if you purchased and stored the wire? Should you make the purchase? (See thesolution at the end of the book.)

The title of this chapter refers to the time value of money. But why might money change values, andwhy does it depend on time? The term “time value of money” really refers to the difference in buyingpower for a dollar over time. Consider that $100 can buy you an assortment of food and drinks today. Willyou be able to buy those same items in five years with the same $100? Probably not. Inflation mightcause these items to cost $120. If so, in terms of buying “stuff,” the dollar would have lost value over thefive years. If you don’t need to spend your money today, putting it in your mattress will only cause it tolose value over time. Instead, there are banks that would like to use your money and pay you back later,with interest. This interest is your compensation to offset the money’s decline in value. Each dollar will beworth less in the future, but you’ll get more dollars. So you’ll be able to buy the same items as before.

The basic idea behind the time value of money is that $1 today is worth more than $1 promised nextyear. But how much more? Is $1 today worth $1.05 next year? $1.08? $1.12? The answer variesdepending on current interest rates. This chapter describes the time value of money concept and providesthe tools needed to analyze single cash flows at different points in time.■

4.1 • ORGANIZING CASH FLOWS LG4-1Managing cash flow timing is one of the most important tasks in successfully operating a business. A helpful toolfor organizing our analysis is the time line, which shows the magnitude of cash flows at different points in time, such

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as monthly, quarterly, semiannually, or yearly. Cash we receive is called an inflow, and we denote it with a positivenumber. Cash that leaves us, such as a payment or contribution to a deposit, is an outflow designated with a negativenumber.

time line A graphical representation showing the size and timing of cash flows through time.

inflow Cash received, often from income or sale of an investment.

outflow Cash payment, often a cost or the price of an investment or deposit.

The following time line illustrates a $100 deposit you made at a bank that pays 5 percent interest. In one year, the$100 has become $105. Given that interest rate, having $100 now (in year 0) has the same value as having $105 inone year.

Here’s a simple example: Suppose you allowed the bank to rent your $100 for a year at a cost of 5 percent, or $5.This cost is known as the interest rate.

interest rate The cost of borrowing money denoted as a percent.

personal APPLICATIONPayday lending has become a multibillion-dollar industry across the United States in just a few years. It provides people with short-term loans and gets its name from the fact that the loan is to be paid back at the borrower’s next payday. Anthony is short a fewhundred dollars and his next paycheck is two weeks away. For a $300 loan, Anthony must pay a $50 “fee” in advance and repay the$300 loan in two weeks. What implied interest rate would Anthony pay for this two-week period? Is this a good deal? (See thesolution at the end of the book.)

But what if Anthony can’t pay the loan back on time?

Interest rates will affect you throughout your life, both in business and in your personal life. Companies borrowmoney to build factories and expand into new locations and markets. They expect the future revenues generated bythese activities to more than cover the interest payments and repay the loan. People borrow money on credit cardsand obtain loans for cars and home mortgages. They expect their purchases to give them the satisfaction in the futurethat compensates them for the interest payments charged on the loan. Understanding the dynamics between interestrates and cash inflows and outflows over time is key to financial success. The best place to start learning theseconcepts lies in understanding how money grows over time.

4.2 • FUTURE VALUE LG4-2The $105 one-time cash flow that your bank credits to your account in one year is known as a future value (FV) of$100 in one year at a 5 percent annual interest rate. If interest rates were higher than 5 percent, then the future valueof your $100 would also be higher. If you left your money in the bank for more than one year, then its future valuewould continue to grow over time. Let’s see why.

future value (FV) The value of an investment after one or more periods.

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time out!4-1 Why is a dollar worth more today than a dollar received one year from now?4-2 Drawing on your past classes in accounting, explain why time lines must show one negative cash flow and one positive

cash flow.

4-3 Set up a time line, given a 6 percent interest rate, with a cash inflow of $200 today and a cash outflow of $212 in one year.

Single-Period Future ValueComputing the future value of a sum of money one year from today is straightforward: Add the interest earned totoday’s cash flow. In this case

We computed the $5 interest figure by multiplying the interest rate by today’s cash flow ($100 × 5%). Note that inequations, interest rates appear in decimal format. So we use 0.05 for 5 percent:

Note that this is the same as

We need the 1 in the parentheses to recapture the original deposit and the 0.05 is for the interest earned. We cangeneralize this computation to any amount of today’s cash flow. In the general form of the future value equation, wecall cash today present value, or PV. We compute the future value one year from now, called FV1, using the interestrate, i:

present value (PV) The amount a future cash flow is worth today.

(4-1)

▼ TABLE 4.1 Higher Interest Rates and Cash Flows Lead to Higher Future Values

A B C D

1 Higher Interest Rates Lead to Higher Future Values

2 Today’s Cash Flow Interest Rate Interest Earned Next Year’s Future Value

3 $100.00 5% $5.00 $105.00

4 $100.00 6% $6.00 $106.00

5 $15,000.00 5% $750.00 $15,750.00

6 $15,000.00 6% $900.00 $15,900.00

7

8 Higher Cash Flows Today Lead to Higher Future Values

9 Today’s Cash Flow Interest Rate Interest Earned Next Year’s Future Value

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10 $500.00 7.50% $37.50 $537.50

11 $750.00 7.50% $56.25 $806.25

Notice that this is the same equation we used to figure the future value of your $100. We’ve simply made it genericso we can use it over and over again. The 1 subscript means that we are calculating for only one period—in thiscase, one year. If interest rates were 6 percent instead of 5 percent per year, for instance, we could use equation 4-1to find that the future value of $100 in one year is $106 [= $100 × (1 + 0.06)].

Of course, the higher the interest rate, the larger the future value will be. Table 4.1 shows the interest earned andfuture value for a sample of different cash flows and interest rates. Notice from the first two lines of the table that,while the difference in interest earned between 5 percent and 6 percent ($1) doesn’t seem like much on a $100deposit, the difference on a $15,000 deposit (the following two lines) is substantial ($150).

Compounding and Future Value LG4-3After depositing $100 for one year, you must decide whether to take the $105 or leave the money at the bank foranother year to earn another 5 percent (or whatever interest rate the bank currently pays). In the second year at thebank, the deposit earns 5 percent on the $105 value, which is $5.25 (= $105 × 0.05). Importantly, you get more thanthe $5 earned the first year, which would be a simple total of $110. The extra 25 cents earned in the second year isinterest on interest that was earned in the first year. We call this process of earning interest both on the originaldeposit and on the earlier interest payments compounding.

compounding The process of adding interest earned every period on both the original investment and the reinvested earnings.

So, let’s illustrate a $100 deposit made for two years at 5 percent

LG4-1

The question mark denotes the amount we want to solve for. As with all TVM problems, we simply have to identifywhat element we’re solving for; in this case, we’re looking for the FV. To compute the two-year compounded futurevalue, simply use the 1-year equation (4-1) twice.

So the future value of $100 deposited today at 5 percent interest is $110.25 in period 2. You can see that thisrepresents $10 of interest payments generated from the original $100 ($5 each year) and $0.25 of interest earned inthe second year on previously earned interest payments. The $5 of interest earned every year on the original depositis called simple interest. Any amount of interest earned above the $5 in any given year comes fromcompounding. Over time, the new interest payments earned from compounding can become substantial.The multiyear form of equation (4-1) is the future value in year N, shown as:

simple interest Interest earned only on the original deposit.

(4-2)

We can solve the two-year deposit problem more directly using equation 4-2 as $110.25 = $100 × (1.05)2. Here,solving for FV in the equation requires solving for only one unknown. In fact, all TVM equations that you willencounter only require figuring out what is unknown in the situation and solving for that one unknown factor.

We can easily adapt equation 4-2 to many different future value problems. What is the future value in 30 years ofthat $100 earning 5 percent per year? Using equation 4-2, we see that the future value is $100 × (1.05)30 = $432.19.

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The money has increased substantially! You have made a profit of $332.19 over and above your original $100. Ofthis profit, only $150 (= $5 × 30 years) came from simple interest earned on the original deposit. The rest, $182.19(= $332.19 − $150), is from the compounding effect of earning interest on previously earned interest.

Remember that the difference between earning 5 percent and 6 percent in interest on the $100 was only $1 the firstyear. So what is the future value difference after 15 years? Is it $15? No, as Figure 4.1 shows, the difference infuture value substantially increases over time. The difference is $31.76 in year 15 and $142.15 in year 30.

The Power of Compounding LG4-3 Compound interest is indeed a powerful tool for building wealth.Albert Einstein, the German-born American physicist who developed the special and general theories of relativityand won the Nobel Prize for Physics in 1921, is supposed to have said, “The most powerful force in the universe iscompound interest.”1 Figure 4.2 illustrates this point. It shows the original $100 deposited, the cumulative interestearned on that deposit, and the cumulative interest-on-interest earned. By the 27th year, the money from the interest-on-interest exceeds the interest earned on the original deposit. By the 40th year, interest-on-interest contributes morethan double the interest on the deposit. The longer money can earn interest, the greater the compounding effect.

FIGURE 4-1 The Future Value of $100

Small differences in interest rates can really add up over time!

FIGURE 4-2 Interest Earned on Prior Interest at a 5 Percent Rate

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The money from interest-on-interest will eventually exceed the interest from the original deposit.

Earning higher interest rates on the investment for additional time periods magnifies compounding power. Considerthe future value of $100 deposited at different interest rates and over different time periods as shown in Table 4.2.The future value of $100 earning 5 percent per year for five years is $127.63, for a gain of $27.63. Would youdouble your gain by simply investing that same $100 at double the interest rate, 10 percent? No, becausecompounding changes the nature of the investment so that your money grows exponentially, not in a simple linearrelationship. The future value of $100 in five years at 10 percent is $161.05. The $61.05 gain is more than doublethe gain of $27.63 earned at 5 percent. Tripling the interest rate to 15 percent shows a gain of $101.14 that is nearlyquadruple the gain earned at 5 percent.

The same effect occurs when we increase the time. When the deposit earns 10 percent per year for five years, thegain is $61.05. When we double the amount of time to 10 years, the gain more than doubles to $159.37. If we doublethe time again to 20 years, the gain increases not to just $318.74 (= $159.37 × 2) but to $572.75. At 10 percent for30 years, the gain on $100 is a whopping $1,644.94. Interest rates and time are both important factors incompounding! These relationships are illustrated in Figure 4.3.

▼ TABLE 4.2 Compounding Builds Wealth Over Time

A B C D E

1 Future Value of $100 Deposited at 5%, 10%, and 15% Interest Rates

2

3 Future Value

4 Interest Rate Earned 5 years 10 years 20 years 30 years

5 5% $127.63 $162.89 $265.33 $432.19

6 10% $161.05 $259.37 $672.75 $1,744.94

7 15% $201.14 $404.56 $1,636.65 $6,621.18

8

9 =FV(A7, 5, 0, −100) =FV(A6, 30, 0, −100)

▼FIGURE 4-3 The Impact of Time and the Magnitude of the Interest Rate

Future value of $100 deposited at 5%, 10%, and 15% interest rates: The future value differences between compounding interest ratesexpand exponentially over time.

EXAMPLE4-1 Graduation Celebration Loan LG4-3

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

Dominic is a fourth-year business student who wants to go on a graduationcelebration/vacation in Mexico but he has no money to pay for the trip. Afterthe vacation, Dominic will start his career. His job will require moving to a newtown and buying professional clothes. He asked his parents to lend him$1,500, which he figures he will be able to pay back in three years. Hisparents agree to lend him the money, but they will charge 7 percent interestper year. What amount will Dominic need to pay back? How much interest willhe pay? How much of what he pays is interest-on-interest?

SOLUTION:

Dominic will have to pay:

Of the $1,837.56 he owes his parents, $337.56 (= $1,837.56 − $1,500) isinterest. We can illustrate this time-value problem in the following time line.

Compare this compound interest with simple interest. Simple interest wouldbe 7 percent of $1,500 (which is $105) per year. The three-year cost would

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then be $315 (= 3 × $105). The difference between the compound interest of$337.56 and the total simple interest of $315 is the interest-on-interest of$22.56.

Similar to Problems 4-3, 4-4, 4-5, 4-6, 4-21, 4-22, 4-33, 4-34, Self-TestProblem 1

Compounding at Different Interest Rates Over Time LG4-4

We already know that the $100 deposit will grow to $105 at the end of the first year. This $105 will then earn 6percent in the second year and have a value of $111.30 (= $105 × 1.06). If we put the two steps together into oneequation, the solution appears as $111.30 = $100 × 1.05 × 1.06. From this you should not be surprised that a generalequation for future value of multiple interest rates is

(4-3)

Note that the future value equation 4-2 is a special case of the more general equation 4-3. If the interest rate everyperiod is the same, we can write equation 4-3 as equation 4-2.

time out!4-4 How does compounding help build wealth (or increase debt) over time?4-5 Why does doubling the interest rate or time quickly cause more than a doubling of the future value?

EXAMPLE 4-2Celebration Loan with PaybackIncentive LG4-3

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Reexamine the loan Dominic was seeking from his parents in theprevious example. His parents want to give him an incentive to pay offthe loan as quickly as possible. They structure the loan so they charge7 percent interest the first year and increase the rate 1 percent eachyear until the loan is paid. How much will Dominic owe if he waits threeyears to pay off the loan? Say that in the third year he considerswhether to pay off the loan or wait one more year. How much more willhe pay if he waits one more year?

SOLUTION:

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For a payment in the third year, Dominic will pay interest of 7 percentthe first year, 8 percent the second year, and 9 percent the third year.He will have to pay

The cash flow time line is

Even worse, if he waits until the fourth year, he will pay one year ofinterest at 10 percent. The total payment will be

Because of both the escalating interest rate and the compoundingeffect, Dominic must make timely and increasing payments the longerhe delays in paying off the loan. Deciding in the third year to put off thepayment an extra year would cost him an additional $188.94 (=$2,078.35 − $1,889.41).

Similar to Problems 4-7, 4-8

Math CoachUsing a Financial Calculator

Financial, or business, calculators are programmed to perform the time value of money equations we develop in this chapter and thenext. The two most common types of inexpensive financial calculators that can perform such functions are the Hewlett-Packard 10B IIBusiness Calculator and the Texas Instruments BA II (Plus or Professional). Among many useful financial shortcuts these calculatorshave five specific financial buttons. The relevant financial buttons for time value of money (TVM) calculations are listed below. The HP10B II calculator buttons look like this:

1. N (for the number of periods),

2. I/YR (for the interest rate),3. PV (for present value),

4. PMT (for a constant payment every period), and5. FV (for future value).

Notice that the TI BA II Plus financial calculator buttons appear to be very similar:

To get to the TVM menu, select APPLICATIONS and then choose FINANCE, and finally 1 TVM SOLVER on the previous screens.A common, more sophisticated and expensive calculator is the TI-83. This calculator has a menu system that includes the financialfunctions as shown:

Setting up Your CalculatorThese calculators come from the factory with specific settings. You will find it useful to change two of them. The first is to set thenumber of digits shown after the decimal point on the calculator display. The factory setting is for two digits. However, consider aproblem in which we use a 5.6 percent interest rate. The decimal version of this percentage is 0.056, which a two-digit display wouldround to 0.06. It’s less worrisome to set the calculator to display the number of digits necessary to show the right number; this is calleda floating point display. To set a floating point display for the HP calculator, press the color button, then the DISP button, and finally thedecimal (.) button. To set the display for a floating point decimal on the TI calculator, push the 2ND button, followed by the FORMATbutton, followed by the 9 button, and finally the ENTER button.

The second change you’ll want to make is to set the number of times the calculator compounds each period. The settings may bepreset to 12 times per period. Reset this to one time per period. To change the HP calculator to compound once per period, push the 1button, then the color button, and finally the P/YR button. On the TI calculator, simply push the 2ND button, the P/Y button, the numberone, and the ENTER button. These new settings will remain in the calculator until you either change them or remove the calculator’sbatteries.

Using Your Calculator

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The calculators compute time-value problems in similar ways. Enter the cash flows into the time-value buttons (PV, PMT, and FV)consistent with the way they are shown in a time line. In other words, cash inflows should be positive and cash outflows negative. Thus,PV and FV cash flows are nearly always opposite in sign. Enter interest rates (I) in the percentage form, not the decimal form. Alsoenter the number of periods in the problem (N).

Consider our earlier example of the $100 deposit for two years earning a 5 percent interest rate.

1. To set the number of years, press 2 and then the N button.2. To set the interest rate, press 5 and then the I button. (Note that interest rates are in percentage format for using a financial

calculator and in decimal format for using the equations.)

3. To enter the current cash flow: press 100, then make it negative by pressing the +/− button, then press the PVbutton.

4. We won’t use the PMT button, so enter 0 and then the PMT button.

5. To solve for future value, press the compute button (CPT) [for the TI] and then the FV button [press the FV button only for theHP].

6. Solution: the display should show FV = 110.25

Note that the answer is positive, consistent with an inflow and the time line diagram. These values remain in the TVM registers evenafter the calculator is turned off. So when you start a new problem, you should clear out old values first. For the HP calculator, clear theregisters by pressing the shift/orange key before pressing C. You can clear the BAII Plus calculator using 2ND and CLR TVM.

You’ll notice that throughout this book we use the equations in the main text to solve time value of money problems. We provide thecalculator solutions in the margins.

4.3 • PRESENT VALUE LG4-4We asked earlier what happens when you deposit $100 cash in the bank to earn 5 percent interest for one year—thebank pays you a $105 future value. However, we could have asked the question in reverse. That is, if the bank willpay $105 in one year and interest rates are 5 percent, how much would you be willing to deposit now, to receive thatpayment in a year? Here, we start with a future value and must find the present value—a different kind ofcalculation called discounting.

How much would you be willing to deposit now to receive a certain payment in a year?©Ryan McVay/Getty Images

DiscountingWhile the process of a present value growing over time into the future is called compounding, the process offiguring out how much an amount that you expect to receive in the future is worth today is discounting. Just ascompounding significantly increases the present value into the future, discounting significantly decreases the valueof a future amount to the present. Since discounting is the reverse of compounding, we can rearrange equation 4-1 tosolve for the present value of a cash flow received one year in the future.

(4-4)

discounting The process of finding present value by reducing future values using the discount, or interest, rate.

Suppose the bank is going to pay $105 in one year and interest rates are 5 percent. Then the present value of thepayment is $105/1.05 = $100. Present values are always smaller than future values (as long as interest rates aregreater than zero!), and the difference between what an investment is worth today and what it’s worth when you’resupposed to redeem it gets larger as the interest rate increases. Likewise, if the amount of time until the expectedpayment date increases, the difference will also increase in value.

Discounting Over Multiple Periods Discounting over multiple periods is the reverse process of compoundingover multiple periods. Knowing this, we can find the general equation for present value by rearranging the terms inequation 4-2 to form:

(4-5)

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The interest rate, i, which we use to calculate present value, is often referred to as the discount rate. How much is a$100 payment to be received in the future worth today? Of course, it depends on how far into the future you expectto receive the payment and the discount rate used. If you receive a $100 cash flow in five years, then its presentvalue is $78.35, discounted at 5 percent:

discount rate The interest rate used to discount future cash flow(s) to the present.

The time line looks like this:

LG4-1

If the discount rate rises to 10 percent, the present value of our $100 to be paid to us in five years is only $62.09today. At a 15 percent interest rate, the present value declines to less than half the future cash flow: $49.72. Higherinterest rates discount future cash flows more quickly and dramatically. You can see this principle illustrated inFigure 4.4.

Moving right from point A in Figure 4.4, notice that if interest rates are 0 percent, the present value will equal thefuture value. Also note from the curved lines that when the discount rate is greater than zero, the discounting topresent value is not linear through time. The higher the discount rate, the more quickly the cash flow value falls. Ifthe discount rate is 10 percent, a $100 cash flow that you would receive in 25 years is worth less than $10 today, asshown at point B in the figure. With a 15 percent discount rate, the $100 payment to be received in 33 years, at pointC, is worth less than $1 today.

the Math Coach on…

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“When using a financial calculator, be sure to either clearthe time value of money buttons or enter a zero for thefactors that you won’t use to solve the problem.„

FIGURE 4-4 Present Value of a $100 Cash Flow Made in the Future

The higher the discount rate, the more quickly the cash flow value falls.

EXAMPLE 4-3Buy Now and Don’t Pay for TwoYears LG4-4

For interactive versionsof this example, log in

to Connect or go to

Suppose that a marketing manager for a retail furniture companyproposes a sale. Customers can buy now but don’t have to pay for theirfurniture purchases for two years. From a time value of moneyperspective, selling furniture at full price with payment in two years isequivalent to selling furniture at a sale, or discounted, price withimmediate payment. If interest rates are 7.5 percent per year, what isthe equivalent sale price of a $1,000 sleeper-sofa when the customertakes the full two years to pay for it?

SOLUTION:

mhhe.com/CornettM4e. The time line for this problem is:

Using equation 4-5, the present value computation is

In this case, the marketing proposal for delaying payment for two yearsis equivalent to selling the $1,000 sleeper-sofa for a sale price of$865.33, or a 13.5 percent discount. When stores promote such sales,they often believe that customers will not be able to pay the full amountat the end of the two years and then must pay high interest ratecharges and late fees. Customers who do pay on time are getting agood deal.

Similar to Problems 4-9, 4-10, 4-11, 4-12, Self-Test Problem 2

Discounting with Multiple Rates LG4-4 We can also discount a future cash flow at different interest ratesper period. We find the general form of the equation for present value with multiple discount rates by rearrangingequation 4-3:

Present value with different discount rates = Future cash flow ÷ Each period’s discounting

(4-6)

LG4-1

Suppose that we expect interest rates to increase over the next few years, from 7 percent this year, to 8 percent nextyear, to 8.5 percent in the third year. In this environment, how would we work out the present value of a future$2,500 cash flow in year 3? The time line for this problem is

time out!4-6 How are interest rates in the economy related to the way people value future cash payments?4-7 Explain how discounting is the reverse of compounding.

Using equation 4-6 shows that the present value is $1,993.90:

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4.4 • USING PRESENT VALUE AND FUTURE VALUE LG4-5Moving Cash FlowsAs managers analyze investment projects, debt management, and cash flows, they frequently find it useful to movecash flows to different points in time. While you may be planning to keep money deposited in the bank for threeyears when you will buy a car, life often has a way of altering plans. What type of car might you purchase if themoney earns interest for only two years, or for four years? How is a corporate financial forecast affected if the firmneeds to remodel a factory two years sooner than planned? Moving cash flows around in time is important tobusinesses and individuals alike for sound financial planning and decision making.

LG4-1

Moving cash flows from one point in time to another requires us to use both present value and future valueequations. Specifically, we use the present value equation for moving cash flows to an earlier point in time, and thefuture value cash flows for moving cash flows to a later point in time. For example, what’s the value in year 2 of a$200 cash flow to be received in three years, when interest rates are 6 percent? This problem requires moving the$200 payment in the third year to a value in the second year, as shown in the time line:

Since the cash flow is to be moved one year earlier in time, we use the present value equation:

When interest rates are 6 percent, a $188.68 payment in year 2 equates to a $200 payment in year 3.

What about moving the $200 cash flow to year 5? Since this requires moving the cash flow later in time by twoyears, we use the future value equation. In this case, the equivalent of $200 in the third year is a fifth-year paymentof:

Table 4.3 illustrates how we might move several cash flows. At an 8 percent interest rate, a $1,000 cash flow due in

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year 5 compounded to year 10 equals $1,469.33. We could also discount that same $1,000 cash flow to a value of$793.83 in year 2. At an 8 percent interest rate, the three cash flows ($793.83 in year 2, $1,000 in year 5, and$1,469.33 in year 10) become equivalent. Table 4.3 illustrates the movement of other cash flows given differentinterest rates and time periods.Moving cash flows from one year to another creates an easy way to compare or combine two cash flows. Would yourather receive $150 in year 2 or $160 in year 2? Since both cash flows occur in the same year, the comparison isstraightforward. But we can’t directly add or compare cash flows in different years until we consider their timevalue. We can compare cash flows in different years by moving one cash flow to the same time as the other usingthe present value or future value equations. Once you have the value of each cash flow in the same year, you candirectly compare or combine them.

Rule of 72 LG4-6 Albert Einstein is also credited with popularizing compound interest by introducing asimple mathematical approximation for the number of years required to double an investment. It’s called the Rule of72.

Rule of 72 An approximation for the number of years needed for an investment to double in value.

▼ TABLE 4.3 Equivalent Cash Flows in Time

When InterestRates Are

A Cash Flowof In Year

Can beMoved to

Year With EquationEquivalent Cash

Flow

Moving Later versus Moving Earlier

8% $1,000 5 10FV10 = PV5 × (1 + i )

5 =

$1,000 × (1.08)5 =$1,469.33

8 1,000 5 2PV2 = FV5 / (1 + i)

3 =

$1,000 / (1.08)3 =793.83

Moving Earlier

10 500 9 8PV8 = FV9 / (1 + i )

1 =

$500 / (1.10)1 =454.55

10 500 9 0PV0 = FV9 / (1 + i)

9 =

$500 / (1.10)9 =212.05

Moving Later

12 100 4 20FV20 = PV4 × (1 + i )

16 =

$100 × (1.12)16 =613.04

12 100 4 30

FV30 = PV4 × (1 + i

)26 = $100 ×(1.12)26 =

1,904.01

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(4-7)

The Rule of 72 illustrates the power of compound interest. How many years will it take to double money depositedat 6 percent per year? Using the Rule of 72, we find the answer is 12 years (= 72/6). A higher interest rate causesfaster increases in future value. A 9 percent interest rate allows money to double in just eight years (= 72/9).Remember that this rule provides only a mathematical approximation. It’s more accurate with lower interest rates.After all, with a 72 percent interest rate, the rule predicts that it will take one year to double the money (= 72/72).However, we know that it actually takes a 100 percent rate to double money in one year.

We can also use the Rule of 72 to approximate the interest rate needed to double an investment in a specific amountof time. What rate do we need to double an investment in five years? Rearranging equation 4-7 shows that the rateneeded is 14.4 percent (= 72/5) per year.

time out!4-8 In Example 4-4, could Timber, Inc., have performed its analysis by moving the $175,000 to year 2 and comparing? Would

the firm then have made the same decision?

4-9 At what interest rate (and number of years) does the Rule of 72 become too inaccurate to use?

EXAMPLE 4-4 Pay Damages or Appeal? LG4-5

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Timber, Inc., lost a lawsuit in a business dispute. The judge ordered thecompany to pay the plaintiff $175,000 in one year. Timber’s attorneyadvises Timber to appeal the ruling. If so, Timber will likely lose againand will still have to pay the $175,000. But by appealing, Timber movesthe $175,000 payment to year 2, along with the attorney’s fee of$20,000 for the extra work. The interest rate is 7 percent. Whatdecision should Timber make?

SOLUTION:

Timber executives must decide whether to pay $175,000 in one year or$195,000 in two years. To compare the two choices more directly,move the payment in year 2 to year 1 and then compare it to $175,000.Timber should choose to make the smaller payment. The computationis

The value in year 1 of a year 2 payment of $195,000 is $182,242.99,which is clearly more than the $175,000 year 1 payment. So Timbershould not appeal and should pay the plaintiff $175,000 in one year(and may want to look for another attorney).

Similar to Problems 4-23, 4-24, 4-25, 4-26, 4-27, 4-28, 4-41

finance at work //: investmentsTVM Caveat Emptor

©Trevor Lush/Blend Images LLC

Not making your payments on time can get very expensive. Reconsider the furniture selling experience in Example 4-3. The store hasgiven customers the opportunity to buy the sleeper-sofa today and not pay the $1,000 price for two years. But what happens if you forgetto pay on time? Indeed, many people do forget. Others simply haven’t saved $1,000 and can’t make the payment. The fine print in thesedeals provides the penalties for late payment. For example, the late clause might require a 10 percent annually compounded interestrate to apply to any late payment—retroactive to the sale date. Thus, being one day late with the payment will automatically incur aninterest charge for the entire two years of $210 (= $1,000 × 1.12 − $1,000), which is in addition to the original $1,000 still owed, ofcourse.

The impact of making late payments can also show up later when you apply for credit cards, auto loans, and other credit. Creditrating agencies gather information on us from companies, banks, and landlords to grade our payment history. If you consistently makelate payments on your apartment, credit card, or electric bill, these agencies will give you a poor grade. The higher your grade, called acredit score, the more likely you are to be able to get a loan and pay a lower interest rate on that loan. People with lower credit scoresmay not be able to borrow money and when they can, they will pay higher interest rates on their credit cards and auto loans. Paying ahigher interest rate can really cost you a lot of money. Remember the future value differences between interest rates illustrated in Table4.2 and Figure 4.3. Those people who have really bad credit scores can’t get loans from banks and merchants and have to rely onpayday lending places that charge enormously high rates, as highlighted in this chapter’s Personal Application Viewpoint.

Making a late payment might not seem like a big deal at the time, but it can really cost you!

Want to know more?Key Words to Search for Updates: housing bubble, subprime lending, mortgage-backed securities, AIG, Countrywide Financial

4.5 • COMPUTING INTEREST RATES LG4-7Time value of money calculations come in handy when we know two cash flows and need to find the interest rate.The investment industry often uses this analysis. Solving for the interest rate, or rate of return,2 can answer questionslike, “If you bought a gold coin for $350 three years ago and sell it now for $475, what rate of return have youearned?” The time line for this problem looks like this:

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LG4-1

In general, computing interest rates is easiest with a financial calculator. To compute the answer using the time-value equations, consider how the cash flows fit into the future value equation 4-2:

the Math Coach on…

“When using a financial calculator to compute an interest rate between two cashflows, you must enter one cash flow as a negative number. This is because youmust inform the calculator which payments are cash inflows and which are cashoutflows. If you input all the cash flows as the same sign, the calculator will showan error when asked to compute the interest rate.„

Rearranging gives

To solve for the interest rate, i, take the third root of both sides of the equation. To do this, take 1.357 to the 1/3power using the yx button on your calculator.3 Doing this leads to

If you buy a gold coin for $350 and sell it three years later for $475, you earn a 10.7 percent return per year.

LG4-6

Time is an important factor in computing the return that you’re earning per year. Turning a $100 investment into

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$200 is a 100 percent return. If your investments earn this much in two years, then they earned a 41.42 percent rateof return per year [$100 × (1.4142)2 = $200]. Table 4.4 shows the annual interest rate earned for doubling aninvestment over various time periods. Notice how compounding complicates the solution: It’s not as simple as justdividing by the number of years. Getting a 100 percent return in two years means earning 41.42 percent per year, not50 percent per year. Table 4.4 also shows the Rule of 72 interest rate estimate.

▼ TABLE 4.4 Interest Rate per Year to Double an Investment

Return AsymmetriesSuppose you bought a gold coin for $700 last year and now the market will pay you only $350. Clearly, theinvestment earned a negative rate of return. Use a financial calculator or a time-value equation to verify that this is areturn of −50 percent. You lost half your money! So, in order to break even and get back to $700, you need to earn apositive 50 percent, right? Wrong. Note that to get from $350 to $700, your money needs to double! You need a 100percent return to make up for a 50 percent decline. Similarly, you need a gain of 33.33 percent to make up for a 25percent decline. If your investment declines by 10 percent, you’ll need an 11.11 percent gain to offset the loss. Ingeneral, only a higher positive return can offset any given negative return.

time out!4-10 Say you double your money in three years. Explain why the rate of return is NOT 33.3 percent per year.4-11 Show that you must earn a 25 percent return to offset a 20 percent loss.

4.6 • SOLVING FOR TIME LG4-8Sometimes you may need to determine the time period needed to accumulate a specific amount of money. If youknow the starting cash flow, the interest rate, and the future cash flow (the amount you will need), you can solve thetime value equations for the number of years that you will need to accumulate that money. Just as with solving fordifferent interest rates, solving for the number of periods is complicated and requires using natural logarithms.4Many people prefer to use a financial calculator to solve for the number of periods.

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When interest rates are 9 percent, how long will it take for a $5,000 investment to double? Finding the solution witha financial calculator entails entering

I = 9

PV = −5,000PMT = 0

FV = 10,000

The answer is 8.04 years, or eight years and two weeks. The Rule of 72 closely approximates the answer, whichpredicts eight years (= 72/9).

time out!4-12 In Example 4-5, how long will it take your company to double its sales?4-13 In what other areas of business can these time-value concepts be used?

EXAMPLE 4-5 Growth in Staffing Needs LG4-8

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Say that you are the sales manager of a company that producessoftware for human resource departments. You are planning yourstaffing needs, which depend on the volume of sales over time. Yourcompany currently sells $350 million of merchandise per year and hasgrown 7 percent per year in the past. If this growth rate continues, howlong will it be before the firm reaches $500 million in sales? How longbefore it reaches $600 million?

SOLUTION:

You could set up the following time line to illustrate the problem:

As shown in the margin, $350 million of sales growing at 7 percent peryear will reach $500 million in five years and three months. To reach$600 million will take just two weeks short of eight years.

Similar to Problems 4-31, 4-32, Self-Test Problem 4

page 107

the Math Coach on…Simple TVM Spreadsheet Functions

Common spreadsheet programs include time value of money functions. The functions are

Compute a future value = FV(rate,nper,pmt,pv,type)

Compute a present value = PV(rate,nper,pmt,fv,type)

Compute the number of periods = NPER(rate,pmt,pv,fv,type)

Compute an interest rate = RATE(nper,pmt,pv,fv,type)

Compute a repeating payment = PMT(rate,nper,pv,fv,type)

The five input/outputs (FV, PV, NPER, RATE, PMT) work similarly to the five TVM buttons on a business calculator. The type inputdefaults to 0 for normal situations, but can be set to 1 for computing annuity due problems (see Chapter 5). Different spreadsheetprograms might have slightly different notations for these five functions.

Consider the future value problem of Example 4-1. The spreadsheet solution is the same as the TVM calculator solution. Note thatsince the PV is listed as a positive number, the FV output is a negative number.

The inputs to the function can be directed to other cells, like the rate, nper, and pv in the this illustration. Or the input can be the actualnumber, like pmt and type.This spreadsheet solves for the interest rate in the preceding example in the text. Just like using the TVM calculator, the PV and FVmust be of opposite signs to avoid getting an error message.

See this textbook’s online student center to watch instructional videos on using spreadsheets. Also note that the solution for all theexamples in the book are illustrated using spreadsheets in videos that are available in Connect.

Get Online

©JGI/Jamie Grill/Blend Images LLC.

Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow.Which cash flows should be negative and which positive? Why? (LG4-1)

2. How are the present value and future value related? (LG4-2)

3. Would you prefer to have an investment earning 5 percent for 40 years or an investment earning 10 percent for20 years? Explain. (LG4-3)

4. How are present values affected by changes in interest rates? (LG4-4)

5. What do you think about the following statement? “I am going to receive $100 two years from now and $200three years from now, so I am getting a $300 future value.” How could the two cash flows be compared orcombined? (LG4-5)

6. Show how the Rule of 72 can be used to approximate the number of years to quadruple an investment. (LG4-6)

7. Without making any computations, indicate which of each pair has a higher interest rate: (LG4-7)

a. $100 doubles to $200 in five years or seven years.b. $500 increases in four years to $750 or to $800.c. $300 increases to $450 in two years or increases to $500 in three years.

page 108

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8. A $1,000 investment has doubled to $2,000 in eight years because of a 9 percent rate of return. How muchlonger will it take for the investment to reach $4,000 if it continues to earn a 9 percent rate? (LG4-8)

ProblemsBASIC PROBLEMS

4-1 Time Line Show the time line for a $500 cash inflow today, a $605 cash outflow in year 2, and a 10percent interest rate. (LG4-1)

4-2 Time Line Show the time line for a $400 cash outflow today, a $518 cash inflow in year 3, and a 9percent interest rate. (LG4-1)

4-3 One Year Future Value What is the future value of $500 deposited for one year earning an 8 percentinterest rate annually? (LG4-2)

4-4 One Year Future Value What is the future value of $400 deposited for one year earning an interest rateof 9 percent per year? (LG4-2)

4-5 Multiyear Future Value How much would be in your savings account in 11 years after depositing $150today if the bank pays 8 percent per year? (LG4-3)

4-6 Multiyear Future Value Compute the value in 25 years of a $1,000 deposit earning 10 percent per year.(LG4-3)

4-7 Compounding with Different Interest Rates A deposit of $350 earns the following interest rates:a. 8 percent in the first year.b. 6 percent in the second year.c. 5.5 percent in the third year.

What would be the third year future value? (LG4-3)4-8 Compounding with Different Interest Rates A deposit of $750 earns interest rates of 9 percent in the

first year and 12 percent in the second year. What would be the second year future value? (LG4-3)4-9 Discounting One Year What is the present value of a $350 payment in one year when the discount rate is

10 percent? (LG4-4)4-10 Discounting One Year What is the present value of a $200 payment in one year when the discount

rate is 7 percent? (LG4-4)4-11 Present Value What is the present value of a $1,500 payment made in nine years when the discount

rate is 8 percent? (LG4-4)4-12 Present Value Compute the present value of an $850 payment made in 10 years when the discount

rate is 12 percent. (LG4-4)4-13 Present Value with Different Discount Rates Compute the present value of $1,000 paid in three

years using the following discount rates: 6 percent in the first year, 7 percent in the second year, and 8percent in the third year. (LG4-4)

4-14 Present Value with Different Discount Rates Compute the present value of $5,000 paid in twoyears using the following discount rates: 8 percent in the first year and 7 percent in the second year.(LG4-4)

4-15 Rule of 72 Approximately how many years are needed to double a $100 investment wheninterest rates are 7 percent per year? (LG4-6)

4-16 Rule of 72 Approximately how many years are needed to double a $500 investment when interestrates are 10 percent per year? (LG4-6)

4-17 Rule of 72 Approximately what interest rate is needed to double an investment over five years? (LG4-6)

4-18 Rule of 72 Approximately what interest rate is earned when an investment doubles over 12 years?(LG4-6)

4-19 Rates over One Year Determine the interest rate earned on a $1,400 deposit when $1,800 is paidback in one year. (LG4-7)

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4-20 Rates over One Year Determine the interest rate earned on a $2,300 deposit when $2,900 is paidback in one year. (LG4-7)

INTERMEDIATE PROBLEMS

4-21 Interest-on-Interest Consider a $2,000 deposit earning 8 percent interest per year for five years.What is the future value, and how much total interest is earned on the original deposit versus howmuch is interest earned on interest? (LG4-3)

4-22 Interest-on-Interest Consider a $5,000 deposit earning 10 percent interest per year for 10 years.What is the future value, how much total interest is earned on the original deposit, and how much isinterest earned on interest? (LG4-3)

4-23 Comparing Cash Flows What would be more valuable, receiving $500 today or receiving $625 inthree years if interest rates are 7 percent? Why? (LG4-5)

4-24 Comparing Cash Flows Which cash flow would you rather pay, $425 today or $500 in two years ifinterest rates are 10 percent? Why? (LG4-5)

4-25 Moving Cash Flows What is the value in year 3 of a $700 cash flow made in year 6 if interest ratesare 10 percent? (LG4-5)

4-26 Moving Cash Flows What is the value in year 4 of a $1,000 cash flow made in year 6 if interest ratesare 8 percent? (LG4-5)

4-27 Moving Cash Flows What is the value in year 10 of a $1,000 cash flow made in year 3 if interestrates are 9 percent? (LG4-5)

4-28 Moving Cash Flows What is the value in year 15 of a $250 cash flow made in year 3 if interest ratesare 11 percent? (LG4-5)

4-29 Solving for Rates What annual rate of return is earned on a $1,000 investment when it grows to$1,800 in six years? (LG4-7)

4-30 Solving for Rates What annual rate of return is earned on a $5,000 investment when it grows to$9,500 in five years? (LG4-7)

4-31 Solving for Time How many years (and months) will it take $2 million to grow to $5 million with anannual interest rate of 7 percent? (LG4-8)

4-32 Solving for Time How long will it take $2,000 to reach $5,000 when it grows at 10 percent per year?(LG4-8)

ADVANCED PROBLEMS

4-33 Future Value At age 30 you invest $1,000 that earns 8 percent each year. At age 40 you invest$1,000 that earns 12 percent per year. In which case would you have more money at age 60?(LG4-2)

4-34 Future Value At age 25 you invest $1,500 that earns 8 percent each year. At age 40 you invest$1,500 that earns 11 percent per year. In which case would you have more money at age 65? (LG4-2)

4-35 Solving for Rates You invested $2,000 in the stock market one year ago. Today, the investment isvalued at $1,500. What return did you earn? What return would you need to get next year to breakeven overall? (LG4-7)

4-36 Solving for Rates You invested $3,000 in the stock market one year ago. Today, the investment isvalued at $3,750. What return did you earn? What return would you suffer next year for yourinvestment to be valued at the original $3,000? (LG4-7)

4-37 Solving for Rates What annual rate of return is earned on a $4,000 investment made in year 2 whenit grows to $6,500 by the end of year 7? (LG4-7)

4-38 Solving for Rates What annual rate of return is implied on a $2,500 loan taken next year when$3,500 must be repaid in year 4? (LG4-7)

4-39 General TVM Ten years ago, Hailey invested $2,000 and locked in a 9 percent annual interest ratefor 30 years (ending 20 years from now). Aidan can make a 20-year investment today and lock in a 10percent interest rate. How much money should he invest now in order to have the same amount ofmoney in 20 years as Hailey? (LG4-2, LG4-4)

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4-40 General TVM Ten years ago, Hailey invested $3,000 and locked in an 8 percent annual interest ratefor 30 years (ending 20 years from now). Aidan can make a 20-year investment today and lock in a 10percent interest rate. How much money should he invest now in order to have the same amount ofmoney in 20 years as Hailey? (LG4-2, LG4-4)

4-41 Moving Cash Flows You are scheduled to receive a $500 cash flow in one year, a $1,000 cash flowin two years, and pay an $800 payment in three years. If interest rates are 10 percent per year, what isthe combined present value of these cash flows? (LG4-5)

4-42 Spreadsheet Problem Oil prices have increased a great deal in the last decade. The following tableshows the average oil price for each year since 1949. Many companies use oil products as a resourcein their own business operations (like airline firms and manufacturers of plastic products). Managersof these firms will keep a close watch on how rising oil prices will impact their costs. The interest ratein the PV/FV equations can also be interpreted as a growth rate in sales, costs, profits, and so on (seeExample 4-5).

a. Using the 1949 oil price and the 1969 oil price, compute the annual growth rate in oil prices duringthose 20 years.

b. Compute the annual growth rate between 1969 and 1989 and between 1989 and 2015.c. Given the price of oil in 2015 and your computed growth rate between 1989 and 2015, compute the

future price of oil in 2018 and 2025.

Average Oil Prices

Year Per Barrel Year Per Barrel Year Per Barrel

1949 $2.54 1971 $ 3.39 1993 $14.25

1950 $2.51 1972 $ 3.39 1994 $13.19

1951 $2.53 1973 $ 3.89 1995 $14.62

1952 $2.53 1974 $ 6.87 1996 $18.46

1953 $2.68 1975 $ 7.67 1997 $17.23

1954 $2.78 1976 $ 8.19 1998 $10.87

1955 $2.77 1977 $ 8.57 1999 $15.56

1956 $2.79 1978 $ 9.00 2000 $26.72

1957 $3.09 1979 $12.64 2001 $21.84

1958 $3.01 1980 $21.59 2002 $22.51

1959 $2.90 1981 $31.77 2003 $27.54

1960 $2.88 1982 $28.52 2004 $38.93

1961 $2.89 1983 $26.19 2005 $46.47

1962 $2.90 1984 $25.88 2006 $58.30

1963 $2.89 1985 $24.09 2007 $64.67

1964 $2.88 1986 $12.51 2008 $91.48

1965 $2.86 1987 $15.40 2009 $53.48

1966 $2.88 1988 $12.58 2010 $71.21

1967 $2.92 1989 $15.86 2011 $87.04

1968 $2.94 1990 $20.03 2012 $93.02

1969 $3.09 1991 $16.54 2013 $97.91

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1970 $ 3.18 1992 $15.99 2014 $93.26

2015 $48.79

4-43 Spreadsheet Problem Consider that you are the marketing manager of a firm. You need to haveapproximately one additional salesperson for every $10 million in sales. You currently have $50million in sales and have five employees handling the sales accounts. In order to plan ahead, you wantto get an idea of when you may need to hire more salespeople. Build a table that shows the sales foreach of the next 10 years for sales growth of 5%, 10%, 15%, and 20% (see Example 4-5).

Comment on when new sales staff should be hired for each growth rate.

A B C D E F G H I J K L

1 Growth Rate Today Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10

2 5% $50 $52.50

3 10% $50 $55.00

4 15% $50 $57.50

5 20% $50 $60.00

NotesCHAPTER 41 No one seems to know exactly what he said, when he said it, or to whom. Similar statements commonly attributed to Einstein are: (1)

compound interest is the greatest wonder of the universe, (2) compound interest is the ninth wonder of the world, and (3) it is thegreatest mathematical discovery of all time. If he did not say any of these things, he (or someone else) should have!

2 The terms interest rate and rate of return are referring to the same thing. However, it is a common convention to refer to interest ratewhen you are the one paying the cash flows and refer to rate of return when you are the one receiving the cash flows.

3 The general equation for computing the interest rate is

4 The equation for solving for the number of periods is

W

Chapter fivetime value of money 2:analyzing annuity cash flows

©Stuart Monk/Shutterstock

e explained basic time value computations in the previous chapter. Those TVM equations coveredmoving a single cash flow from one point in time to another. While this circumstance doesdescribe some problems that businesses and individuals face, most debt and investment

applications of time value of money feature multiple cash flows. In fact, most situations require manyequal payments over time. Since these situations require a bit more complicated analysis, this chaptercontinues the TVM topic for applications that require many equal payments over time. For example, carloans and home mortgage loans require the borrower to make the same monthly payment for manymonths or years. People save for the future through monthly contributions to their pension portfolios.People in retirement must convert their savings into monthly income. Companies also make regularpayments. Johnson & Johnson (ticker: JNJ) will pay level semiannual interest payments through 2033 onmoney it borrowed. The Boeing Company (ticker: BA) paid a $0.42 per share quarterly dividend tostockholders for three straight years until 2012, when it switched to a $0.44 dividend. These examples

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require payments (and compounding) over different time intervals (monthly for car loans andsemiannually for company debt). How are we to value these payments into common or comparableterms? In this chapter, we illustrate how to value multiple cash flows over time, including equal anduneven payments, and how to incorporate different compounding frequencies.

LEARNING GOALS

LG5-1 Compound multiple cash flows to the future.LG5-2 Compute the future value of frequent, level cash flows.LG5-3 Discount multiple cash flows to the present.LG5-4 Compute the present value of an annuity.LG5-5 Figure cash flows and present value of a perpetuity.LG5-6 Adjust values for beginning-of-period annuity payments.LG5-7 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.LG5-8 Compute the interest rate of annuity payments.LG5-9 Compute payments and amortization schedules for car and mortgage loans.LG5-10 Calculate the number of payments on a loan.

viewpointsbusiness APPLICATIONWalkabout Music, Inc., issued $20 million in debt 10 years ago to finance its factory construction. The debt allows Walkabout to makeinterest-only payments at a 7 percent coupon rate, paid semiannually for 30 years. Debt issued today would carry only 6 percentinterest. The company’s CFO is considering whether or not to issue new debt (for 20 years) to pay off the old debt. To pay off the olddebt early, Walkabout would have to pay a special “call premium” totaling $1.4 million to its debt holders. To issue new debt, the firmwould have to pay investment bankers a fee of $1.2 million. Should the CFO replace the old debt with new debt? (See the solution atthe end of the book.)

5.1 • FUTURE VALUE OF MULTIPLE CASH FLOWS LG5-1Chapter 4 illustrated how to take single payments and compound them into the future. To save enough money for adown payment on a house or for retirement, people typically make many contributions over time to their savingsaccounts. We can add the future value of each contribution together to see what the total will be worth at somefuture point in time—such as age 65 for retirement or in two years for a down payment on a house.

Finding the Future Value of Several Cash FlowsConsider the following contributions to a savings account over time. You make a $100 deposit today, followed by a$125 deposit next year, and a $150 deposit at the end of the second year. If interest rates are 7 percent, what’s thefuture value of your deposits at the end of the third year? The time line for this problem is illustrated as

Note that the first deposit will compound for three years. That is, the future value in year 3 of a cash flow in year 0will compound 3 v(= 3 − 0) times. The deposit at the end of the first year will compound twice (= 3 − 1). In general,a deposit in year m will compound N−m times for a future value in year N. We can find the total amount at the endof three years by computing the future value of each deposit and then adding them together. Using the future valueequation from Chapter 4, the future value of today’s deposit is $100 ×  (1 + 0.07) 3 = $122.50. Similarly, the future

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value of the next two deposits are $125 ×  (1 + 0.07) 2 = $143.11 and $150 ×  (1 + 0.07) 1 = $160.50, respectively.

Putting these three individual future value equations together would yield

personal APPLICATIONSay that you obtained a mortgage for $150,000 three years ago when you purchased your home. You’ve been paying monthlypayments on the 30-year mortgage with a fixed 8 percent interest rate and have $145,920.10 of principal left to pay. Recently, yourmortgage broker called to mention that interest rates on new mortgages have declined to 7 percent. He suggested that you could savemoney every month if you refinanced your mortgage. You could find a 27-year mortgage at the new interest rate for a $1,000 fee.Should you refinance your mortgage? (See the solution at the end of the book.)

But what if you want to move in the next few years? Is it still a good idea?

The general equation for computing the future value of multiple and varying cash flows (or payments) is

(5-1)

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In this equation, the letters m, n, and p denote when the cash flows occur in time, so N − m etc. represent the lengthof time that the respective cash flow will get to earn compound interest. Each deposit can be different from theothers.

EXAMPLE 5-1 Saving for a Car LG5-1

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Say that, as a freshman in college, you will be working as a housepainter for each of the next three summers. You intend to set asidesome money from each summer’s paycheck to buy a car for yoursenior year. If you can deposit $2,000 at the end of the first summer,$2,500 at the end of the second summer, and $3,000 at the end of thelast summer, how much money will you have to buy a car at the end ofthe last summer if interest rates are 5 percent?

SOLUTION:

The time line for the forecast is

The first cash flow, which occurs at the end of the first year, willcompound for two years. The second cash flow will be invested for onlyone year. The last contribution will not have any time to grow before thepurchase of the car. Using equation 5-1, the solution is

You will have $7,830 in cash to purchase a car for your senior year.

Similar to Problems 5-1, 5-2, 5-17, 5-18, 5-43, 5-44

Future Value of Level Cash Flows LG5-2Now suppose that each cash flow is the same and occurs every year. Level sets of frequent cash flows are commonin finance—we call them annuities. The first cash flow of an annuity occurs at the end of the first year (or other timeperiod) and continues every year to the last year. We derive the equation for the future value of an annuity from thegeneral equation for future value of multiple cash flows, equation 5-1. Since each cash flow is the same, and thecash flows are every period, the equation appears as

annuity A stream of level and frequent cash flows paid at the end of each time period—often referred to as an ordinary annuity.

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The term FVA is used to denote that this is the future value of an annuity. Factoring out the common level cash flow,PMT, we can summarize and reduce the equation as

(5-2)

Suppose that $100 deposits are made at the end of each year for five years. If interest rates are 8 percent per year, thefuture value of this annuity stream is computed using equation 5-2 as

We can show these deposits and future value on a time line as

Five deposits of $100 each were made. So, the $586.66 future value represents $86.66 of interest paid. As withalmost any TVM problem, the length of time of the annuity and the interest rate for compounding are very importantfactors in accumulating wealth within the annuity. Consider the examples in Table 5.1. A $50 deposit made everyyear for 20 years will grow to $1,839.28 with a 6 percent interest rate. Doubling the annual deposits to $100 alsodoubles the future value to $3,678.56. However, making $100 deposits for twice the amount of time, 40 years, morethan quadruples the future value to $15,476.20! Longer time periods lead to more total compounding and muchmore wealth. Interest rates also have this effect. Doubling the interest rate from 6 to 12 percent on the 40-yearannuity results in nearly a five-fold increase in the future value to $76,709.14. Think about it: Depositing only $100per year (about 25 lattes per year) can generate some serious money over time. See Figure 5.1. How much would$2,000 annual deposits generate?

▼ TABLE 5.1 Magnitude of Periodic Payments, Number of Years Invested, and Interest Rate on FV of Annuity

FIGURE 5-1 Future Value of a $100 Annuity at 6 Percent

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Longer time periods lead to more total compounding and much more wealth.

the Math Coach on…Annuities and the Financial Calculator

“In the previous chapter, the level payment button (PMT) in the financial calculator was always set to zerobecause no constant payments were made every period. We use the PMT button to input the annuity amount.For calculators, the present value is of the opposite sign (positive versus negative) from the future value. Thisis also the case with annuities. The level cash flow will be of the opposite sign as the future value, as the timeline on page 118 shows.

You would use the financial calculator to solve the problem of depositing $100 for five years via the followinginputs: N = 5, I = 8, PV = 0, PMT = –100. In this case, the input for present value is zero because no deposit ismade today. The result of computing the future value is 586.66.„

Future Value of Multiple AnnuitiesAt times, multiple annuities can occur in both business and personal life. For example, you may find that you canincrease the amount of money you save each year because of a promotion or a new and better job. As an illustration,reconsider the annual $100 deposits made for five years at 8 percent per year. This time, the deposit can be increasedto $150 for the fourth and fifth years. How can we use the annuity equation to compute the future value when wehave two levels of cash flows? In this case, the cash flow can be categorized as two annuities. The first annuity is a$100 cash flow for five years. The second annuity is a $50 cash flow for two years. We demonstrate this as

the Math Coach on…Solving Multiple Annuities

“The trick to solving multiple annuity problems is to disentangle cash flows into groups of level paymentsending in the future value year that we’ve designated.„

To determine the future value of these two annuities, compute the future value of each one separately, and thensimply add them together. The future value of the $100 annuity is the same as computed before, $586.66. The futurevalue of the $50 annuity, using the TVM equation for the future value of a cash stream, is

EXAMPLE 5-2Saving in the Company PensionPlan LG5-2

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

You started your first job after graduating from college. Your companyoffers a retirement plan for which the company contributes 50 percentof what you contribute each year. So, if you contribute $3,000 per yearfrom your salary, the company adds another $1,500. You get to decidehow to invest the total annual contribution from several portfoliochoices that the plan administrator provides. Suppose that you pick amixture of stocks and bonds that is expected to earn 7 percent peryear. If you plan to retire in 40 years, how big will you expect thatretirement account to be? If you could earn 8 percent per year, howmuch money would be available?

SOLUTION:

Every year, you and your employer will set aside a total of $4,500 foryour retirement. Using equation 5-2 shows that the future value of thisannuity is

Note that you can build a substantial amount of wealth ($898,358)

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through your pension plan at work. If you can earn just 1 percent moreeach year, 8 percent total, you could be a millionaire!

Similar to Problems 5-3, 5-4, Self-Test Problem 1

finance at work //: personalWho Will Save for Their Future?

©Chris Ryan/Age Fotostock

Though it seems way too early for you to think about planning for your “golden years,” financially wise people realize that it’s never tooearly to start. Unfortunately, most people save little for their retirement years. Twenty-nine percent of households age 55 and older haveno pension or retirement savings. About 23 percent have no savings, but do have a pension. Of the 48 percent that have retirementsavings, the median amount is $109,000. How far does that get you? Using a 6 percent investment return, $109,000 can generate amonthly income of only $653.51 for 30 years, at which time it is used up. That is less than $8,000 per year! The average Social Securitymonthly benefit is just over $1,318 per month, or about $15,816 per year. Few people will have the lifestyle they wanted in theirretirement years. However, that doesn’t have to be true for you if you start saving early!

This chapter illustrates that much higher amounts of wealth can be accumulated if you start early. One easy way to do this is througha retirement plan at work. Most company and government employers offer their employees defined contribution plans. (The corporateversion is called a 401(k) plan; a nonbusiness plan is usually referred to as a 403(b) plan—both named after the legislation that createdthe plans.) These plans place all of the responsibility on employees to provide for their retirement. Employees contribute from their ownpaychecks and decide how to invest. Employees’ decisions about how much to contribute and how early to start contributing have adramatic impact on retirement wealth.

Consider employees who earn $50,000 annually for 40 years and then retire. Note that if the employees contribute for 40 years, theymust start by age 25 or so—starting early is vitally important! Contributing 5 percent of their salaries ($2,500) to the 401(k) plan everyyear and having it earn a 4 percent return will generate $237,564 for retirement. A 10 percent contribution ($5,000) would create$475,128 for retirement. Finally, investment decisions that yield an 8 percent return would yield $1.3 million with a 10 percentcontribution. This is quite a range of retirement wealth generated from just three important decisions each employee must make—howmuch to contribute, how to invest the funds, and when to start! Unfortunately, too many people make poor decisions. Their first mistakeis to start making 401(k) contributions too late to allow the funds to generate significant compounding.

Saving and investing money through a defined contribution plan is a good way to build wealth for retirement. But you must followthese rules: Start early, save much, and don’t touch!

Want to know more?Key Words to Search for Updates: Employee Benefit Research Institute (go to www.ebri.org), retirement income

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Source: “Retirement Security: Most Households Approaching Retirement Have Low Savings,” Government Accountability Office, GAO-15-419, May 12, 2015. http://www.gao.gov/products/GAO-15-419.

So, the future value of both of the annuities is $690.66 (= $586.66 + $104). In the same way, we could easilycompute the future value if the last two cash flows are $50 lower ($50 each), instead of $50 higher ($150 each). Tosolve this alternative version, we would simply subtract the $104 future value instead of adding it.

EXAMPLE 5-3Growing RetirementContributions LG5-2

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

In the previous example, you are investing a total of $4,500 per year for40 years in your employer’s retirement program. You believe that withraises and promotions, you will eventually be able to contribute moremoney each year. Consider that halfway through your career, you areable to increase your investment in the retirement program to $6,000per year (your contribution plus the company match). What would bethe future value of your retirement wealth from this program ifinvestments are compounded at 7 percent?

SOLUTION:

You can compute the future value using two annuities. The first annuityis one with payments of $4,500 that lasts 40 years. The second is a$1,500 (= $6,000 – $4,500) annuity that lasts only 20 years. Wealready computed the future value of the first annuity in the previousexample: $898,358. The future value of the second annuity is

So, your retirement wealth from this program would be $959,851 (=$898,358 + $61,493).

Similar to Problems 5-19, 5-20, Self-Test Problem 1

time out!5-1 Describe how compounding affects the future value computation of an annuity.5-2 Reconsider your original retirement plan example to invest $4,500 per year for 40 years. Now consider the result if you don’t

contribute anything for four years (years 19 to 22) while your child goes to college. How many annuity equations will youneed to find the future value of your 401(k) in this situation?

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5.2 • PRESENT VALUE OF MULTIPLE CASH FLOWS LG5-3The future value concept is very useful to understand how to build wealth for the future. The present value conceptwill help you most particularly for personal applications such as evaluating loans (like car and mortgage loans) andbusiness applications (like determining the value of business opportunities).

Finding the Present Value of Several Cash FlowsConsider the cash flows that we showed at the very beginning of the chapter: You deposit $100 today, followed by a$125 deposit next year, and a $150 deposit at the end of the second year. In the previous situation, we sought thefuture value when interest rates are 7 percent. Instead of future value, we compute the present value of thesethreecash flows. The time line for this problem appears as

The first cash flow is already in year zero, so its value will not change. We will discount the second cash flow oneyear and the third cash flow two years. Using the present value equation from the previous chapter, the present valueof today’s payment is simply $100 ÷ (1 + 0.07)0 = $100. Similarly, the present value of the next two cash flows are$125 ÷ (1 + 0.07)1 = $116.82 and $150 ÷ (1 + 0.07)2 = $131.02, respectively. Therefore, the present value of thesecash flows is $347.84 (= $100 + $116.82 + $131.02).

Putting these three individual present value equations together would yield

The general equation for discounting multiple and varying cash flows is

(5-3)

In this equation, the letters m, n, and p denote when the cash flows occur in time. Each deposit can differ from theothers in terms of size and timing.

Present Value of Level Cash Flows LG5-4You will find that this present value of an annuity concept will have many business and personal applicationsthroughout your life. Most loans are set up so that the amount borrowed (the present value) is repaid through levelpayments made every period (the annuity). Lenders will examine borrowers’ budgets and determine how much eachborrower can afford as a payment. The maximum loan offered will be the present value of that annuity payment. Theequation for the present value of an annuity can be derived from the general equation for the present value ofmultiple cash flows, equation 5-3. Since each cash flow is the same, and the borrower pays the cash flows everyperiod, the present value of an annuity, PVA, can be written as

(5-4)

Suppose that someone makes $100 payments at the end of each year for five years. If interest rates are 8 percent peryear, the present value of this annuity stream is computed using equation 5-4 as

The time line for these payments and present value appears as

Notice that although five payments of $100 each were made, $500 total, the present value is only $399.27. As we’venoted previously, the span of time over which the borrower pays the annuity and the interest rate for discountingstrongly affect present value computations. When you borrow money from the bank, the bank views the amount itlends as the present value of the annuity it receives over time from the borrower. Consider the examples in Table5.2.

A $50 deposit made every year for 20 years is discounted to $573.50 with a 6 percent discount rate. Doubling theannual cash flow to $100 also doubles the present value to $1,146.99. But extending the time period does not impactthe present value as much as you might expect. Making $100 payments for twice the amount of time—40 years—does not double the present value. As you can see in Table 5.2, the present value increases less than 50 percent toonly $1,504.63! If the discount rate increases from 6 percent to 12 percent on the 40-year annuity, the present valuewill shrink to $824.38.

The present value of a cash flow made far into the future is not very valuable today, as Figure 5.2 illustrates. Thatswhy doubling the number of years in the table from 20 to 40 only increased the present value by approximately 30percent. Notice how the present value of $100 annuity payments declines for the cash flows made later in time,especially at higher discount rates. The $100 cash flow in year 20 is worth less than $15 today if we use a 10 percentdiscount rate; they’re worth more than double, at nearly $38 today, if we use a discount rate of 5 percent. The figurealso shows how quickly present value declines with a higher discount rate relative to a lower rate. As we showedabove, the present values of the annuities in the figure are the sums of the present values shown. Since the presentvalues for the 10 percent discount rate are smaller, the present value of an annuity is smaller as interest rates rise.

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▼ TABLE 5.2 Magnitude of the Annuity, Number of Years Invested, and Interest Rate on PV

Present Value of Multiple AnnuitiesJust as we can combine annuities to solve various future value problems, we can also combine annuities to solvesome present value problems with changing cash flows. Consider David Price’s Major League Baseball contractsigned in 2015 with the Boston Red Sox. This was the largest contract for a pitcher ever. It was reported as having a$217 million value. The contract was structured so that the Red Sox paid Price $30 million per year in 2016 through2018, $31 million in 2019, and $32 million per year in 2020 through 2022.1 However, we know that future cashflows have lower present values. So, using a 5 percent discount rate, what is the present value of Prices contract?

FIGURE 5-2 Present Value of Each Annuity Cash Flow

the Math Coach on…Using a Financial Calculator—Part 2

The five TVM buttons/functions in financial calculators have been fine, so far, for the types of TVM problems we’ve been solving.Sometimes we had to use them two or three times for a single problem, but that was usually because we needed an intermediatecalculation to input into another TVM equation.

Luckily, most financial calculators also have built-in worksheets specifically designed for computing TVM in problems with multiplenonconstant cash flows.

To make calculator worksheets as flexible as possible, they are usually divided into two parts: one for input, which we’ll refer to as theCF (cash flow) worksheet, and one or more for showing the calculator solutions. We’ll go over the conventions concerning the CFworksheet here, and we’ll discuss the output solutions in Chapter 13.

The CF worksheet is usually designed to handle inputting sets of multiple cash flows as quickly as possible. As a result, it normallyconsists of two sets of variables or cells—one for the cash flows and one to hold a set of frequency counts for the cash flows, so thatwe can tell it we have seven $1,500 cash flows in a row instead of having to enter $1,500 seven times.

Using the frequency counts to reduce the number of inputs is handy, but you must take care. Frequency counts are only good forembedded annuities of identical cash flows. You have to ensure that you don’t mistake another kind of cash flow for an annuity.

Also, using frequency counts will usually affect the way that the calculator counts time periods. As an example, let’s talk about how wewould put the set of cash flows shown here into a CF worksheet:

To designate which particular value we’ll place into each particular cash flow cell in this worksheet, we’ll note the value and the cellidentifier, such as CF0, CF1, and so forth. We’ll do the same for the frequency cells, using F1, F2, etc., to identify which CF cell thefrequency cell goes with. (Note that, in most calculators, CF0 is treated as a unique value with an unalterable frequency of 1; we’regoing to make the same assumption here so you’ll never see a listing for F0.) For this sample time line, our inputs would be

−$800 [CF0]

$150 [CF1] 1 [F1]

$200 [CF2] 1 [F2]

$  0 [CF3] 1 [F3]

$150 [CF4] 3 [F4]

$ 75 [CF5] 2 [F5]

To compute the present value of these cash flows, use the NPV calculator function. The NPV function computes the present value of allthe future cash flows and then adds the year 0 cash flow. Then, on the NPV worksheet, you would simply need to enter the interest rateand solve for the NPV:

10% [I]

[CPT] [NPV] = −$144.61

Note a few important things about this example:

1. We had to manually enter a value of $0 for CF3. If we hadn’t, the calculator wouldn’t have known about it and would haveimplicitly assumed that CF4 came one period after CF2.

2. Once we use a frequency cell for one cash flow, all numbering on any subsequent cash flows that we enter into the calculator isgoing to be messed up, at least from our point of view. For instance, the first $75 isn’t what we would call “CF5,” is it? We’d call it“CF7” because it comes at time period 7; but calculators usually treat CF5 as “the fifth set of cash flows,” so we’ll just have to tryto do the same to be consistent.

3. If we really don’t need to use frequency cells, we will usually just leave them out of the guidance instructions in this chapter tosave space.

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The reported value for many sports contracts may be misleading in present value terms.©Akihiro Sugimoto/age fotostock

We begin by showing the salary cash flows with the time line

First create a $32 million, seven-year annuity. Here are the associated cash flows:

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Now create a –$1 million, four-year annuity:

Notice that creating the –$1 million annuity also resulted in the third annuity of –$1 million for three years. Thistime line shows three annuities. If you add the cash flows in any year, the sum is Price’s salary for that year. Nowwe can find the present value of each annuity using equation 5-4 three times.

Adding the value of the three annuities reveals that the present value of Price’s salary was $178.89 million(= $185.16m – $3.55m – $2.72m). So, the present value of Price’s contract turns out to be quiteconsiderable, but it is not the $217 million contract value advertised!

EXAMPLE 5-4 Value of Payments LG5-4

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Your firm needs to buy additional physical therapy equipment that costs$20,000. The equipment manufacturer will give you the equipment nowif you will pay $6,000 per year for the next four years. If your firm canborrow money at a 9 percent interest rate, should you pay themanufacturer the $20,000 now or accept the four-year annuity offer of$6,000?

SOLUTION:

We can find the cost of the four-year, $6,000 annuity in present valueterms using equation 5-4:

The cost of paying for the equipment over time is $19,438.32. This isless, in present value terms, than paying $20,000 cash. The firm shouldtake the annuity payment plan.

Similar to Problems 5-7, 5-8, Self-Test Problem 2

Perpetuity—A Special Annuity LG5-5A perpetuity is a special type of annuity with a stream of level cash flows that are paid forever. These arrangementsare called perpetuities because payments are perpetual. Assets that offer investors perpetual payments are preferredstocks and British 2½% Consolidated Stock, a debt referred to as consols.

perpetuity An annuity with cash flows that continue forever.

consols Investment assets structured as perpetuities.

The value of an investment like this is the present value of all future annuity payments. As the cash flow continuesindefinitely, we can’t use equation 5-4. Luckily, mathematicians have figured out that when the number of periods,N, in equation 5-4 goes to infinity, the equation reduces to a very simple one:

(5-5)

For example, the present value of an annual $100 perpetuity discounted at 10 percent is $1,000 (= $100 ÷ 0.10).Compare this to the present value of a $100 annuity of 40 years as shown in Table 5.2. The 40-year annuity’s valueis $977.91. You’ll see that extending the payments from 40 years to an infinite number of years adds only $22.09 (=$1,000 − $977.91) of value. This demonstrates once again how little value today is placed on cash flows paid manyyears into the future.

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5.3 • ORDINARY ANNUITIES VERSUS ANNUITIES DUE LG5-6So far, we’ve assumed that every cash flow comes in at the end of every period. But in many instances, cash flowscome in at the beginning of each period. An annuity in which the cash flows occur at the beginning of each period iscalled an annuity due.

annuity due An annuity in which cash flows are paid at the beginning of each time period.

Consider the five-year $100 annuity due. The cash flow in the beginning of year 1 looks like it’s actually a cash flowtoday. Annuity due moved the cash flow from the end of the year to the beginning, which looks like the end of theprevious year.

Note that these five annuity-due cash flows are essentially the same as a payment today and a four-year ordinaryannuity.

time out!5-3 How important is the magnitude of the discount rate in present value computations? Do significantly higher interest rates

lead to significantly higher present values?

5-4 Reconsider the physical therapy equipment example. If interest rates are only 7 percent, should you pay the up-front fee orthe annuity?

Future Value of an Annuity Due So, how do we calculate the future value of the five-year annuity due shown inthe time line? The first cash flow of an ordinary five-year annuity can compound for four years. The last cash flowdoes not compound at all. From the time line, you can see that the first cash flow of the annuity due essentiallyoccurs in year zero, or today. So the first cash flow compounds for five years. The last cash flow of an annuity duecompounds one year. The main difference between an annuity due and an ordinary annuity is that all the cash flowsof the annuity due compound one more year than the ordinary annuity. The future value of the annuity due willsimply be the future value of the ordinary annuity multiplied by (1 + i):

(5-6)

Earlier in the chapter, the future value of this ordinary annuity was shown to be $586.66. Therefore, the future valueof the annuity due is $633.59 (= $586.66 × 1.08).

finance at work //: behavioralTake Your Lottery Winnings Now or Later?

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©McGraw-Hill Education

On January 13, 2016, three lottery tickets co-won a record Powerball jackpot of $1.5 billion. So each ticket won $500 million. Thewinners had two choices for payment: They could take a much-discounted lump sum cash payment immediately or take 30 annuitypayments (one immediately and then one every year for 29 years, which is a 30-year annuity due). The annuity payment would be$16.67 million (= $500 million ÷ 30) for 30 years. The alternative immediate lump sum was $309.97 million before taxes. One way todecide between the two alternatives would be to use the time value of money concepts. The winners might have computed the presentvalue of the annuity and compared it to the lump sum cash payment.

At the time, long-term interest rates were 3.9 percent. The present value of the annuity offered was $303.11 million per winning ticket.(Compute this yourself.) Notice that winning $500 million does not deliver $500 million of value! If the decision was made from thisperspective, the group should choose to take the lump sum because it has more value than the annuity alternative, and that is what thethree winners did. In fact, most winners do. Financial advisors tend to recommend that lottery winners take the lump sum because theybelieve that the money can earn a higher return than the 3.9 percent interest rate. Of course, you pay income taxes too. The 39.6%federal tax rate brings the lump sum payment down to $187.2 million.

Good reasons arise for taking the annuity, however. To earn the higher return on the lump sum, the advisor (and the group ofowners) would have to take risks. In addition, most of the lump sum would have to be invested. But most people who choose the lumpsum end up spending much of it in the first couple of years. Stories abound about lottery winners who declare bankruptcy a few yearsafter receiving their money. Choosing the annuity helps instill financial discipline, since the winners can’t waste money today that theywon’t receive for years.

Want to know more?Key Words to Search for Updates: Powerball winners (go to www.powerball.com)

Source: Riley, Charles, Sara Sidner, and Tina Burnside, “We Have Powerball Winners!,” CNN Money, January 13, 2016,http://money.cnn.com/2016/01/13/news/powerball-winner-lottery.

Present Value of an Annuity Due What is a five-year annuity due, shown previously, worth today? Rememberthat we discount the first cash flow of an ordinary five-year annuity one year. We discount the last cash flow for thefull five years. But since the first cash flow of the annuity due is already paid today, we don’t discount it at all. Wediscount the last cash flow of an annuity due only four years. Indeed, we discount all the cash flows of the annuitydue one year less than we would discount the ordinary annuity. Therefore, the present value of the annuity due issimply the present value of the ordinary annuity multiplied by (1 + i):

(5-7)

the Math Coach on…Setting Financial Calculators for Annuity Due

“Financial calculators can be set for beginning-of-period payments. Once set, you compute future andpresent values of annuities due just as you would the ordinary annuity. To set the HP calculator, press thecolor button followed by the BEG/END button. To set the TI calculator for an annuity due, push the 2NDbutton, followed by the BGN button, followed by the 2ND button again, followed by the SET button, andfollowed by the 2ND button a third time, finally the QUIT button. To set the HP and TI calculators back to end-of-period cash flows, repeat these procedures.„

Earlier in the chapter, we discovered that the present value of this ordinary annuity was $399.27. So the presentvalue of the annuity due is $431.21 (= $399.27 × 1.08).

Interestingly, we make the same adjustment, (1 + i), to both the ordinary annuity present value and future value tocompute the annuity due value.

5.4 • COMPOUNDING FREQUENCY LG5-7So far, all of our examples and illustrations have used annual payments and annual compounding or discountingperiods. But many situations that use cash flow time-value-of-money analysis require more frequent or less frequenttime periods than simple yearly entries. Bonds make semiannual interest payments; stocks pay quarterly dividends.Most consumer loans require monthly payments. Monthly payments require monthly compounding. In this section,we’ll discuss the implications of compounding more than once a year.

time out!5-5 In what situations might you need to use annuity due analysis instead of an ordinary annuity analysis?5-6 Reconsider your retirement plan earlier in this chapter. What would your retirement wealth grow to be if you started

contributing today?

Effect of Compounding FrequencyConsider a $100 deposit made today with a 12 percent annual interest rate. What’s the future value of this deposit inone year? Equation 4-2 from the previous chapter shows that the answer is $112. What would happen if the bankcompounded the interest every six months instead of at the end of the year? Halfway through the year, the bankwould compute that the deposit has grown 6 percent (half the annual 12 percent rate) to $106. At the end of the year,the bank would compute another 6 percent interest payment. However, this 6 percent is earned on $106, not theoriginal $100 deposit. The end-of-year value is therefore $112.36 (= $106 × 1.06). By compounding twice per yearinstead of just once, the future value is $0.36 higher. Though this amount may seem negligible, you might besurprised to see how quickly the difference becomes significant.

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Instead of compounding annually or semiannually, what might happen if compounding were quarterly? Since eachyear contains four quarters, the interest rate per quarter would be 3 percent (= 12 percent ÷ 4 quarters). The futurevalue in one year, compounded quarterly, is $112.55 (= $100 × 1.034). Again, the compounding frequency increasedand so did the future value. Table 5.3 shows the effect of various compounding frequencies. We’d like to draw yourattention to two important points in the table. First, the higher the compound frequency, the higher the future valuewill be. Second, the relative increase in value from increasing compounding frequency seems to diminish withincreasing frequencies. For example, increasing frequency from annual to semiannual increased the future value by36 cents. However, increasing frequency from daily to hourly compounding increases the future value by only 0.1cent.2

▼ TABLE 5.3 Future Value in One Year and Compounding Frequency of $100 at 12 percent

A B C D

1 Frequency Period Interest Rate Future Value Equation Future Value

2 Annual 12% $100 × 1.121$ 112.00

3 Semiannual 6 $100 × 1.062112.36

4 Quarterly 3 $100 × 1.034112.55

5 Monthly 1 $100 × 1.0112112.68

6 Daily 0.032877 $100 × 1.00032877365112.748

7 Hourly 0.00136986 $100 × 1.00001369868760112.749

The higher the compound frequency, the higher the future value will be.

When we work with annuity cash flows, the compound frequency used is the same as the timing of the cash flows.When annuity cash flows are paid monthly, then interest is also compounded monthly, as seen in Examples 5-5 and5-6.

EARs and APRs If you borrowed $100 at a 12 percent interest rate, you would expect to pay $112 in one year. Ifthe loan compounded monthly, then you would owe $112.68 at the end of the year, as Table 5.3 shows. So a 12percent loan compounded monthly means that you really pay more than 12 percent. In fact, you would pay 12.68percent. In this example, the 12 percent rate is called the annual percentage rate (APR). The 12.68 percent is called theeffective annual rate (EAR)—a more accurate measurement of what you will actually pay.

annual percentage rate (APR) The interest rate per period times the number of periods in a year.

effective annual rate (EAR) The interest rate per period times the number of periods in a year.

Lenders are legally required to show potential borrowers the APR on any loan offered. While the difference in APRand EAR is not that large in this example, it’s interesting that the law requires only the less accurate (and lower) oneto be shown. Since the EAR is a more accurate measure of what you will pay, it’s useful to know how to convert astated APR to an EAR. Equation 5-8 shows this conversion with a compounding frequency of m times per year:

(5-8)

Table 5.4 shows various EAR conversions. If compounding occurs annually, you will see that the EAR and the APRwill be the same. If compounding happens more than once a year, then the EAR will be higher than the APR. Thetable also demonstrates that the compound frequency effect grows substantially for higher interest rates or longerterm loans. Compounded quarterly, the EAR is hardly different at all from a 5 percent APR: 5.09 percent versus 5

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percent. The difference is larger when the APR is 12 percent. Compounded quarterly, the EAR is higher at 12.55percent.

the Math Coach on…Annuity Computations in Spreadsheets

“The TVM functions in a spreadsheet handle annuity payments similar to financial calculators. Thespreadsheet Math Coach in Chapter 4 shows the functions. The functions have an annuity input.

The example illustrated earlier in this chapter asks for the FV of annual $100 deposits earning 8 percent. Thespreadsheet solution is the same as the equation and calculator solutions. If you want the FV of an annuitydue, just change the type from 0 to 1.

See this textbook’s online student center to watch instructional videos on using spreadsheets.„

EXAMPLE 5-5 Car Loan Debt LG5-4

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Now you would like to buy a car. You have reviewed your budget anddetermined that you can afford to pay $500 per month as a carpayment. How much can you borrow if interest rates are 9 percent andyou pay the loan over four years? How much could you borrow if youagree to pay for six years instead?

SOLUTION:

The loan amount is the present value of the 48-month, $500 annuity.Note that the loan term will be 48 (= 4 × 12) months and the interestrate is 0.75 (= 9 ÷ 12) percent. Using equation 5-4, you discover thatyou can borrow up to $20,092 to buy a car:

If you are willing to borrow money for six years instead of four, thesmall change to the equation results in your ability to borrow $27,738.Although this would allow you to buy a more expensive car, it would

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also require two more years of $500 payments (an additional $12,000of payments!).

Similar to Problems 5-25, 5-26, Self-Test Problem 4

EXAMPLE 5-6Making Monthly PensionContributions LG5-7

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Reexamine your original plan to contribute to your company retirementplan. Instead of a total contribution of $4,500 per year for 40 years, youare able to contribute monthly. Given your expected 7 percent per yearinvestment return, how much money can you expect in your retirementaccount?

SOLUTION:

Now your total monthly contribution will be $375 (= $4,500 ÷ 12), whichwill continue for 480 months and earn a 0.58333 (= 7 ÷ 12) percentmonthly return. The results of equation 5-2 show that the future valueof this annuity is

When you made contributions annually, the future value was $898,358(Example 5-2). By changing to monthly contributions, your retirementnest egg increased by nearly $86,000 to $984,305!

Similar to Problems 5-51, 5-52, Self-Test Problem 3

the Math Coach on…Common Mistakes

“As you figure present and future values of annuity cash flows, check that all terms are consistent: thenumber of payments, interest rate, and payment size all need to use common terms. If your payments aremonthly, then the number of payments must reflect the number of months; the interest rate must be stated asa per-month rate, and the payment register must reflect that monthly payment.„

time out!5-7 Why is EAR a more accurate measure of the rate actually paid than APR?

5-8 What would have a smaller present value: a future sum discounted annually or one discounted monthly?

▼ TABLE 5.4 The EAR Is Higher than the APR

A B C D

1 APR Compounding Periods Equation = EAR

2 Varying the Compounding Periods

3 5%  1     (1 + 0.05/1)1 − 1 5.00% 

4 5 4     (1 + 0.05/4)4 − 1 5.09

5 5 12     (1 + 0.05/12)12 − 1 5.12

6 Varying APR and Compounding Periods

7 9 4     (1 + 0.09/4)4 − 1 9.31

8 9 12     (1 + 0.09/12)12 − 1 9.38

9 12 4     (1 + 0.12/4)4 − 1 12.55

10 12 12     (1 + 0.12/12)12 − 1 12.68

Note: This compound frequency effect grows substantially for higher interest rates or longer term loans.

EXAMPLE 5-7Evaluating Credit CardOffers LG5-7

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

As a college student, you probably receive many credit card offers inthe mail. Consider these two offers. The first card charges a 16 percentAPR. An examination of the footnotes reveals that this card compoundsmonthly. The second credit card charges 15.5 percent APR andcompounds weekly. Which card has a lower effective annual rate?

SOLUTION:

Compute the EAR of each card to compare them in common (andrealistic) terms. The first card has an EAR of

The EAR of the second card is

You should pick the second credit card because it has a lower effectiveannual rate. But note also that you will always be better off if you pay

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your credit card balance whenever the bill comes due.

Similar to Problems 5-15, 5-16, Self-Test Problem 3

5.5 • ANNUITY LOANS LG5-8In this chapter, we’ve focused on computing the future and present value of annuities. But in many situations, thesevalues are already known and what we really need to compare are the payments or implied interest rate—usually,the highest interest rate offered.

the Math Coach on…Common Mistakes

“As we noted in Chapter 4, when computing the interest rate, make sure that the present value and theannuity payments are of different signs (positive versus negative). Otherwise, the calculator will show an error.

What Is the Interest Rate?Many business and personal applications already state the cost of an investment, as well as the annuity cash flowsand time period. We need, then, to solve for the implied interest rate of this investment. Unfortunately, we have nogeneral, easy equation to solve for the interest rate. Even financial calculators use an iterating process, which causesthem to “think” a little longer before displaying the estimated interest rate result.

Consider the plight of a manager of a small doctor’s office who has the opportunity to buy a piece of imagingequipment for $100,000. The equipment will allow the office to generate $25,000 in profits for six years, at whichtime the equipment will be worn out and without value in the United States. What rate of return does this purchaseoffer the doctor’s office? The time line for this problem appears as

For the financial calculator solution, input N = 6, PV = –100000, PMT = 25000, and FV = 0. The interest rate resultis then 12.98 percent. So, if this is a high enough return relative to other uses of the $100,000, the doctor’s officeshould seriously consider purchasing the imaging machine.

EXAMPLE 5-8Computing Interest RateNeeded LG5-8

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

After saving diligently throughout your entire career, you and yourspouse are finally ready to retire with a nest egg of $800,000. You needto invest this money in a mix of stocks and bonds that will allow you towithdraw $6,000 per month for 30 years. What interest rate do you

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need to earn?

SOLUTION:

Use a financial calculator and input N = 360, PV = –800000, PMT =6000, and FV = 0. The interest rate result is 0.6860 percent. Butremember, since the periods and payments are in months, the interestrate is too. It is customary to report this as an APR: 8.23 percent (=0.6860 percent × 12). However, the EAR more accurately reflects thetrue interest rate, 8.55 percent (= 1.0068612 – 1). In order for yourmoney to last for 30 years while funding a $6,000 per month income,you must earn at least an 8.23 APR per year return.

If you have uneven cash flows, use the calculator CF worksheet andthen solve with the IRR function.

Similar to Problems 5-33, 5-34, 5-35, 5-36

Finding Payments on an Amortized Loan LG5-9

©Phillip Spears/Getty Images

Many consumers and small business owners already know how much money they want to borrow and the level ofcurrent interest rates. Usually, they need to translate this information into the actual payments to determine if theycan really afford the purchase. A loan structured for annuity payments that completely pay off the debt is called anamortized loan. To compute the annuity cash flow of an amortized loan, rearrange the present value of an annuityformula, equation 5-4, to solve for the payment:

amortized loan A loan in which the borrower pays interest and principal over time.

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(5-9)

Most car loans require monthly payments for three to five years. Assume that you need a $10,000 loan to buy a car.The loan is for four years and interest rates are 9 percent per year APR. To implement equation 5-9, use an interestrate of 0.75 percent (= 9 percent/12) and 48 periods (= 4 × 12) as

So, when interest rates are 9 percent, it takes monthly payments of $248.85 to pay off a $10,000 loan in four years.

Interest rate levels and loan length strongly affect how large your payments will be. Table 5.5 shows the monthlypayments needed to pay off a mortgage debt at various interest rates and lengths of time. (Try computing thepayments yourself!) Note that as the interest rate declines, the monthly payment also declines. This is why peoplerush to refinance their mortgages after interest rates fall. A decline of 1 or 2 percent can save a homeowner hundredsof dollars every month. You will also see from the table that paying off a mortgage in only 15 years requires largerpayments, but generally saves thousands in interest.

Amortized Loan Schedules When you pay a car loan or home mortgage, you will often find it useful to knowhow much of the debt, or loan principal, you still owe. For example, consider a case wherein you bought a car twoyears ago using a four-year loan. In order to sell the car now, the loan balance will have to be paid off.Being able to compute this principal balance may influence your chances of selling the car.

loan principal The balance yet to be paid on a loan.

▼ TABLE 5.5 Monthly Payments on a $225,000 Loan

An interest-only loan allows the borrower to make payments that consist totally of interest payments, so none of thedebt is reduced. A $10,000 interest-only loan with a 9 percent APR paid monthly will cost $75 per month (=$10,000 × 0.09 ÷ 12). Amortizing this loan over four years requires monthly payments of $248.85 (see earlier carloan problem). The difference in the first month’s payment on the two loans is $173.85 (= $248.85 – $75) andrepresents the amount of the regular amortized loan’s payment that goes to reducing the principal balance. So afterthe first month’s payment, the amortized loan’s balance has fallen to $9,826.15, while the interest-only loan still hasa balance of $10,000.

In the second month, the interest incurred on the regular amortized loan is $73.70 (= $9,826.15 × 0.09 ÷ 12), so the$248.85 second-month payment represents principal payment of $175.15. These numbers are shown in theamortization schedule of Table 5.6. The table will show you that the early payments on a car loan go mostly to payingthe interest rather than reducing the principal. That interest component declines over time, and then the principalbalance declines.

amortization schedule A table detailing the periodic loan payment, interest payment, and debt balance over the life of the loan.

The amortization schedule shows that if you wish to sell the car after two years, you will have to pay the loancompany a car loan (principal) debt of $5,447.13. Of course, if you had an interest-only loan, you would still owethe full principal of $10,000 after two years. Amortization schedules are also useful for determining other things,like the total amount of interest that you will pay over the life of the loan. In this case, if you take a regular loan inwhich you pay both principal and interest, you pay $10,000 in principal and nearly $1,945 in interest during the fouryears of the loan. The interest component is an even larger component of longer-term loans, like 30-year mortgages.Depending on the interest rate charged, the first payment in a mortgage consists of 75 percent to 95 percent interest.The home mortgage principal balance falls very slowly in the first years of the loan.

▼ TABLE 5.6 Amortization Schedule over Four Years (9 percent APR)

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EXAMPLE 5-9Monthly MortgagePayments LG5-9

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to Connect or go tomhhe.com/CornettM4e.

Say that you have your heart set on purchasing a beautiful, old Tudor-style house for $250,000. A mortgage broker says that you can qualifyfor a mortgage for 80 percent (or $200,000) of the price. If you get a15-year mortgage, the interest rate will be 6.1 percent APR. A 30-yearmortgage costs 6.4 percent. One of the factors that will help you decidewhich mortgage to take is the magnitude of the monthly payments.What will they be?3

SOLUTION:

To pay off the mortgage in only 15 years, the payments would have tobe larger than for the 30-year mortgage. The higher payment will beeased somewhat because the interest rate is lower on the 15-yearmortgage. The interest rate would be i = 0.061 ÷ 12 = 0.0050833, or0.50833% per month. The payment for the 15-year mortgage is

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The payment for the 30-year mortgage would be

So, the payments on the 15-year mortgage are nearly $450 more eachmonth than the 30-year mortgage payments. You must decide whetherthe cost of paying the extra $450 each month is worth it to own thehouse with no debt 15 years sooner. The decision would depend onyour financial budget and the strength of your desire to be debt free.

Similar to Problems 5-39, 5-40, Self-Test Problems 1 and 4

We construct amortization schedules by showing the loan’s principal balance at the beginning of the month. This isthe same as the balance at the end of the previous month (except for the very first payment). Then we compute theinterest owed on that balance for the month. After paying that interest, what’s left of the monthly payment reducesthe loan balance for the next month. Because of these repetitive computations, spreadsheets make amortizationschedules easy to construct.

time out!5-9 How might credit card companies keep their cardholders in debt for a long time? What payment do the credit card

companies expect your friend to make so that he never pays down the debt?5-10 Can you find the interest rate if you know the annuity payments and a future value? Under what circumstances might you

want to solve this kind of problem? Which equation would you use?

Compute the Time Period You might also find it useful to know how long it will take to pay off a loan withspecific annuity payments. To find the number of periods, you can solve equation 5-9 for N—the number ofpayments—but the equation becomes quite complicated.4 Many people just use a financial calculator or spreadsheet.We can check to see if the $248.85 monthly payment would indeed pay off the $10,000, 9 percent car loan in fouryears. Finding the solution with a financial calculator entails entering I = 0.75, PV = 10000, PMT = –248.85, and FV= 0. The answer is 48 months.

Add-On Interest One method of calculating payments of a loan that is popular in payday lending is called add-oninterest. This method computes the amount of the interest payable at the beginning of the loan, which is then addedto the principal of the loan. This total is then divided into the number of payments to be made. Consider a loan of$1,000 to be paid with 9 percent add-on interest and repaid in six monthly payments.

add-on interest A calculation of the amount of interest determined at the beginning of the loan and then added to the principal.

the Math Coach on…

Using the AMORT Function in TVM Calculators

“TVM calculators have preprogrammed functions to compute the amount of principal paid part way through amortgage. For example, if you took out a 30-year, $200,000 mortgage at a 6 percent APR, how much principalhave you paid after five years? How much do you still owe? How much interest have you paid?

To answer these questions, first enter the mortgage information to compute the monthly payments. Then usethe AMORT function. This example uses the Texas Instruments BA II + as an example. The Hewlett-Packardand other TVM calculators have similar functions. The AMORT function allows you to compute the loanbalance at any time during the mortgage period. It also computes the amount of principal and interest that hasbeen paid during any time period. To answer the questions above

1. Press 2nd AMORT and P1 = 1 appears. (This refers to the first payment of the mortgage.)2. Press the down arrow ↓, P2 = appears. (This refers to the last payment made.)

3. The question refers to 5 years of payments, which is 60 months. Enter 60 and press ENTER.The calculator has now computed the loan balance after the 60th payment and the amount of principal andinterest that have been paid between the 1st and the 60th payments.

4. Press the down arrow ↓, displayed is BAL = 186,108.71, which is the loan balance.5. Press the down arrow ↓, displayed is PRN = 13,891.29, which is the principal paid in the first five years.

6. Press the down arrow ↓, displayed is INT = –58,054.78, which is the interest paid in the first five years.

Note that in the beginning of a mortgage, far more interest is paid than principal.„The total interest for this loan is computed as 9 percent of $1,000 for six months, or $45 (= 0.09 × $1,000 × ½). Thisis added to the principal for a total of $1,045. Each of the six monthly payments is then $1,045 ÷ 6 = $174.17. Bealert that the add-on interest method seriously understates the real interest rate that is being paid! If you borrow$1,000 and repay a $174.17 monthly annuity for six months, the monthly interest rate is 1.27 percent. This is a 15.27percent APR (= 1.27% × 12) and a 16.39 percent EAR (= 1.012712 − 1)—both much higher than the advertised 9percent interest rate of this loan.

EXAMPLE 5-10

Time to Pay Off a Credit CardBalance LG5-10

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Through poor financial management, your friend has racked up $5,000in debt on his credit card. The card charges a 19 percent APR andcompounds monthly. His latest bill shows that he must pay a minimumof $150 this month. At this rate, how long will it take your friend to payoff his credit card debt?

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SOLUTION:

Using the financial calculator, input I = 1.58333 (= 19/12), PV = 5000,PMT = –150, FV = 0. The answer is 48 months, or 4 years. If the friendpays the minimum payment, then it will be a long time before he will beout of debt. The credit card company is very content to continue to earnthe high return for many years—essentially, the interest on the loanand a very small portion of the principal. Your friend should pay morethan the minimum charge to reduce his debt quicker.

Similar to Problems 5-41, 5-42, Self-Test Problem 4

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Your Turn…Questions

1. How can you add a cash flow in year 2 and a cash flow in year 4? In year 7? (LG5-1)

2. People can become millionaires in their retirement years quite easily if they start saving early in employer

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401(k) or 403(b) programs (or even if their employers don’t offer such programs). Demonstrate the growth of a$250 monthly contribution for 40 years earning 9 percent APR. (LG5-2)

3. When you discount multiple cash flows, how does the future period that a cash flow is paid affect its presentvalue and its contribution to the value of all the cash flows? (LG5-3)

4. How can you use the present value of an annuity concept to determine the price of a house you can afford?(LG5-4)

5. Since perpetuity payments continue forever, how can a present value be computed? Why isn’t the present valueinfinite? (LG5-5)

6. Explain why you use the same adjustment factor, (1 + i), when you adjust annuity due payments for both futurevalue and present value. (LG5-6)

7. Use the idea of compound interest to explain why EAR is larger than APR. (LG5-7)

8. Would you rather pay $10,000 for a five-year, $2,500 annuity or a 10-year, $1,250 annuity? Why? (LG5-8)

9. The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful inreducing taxes than in the later years? (LG5-9)

10. How can you use the concepts illustrated in computing the number of payments in an annuity to figure how topay off a credit card balance? How does the magnitude of the payment impact the number of months? (LG5-10)

ProblemsBASIC PROBLEMS

5-1 Future Value Compute the future value in year 9 of a $2,000 deposit in year 1 and another $1,500 depositat the end of year 3 using a 10 percent interest rate. (LG5-1)

5-2 Future Value Compute the future value in year 7 of a $2,000 deposit in year 1 and another $2,500 depositat the end of year 4 using an 8 percent interest rate. (LG5-1)

5-3 Future Value of an Annuity What is the future value of a $900 annuity payment over five years if interestrates are 8 percent? (LG5-2)

5-4 Future Value of an Annuity What is the future value of a $700 annuity payment over six years if interestrates are 10 percent? (LG5-2)

5-5 Present Value Compute the present value of a $2,000 deposit in year 1 and another $1,500 deposit at theend of year 3 if interest rates are 10 percent. (LG5-3)

5-6 Present Value Compute the present value of a $2,000 deposit in year 1 and another $2,500 deposit at theend of year 4 using an 8 percent interest rate. (LG5-3)

5-7 Present Value of an Annuity What’s the present value of a $900 annuity payment over five years ifinterest rates are 8 percent? (LG5-4)

5-8 Present Value of an Annuity What’s the present value of a $700 annuity payment over six years ifinterest rates are 10 percent? (LG5-4)

5-9 Present Value of a Perpetuity What’s the present value, when interest rates are 7.5 percent, of a $50payment made every year forever? (LG5-5)

5-10 Present Value of a Perpetuity What’s the present value, when interest rates are 8.5 percent, of a $75payment made every year forever? (LG5-5)

5-11 Present Value of an Annuity Due If the present value of an ordinary, seven-year annuity is $6,500and interest rates are 7.5 percent, what’s the present value of the same annuity due? (LG5-6)

5-12 Present Value of an Annuity Due If the present value of an ordinary, six-year annuity is $8,500 andinterest rates are 9.5 percent, what’s the present value of the same annuity due? (LG5-6)

5-13 Future Value of an Annuity Due If the future value of an ordinary, seven-year annuity is $6,500 andinterest rates are 7.5 percent, what is the future value of the same annuity due? (LG5-6)

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5-14 Future Value of an Annuity Due If the future value of an ordinary, six-year annuity is $8,500 andinterest rates are 9.5 percent, what’s the future value of the same annuity due? (LG5-6)

5-15 Effective Annual Rate A loan is offered with monthly payments and a 10 percent APR. What’s theloan’s effective annual rate (EAR)? (LG5-7)

5-16 Effective Annual Rate A loan is offered with monthly payments and a 13 percent APR. What’s theloan’s effective annual rate (EAR)? (LG5-7)

INTERMEDIATE PROBLEMS

5-17 Future Value Given a 4 percent interest rate, compute the year 6 future value of deposits made inyears 1, 2, 3, and 4 of $1,100, $1,200, $1,200, and $1,500. (LG5-1)

5-18 Future Value Given a 5 percent interest rate, compute the year 6 future value of deposits made inyears 1, 2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400. (LG5-1)

5-19 Future Value of Multiple Annuities Assume that you contribute $200 per month to a retirement planfor 20 years. Then you are able to increase the contribution to $300 per month for another 30 years.Given a 7 percent interest rate, what is the value of your retirement plan after the 50 years? (LG5-2)

5-20 Future Value of Multiple Annuities Assume that you contribute $150 per month to aretirement plan for 15 years. Then you are able to increase the contribution to $350 per monthfor the next 25 years. Given an 8 percent interest rate, what is the value of your retirement plan afterthe 40 years? (LG5-2)

5-21 Present Value Given a 6 percent interest rate, compute the present value of payments made in years 1,2, 3, and 4 of $1,000, $1,200, $1,200, and $1,500. (LG5-3)

5-22 Present Value Given a 7 percent interest rate, compute the present value of payments made in years 1,2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400. (LG5-3)

5-23 Present Value of Multiple Annuities A small business owner visits her bank to ask for a loan. Theowner states that she can repay a loan at $1,000 per month for the next three years and then $2,000 permonth for two years after that. If the bank is charging customers 7.5 percent APR, how much would itbe willing to lend the business owner? (LG5-4)

5-24 Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan. Theowner states that he can repay a loan at $1,500 per month for the next three years and then $500 permonth for two years after that. If the bank is charging customers 8.5 percent APR, how much would itbe willing to lend the business owner? (LG5-4)

5-25 Present Value You are looking to buy a car. You can afford $450 in monthly payments for four years.In addition to the loan, you can make a $1,000 down payment. If interest rates are 5 percent APR,what price of car can you afford? (LG5-4)

5-26 Present Value You are looking to buy a car. You can afford $650 in monthly payments for five years.In addition to the loan, you can make a $750 down payment. If interest rates are 8 percent APR, whatprice of car can you afford? (LG5-4)

5-27 Present Value of a Perpetuity A perpetuity pays $100 per year and interest rates are 7.5 percent.How much would its value change if interest rates increased to 9 percent? Did the value increase ordecrease? (LG5-5)

5-28 Present Value of a Perpetuity A perpetuity pays $50 per year and interest rates are 9 percent. Howmuch would its value change if interest rates decreased to 7.5 percent? Did the value increase ordecrease? (LG5-5)

5-29 Future and Present Value of an Annuity Due If you start making $50 monthly contributions todayand continue them for five years, what’s their future value if the compounding rate is 10 percent APR?What is the present value of this annuity? (LG5-6)

5-30 Future and Present Value of an Annuity Due If you start making $75 monthly contributions todayand continue them for four years, what is their future value if the compounding rate is 12 percentAPR? What is the present value of this annuity? (LG5-6)

5-31 Compound Frequency Payday loans are very short-term loans that charge very high interest rates.You can borrow $225 today and repay $300 in two weeks. What is the compounded annual rateimplied by this 33.33 percent rate charged for only two weeks? (LG5-7)

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5-32 Compound Frequency Payday loans are very short-term loans that charge very high interest rates.You can borrow $500 today and repay $590 in two weeks. What is the compounded annual rateimplied by this 18 percent rate charged for only two weeks? (LG5-7)

5-33 Annuity Interest Rate What’s the interest rate of a six-year, annual $5,000 annuity with present valueof $20,000? (LG5-8)

5-34 Annuity Interest Rate What’s the interest rate of a seven-year, annual $4,000 annuity with presentvalue of $20,000? (LG5-8)

5-35 Annuity Interest Rate What annual interest rate would you need to earn if you wanted a$1,000 per month contribution to grow to $75,000 in six years? (LG5-8)

5-36 Annuity Interest Rate What annual interest rate would you need to earn if you wanted a $600 permonth contribution to grow to $45,000 in six years? (LG5-8)

5-37 Add-On Interest Payments To borrow $500, you are offered an add-on interest loan at 8 percent.Two loan payments are to be made, one at six months and the other at the end of the year. Computethe two equal payments. (LG5-8)

5-38 Add-On Interest Payments To borrow $800, you are offered an add-on interest loan at 7 percent.Three loan payments are to be made, one at four months, another at eight months, and the last one atthe end of the year. Compute the three equal payments. (LG5-8)

5-39 Loan Payments You wish to buy a $25,000 car. The dealer offers you a four-year loan with a 9percent APR. What are the monthly payments? How would the payment differ if you paid interestonly? What would the consequences of such a decision be? (LG5-9)

5-40 Loan Payments You wish to buy a $10,000 dining room set. The furniture store offers you a three-year loan with an 11 percent APR. What are the monthly payments? How would the payment differ ifyou paid interest only? What would the consequences of such a decision be? (LG5-9)

5-41 Number of Annuity Payments Joey realizes that he has charged too much on his credit card and hasracked up $5,000 in debt. If he can pay $150 each month and the card charges 17 percent APR(compounded monthly), how long will it take him to pay off the debt? (LG5-10)

5-42 Number of Annuity Payments Phoebe realizes that she has charged too much on her credit card andhas racked up $6,000 in debt. If she can pay $200 each month and the card charges 18 percent APR(compounded monthly), how long will it take her to pay off the debt? (LG5-10)

ADVANCED PROBLEMS

5-43 Future Value Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,000and $2,000 are made in years 1 and 3, respectively, and a withdrawal of $700 is made in year 4. (LG5-10)

5-44 Future Value Given a 9 percent interest rate, compute the year 6 future value if deposits of $1,500and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $600 is made in year 5. (LG5-1)

5-45 EAR of Add-On Interest Loan To borrow $2,000, you are offered an add-on interest loan at 10percent with 12 monthly payments. First compute the 12 equal payments and then compute the EARof the loan. (LG5-7, LG5-8)

5-46 EAR of Add-On Interest Loan To borrow $700, you are offered an add-on interest loan at 9 percentwith 12 monthly payments. First compute the 12 equal payments and then compute the EAR of theloan. (LG5-7, LG5-8)

5-47 Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $500cash back on the purchase or a 3 percent APR, four-year loan. The price of the car is $15,000 and youcould obtain a four-year loan from your credit union, at 6 percent APR. Which deal is cheaper? (LG5-4, LG5-9)

5-48 Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $1,000cash back on the purchase, or a 2 percent APR, five-year loan. The price of the car is $20,000 and youcould obtain a five-year loan from your credit union, at 7 percent APR. Which deal is cheaper? (LG5-4, LG5-9)

5-49 Amortization Schedule Create the amortization schedule for a loan of $15,000, paid monthly

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over three years using a 9 percent APR. (LG5-9)5-50 Amortization Schedule Create the amortization schedule for a loan of $5,000, paid monthly over two

years using an 8 percent APR. (LG5-9)5-51 Investing for Retirement Monica has decided that she wants to build enough retirement wealth that,

if invested at 8 percent per year, will provide her with $3,500 of monthly income for 20 years. To date,she has saved nothing, but she still has 30 years until she retires. How much money does she need tocontribute per month to reach her goal? (LG5-4, LG5-9)

5-52 Investing for Retirement Ross has decided that he wants to build enough retirement wealth that, ifinvested at 7 percent per year, will provide him with $3,000 of monthly income for 30 years. To date,he has saved nothing, but he still has 20 years until he retires. How much money does he need tocontribute per month to reach his goal? (LG5-4, LG5-9)

5-53 Loan Balance Rachel purchased a $15,000 car three years ago using an 8 percent, four-year loan. Shehas decided that she would sell the car now, if she could get a price that would pay off the balance ofher loan. What is the minimum price Rachel would need to receive for her car? (LG5-9)

5-54 Loan Balance Hank purchased a $20,000 car two years ago using a 9 percent, five-year loan. He hasdecided that he would sell the car now, if he could get a price that would pay off the balance of hisloan. What’s the minimum price Hank would need to receive for his car? (LG5-9)

5-55 Teaser Rate Mortgage A mortgage broker is offering a $183,900 30-year mortgage with a teaser rate.In the first two years of the mortgage, the borrower makes monthly payments on only a 4 percent APRinterest rate. After the second year, the mortgage interest rate charged increases to 7 percent APR.What are the monthly payments in the first two years? What are the monthly payments after thesecond year? (LG5-9)

5-56 Teaser Rate Mortgage A mortgage broker is offering a $279,000 30-year mortgage with a teaser rate.In the first two years of the mortgage, the borrower makes monthly payments on only a 4.5 percentAPR interest rate. After the second year, the mortgage interest rate charged increases to 7.5 percentAPR. What are the monthly payments in the first two years? What are the monthly payments after thesecond year? (LG5-9)

5-57 Spreadsheet Problem Consider a person who begins contributing to a retirement plan at age 25 andcontributes for 40 years until retirement at age 65. For the first 10 years, she contributes $3,000 peryear. She increases the contribution rate to $5,000 per year in years 11 through 20. This is followed byincreases to $10,000 per year in years 21 through 30 and to $15,000 per year for the last 10 years. Thismoney earns a 9 percent return. First compute the value of the retirement plan when she turns age 65.Then compute the annual payment she would receive over the next 40 years if the wealth wasconverted to an annuity payment at 8 percent. (LG5-2, LG5-9)

5-58 Spreadsheet Problem When paying off a home mortgage, extra principle payments can have adramatic impact on the time needed to pay off the mortgage. (LG5-9)a. Create an amortization schedule for a $200,000, three-year mortgage, with a 6% APR.b. After the fifth year, add an extra $100 to each monthly payment. When is the loan paid off?

Combined Chapter 4 and Chapter 5 Problems4&5-1 Future Value Consider that you are 35 years old and have just changed to a new job. You have

$80,000 in the retirement plan from your former employer. You can roll that money into theretirement plan of the new employer. You will also contribute $3,600 each year into your newemployer’s plan. If the rolled-over money and the new contributions both earn a 7 percent return,how much should you expect to have when you retire in 30 years?

4&5-2 Future Value Consider that you are 45 years old and have just changed to a new job. You have$150,000 in the retirement plan from your former employer. You can roll that money into theretirement plan of the new employer. You will also contribute $7,200 each year into your new

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employer’s plan. If the rolled-over money and the new contributions both earn an 8 percentreturn, how much should you expect to have when you retire in 20 years?

4&5-3 Future Value and Number of Annuity Payments Your client has been given a trust fundvalued at $1 million. He cannot access the money until he turns 65 years old, which is in 25years. At that time, he can withdraw $25,000 per month. If the trust fund is invested at a 5.5percent rate, how many months will it last your client once he starts to withdraw the money?

4&5-4 Future Value and Number of Annuity Payments Your client has been given a trust fundvalued at $1.5 million. She cannot access the money until she turns 65 years old, which is in 15years. At that time, she can withdraw $20,000 per month. If the trust fund is invested at a 5percent rate, how many months will it last your client once she starts to withdraw the money?

4&5-5 Present Value and Annuity Payments A local furniture store is advertising a deal in which youbuy a $3,000 dining room set and do not need to pay for two years (no interest cost is incurred).How much money would you have to deposit now in a savings account earning 5 percent APR,compounded monthly, to pay the $3,000 bill in two years? Alternatively, how much would youhave to deposit in the savings account each month to be able to pay the bill?

4&5-6 Present Value and Annuity Payments A local furniture store is advertising a deal in which youbuy a $5,000 living room set with three years before you need to make any payments (no interestcost is incurred). How much money would you have to deposit now in a savings account earning4 percent APR, compounded monthly, to pay the $5,000 bill in three years? Alternatively, howmuch would you have to deposit in the savings account each month to be able to pay the bill?

4&5-7 House Appreciation and Mortgage Payments Say that you purchase a house for $200,000 bygetting a mortgage for $180,000 and paying a $20,000 down payment. If you get a 30-yearmortgage with a 7 percent interest rate, what are the monthly payments? What would the loanbalance be in 10 years? If the house appreciates at 3 percent per year, what will be the value ofthe house in 10 years? How much of this value is your equity?

4&5-8 House Appreciation and Mortgage Payments Say that you purchase a house for $150,000 bygetting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-yearmortgage with a 7 percent interest rate, what are the monthly payments? What would the loanbalance be in five years? If the house appreciates at 4 percent per year, what will be the value ofthe house in five years? How much of this value is your equity?

4&5-9 Construction Loan You have secured a loan from your bank for two years to build your home.The terms of the loan are that you will borrow $200,000 now and an additional $100,000 inone year. Interest of 10 percent APR will be charged on the balance monthly. Since nopayments will be made during the two-year loan, the balance will grow at the 10 percentcompounded rate. At the end of the two years, the balance will be converted to a traditional 30-year mortgage at a 6 percent interest rate. What will you be paying as monthly mortgagepayments (principal and interest only)?

4&5-10 Construction Loan You have secured a loan from your bank for two years to build your home.The terms of the loan are that you will borrow $100,000 now and an additional $50,000 in oneyear. Interest of 9 percent APR will be charged on the balance monthly. Since no payments willbe made during the two-year loan, the balance will grow. At the end of the two years, the balancewill be converted to a traditional 15-year mortgage at a 7 percent interest rate. What will you payas monthly mortgage payments (principal and interest only)?

NotesCHAPTER 51. The contract actually contains some complications like incentives to play well and salary deferral. We ignore those complicating factors

here.

2. It is also possible to continuously compound. The future value of a continuously compounded deposit is , where ehas a value of 2.7183.

3. Most homeowners are actually most interested in their total payment, which will include hazard insurance for the home and propertytaxes. Such payments are referred to as PITI—principal, interest, taxes, and insurance. For simplicity, we use only PI payments here—principal and interest.

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4. The equation for solving for the number of periods in an annuity is:

chapter sixunderstanding financialmarkets and institutions

©Steve Allen/Stockbyte/Getty Images

H

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ow do funds flow throughout the economy? How do financial markets operate and relate to oneanother? As an individual investor or a financial manager you need to know. Your future decision-making skills depend on it. Investors’ funds flow through financial markets such as the New York

Stock Exchange and mortgage markets. Financial institutions—commercial banks (e.g., Bank ofAmerica), investment banks (e.g., Morgan Stanley), and mutual funds (e.g., Fidelity)—act asintermediaries to channel funds from individual savers or investors through financial markets. This chapterlooks at the nature and operations of financial markets and discusses the financial institutions (FIs) thatparticipate in those markets. Bonds, stocks, and other securities that trade in the markets are covered inChapters 7 and 8.

In this chapter we also examine how significant changes in the way financial institutions deliverservices played a major role in forming the severe financial crisis that began in late 2008. We examinesome of the crisis’s underlying causes, review some of the major events that occurred during that time,and discuss some resulting regulatory and industry changes that are in effect today in Appendix 6A,available in Connect or at mhhe.com/Cornett4e.

LEARNING GOALS

LG6-1 Differentiate between primary and secondary markets and between money and capital markets.LG6-2 List the types of securities traded in money and capital markets.LG6-3 Identify different types of financial institutions and the services that each provides.LG6-4 Know the main suppliers and demanders of loanable funds.LG6-5 Understand how equilibrium interest rates are determined.LG6-6 Analyze specific factors that influence interest rates.LG6-7 Offer different theories that explain the shape of the term structure of interest rates.LG6-8 Demonstrate how forward interest rates derive from the term structure of interest rates.

viewpointsbusiness APPLICATIONDPH Corporation needs to issue new bonds either this year or in two years. DPH Corp. is a profitable firm, but if the U.S. economywere to experience a downturn, the company would see a big drop in sales over the next two years as its products are very sensitiveto changes in the overall economy. DPH Corp. currently has $10 million in public debt outstanding, but its bonds are not activelytraded. What questions must DPH Corp. consider as its managers decide whether to issue bonds today or in two years? How canDPH Corp. get these bonds to potential buyers and thus raise the needed capital? (See the solution at the end of the book.)

6.1 • FINANCIAL MARKETS LG6-1Financial markets exist to manage the flow of funds from investors to borrowers as well as from one investor toanother. We generally differentiate financial markets by their primary financial instruments’ characteristics (such asbond maturities) or the market’s location. Specifically, we can distinguish markets along two major dimensions:

financial markets The arenas through which funds flow.

1. Primary versus secondary markets.2. Money versus capital markets.

Primary Markets versus Secondary Markets

Primary Markets Primary markets provide a forum in which demanders of funds (e.g., corporations such as IBM or

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government entities such as the U.S. Treasury) raise funds by issuing new financial instruments, such as stocks andbonds. Corporations or government entities continually have new projects or expanded production needs, but do nothave sufficient internally generated funds (such as retained earnings) to support their capital needs. Thus,corporations and governments issue securities in external primary markets to raise additional funds. These entitiessell the new financial instrument issues to initial fund suppliers (e.g., households) in exchange for the funds (money)that the issuer requires.

primary markets Markets in which corporations raise funds through new issues of securities.

In the United States, financial institutions called investment banks arrange most primary market transactions forbusinesses. Some of the best-known examples of U.S. investment banks include Morgan Stanley, Goldman Sachs,or Merrill Lynch (owned by Bank of America, a commercial bank). These firms intermediate between issuing parties(fund demanders) and investors (fund suppliers). Investment banks provide fund demanders with a number ofservices, including advising the company or government agency about the securities issue (such as an appropriateoffer price and number of securities to issue) and attracting initial public purchasers of the customer’s securitiesofferings. Firms that need funds are seldom expert at raising capital themselves, so they avert risk and lower theircosts by turning to experts at investment banks to issue their primary market securities.

investment banks Banks that help companies and governments raise capital.

commercial bank Depository institutions whose major assets are loans and whose major liabilities are deposits.

The initial (or primary market) sale of securities occurs either through a public offering or as a private placement toa small group of investors. An investment bank serves as a security underwriter in a public offering. In a privateplacement, the security issuer engages the group of buyers (usually fewer than 10) to purchase the whole issue.Buyers are typically financial institutions. To protect smaller individual investors against a lack of disclosure,publicly traded securities must be registered with the Securities and Exchange Commission (SEC). Privateplacements, on the other hand, can be unregistered and resold to large, financially sophisticated investors only.Large investors supposedly possess the resources and expertise to analyze a security’s risk. Privately placed bondsand stocks traditionally have been among the most illiquid securities in the securities markets; only the very largestfinancial institutions or institutional investors are able or willing to buy and hold them in the absence of an activesecondary market. Issuers of privately placed securities tend to be less well known (e.g., medium-sizedmunicipalities and corporations). Because of this lack of information and its associated higher risk, returns paid toholders of privately placed securities tend to be higher than those on publicly placed securities issues.

personal APPLICATIONJohn Adams wants to invest in one of two corporate bonds issued by separate firms. One bond yields 8.00 percent with a 10-yearmaturity; the other offers a 10.00 percent yield and a 9-year maturity. The second bond seems to be the better deal if one only looksat the interest rate. Is it necessarily the bond in which John should invest? Once he decides which bond represents the betterinvestment, how can John go about buying the bond? (See the solution at the end of the book.)

Should John consider bonds from other countries?

Figure 6.1 illustrates a time line for the primary market exchange of funds for a new issue of corporate bonds orequity. We will further discuss how companies, the U.S. Treasury, and government agencies that market primarygovernment securities, such as Ginnie Mae and Freddie Mac, go about selling primary market securities in Chapter8. Throughout this text, we focus on government securities from the buyer’s, rather than the seller’s, point of view.You can find in-depth discussions of government securities from the seller’s point of view in a public finance text.

Primary market financial instruments include stock issues from firms initially going public (e.g., allowing theirequity shares to be publicly traded on stock markets for the first time). We usually refer to these first-time issues as

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initial public offerings (IPOs). For example, on June 16, 2015, Fitbit announced a $732 million IPO of its commonstock. Fitbit used several investment banks, including Morgan Stanley, Deutsche Bank, and Bank ofAmerica Merrill Lynch, to underwrite the company’s stock. Publicly traded firms may issue additionalbonds or stocks as primary market securities. For example, on February 25, 2015, American Tower Groupannounced that it would sell an additional 23.5 million shares of common stock (at $97.00 per share) underwrittenby investment banks such as Goldman Sachs, Bank of America Merrill Lynch, Barclays, Citigroup and J.P. Morgan.The funds were used to finance the acquisition of Verizon. If the acquisition of Verizon was not completed,American Tower expected to use the net proceeds from the offering for general corporate purposes.

initial public offerings (IPOs)  A first-time issue of stock by a private firm going public (e.g., allowing its equity, some of which was heldprivately by managers and venture capital investors, to be publicly traded in stock markets for the first time).

FIGURE 6.1 Primary Market Transfer of Funds

Secondary Markets Once firms issue financial instruments in primary markets, these same stocks and bonds arethen traded—that is, bought and resold—in secondary markets. The New York Stock Exchange (NYSE) and theNASDAQ are two well-known examples of secondary markets for trading stocks (see Chapters 7 and 8). In additionto stocks and bonds, secondary markets also exist for financial instruments backed by mortgages and other assets,foreign exchange, and futures and options (i.e., derivative securities, discussed later in the chapter).

secondary markets Markets that trade financial instruments once they are issued.

Buyers find sellers of secondary market securities in economic agents that need funds (fund demanders). Secondarymarkets provide a centralized marketplace where economic agents know that they can buy or sell most securitiesquickly and efficiently. Secondary markets, therefore, save economic agents the search costs of finding buyers orsellers on their own. Figure 6.2 illustrates a secondary market transfer of funds. Secondary market buyers often usesecurities brokers such as Charles Schwab or other brokerage firms to act as intermediaries as they exchange fundsfor securities (see Chapter 8). An important note: The firm that originally issued the stock or bond is not involved insecondary market transactions in any way—no money accrues to the company itself when its stock trades in asecondary market.

Secondary markets offer benefits to both investors (fund suppliers) and issuers (fund demanders). Investors gainliquidity and diversification benefits (see Chapter 10). Although corporate security issuers are not directly involvedin secondary market transactions, issuers do gain information about their securities’ current market value. Publiclytraded firms can thus observe how investors perceive their corporate value and their corporate decisions by trackingtheir firms’ securities’ secondary market prices. Such price information allows issuers to evaluate how well they areusing internal funds as well as the funds generated from previously issued stocks and bonds and provides indicationsabout how well any subsequent bond or stock offerings might be received—and at what price.

FIGURE 6.2 Secondary Market Transfer of Funds

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Secondary market trading volume can be quite large. Trading volume is defined as the number of shares of a securitythat are simultaneously bought and sold during a given period. Each seller and each buyer actually contract with theexchange’s clearinghouse, which then matches sell and buy orders for each transaction. The clearinghouse is acompany whose stock trades on the exchange, and the clearinghouse runs on a for-profit basis.

trading volume The number of shares of a security that are simultaneously bought and sold during a period.

FIGURE 6.3 Money versus Capital Market Maturities

The exchange and the clearinghouse can process many transactions in a single day. For example, on October 28,1997, NYSE trading volume exceeded 1 billion shares for the first time ever. On October 10, 2008 (at theheight of the financial crisis), NYSE trading volume topped 7.3 billion shares, the highest level to date. Incontrast, during the mid-1980s, a NYSE trading day during which 250 million shares traded was considered a high-volume day.

Money Markets versus Capital MarketsWe noted that financial markets are differentiated in part by the maturity dates of the instruments traded. Thisdistinction becomes important when we differentiate money markets from capital markets. Both of these marketsdeal in debt securities (capital markets also deal in equity securities); the question becomes one of when thesecurities come due.

Money Markets Money markets feature debt securities or instruments with maturities of one year or less (see Figure6.3). In money markets, agents with excess short-term funds can lend (or supply) to economic agents who need (ordemand) short-term funds. The suppliers of funds buy money market instruments and the demanders of funds sellmoney market instruments. Because money market instruments trade for only short periods of time, fluctuations insecondary-market prices are usually quite small. With less volatility, money market securities are thus less riskythan longer-term instruments. In the United States, many money market securities do not trade in a specific location;rather, transactions occur via telephones, wire transfers, and computer trading. Thus, most U.S. money markets aresaid to be over-the-counter (OTC) markets.

money markets Markets that trade debt securities or instruments with maturities of less than one year.

over-the-counter market Markets that do not operate in a specific fixed location—rather, transactions occur via telephones, wiretransfers, and computer trading.

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Money Market Instruments LG6-2 Corporations and government entities issue a variety of money marketsecurities to obtain short-term funds. These securities include

Treasury bills.

Federal funds and repurchase agreements.Commercial paper.

Negotiable certificates of deposit.Banker’s acceptances.

Table 6.1 lists and defines each money market security. Figure 6.4 graphically depicts the proportion of U.S. moneymarket instruments outstanding across three decades. Notice that, in 2016, federal funds and repurchase agreementscommanded the highest dollar value of all money market instruments, followed by negotiable CDs, Treasury bills,and commercial paper.

Capital Markets Capital markets are markets in which parties trade equity (stocks) and debt (bonds) instrumentsthat mature in more than one year (see Figure 6.3). Given their longer maturities, capital market instruments aresubject to wider price fluctuations than are money market instruments (see the term structure discussion below andin Chapter 7).

capital markets Markets that trade debt (bonds) and equity (stock) instruments with maturities of more than one year.

▼ TABLE 6.1 Money Market Instruments

Treasury bills: Short-term U.S. government obligations.

Federal funds: Short-term funds transferred between financial institutions, usually for no more than one day.

Repurchase agreements (repos): Agreements involving security sales by one party to another, with the promise to reverse thetransaction at a specified date and price, usually at a discounted price.

Commercial paper: Short-term unsecured promissory notes that companies issue to raise short-term cash (sometimes calledPaper).

Negotiable certificates of deposit: Bank-issued time deposits that specify an interest rate and maturity date and are negotiable—that is, traded on an exchange. Their face value is usually at least $100,000.

Banker acceptances (BAs): Bank-guaranteed time drafts payable to a vendor of goods.

FIGURE 6.4 Money Market Instruments Outstanding

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Here we see how the percentage of each money market instrument traded changes across three decades.Source: Federal Reserve Board, “Financial Accounts of the United States,” Statistical Releases, Washington, DC, various issues.www.federalreserve.gov

Capital Market Instruments Capital market securities includeU.S. Treasury notes and bonds.

U.S. government agency bonds.State and local government bonds.

Mortgages and mortgage-backed securities.Corporate bonds.

Corporate stocks.

Table 6.2 lists and defines each capital market security. Figure 6.5 graphically depicts U.S. capital marketinstruments outstanding over several decades. Note that corporate stocks (equities) represent the largest capitalmarket instrument, followed by mortgages and mortgage-backed securities and then corporate bonds. The relativesize of capital markets depends on two factors: the number of securities issued and their market prices. The 1990ssaw consistently rising bull markets; hence the sharp increase in equities’ dollar value outstanding. Stock values fellin the early 2000s as the U.S. economy experienced a downturn—partly because of 9/11 and partly because interestrates began to rise—and stock prices fell. Stock prices in most sectors subsequently recovered and, by 2007, evensurpassed their 1999 levels. Stock prices fell precipitously during the financial crisis of 2008 and 2009. As of mid-March 2009, the Dow Jones Industrial Average (DJIA) had fallen in value 53.8 percent in less than 1½ year’s time.This was greater than the decline during the market crash of 1937 and 1938, when it fell 49 percent. However, stockprices recovered along with the economy in the last half of 2009 and first half of 2010, rising 71.1 percent betweenMarch 2009 and April 2010. However, it took until March 5, 2013, for the DJIA to surpass its pre-crisis high of14,164.53, closing at 14,253.77 for the day.

▼ TABLE 6.2 Capital Market Instruments

Treasury notes and bonds: U.S. Treasury long-term obligations issued to finance the national debt and pay for other federalgovernment expenditures.

U.S. government agency bonds: Long-term debt securities collateralized by a pool of assets and insured by agencies of theU.S. government.

State and local government bonds: Debt securities issued by state and local (e.g., county, city, school) governments, usuallyto cover capital (long-term) improvements.

Mortgages: Long-term loans issued to individuals or businesses to purchase homes, pieces of land, or other real property.

Mortgage-backed securities: Long-term debt securities that offer expected principal and interest payments as collateral. Thesesecurities, made up of many mortgages, are gathered into a pool and are thus “backed” by promised principal and interest cashflows.

Corporate bonds: Long-term debt securities issued by corporations.

Corporate stocks: Long-term equity securities issued by public corporations; stock shares represent fundamental corporateownership claims.

FIGURE 6.5 Capital Market Instruments Outstanding

Source: Federal Reserve Board, “Financial Accounts of the United States,” Statistical Releases, Washington, DC, various issues.www.federalreserve.gov

Other Markets

Foreign Exchange Markets Today, most U.S.-based companies operate globally. Competent financialmanagers understand how events and movements in financial markets in other countries can potentially affect theirown companies’ profitability and performance. For example, in 2015, IBM experienced a drop in revenue of 9percent due to foreign exchange trends. Coca-Cola, which gets the majority of its sales from outside the UnitedStates, also saw revenues decrease by approximately 6 percent as the U.S. dollar strengthened relative to foreigncurrencies.

©Jack Star/PhotoLink/Getty Images

Foreign exchange markets trade currencies for immediate (also called “spot”) or some future stated delivery. When aU.S. corporation sells securities or goods overseas, the resulting cash flows denominated in a foreign currency

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expose the firm to foreign exchange risk. This risk arises from the unknown value at which foreign currency cashflows can be converted into U.S. dollars. Foreign currency exchange rates vary day to day with worldwide demandand supply of foreign currency and U.S. dollars. Investors who deal in foreign-denominated securities face the samerisk.

foreign exchange risk Risk arising from the unknown value at which foreign currency cash flows can be converted into U.S. dollars.

foreign exchange markets Markets in which foreign currency is traded for immediate or future delivery.

The actual number of U.S. dollars that a firm receives on a foreign investment depends on the exchange ratebetween the U.S. dollar and the foreign currency just as much as it does on the investment’s performance. Firms willhave to convert the foreign currency into U.S. dollars at the prevailing exchange rate. If the foreign currencydepreciates (falls in value) relative to the U.S. dollar (say from 0.1679 dollar per unit of foreign currency to0.1550 dollar per unit of foreign currency) over the investment period (i.e., the period between when aforeign investment is made and the time it comes to fruition), the dollar value of cash flows received will fall. If theforeign currency appreciates, or rises in value, relative to the U.S. dollar, the dollar value of cash flows receivedfrom the foreign investment will increase.

Foreign currency exchange rates are variable. They vary day to day with demand for and supply of foreign currencyand with demand for and supply of dollars worldwide. Central governments sometimes intervene in foreignexchange markets directly—such as China’s valuing of the yuan at artificially high rates relative to the dollar.Governments also affect foreign exchange rates indirectly by altering prevailing interest rates within their owncountries. You will learn more about foreign exchange markets in Chapter 19.

Derivative Securities Markets A derivative security is a financial security (such as a futures contract, optioncontract, or mortgage-backed security) with a value that is linked to another, underlying security, such as a stocktraded in capital markets or British pounds traded in foreign exchange (forex) markets. Derivative securitiesgenerally involve an agreement between two parties to exchange a standard quantity of an asset or cash flow at apredetermined price and at a specified date in the future. As the value of the underlying security changes, the valueof the derivative security changes.

derivative security A security formalizing an agreement between two parties to exchange a standard quantity of an asset at apredetermined price on a specified date in the future.

While derivative security contracts, especially for physical commodities like corn or gold, have existed for centuries,derivative securities markets grew increasingly popular in the 1970s, 1980s, and 1990s as traders, firms, andacademics figured out how to spread risk for more and more underlying commodities and securities by usingderivative contracts. Derivative contracts generally feature a high degree of leverage; that is, the investor only has toput up a very small portion of the underlying commodity or security’s value to affect or control the underlyingcommodity or security.

Derivative securities traders can be either users of derivative contracts (for hedging and other purposes) or dealers(such as banks) that act as counterparties in customer trades for fees. An example of hedging involves commoditiessuch as corn, wheat, or soybeans. For example, suppose you run a flour mill and will need to buy either soft wheat(Chicago) or hard red winter wheat (Kansas City) in the future. If you are concerned that the price of wheat will rise,you might lock in a price today to meet your needs six months from now by buying wheat futures on a commoditiesexchange. If you are correct and wheat prices rise over the six months, you may purchase the wheat by closing outyour futures positions, buying the wheat at the futures price rather than the higher market price. Likewise, if youknow that you will be delivering a large shipment to, say, Europe, in three months, you might take an offsettingposition in euro futures contracts to lock in the exchange rate between the dollar and the euro as it stands today—and (you hope) eliminate foreign exchange risk from the transaction.

Derivative securities markets are the newest—and potentially the riskiest—of the financial security markets. Lossesassociated with off-balance-sheet mortgage-backed securities created and held by FIs were at the very heart of thefinancial crisis. Signs of significant problems in the U.S. economy first appeared in late 2006 and early 2007 whenhome prices plummeted and defaults began to affect the mortgage lending industry as a whole, as well as other partsof the economy noticeably. Mortgage delinquencies, particularly on subprime mortgages, surged in the last quarterof 2006 through 2008 as homeowners who had stretched themselves to buy or refinance a home in the early 2000sfell behind on their loan payments. As mortgage borrowers defaulted, the financial institutions that held their

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mortgages and credit derivative securities (in the form of mortgage-backed securities) started announcing hugelosses on them. These losses reached $700 billion worldwide by early 2009. The situation resulted in the failure,acquisition, or bailout of some of the largest FIs and a near meltdown of the world’s financial and economicsystems. More recently, as the nearby Finance at Work box highlights, JPMorgan Chase experienced huge lossesfrom positions in the derivative securities markets.

time out!6-1 How do primary and secondary markets differ?6-2 What are foreign exchange markets?6-3 What are derivativeas securities?

6.2 • FINANCIAL INSTITUTIONS LG6-3Financial institutions (e.g., banks, thrifts, insurance companies, mutual funds) perform vital functions to securitiesmarkets of all sorts. They channel funds from those with surplus funds (suppliers of funds) to those with shortagesof funds (demanders of funds). In other words, FIs operate financial markets. FIs allow financial markets to functionby providing the least costly and most efficient way to channel funds to and from these markets. FIs play a secondcrucial role by spreading risk among market participants. This risk-spreading function is vital to entrepreneurialefforts, for few firms or individuals could afford the risk of launching an expensive new product or process bythemselves. Individual investors take on pieces of the risk by buying shares in risky enterprises. Investors thenmitigate their own risks by diversifying their holdings into appropriate portfolios, which we cover in Chapters 9 and10. Table 6.3 lists and summarizes the various types of FIs.

financial institutions Institutions that perform the essential function of channeling funds from those with surplus funds to those withshortages of funds.

To understand just how important FIs are to the efficient operation of financial markets, imagine a simple world inwhich FIs did not exist. In such a world, suppliers of funds (e.g., households), generating excess savings byconsuming less than they earn, would have a basic choice. They could either hold cash as an asset or invest that cashin the securities issued by users of funds (e.g., corporations, governments, or retail borrowers). In general,demanders (users) of funds issue financial claims (e.g., equity and debt securities) to finance the gap between theirinvestment expenditures and their internally generated savings, such as retained earnings. As shown in Figure 6.6, ina world without financial institutions, we would have direct transfers of funds from fund suppliers to fund users. Inreturn, financial claims would flow directly from fund users to fund suppliers.

direct transfer The process used when a corporation sells its stock or debt directly to investors without going through a financialinstitution.

FIGURE 6.6 Flow of Funds in a World without FIs

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▼ TABLE 6.3 Types of Financial Institutions

Commercial banks: Depository institutions whose major assets are loans and whose major liabilities are deposits. Commercialbank loans cover a broader range, including consumer, commercial, and real estate loans, than do loans from other depositoryinstitutions. Because they are larger and more likely to have access to public securities markets, commercial bank liabilitiesgenerally include more nondeposit sources of funds than do those of other depository institutions.

Thrifts: Depository institutions including savings associations, savings banks, and credit unions. Thrifts generally performservices similar to commercial banks, but they tend to concentrate their loans in one segment, such as real estate loans orconsumer loans. Credit unions operate on a not-for-profit basis for particular groups of individuals, such as a labor union or aparticular company’s employees.

Insurance companies: Protect individuals and corporations (policyholders) from financially adverse events. Life insurancecompanies provide protection in the event of untimely death or illness, and help in planning retirement. Property casualtyinsurance protects against personal injury and liability due to accidents, theft, fire, and so on.

Securities firms and investment banks: Underwrite securities and engage in related activities such as securities brokerage,securities trading, and making markets in which securities trade.

Finance companies: Make loans to both individuals and businesses. Unlike depository institutions, finance companies do notaccept deposits, but instead rely on short- and long-term debt for funding, and many of their loans are collateralized with somekind of durable good, such as washer/dryers, furniture, carpets, and the like.

Mutual funds: Pool many individuals’ and companies’ financial resources and invest those resources in diversified assetportfolios.

Pension funds: Offer savings plans through which fund participants accumulate savings during their working years. Participantsthen withdraw their pension resources (which have presumably earned additional returns in the interim) during their retirementyears. Funds originally invested in and accumulated in a pension fund are exempt from current taxation. Participants pay taxeson distributions taken after age 55, when their tax brackets are (presumably) lower.

In this economy without FIs, the amount of funds flowing between fund suppliers and fund users through financialmarkets would likely be quite low for several reasons:

Once they have lent money in exchange for financial claims, fund suppliers would need to continually monitor the use of their funds. Fundsuppliers must ensure that fund users neither steal the funds outright nor waste the funds on projects that have low or negative returns,since either theft or waste would lower fund suppliers’ chances of being repaid and/or earning a positive return on theirinvestments (such as through the receipt of dividends or interest). Monitoring against theft, misuse, or underuse of their fundswould cost any given fund supplier a lot of time and effort, and of course each fund supplier, regardless of the dollar value of theinvestment, would have to carry out the same costly and time-consuming process. Further, many investors do not have the financialtraining to understand the necessary business information to assess whether a securities issuer is making the best use of their funds. Infact, so many investment opportunities are available to fund suppliers, that even those trained in financial analysis rarely have the time tomonitor how their funds are used in all of their investments. The resulting lack of monitoring increases the risk of directly investing infinancial claims. Given these challenges, fund suppliers would likely prefer to delegate the task of monitoring fund borrowers to ensuregood performance to others.

Many financial claims feature a long-term commitment (e.g., mortgages, corporate stock, and bonds) for fund suppliers, but suppliers maynot wish to hold these instruments directly. Specifically, given the choice between holding cash or long-term securities, fund suppliers maychoose to hold cash for its liquidity. This is especially true if the suppliers plan to use their savings to finance consumption expendituresbefore their creditors expect to repay them. Fund suppliers may also fear that they will not find anyone to purchase their financial claim andfree up their funds. When financial markets are not very developed, or deep, in terms of the number of active buyers and sellers in themarket, such liquidity concerns arise.

liquidity The ease with which an asset can be converted into cash.

Even though real-world financial markets provide some liquidity services by allowing fund suppliers to trade financial securities amongthemselves, fund suppliers face price risk when they buy securities—fund suppliers may not get their principal back, let alone any returnon their investment. The price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE)or NASDAQ may well differ from the price they initially paid for the security. The investment community as a whole may change thesecurity’s valuation between the time the fund supplier bought it and the time the fund supplier sold it. Also, dealers, acting asintermediaries between buyers and sellers, charge transaction costs for completing a trade. So even if an investor bought a security andthen sold it the next day, the investor would likely lose money from transaction and other costs.

price risk The risk that an asset’s sale price will be lower than its purchase price.

Unique Economic Functions Performed by Financial InstitutionsBecause of (1) monitoring costs, (2) liquidity costs, and (3) price risk, most average investors may well view directinvestment in financial claims and markets as an unattractive proposition and, as fund suppliers, they will likelyprefer to hold cash. As a result, financial market activity (and therefore savings and investment) would likely remainquite low. However, the financial system has developed an alternative, indirect way for investors (or fund suppliers)to channel funds to users of funds: Financial intermediaries indirectly transfer funds to ultimate fund users. Because of

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monitoring, liquidity risk, and price risk costs, fund suppliers often prefer to hold financial intermediaries’ financialclaims rather than those directly issued by the ultimate fund users. Consider Figure 6.7, which more closelyrepresents the way that funds flow in the U.S. financial system than does Figure 6.6. Notice how financialinstitutions stand—or intermediate—between fund suppliers and fund users. That is, FIs channel funds fromultimate suppliers to ultimate fund users. Fund suppliers and users use these FIs to channel funds because offinancial intermediaries’ unique ability to measure and manage risk, and thus reduce monitoring costs, liquiditycosts, and price risk.

indirect transfer A transfer of funds between suppliers and users of funds through a financial institution.

FIGURE 6.7 Flow of Funds in a World with FIs

Financial institutions stand between fund suppliers and users.

finance at work //: marketsJP Morgan’s $2 Billion Blunder

©Monica and Michael Sweet/Getty Images

JP Morgan Chase & Co. is reeling after a huge trading bet backfired and left the bank with at least $2 billion in losses from the bad trade.This may be the end of chief executive James Dimon’s run as the so-called “King of Wall Street.” The bank’s Chief Investment Office(CIO), responsible for managing the New York company’s risk, placed a series of risky bets and trades. In an article published lastmonth, The Wall Street Journal reported that “large positions taken in that office by a trader nicknamed ‘the London whale’ had roiled asector of the debt markets. The bank, betting on a continued economic recovery with a complex web of trades tied to the values ofcorporate bonds, was hit hard when prices moved against it starting last month, causing losses in many of its derivatives positions. Thelosses occurred while J.P. Morgan tried to scale back that trade.”

In April of 2012, The Wall Street Journal reported that investors and hedge funds were trying to take advantage of trades made byChase’s London whale, Bruno Iksil, who worked out of the CIO, by making bets in the market on credit default swaps (CDSs). The CIOgroup previously had stopgaps in place to protect and prevent the company from significant losses during periods of downturn in theeconomy. However, the Journal reports that earlier in 2012, “it began reducing that position, [taking] a bullish stance on the financialhealth of certain companies and selling protection that would compensate buyers if those companies defaulted on debts. Mr. Iksil was aheavy seller of CDS contracts tied to a basket, or index, of companies.” In April of 2012, these protection costs began to go up, which

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further contributed to the bank’s losses.According to JP Morgan Chase company filings, Mr. Iksil’s group had approximately $350 billion in investment securities, about 15%

of the bank’s total assets, on December 31, 2011. Mr. Dimon said the bank has an extensive review under way of what went wrong.“These were grievous mistakes, they were self-inflicted, we were accountable and we happened to violate our own standards andprinciples by how we want to operate the company. This is not how we want to run a business.”

Mr. Dimon held a conference call with investors and analysts on May 10, stating, “In hindsight, the . . . strategy was flawed, complex,poorly reviewed, poorly executed, and poorly monitored. The portfolio has proven to be riskier, more volatile and less effective . . . thanwe thought.” Dimon resolves, “We will learn from it, we will fix it, we will move on, hopefully in the end, it will make us a better company.”Though JP Morgan Chase came through the financial crisis better off than many other financial institutions, this trading loss certainlytarnishes their reputation. Mr. Dimon reports that the loss is “slightly more than $2 billion” in the second quarter of this year.

Want to know more?Key Words to Search for Updates: JPMorgan, London whale, derivative trading losses

Sources: Fitzpatrick, Dan, Gregory Zuckerman, and Liz Rappaport, “J.P. Morgan’s $2 Billion Blunder,” The Wall Street Journal Online,May 11, 2012. JP Morgan Chase & Co. Business Update Call, May 10, 2012.

Monitoring Costs As we noted above, a fund supplier who directly invests in a fund user’s financial claims facesa high cost of comprehensively monitoring the fund user’s actions in a timely way. One solution to this problem isthat a large number of small investors can group their funds together by holding claims issued by an FI. In turn, theFI will invest in direct financial claims that fund users issue. Financial institutions’ aggregation of funds from fundsuppliers resolves a number of problems:

First, large FIs now have much greater incentive to collect information and monitor the ultimate fund user’s actions, because the FI has farmore at stake than any small individual fund supplier would have.Second, the FI performs the necessary monitoring function via its own internal experts. In an economic sense, fund suppliers appoint theFI as a delegated monitor to act on their behalf. For example, full-service securities firms such as Bank of America Merrill Lynch carry outinvestment research on new issues and make investment recommendations for their retail clients (investors), whilecommercial banks collect deposits from fund suppliers and lend these funds to ultimate users, such as corporations. Animportant part of these FIs’ functions is their ability and incentive to monitor ultimate fund users.

delegated monitor An economic agent appointed to act on behalf of smaller investors in collecting information and/or investing funds ontheir behalf.

Liquidity and Price Risk In addition to providing more and better information about fund users’ activities,financial intermediaries provide additional liquidity to fund suppliers, acting as asset transformers as follows: FIspurchase the financial claims that fund users issue—primary securities such as mortgages, bonds, and stocks—andfinance these purchases by selling financial claims to household investors and other fund suppliers as deposits,insurance policies, or other secondary securities. The secondary securities—packages or pools of primary claims—that FIs collect and then issue are often more liquid than are the primary securities themselves. For example, banksand thrift institutions (e.g., savings associations) offer draft deposit accounts with fixed principal values and (often)guaranteed interest rates. Fund suppliers can generally access the funds in those accounts on demand. Money marketmutual funds issue shares to household savers that allow the savers to maintain almost fixed principal amounts whileearning somewhat higher interest rates than on bank deposits. Further, savers can also withdraw these funds ondemand whenever the saver writes a check on the account. Even life insurance companies allow policyholders toborrow against their company-held policy balances with very short notice.

asset transformer Service provided by financial institutions in which financial claims issued by an FI are more attractive to investorsthan are the claims directly issued by corporations.

secondary securities Packages or pools of primary claims.

The Shift Away from Risk Measurement and Management and the Financial Crisis Certainly, a majorevent that changed and reshaped the financial services industry was the financial crisis of the late 2000s. As FIsadjusted to regulatory changes brought about in the 1980s and 1990s, one result was a dramatic increase in systemicrisk of the financial system, caused in large part by a shift in the banking model from that of “originate and hold” to“originate to distribute.” In the traditional model, banks take short-term deposits and other sources of funds and usethem to fund longer term loans to businesses and consumers. Banks typically hold these loans to maturity, and thushave an incentive to screen and monitor borrower activities even after a loan is made. However, the traditionalbanking model exposes the institution to potential liquidity, interest rate, and credit risk. In attempts to avoid these

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risk exposures and generate improved return-risk trade-offs, banks have shifted to an underwriting model in whichthey originate or warehouse loans, and then quickly sell them. Figure 6.8 shows the growth in bank loan secondarymarket trading from 1991 through 2015. Note the huge growth in bank loan trading even during the financial crisisof 2008 and 2009. When loans trade, the secondary market produces information that can substitute for theinformation and monitoring of banks. Further, banks may have lower incentives to collect information and monitorborrowers if they sell loans rather than keep them as part of the bank’s portfolio of assets. Indeed, most large banksare organized as financial service holding companies to facilitate these new activities.

More recently activities of shadow banks, nonfinancial service firms that perform banking services, have facilitatedthe change from the “originate and hold” model of commercial banking to the “originate and distribute” bankingmodel. Participants in the shadow banking system include structured investment vehicles (SIVs), special purposevehicles (SPVs), asset-backed commercial paper (ABCP) conduits, limited-purpose finance companies, moneymarket mutual funds (MMMFs), and credit hedge funds. In the shadow banking system, savers place their fundswith money market mutual and similar funds, which invest these funds in the liabilities of other shadow banks.Borrowers get loans and leases from shadow banks such as finance companies rather than from banks. Like thetraditional banking system, the shadow banking system intermediates the flow of funds between net savers and netborrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, orshadow bank, that intermediates. Further, unlike the traditional banking system, where the complete creditintermediation is performed by a single bank, in the shadow banking system it is performed through a series of stepsinvolving many nonbank, unregulated financial service firms.

FIGURE 6.8 Bank Loan Secondary Market Trading

Bank loan sales have increased dramatically over the last 20 years.

These innovations remove risk from the balance sheet of financial institutions and shift risk off the balance sheet andto other parts of the financial system. Since the FIs, acting as underwriters, are not exposed to the credit, liquidity,and interest rate risks of traditional banking, they have little incentive to screen and monitor activities of borrowersto whom they originate loans. Thus, FIs’ role as specialists in risk measurement and management is reduced.

The economy relies on financial institutions to act as specialists in risk measurement and management. The

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importance of this was demonstrated during the global financial crisis. When FIs failed to perform their critical riskmeasurement and management functions, a crisis of confidence that disrupted financial markets ensued. The resultwas a worldwide breakdown in credit markets, as well as an enhanced level of equity market volatility.

time out!6-4 List the major types of financial institutions.6-5 What three main issues would deter fund suppliers from directly purchasing securities?6-6 What events resulted in banks’ shift from the traditional banking model of “originate and hold” to a model of “originate and

distribute”?

6.3 • INTEREST RATES AND THE LOANABLE FUNDSTHEORY LG6-3We often speak of “the interest rate” as if only one rate applies to all financial situations or transactions. In fact, wecan list tens or hundreds of interest rates that are appropriate in various conditions or situations within the U.S.economy on any particular day. Let’s explore a bit how the financial sector sets these rates and how the rates relateto one another. We actually observe nominal interest rates in financial markets—these are the rates most often quotedby financial news services. As we will see in Chapters 7 and 8, nominal interest rates (or, simply, interest rates)directly affect most tradable securities’ value or price. Since any change in nominal interest rates has such profoundeffects on security prices, financial managers and individual investors spend a lot of time and effort trying to identifyfactors that may influence future interest rate levels.

nominal interest rates The interest rates actually observed in financial markets.

Of course, interest rate changes influence investment performance and trigger buy or sell decisions for individualinvestors, businesses, and governmental units alike. For example, in 2008 and 2009, the Federal Reserve,in an effort to address the severe financial crisis, unexpectedly announced that it would drop its target fedfunds rate to a range between 0 and 0.25 percent and lowered its discount window rate to 0.5 percent, the lowestlevel since the 1940s. These rates remained at historically low levels until December 2015 when the Federal Reserveraised the fed funds rate to a range of 0.25 to 0.5 percent and the discount window rate to 1 percent. This was thefirst interest rate increase since 2006.

Figure 6.9 illustrates the movement of the following key U.S. interest rates over the past 44 years:The prime commercial loan rate.The three-month T-bill rate.

The home mortgage rate.The high-grade corporate bond rate.

Figure 6.9 shows how interest rates vary over time. For example, the prime rate hit highs of over 20 percent in theearly 1980s, yet fell as low as 4.75 percent in the early 1970s. The prime rate stayed below 10 percent throughoutmuch of the 1990s, fell back further to 4.00 percent in the early 2000s, then rose to as high as 8.25 percent in themid-2000s. During the financial crisis of 2008 and 2009, the Fed took aggressive actions to stimulate theeconomy, including dropping interest rates to historic lows. As a result, the prime rate fell to 3.25 percentand stayed there until December 2015.

FIGURE 6.9 Key U.S. Interest Rates, 1972–2016

Loan rates tend to move together over time.

Source: Federal Reserve Board, website, various dates. www.federalreserve.gov

Interest rates play a major part in the determination of the value of financial instruments. For example, in September2015 the Federal Reserve unexpectedly announced that it would not raise interest rates. The financial marketsreacted significantly: The Dow Jones Industrial Average declined almost 300 points, 1.75 percent in value; theinterest rate on Treasury securities decreased (i.e., the yield on 10-year T-notes decreased 0.123 percent); gold pricesincreased 1.6 percent; and the U.S. dollar strengthened against foreign currencies. Given the impact a change ininterest rates has on security values, financial institution and other firm managers spend much time and effort tryingto identify factors that determine the level of interest rates at any moment in time, as well as what causes interest ratemovements over time.

One model that is commonly used to explain interest rates and interest rate movements is the loanable funds theory.The loanable funds theory views the level of interest rates as resulting from factors that affect the supply of anddemand for loanable funds. It categorizes financial market participants—consumers, businesses, governments, andforeign participants—as net suppliers or demanders of funds.

loanable funds theory A theory of interest rate determination that views equilibrium interest rates in financial markets as a result of thesupply of and demand for loanable funds.

Supply of Loanable Funds LG6-4The supply of loanable funds is a term commonly used to describe funds provided to the financial markets by netsuppliers of funds. In general, the quantity of loanable funds supplied increases as interest rates rise. Figure 6.10illustrates the supply curve for loanable funds. Other factors held constant, more funds are supplied as interest ratesincrease (the reward for supplying funds is higher). Table 6.4 presents data on the supply of loanable funds from thevarious groups of market participants from U.S. flow of funds data as of 2015.

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The household sector (consumer sector) is the largest supplier of loanable funds in the United States—$70.27 trillionin 2015. Households supply funds when they have excess income or want to reallocate their asset portfolio holdings.For example, during times of high economic growth, households may replace part of their cash holdings withearning assets (i.e., by supplying loanable funds in exchange for holding securities). As the total health of aconsumer increases, the total supply of loanable funds from that consumer will also generally increase.Households determine their supply of loanable funds not only on the basis of the general level of interestrates and their total wealth, but also on the risk of securities investments. The greater the perceived risk of securitiesinvestments, the less households are willing to invest at each interest rate. Further, the supply of loanable funds fromhouseholds also depends on their immediate spending needs. For example, near-term educational or medicalexpenditures will reduce the supply of funds from a given household.

FIGURE 6.10 Supply of and Demand for Loanable Funds

The demand and supply of loanable funds varies with interest rates.

▼ TABLE 6.4 Funds Supplied and Demanded by Various Groups (in trillions of dollars)

Funds SuppliedFunds

DemandedNet Funds Supplied (Funds

Supplied − Funds Demanded)

Households $70.27 $23.95 $46.32   

Business—nonfinancial 22.30 58.15 −35.85   

Business—financial 53.69 81.68 −27.99   

Government units 26.61 18.43 8.18   

Foreign participants 23.26 13.92 9.34   

Source: Federal Reserve Board, “Flow of Fund Accounts,” December 2015, www.federalreserve.gov

Higher interest rates will also result in higher supplies of funds from the U.S. business sector ($22.3 trillion fromnonfinancial business and $53.69 trillion from financial business in 2015), which often has excess cash, or workingcapital, that it can invest for short periods of time in financial assets. In addition to the interest rates on theseinvestments, the expected risk on financial securities and their businesses’ future investment needs will affect theiroverall supply of funds.

Loanable funds are also supplied by some governments ($26.61 trillion in 2015). For example, some governments(e.g., municipalities) temporarily generate more cash inflows (e.g., through local taxes) than they have budgeted tospend. These funds can be loaned out to financial market fund users until needed. During the recent financial crisis,the federal government significantly increased the funds it supplied to businesses and consumers as it attempted torescue the U.S. economy from a deep economic recession (see Appendix 6A online in Connect or atmhhe.com/Cornett4e).

Finally, foreign investors increasingly view U.S. financial markets as alternatives to their domestic financial markets($23.26 trillion of funds were supplied to the U.S. financial markets in 2015). When interest rates are higher on U.S.financial securities than they are on comparable securities in their home countries, foreign investors increase their

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supply of funds to U.S. markets. Indeed the high savings rates of foreign households (such as Japanese households)has resulted in foreign market participants being major suppliers of funds to U.S. financial markets in recent years.Similar to domestic suppliers of loanable funds, foreigners assess not only the interest rate offered on financialsecurities, but also their total wealth, the risk on the security, and their future expenditure needs. Additionally,foreign investors alter their investment decisions as financial conditions in their home countries change relative tothe U.S. economy and the exchange rate of their country’s currency changes vis-à-vis the U.S. dollar (see Chapter19). For example, during the recent financial crisis, investors worldwide, searching for a safe haven for their funds,invested huge amounts of funds in U.S. Treasury securities. The amount of money invested in Treasury bills was solarge that the yield on the three-month Treasury bill went below zero for the first time ever; investors wereessentially paying the U.S. government to borrow money.

Demand for Loanable FundsThe demand for loanable funds is a term used to describe the total net demand for funds by fund users. In general,the quantity of loanable funds demanded is higher as interest rates fall. Figure 6.10 also illustrates the demand curvefor loanable funds. Other factors held constant, more funds are demanded as interest rates decrease (the cost ofborrowing funds is lower).

Households (although they are net suppliers of funds) also borrow funds in financial markets ($23.95 trillion in2015). The demand for loanable funds by households reflects the demand for financing purchases of homes (withmortgage loans), durable goods (e.g., car loans, appliance loans), and nondurable goods (e.g., education loans,medical loans). Additional nonprice conditions and requirements (discussed below) also affect a household’sdemand for loanable funds at every level of interest rates.

Businesses demand funds to finance investments in long-term (fixed) assets (e.g., plant and equipment) and forshort-term working capital needs (e.g., inventory and accounts receivable) usually by issuing debt and otherfinancial instruments ($58.15 trillion for nonfinancial businesses and $81.68 trillion for financial businesses in2015). When interest rates are high (i.e., the cost of loanable funds is high), businesses prefer to financeinvestments with internally generated funds (e.g., retained earnings) rather than through borrowed funds.Further, the greater the number of profitable projects available to businesses, or the better the overall economicconditions, the greater the demand for loanable funds.

Governments also borrow heavily in the markets for loanable funds ($18.43 trillion in 2015). For example, state andlocal governments often issue debt instruments to finance temporary imbalances between operating revenues (e.g.,taxes) and budgeted expenditures (e.g., road improvements, school construction). Higher interest rates can causestate and local governments to postpone borrowings and thus capital expenditures. Similar to households andbusinesses, governments’ demand for funds varies with general economic conditions. The federal government isalso a large borrower partly to finance current budget deficits (expenditures greater than taxes) and partly to financepast deficits. The cumulative sum of past deficits is called the national debt, which in the United States in 2015stood at a record $18.94 trillion. Thus, the national debt and especially the interest payments on the national debthave to be financed in large part by additional government borrowing.

Finally, foreign participants (households, businesses, and governments) also borrow in U.S. financial markets($13.92 trillion in 2015). Foreign borrowers look for the cheapest source of dollar funds globally. Most foreignborrowing in U.S. financial markets comes from the business sector. In addition to interest costs, foreign borrowersconsider nonprice terms on loanable funds as well as economic conditions in their home country and the generalattractiveness of the U.S. dollar relative to their domestic currency (e.g., the euro or the yen).

Equilibrium Interest Rate LG6-5The aggregate supply of loanable funds is the sum of the quantity supplied by the separate fund-supplying sectors(e.g., households, businesses, governments, foreign agents) discussed above. Similarly, the aggregate demand forloanable funds is the sum of the quantity demanded by the separate fund-demanding sectors. As illustrated in Figure6.11, the aggregate quantity of funds supplied is positively related to interest rates, while the aggregate quantity offunds demanded is inversely related to interest rates. As long as competitive forces are allowed to operate freely in afinancial system, the interest rate that equates the aggregate quantity of loanable funds supplied with the aggregatequantity of loanable funds demanded for a financial security, Q*, is the equilibrium interest rate for that security, i*,point E in Figure 6.11. For example, whenever the rate of interest is set higher than the equilibrium rate, such as iH,the financial system has a surplus of loanable funds. As a result, some suppliers of funds will lower the interest rate

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at which they are willing to lend and the demanders of funds will absorb the loanable funds surplus. In contrast,when the rate of interest is lower than the equilibrium interest rate, such as iL, there is a shortage of loanable funds inthe financial system. Some borrowers will be unable to obtain the funds they need at current rates. As a result,interest rates will increase, causing more suppliers of loanable funds to enter the market and some demanders offunds to leave the market. These competitive forces will cause the quantity of funds supplied to increase and thequantity of funds demanded to decrease until a shortage of funds no longer exists.

Factors That Cause the Supply and Demand Curves for Loanable Funds to ShiftWhile we have alluded to the fundamental factors that cause the supply and demand curves for loanable funds toshift, in this section we formally summarize these factors. We then examine how shifts in the supply and demandcurves for loanable funds determine the equilibrium interest rate on a specific financial instrument. A shift in thesupply or demand curve occurs when the quantity of a financial security supplied or demanded changes at everygiven interest rate in response to a change in another factor besides the interest rate. In either case, achange in the supply or demand curve for loanable funds causes interest rates to move. Table 6.5 recapsthe factors that affect the supply and demand for loanable funds discussed in this section, their impact on the supplyand demand for loanable funds for a specific security, and the impact on the market clearing (or equilibrium) interestrates holding all other factors constant.

FIGURE 6.11 Determination of Equilibrium Interest Rates

Interest rates always move toward the equilibrium.

Supply of Funds We have already described the positive relation between interest rates and the supply ofloanable funds along the loanable funds supply curve. Factors that cause the supply curve of loanable funds to shift,at any given interest rate, include the wealth of fund suppliers, the risk of the financial security, future spendingneeds, monetary policy objectives, and economic conditions.

Wealth As the total wealth of financial market participants (households, businesses, etc.) increases, the absolutedollar value available for investment purposes increases. Accordingly, at every interest rate, the supply of loanablefunds increases, or the supply curve shifts down and to the right. For example, as the U.S. economy grew in theearly 2010s, total wealth of U.S. investors increased as well. Consequently, the supply of funds available forinvesting (e.g., in stock and bond markets) increased at every available interest rate. We show this shift (increase) inthe supply curve in Figure 6.12(a) as a move from SS to SS”. The shift in the supply curve creates a disequilibriumbetween demand and supply. To eliminate the imbalance or disequilibrium in this financial market, the equilibriuminterest rate falls, from i* to i*”, which is associated with an increase in the quantity of funds loaned between fundsuppliers and fund demanders, from Q* to Q*”. Conversely, as the total wealth of financial marketparticipants decreases, the absolute dollar value available for investment purposes decreases. Accordingly,

at every interest rate, the supply of loanable funds decreases, or the supply curve shifts up and to the left. Thedecrease in the supply of funds due to a decrease in the total wealth of market participants results in an increase inthe equilibrium interest rate and a decrease in the equilibrium quantity of funds loaned (traded).

▼ TABLE 6.5 Factors That Affect the Supply of and Demand for Loanable Funds for a Financial Security

Panel A: The Supply of Funds

Factor Impact on Supply of FundsImpact on Equilibrium InterestRate*

Interest rate Movement along supplycurve

Direct

Total wealth Shift supply curve InverseRisk of financial security Shift supply curve DirectNear-term spending needs Shift supply curve DirectMonetary expansion Shift supply curve InverseEconomic conditions Shift supply curve Inverse

Panel B: The Demand for Funds

Factor Impact on Supply of FundsImpact on Equilibrium InterestRate

Interest rate Movement along demandcurve

Direct

Utility derived from asset purchased withborrowed funds

Shift demand curve Direct

Restrictiveness of nonprice conditions Shift demand curve InverseEconomic conditions Shift demand curve Direct

A “direct” impact on equilibrium interest rates means that as the “factor” increases (decreases), the equilibrium interest rate increases(decreases). An “inverse” impact means that as the factor increases (decreases), the equilibrium interest rate decreases (increases).

Risk As the risk of a financial security decreases (e.g., the probability that the issuer of the security will default onpromised repayments of the funds borrowed), it becomes more attractive to suppliers of funds. At every interest rate,the supply of loanable funds increases, or the supply curve shifts down and to the right, from SS to SS” in Figure6.12(a). Holding all other factors constant, the increase in the supply of funds, due to a decrease in the risk of thefinancial security, results in a decrease in the equilibrium interest rate, from i* to i*”, and an increase in theequilibrium quantity of funds traded, from Q* to Q*”.

Conversely, as the risk of a financial security increases, it becomes less attractive to suppliers of funds. Accordingly,at every interest rate, the supply of loanable funds decreases, or the supply curve shifts up and to the left. Holding allother factors constant, the decrease in the supply of funds due to an increase in the financial security’s risk results inan increase in the equilibrium interest rate and a decrease in the equilibrium quantity of funds loaned (or traded).

FIGURE 6.12 The Effect on Interest Rates from a Shift in the Supply Curve of or a Demand Curve for Loanable Funds

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Changes in the supply of and demand for loanable funds have varying effects.

Near-Term Spending Needs When financial market participants have few near-term spending needs, the absolutedollar value of funds available to invest increases. For example, when a family’s son or daughter moves out of thefamily home to live on his or her own, current spending needs of the family decrease and the supply of availablefunds (for investing) increases. At every interest rate, the supply of loanable funds increases, or the supply curveshifts down and to the right. The financial market, holding all other factors constant, reacts to this increased supplyof funds by decreasing the equilibrium interest rate and increasing the equilibrium quantity of funds traded.

Conversely, when financial market participants have increased near-term spending needs, the absolutedollar value of funds available to invest decreases. At every interest rate, the supply of loanable fundsdecreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in thefinancial market that results in an increase in the equilibrium interest rate and a decrease in the equilibrium quantityof funds loaned (or traded).

Monetary Expansion One method used by the Federal Reserve to implement monetary policy is to alter theavailability of funds, the growth in the money supply, and thus the rate of economic expansion of the economy.

When monetary policy objectives are to allow the economy to expand (as was the case in the late 2000s, during thefinancial crisis, and in the early 2010s), the Federal Reserve increases the supply of funds available in the financialmarkets. At every interest rate, the supply of loanable funds increases, the supply curve shifts down and to the right,and the equilibrium interest rate falls, while the equilibrium quantity of funds traded increases.

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Conversely, when monetary policy objectives are to restrict the rate of economic expansion (and thus inflation), theFederal Reserve decreases the supply of funds available in the financial markets. At every interest rate, the supply ofloanable funds decreases, the supply curve shifts up and to the left, and the equilibrium interest rate rises, while theequilibrium quantity of funds loaned or traded decreases.

Economic Conditions Finally, as the underlying economic conditions themselves (e.g., the inflation rate,unemployment rate, economic growth) improve in a country relative to other countries, the flow of funds to thatcountry increases. This reflects the lower risk (country or sovereign risk) that the country, in the guise of itsgovernment, will default on its obligation to repay funds borrowed. For example, the severe economic crisis inGreece in the early 2010s resulted in a decrease in the supply of funds to that country. An increased inflow offoreign funds to U.S. financial markets increases the supply of loanable funds at every interest rate, and the supplycurve shifts down and to the right. Accordingly, the equilibrium interest rate falls, and the equilibrium quantity offunds loaned or traded increases.

Conversely, when economic conditions in foreign countries improve, domestic and foreign investors take their fundsout of domestic financial markets (e.g., the United States) and invest abroad. Thus, the supply of funds available inthe financial markets decreases and the equilibrium interest rate rises, while the equilibrium quantity of funds tradeddecreases.

Demand for Funds We explained above that the quantity of loanable funds demanded is negatively related tointerest rates. Factors that cause the demand curve for loanable funds to shift include the utility derived from assetspurchased with borrowed funds, the restrictiveness of nonprice conditions on borrowing, and economic conditions.

Utility Derived from Assets Purchased with Borrowed Funds As the utility (i.e., satisfaction or pleasure) derivedfrom an asset purchased with borrowed funds increases, the willingness of market participants (households,businesses, etc.) to borrow increases and the absolute dollar value borrowed increases. Accordingly, at every interestrate, the demand for loanable funds increases, or the demand curve shifts up and to the right. For example, suppose achange in jobs takes an individual from Arizona to Minnesota. The individual currently has a convertibleautomobile. Given the move to Minnesota, the individual’s utility from the convertible decreases, while it wouldincrease for a car with heated seats. Thus, with a potential increased utility from the purchase of a new car, theindividual’s demand for funds in the form of an auto loan increases. We show this shift (increase) in the demandcurve in Figure 6.12(b) as a move from DD to DD”. The shift in the demand curve creates a disequilibrium in thisfinancial market. Holding all other factors constant, the increase in the demand for funds due to an increase in theutility from the purchased asset results in an increase in the equilibrium interest rate, from i* to i*”, and an increasein the equilibrium quantity of funds traded, from Q* to Q*”.

Conversely, as the utility derived from an asset purchased with borrowed funds decreases, the willingness of marketparticipants (households, businesses, etc.) to borrow decreases and the absolute dollar amount borrowed decreases.Accordingly, at every interest rate, the demand for loanable funds decreases, or the demand curve shifts down and tothe left. The shift in the demand curve again creates a disequilibrium in this financial market. As competitive forcesadjust, and holding all other factors constant, the decrease in the demand for funds due to a decrease in the utilityfrom the purchased asset results in a decrease in the equilibrium interest rate and a decrease in the equilibriumquantity of funds loaned or traded.

Restrictiveness of Nonprice Conditions on Borrowed Funds As the nonprice restrictions put on borrowers as acondition of borrowing decrease, the willingness of market participants to borrow increases and the absolute dollarvalue borrowed increases. Such nonprice conditions may include fees or collateral. The lack of such restrictionsmakes the loan more desirable to the user of funds. Accordingly, at every interest rate, the demand forloanable funds increases, or the demand curve shifts up and to the right, from DD to DD”. As competitiveforces adjust, and holding all other factors constant, the increase in the demand for funds due to a decrease in therestrictive conditions on the borrowed funds results in an increase in the equilibrium interest rate, from i* to i*”, andan increase in the equilibrium quantity of funds traded, from Q* to Q*”. Conversely, as the nonprice restrictions puton borrowers as a condition of borrowing increase, market participants’ willingness to borrow decreases, and theabsolute dollar value borrowed decreases. Accordingly, the demand curve shifts down and to the left. The shift inthe demand curve results in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity offunds traded.

Economic Conditions When the domestic economy experiences a period of growth, such as that in the UnitedStates in the mid-2000s and early 2010s, market participants are willing to borrow more heavily. For example, state

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and local governments are more likely to repair and improve decaying infrastructure when the local economy isstrong. Accordingly, the demand curve for funds shifts up and to the right. Holding all other factors constant, theincrease in the demand for funds due to economic growth results in an increase in the equilibrium interest rate andan increase in the equilibrium quantity of funds traded. Conversely, when domestic economic growth is stagnant,market participants reduce their demand for funds. Accordingly, the demand curve shifts down and to the left,resulting in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded.

Movement of Interest Rates over TimeAs discussed in the previous section of this chapter, the loanable funds theory of interest rates is based on the supplyof and demand for loanable funds as functions of interest rates. The equilibrium interest rate (point E in Figure 6.12)is only a temporary equilibrium. Changes in underlying factors that determine the demand and supply of loanablefunds can cause continuous shifts in the supply and/or demand curves for loanable funds. Market forces will react tothe resulting disequilibrium with factors that influence a change in the equilibrium interest rate and quantity of fundstraded in that market. Refer again to Figure 6.12(a), which shows the effects of an increase in the supply curve forloanable funds, from SS to SS” (and the resulting decrease in the equilibrium interest rate, from i* to i*”), whileFigure 6.12(b) shows the effects of an increase in the demand curve for loanable funds, from DD to DD” (and theresulting increase in the equilibrium interest rate, from i* to i*”).

time out!6-7 Who are the main suppliers and demanders of loanable funds?6-8 What happens to the equilibrium interest rate when the demand for (supply of) loanable funds increases?6-9 How do supply and demand together determine interest rates?

6.4 • FACTORS THAT INFLUENCE INTEREST RATES FORINDIVIDUAL SECURITIES LG6-6So far we have looked at the general determination of equilibrium (nominal) interest rates for financial securities inthe context of the loanable demand and supply theory of the flow of funds. In this section, we examine the specificfactors that affect differences in interest rates across the range of real-world financial markets (i.e., differencesamong interest rates on individual securities, given the underlying level of interest rates determined by the demandand supply of loanable funds). These factors include

Inflation.The real risk-free rate.

Default risk.Liquidity risk.

Special provisions regarding the use of funds raised by a particular security issuer.The security’s term to maturity.

We will discuss each of these factors after summarizing them in Table 6.6.

InflationThe first factor that influences interest rates is the economy-wide actual or expected inflation rate. Specifically, thehigher the level of actual or expected inflation, the higher will be the level of interest rates. We define inflation of thegeneral price index of goods and services (or the inflation premium, IP) as the (percentage) increase in the price of astandardized basket of goods and services over a given period of time. The U.S. Department of Commerce measuresinflation using indexes such as the consumer price index (CPI) and the producer price index (PPI). For example, theannual inflation rate using the CPI index between years t and t + 1 would be equal to

inflation The continual increase in the price level of a basket of goods and services.

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(6-1)

The positive relationship between interest rates and inflation rates is fairly intuitive: When inflation raises thegeneral price level, investors who buy financial assets must earn a higher interest rate (or inflation premium) tocompensate for continuing to hold the investment. Holding on to their investments means that they incur highercosts of forgoing consumption of real goods and services today, only to have to buy these same goods and servicesat higher prices in the future. In other words, the higher the rate of inflation, the more expensive the same basket ofgoods and services will be in the future.

Real Risk-Free RateA real risk-free rate is the rate that a risk-free security would pay if no inflation were expected over its holding period(e.g., a year). As such, it measures only society’s relative time preference for consuming today rather thantomorrow. The higher society’s preference to consume today (i.e., the higher its time value of money or rate of timepreference), the higher the real risk-free rate (RFR) will be.

real risk-free rate The interest rate that would exist on a risk-free security if no inflation were expected.

▼ TABLE 6.6 Factors Affecting Nominal Interest Rates

Inflation: A continual increase in the price level of a basket of goods and services throughout the economy as a whole.

Real risk-free rate: Risk-free rate adjusted for inflation; generally lower than nominal risk-free rates at any particular time.

Default risk: Risk that a security issuer will miss an interest or principal payment or continue to miss such payments.

Liquidity risk: Risk that a security cannot be sold at a price relatively close to its value with low transaction costs on short notice.

Special provisions: Provisions (e.g., taxability, convertibility, and callability) that impact a security holder beneficially oradversely and as such are reflected in the interest rates on securities that contain such provisions.

Time to maturity: Length of time until a security is repaid; used in debt securities as the date upon which the security holders gettheir principal back.

Fisher Effect Economists often refer to the relationship among real risk-free rates (RFR), expected inflation(expected IP), and nominal risk-free rates (i), described previously, as the Fisher effect, named for Irving Fisher,who identified these economic relationships early last century. The Fisher effect theorizes that nominal risk-freerates that we observe in financial markets (e.g., the one-year Treasury bill rate) must compensate investorsfor

Any inflation-related reduction in purchasing power lost on funds lent or principal due.

An additional premium above the expected rate of inflation for forgoing present consumption (which reflects the real risk-free rate issuediscussed previously).

(6-2)

Thus, the nominal risk-free rate will equal the real risk-free rate only when market participants expect inflation to bezero: Expected IP = 0. Similarly, the nominal risk-free rate will equal the expected inflation rate only when the realrisk-free rate is zero. We can rearrange the nominal risk-free rate equation to show what determines the real interestrate:1

(6-3)

It needs to be noted that the expected inflation rate is difficult to estimate accurately, so the real risk-free rate can bedifficult to measure accurately. Investors’ expectations are not always realized either.

The one-year T-bill rate in 2015 was 0.32 percent, while the CPI for the year was 0.50 percent, which implies a realrisk-free rate of –0.18 percent—that is, the real risk-free rate was actually negative. Thus, the real value ofinvestments actually decreased in that year.

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Figure 6.13 shows the nominal risk-free rate (one-year T-bill rate) versus the change in the CPI from 1962 through2015. Note that generally the T-bill rate is greater than the CPI, that is, the real risk-free rate earned on securities ispositive. It is during periods of economic slowdowns that the T-bill rate is less than the CPI; that is, real risk-freerates are negative.

Default or Credit RiskDefault risk is the risk that a security issuer may fail to make its promised interest and principal payments to itsbondholders (or its dividend in the case of preferred stockholders). The higher the default risk, the higher the interestrate that security buyers will demand to compensate them for this default (or credit) risk relative to default-risk-freeU.S. Treasury securities. Since the U.S. government has taxation powers and can print currency, the risk of itsdefaulting on debt payments is practically zero. But some borrowers, such as corporations or individuals, have lesspredictable cash flows (and no powers to tax anyone to raise funds immediately). So investors must charge issuersother than the U.S. government a premium for any perceived probability of default and the cost of potentiallyrecovering the amount loaned built into their regular interest rate premium. The difference between a quoted interestrate on a security (security j) and a Treasury security with similar maturity, liquidity, tax, and other features is calleda default or credit risk premium (DRPj). That is

default risk The risk that a security issuer will default on that security by being late on or missing an interest or principal payment.

(6-4)

where ijt = Interest rate on a security issued by a non−Treasury issuer (issuer j) of maturity m at time t.

iTt = Interest rate on a security issued by the U.S. Treasury of maturity m at time t.

Various rating agencies, including Moody’s and Standard & Poor’s, evaluate and categorize the potential defaultrisk on many corporate bonds, some state and municipal bonds, and some stocks. We cover these ratings in moredetail in Chapter 8. For example, in 2015, the 10-year Treasury rate was 2.14 percent. Moody’s Aaa-rated and Baa-rated corporate debt carried interest rates of 3.89 percent and 5.00 percent, respectively. Thus, the average defaultrisk premiums on the Aaa-rated and Baa-rated corporate debt were

Figure 6.14 presents these risk premiums for the stated creditworthiness categories of bonds from 1977 through2015. Notice from this figure and Figure 6.13 that default risk premiums tend to increase when the economy iscontracting and decrease when the economy is expanding. For example, from 2007 to 2008, real risk-free rates (T-bills—CPI in Figure 6.13) increased from 0.43 percent to 1.73 percent. Over the same period, default risk premiumson Aaa-rated bonds increased from 1.39 percent to 1.97 percent. Baa-rated bonds showed a default risk premiumincrease from 2.55 percent to 3.78 percent.

EXAMPLE 6-1Calculating Real Risk-FreeRates LG6-6

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One-year Treasury bill rates in 2007 averaged 4.53 percent andinflation (measured by the consumer price index) for the year was 4.10percent. If investors had expected the same inflation rate as thatactually realized, calculate the real risk-free rate for 2007 according to

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the Fisher effect.

SOLUTION:4.53% − 4.10% = 0.43%

Similar to Problems 6-1, 6-2, Self-Test Problem 1

Liquidity RiskA highly liquid asset can be sold at a predictable price with low transaction costs. That is, the holder can convert theasset at its fair market value on short notice. The interest rate on a security reflects its relative liquidity, with highlyliquid assets carrying the lowest interest rates (all other characteristics remaining the same). Likewise, if a security isilliquid, investors add a liquidity risk premium (LRP) to the interest rate on the security. In the United States,most government securities sell in liquid markets, as do large corporations’ stocks and bonds. Securitiesissued by smaller companies trade in relatively less liquid markets.

liquidity risk The risk that a security cannot be sold at a predictable price with low transaction costs on short notice.

FIGURE 6.13 Nominal Interest Rates versus Inflation

Notice the difference between the nominal risk-free rate and the change in CPI over the last several decades.

Source: Federal Reserve Board and U.S. Department of Labor websites, various dates. www.federalreserve.gov and www.dol.gov.

A different type of liquidity risk premium may also exist if investors dislike long-term securities because their prices(present values, as discussed below and in Chapters 4 and 7) react more to interest rate changes than short-termsecurities do. In this case, a higher liquidity risk premium may be added to a security with a longer maturity becauseof its greater exposure to price risk (loss of capital value) on the longer-term security as interest rates change.

Special Provisions or CovenantsSometimes a security’s issuing party attaches special provisions or covenants to the security issued. Such provisionsaffect the interest rates on these securities relative to securities without such provisions attached to them. Some ofthese special provisions include the security’s taxability, convertibility, and callability. For example, investors payno federal taxes on interest payments received from municipal securities. So a municipal bondholder may demand a

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lower interest rate than that demanded on a comparable taxable bond—such as a Treasury bond (which is taxable atthe federal level but not at the state or local levels) or a corporate bond (the interest on which is taxable at the state,local, and federal levels).Another special covenant is convertibility: A convertible bond offers the holder the opportunity to exchange thebond for another type of the issuer’s securities—usually preferred or common stock—at a preset price (see Chapter7). This conversion option can be valuable to purchasers, so convertible security buyers require lower interest ratesthan a comparable nonconvertible security holder would require (all else equal). In general, special provisions thatbenefit security holders (e.g., tax-free status and convertibility) bring with them lower interest rates, and specialprovisions that benefit security issuers (e.g., callability, by which an issuer has the option to retire, or call, thesecurity prior to maturity at a preset price) require higher interest rates to encourage purchase.

Term to MaturityInterest rates also change—sometimes daily—because of a bond’s term to maturity. Financial professionals refer tothis daily or even hourly changeability in interest rates as the term structure of interest rates, or the yield curve. Theshape of the yield curve derives directly from time value of money principles. The term structure of interest ratescompares interest rates on debt securities based on their time to maturity, assuming that all other characteristics (i.e.,default risk, liquidity risk) are equal. Interest rates change as the maturity of a debt security changes; in general, thelonger the term to maturity, the higher the required interest rate buyers will demand. This addition to the requiredinterest rate is the maturity premium (MP). The MP, which is the difference between the required yield on long-versus short-term securities of the same characteristics except maturity, can be positive, negative, or zero.

term structure of interest rates A comparison of market yields on securities, assuming all characteristics except maturity are the same.

FIGURE 6.14 Default Risk Premiums on Corporate Bonds

Source: Federal Reserve Board website, various dates. www.federalreserve.gov

FIGURE 6.15 Common Shares for Yield Curves on Treasury Securities

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Three common yield curve shapes are (a) upward sloping, (b) downward sloping, and (c) a flat slope.Source: U.S. Treasury, Office of Debt Management, Daily Treasury Yield Curves, various dates. www.ustreas.gov

EXAMPLE 6-2 Determinants of Interest Rates forIndividual Securities LG6-6

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Morningstar Corp.’s eight-year bonds are currently yielding a return of6.85 percent. The expected inflation premium is 1.15 percent annuallyand the real risk-free rate is expected to be 2.25 percent annually overthe next eight years. The default risk premium on Morningstar’s bondsis 1.35 percent. The maturity risk premium is 0.50 percent on two-yearsecurities and increases by 0.05 percent for each additional year tomaturity. Calculate the liquidity risk premium on Morningstar’s eight-year bonds.

SOLUTION:

Similar to Problems 6-3, 6-4, Self-Test Problem 2

The financial industry most often reports and analyzes the yield curve for U.S. Treasury securities. The yield curvefor U.S. Treasury securities has taken many shapes over the years, but the three most common shapes appear inFigure 6.15. In graph (a), the yield curve on January 15, 2016, yields rise steadily with maturity when the yieldcurve slopes upward. This is the most common yield curve. On average, the MP is positive, as you might expect.Graph (b) shows an inverted, or downward-sloping, yield curve, reported on November 24, 2000, in which yieldsdecline as maturity increases. Inverted yield curves do not generally last very long. In this case, the yield curveinverted as the U.S. Treasury began retiring long-term (30-year) bonds as the country began to pay off the nationaldebt. Finally, graph (c) shows a flat yield curve, reported on June 4, 2007, when the yield to maturity is virtuallyunaffected by the term to maturity.

Putting together the factors that affect interest rates in different markets, we can use the following general equationto note the influence of the factors that functionally impact the fair interest rate—the rate necessary to compensateinvestors for all security risks—(ij

*) on an individual (jth) financial security.

(6-5)

where

IP = Inflation premium.RFR = Real risk-free rate.DRPj = Default risk premium on the jth security.LRPj = Liquidity risk premium on the jth security.SCPj = Special covenant premium on the jth security.MPj = Maturity premium on the jth security.

The first two factors, IP and RFR, are common to all financial securities, while the other factors can uniquelyinfluence the price of a single security.

time out!

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6-10 What is the difference between nominal and real risk-free rates?6-11 What does “the term structure of interest rates” mean?6-12 What shape does the term structure usually take? Why?

6.5 • THEORIES EXPLAINING THE SHAPE OF THE TERMSTRUCTURE OF INTEREST RATES2 LG6-7We just explained the necessity of a maturity premium, the relationship between a security’s interest rate and itsremaining term to maturity. We can illustrate these issues by showing that the term structure of interest rates cantake a number of different shapes. As you might expect, economists and financial theorists with various viewpointsdiffer among themselves in theorizing why the yield curve takes different shapes. Explanations for the yield curve’sshape fall predominantly into three categories:

1. The unbiased expectations theory.

2. The liquidity premium theory.3. The market segmentation theory.

Look again at Figure 6.15 (a), which presents the Treasury yield curve as of January 15, 2016. We see that the yieldcurve on this date reflected the normal upward-sloping relationship between yield and maturity. Now let’s turn toexplanations for this shape based on the three predominant theories noted above.

Unbiased Expectations TheoryAccording to the unbiased expectations theory of the term structure of interest rates, at any given point in time, theyield curve reflects the market’s current expectations of future short-term rates. As illustrated in Figure 6.16, theintuition behind the unbiased expectations theory is this: If investors have a four-year investment horizon, they couldeither buy current four-year bonds and earn the current (or spot) yield on a four-year bond (1R4, if held to maturity)each year, or they could invest in four successive one-year bonds [of which they know only the current one-yearspot rate (1R1)]. But investors also expect what the unknown future one-year rates [E(2r1), E(3r1), and E(4r1)] willbe. Note that each interest rate term has two subscripts, e.g., 1R4. The first subscript indicates the period in which thesecurity is bought, so that 1 represents the purchase of a security in period 1. The second subscript indicates thematurity on the security. Thus, 4 represents the purchase of a security with a four-year life. Similarly, E(3r1) is theexpected return on a security with a one-year life purchased in period 3.

According to the unbiased expectations theory, the return for holding a four-year bond to maturity should equal theexpected return for investing in four successive one-year bonds (as long as the market is in equilibrium). If thisequality does not hold, an arbitrage opportunity exists. That is, if investors could earn more on the one-year bondinvestments, they could short (or sell) the four-year bond, use the proceeds to buy the four successive one-yearbonds, and earn a guaranteed profit over the four-year investment horizon. So, according to the unbiasedexpectations theory, if the market expects future one-year rates to rise each successive year into the future,then the yield curve will slope upward. Specifically, the current four-year T-bond rate or return will exceed thethree-year bond rate, which will exceed the two-year bond rate, and so on. Similarly, if the market expects futureone-year rates to remain constant each successive year into the future, then the four-year bond rate will equal thethree-year bond rate. That is, the term structure of interest rates will remain constant (flat) over the relevant timeperiod. Specifically, the unbiased expectation theory states that current long-term interest rates are geometricaverages of current and expected future short-term interest rates. The mathematical equation representing thisrelationship is

(6-6)

therefore

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(6-7)

where 1RN = Actual N-period rate today (i.e., the first day of year 1).

N = Term to maturity.1R1 = Actual 1-year rate today.E(ir1) = Expected 1-year rates for years 2, 3, 4, . . ., N in the future.

Notice that uppercase interest rate terms, 1Rt, are the actual current interest rates on securities purchased today with amaturity of t years. Lowercase interest rate terms, tr1, represent estimates of future one-year interest rates starting tyears into the future.

FIGURE 6.16 Unbiased Expectations Theory of the Term Structure of Interest Rates

Return from buying four 1-year maturity bonds versus buying one 4-year maturity bond.

the Math Coach on…

“When putting interest rates into the equation, enter them in decimal format, not percentage format.Correct: (1 + 0.0294)

Not correct: (1 +2.94)„

EXAMPLE 6-3 Calculating Yield Curves LG6-7

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Suppose that the current one-year rate (one-year spot rate) andexpected one-year T-bond rates over the following three years (i.e.,years 2, 3, and 4, respectively) are as follows:

1R1 = 2.94%, E(1r1) = 4%, E(3r1) = 4.74%, E(4r1) = 5.10%

Construct a yield curve using the unbiased expectations theory.

SOLUTION:

Using the unbiased expectations theory, current (or today’s) rates forone-, two-, three-, and four-year maturity Treasury securities should be

and the current yield to maturity curve will be upward sloping as shown:

This upward-sloping yield curve reflects the market’s expectation ofpersistently rising one-year (short-term) interest rates over the futurehorizon.3

Similar to Problems 6-5, 6-6, 6-7, 6-8, Self-Test Problem 3

Liquidity Premium TheoryThe second popular explanation—the liquidity premium theory of the term structure of interest rates—builds on theunbiased expectations theory. The liquidity premium idea is as follows: Investors will hold long-term maturitiesonly if these securities with longer term maturities are offered at a premium to compensate for future uncertainty inthe security’s value. Of course, uncertainty or risk increases with an asset’s maturity. This theory is thus consistentwith our discussions of market risk and liquidity risk, above. Specifically, in a world of uncertainty, short-termsecurities provide greater marketability (due to their more active secondary markets) and have less price risk thanlong-term securities do. As a result (due to smaller price fluctuations for a given change in interest rates), investorswill prefer to hold shorter-term securities because this kind of paper can be converted into cash with little marketrisk. Said another way, investors face little risk of a capital loss, that is, a fall in the price of the security below itsoriginal purchase price. So, investors must be offered a liquidity premium to buy longer-term securities that carryhigher capital loss risk. This difference in market and liquidity risk can be directly related to the fact that longer-termsecurities are more sensitive to interest rate changes in the market than are shorter-term securities—Chapter 7discusses bond interest rate sensitivity and the link to a bond’s maturity. Because longer maturities on securitiesmean greater market and liquidity risk, the liquidity premium increases as maturity increases.

The liquidity premium theory states that long-term rates are equal to geometric averages of current and expectedshort-term rates (like the unbiased expectations theory), plus liquidity risk premiums that increase with the security’smaturity (this is the extension of the liquidity premium added to the unbiased expectations theory). Figure 6.17illustrates the differences in the shape of the yield curve under the unbiased expectations theory versus the liquiditypremium theory. For example, according to the liquidity premium theory, an upward-sloping yield curve may reflectinvestors’ expectations that future short-term rates will be flat, but because liquidity premiums increase withmaturity, the yield curve will nevertheless slope upward. Indeed, an upward-sloping yield curve may reflectexpectations that future interest rates will rise, be flat, or even fall as long as the liquidity premium increases withmaturity fast enough to produce an upward-sloping yield curve. The liquidity premium theory can be

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mathematically represented as

(6-8)

where Lt = Liquidity premium for a period t and L2 < L3 < LN.

FIGURE 6.17 Yield Curve Using the Unbiased Expectation Theory (UET) versus the Liquidity Premium Theory (LPT)

Notice the differences in the shape of the yield curve under the UET and the LPT.

Let’s compare the yield curves in Examples 6-3 (using the unbiased expectations theory) and 6-4. Notice that theliquidity premium in year 2 (L2 = 0.10%) produces a 0.05 (= 3.52% − 3.47%) percent premium on the yield tomaturity on a two-year T-note, the liquidity premium for year 3 (L3 = 0.20%) produces a 0.10 (= 3.99% − 3.89%)percent premium on the yield to maturity on the three-year T-note, and the liquidity premium for year 4 (L4 =0.30%) produces a 0.15 (= 4.34% − 4.19%) percent premium on the yield to maturity on the four-year T-note.

Market Segmentation TheoryThe market segmentation theory does not build on the unbiased expectations theory or the liquidity premium theory,but rather argues that individual investors and FIs have specific maturity preferences, and convincing them to holdsecurities with maturities other than their most preferred requires a higher interest rate (maturity premium). Themain thrust of the market segmentation theory is that investors do not consider securities with different maturities asperfect substitutes. Rather, individual investors and FIs have distinctly preferred investment horizons dictated by thedates when their liabilities will come due. For example, banks might prefer to hold relatively short-term U.S.Treasury bonds because their deposit liabilities also tend to be short-term—recall that bank customers can accesstheir funds on demand. Insurance companies, on the other hand, may prefer to hold long-term U.S. Treasury bondsbecause life insurance contracts usually expose insurance firms to long-term liabilities. Accordingly, distinct supplyand demand conditions within a particular maturity segment—such as the short end and long end of the bond market

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—determine interest rates under the market segmentation theory.

EXAMPLE 6-4Calculating Yield Curves Usingthe Liquidity PremiumTheory LG6-7

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Suppose that the current one-year rate (one-year spot rate) andexpected one-year T-bond rates over the following three years (i.e.,years 2, 3, and 4, respectively) are as follows:

In addition, investors charge a liquidity premium on longer-termsecurities such that

Using the liquidity premium theory, construct the yield curve.

SOLUTION:

Using the liquidity premium theory, current rates for one-, two-, three-,and four-year maturity Treasury securities should be

and the current yield to maturity curve will be upward sloping as shown:

Similar to Problems 6-9, 6-10, Self-Test Problem 3

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The market segmentation theory assumes that investors and borrowers generally do not want to shift from onematurity sector to another without adequate compensation—that is, an interest rate premium. Figure 6.18demonstrates how changes in supply for short- versus long-term bond market segments result in changing shapes ofthe yield to maturity curve. Specifically, as shown in Figure 6.18, the higher the demand for securities is, the higherthe yield on those securities.4 Further, as the supply of securities decreases in the short-term market and increases inthe long-term market, the slope of the yield curve becomes steeper. If the supply of short-term securities hadincreased while the supply of long-term securities had decreased, the yield curve would have a flatter slope andmight even have sloped downward. Indeed, the U.S. Treasury’s large-scale repurchase of long-term Treasury bonds(i.e., reductions in supply) in early 2000 has been viewed as the major cause of the inverted yield curve thatappeared in February 2000.

FIGURE 6.18 Market Segmentation and Determination of the Slope of the Yield Curve

The higher the demand for securities, the higher the yield on those securities.

time out!6-13 What three theories explain the shape of the yield curve?6-14 Explain how arbitrage plays a role in the unbiased expectations explanation of the shape of the yield curve.

6.6 • FORECASTING INTEREST RATES5 LG6-8We noted in the time value of money (TVM) chapters (Chapters 4 and 5) that as interest rates change, so do thevalues of financial securities. Accordingly, both individual investors and public corporations want to be able topredict or forecast interest rates if they wish to trade profitably. For example, if interest rates rise, the value ofinvestment portfolios of individuals and corporations will fall, resulting in a loss of wealth. So, interest rate forecastsare extremely important for the financial wealth of both public corporations and individuals.

Recall our discussion of the unbiased expectations theory in the previous section of this chapter. That theory

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indicated that the market’s expectation of future short-term interest rates determines the shape of the yield curve. Forexample, an upward-sloping yield curve implies that the market expects future short-term interest rates to rise. So,we can use the unbiased expectations theory to forecast (short-term) interest rates in the future (i.e., forward one-year interest rates). A forward rate is an expected, or implied, rate on a short-term security that will originate at somepoint in the future. Using the equations in the unbiased expectations theory, we can directly derive the market’sexpectation of forward rates from existing or actual rates on spot market securities.

forward rate An expected rate (quoted today) on a security that originates at some point in the future.

To find an implied forward rate on a one-year security to be issued one year from today, we can rewrite the unbiasedexpectations theory equation as follows:

(6-9)

EXAMPLE 6-5 Estimating Forward Rates LG6-8

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In the mid-2010s, the existing or current (spot) one-, two-, three-, andfour-year zero coupon Treasury security rates were as follows:

1R1 = 0.70%, 1R2 = 0.87%, 1R3 = 1.04%, 1R4 = 1.34%

Using the unbiased expectations theory, calculate one-year forwardrates on zero coupon Treasury bonds for years 2, 3, and 4.

SOLUTION:

Similar to Problems 6-15, 6-16, Self-Test Problem 4

where 2 f1 = expected one-year rate for year 2, or the implied forward one-year rate for next year.

Saying that 2 f1 is the expected one-year rate for year 2 is the same as saying that, once we isolate the 2 f1 term, theequation will give us the market’s estimate of the expected one-year rate for year 2. Solving for 2 f1 we get

(6-10)

In general, we can find the forward rate for any year, N, into the future using the following generalized equationderived from the unbiased expectations theory:

(6-11)

time out!

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6-15 What is a forward rate?6-16 How can we obtain an implied forward rate from current short- and long-term interest rates?6-17 Why is it useful to calculate forward rates?

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Your Turn…Questions

1. Classify the following transactions as taking place in the primary or secondary markets (LG6-1):

a. IBM issues $200 million of new common stock.b. The New Company issues $50 million of common stock in an IPO.c. IBM sells $5 million of GM preferred stock out of its marketable securities portfolio.d. The Magellan Fund buys $100 million of previously issued IBM bonds.e. Prudential Insurance Co. sells $10 million of GM common stock.

2. Classify the following financial instruments as money market securities or capital market securities (LG6-2):

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a. Federal fundsb. Common stockc. Corporate bondsd. Mortgagese. Negotiable certificates of depositf. U.S. Treasury billsg. U.S. Treasury notesh. U.S. Treasury bondsi. State and government bonds

3. What are the different types of financial institutions? Include a description of the main servicesoffered by each. (LG6-3)

4. How would economic transactions between suppliers of funds (e.g., households) and users of funds (e.g.,corporations) occur in a world without FIs? (LG6-3)

5. Why would a world limited to the direct transfer of funds from suppliers of funds to users of funds likely resultin quite low levels of fund flows? (LG6-3)

6. How do FIs reduce monitoring costs associated with the flow of funds from fund suppliers to fund users? (LG6-3)

7. How do FIs alleviate the problem of liquidity risk faced by investors wishing to invest in securities ofcorporations? (LG6-3)

8. Who are the suppliers of loanable funds? (LG6-4)

9. Who are the demanders of loanable funds? (LG6-4)

10. What factors cause the supply of funds curve to shift? (LG6-5)

11. What factors cause the demand for funds curve to shift? (LG6-5)

12. What are six factors that determine the nominal interest rate on a security? (LG6-6)

13. What should happen to a security’s equilibrium interest rate as the security’s liquidity risk increases? (LG6-6)

14. Discuss and compare the three explanations for the shape of the yield curve. (LG6-7)

15. Are the unbiased expectations and liquidity premium theories explanations for the shape of the yield curvecompletely independent theories? Explain why or why not. (LG6-7)

16. What is a forward interest rate? (LG6-8)

17. If we observe a one-year Treasury security rate that is higher than the two-year Treasury security rate, what canwe infer about the one-year rate expected one year from now? (LG6-8)

ProblemsBASIC PROBLEMS

6-1 Determinants of Interest Rates for Individual Securities A particular security’s default risk premium is2 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.50percent. The security’s liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent.The security has no special covenants. Calculate the security’s equilibrium rate of return. (LG6-6)

6-2 Determinants of Interest Rates for Individual Securities You are considering an investment in 30-yearbonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reportsthat one-year T-bills are currently earning 1.25 percent. Your broker has determined the followinginformation about economic activity and Moore Corporation bonds:

Real risk-free rate = 0.75%Default risk premium = 1.15%

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Liquidity risk premium = 0.50%Maturity risk premium = 1.75%

a. What is the inflation premium? (LG6-6)b. What is the fair interest rate on Moore Corporation 30-year bonds? (LG6-6)

6-3 Determinants of Interest Rates for Individual Securities Dakota Corporation 15-year bonds have anequilibrium rate of return of 8 percent. For all securities, the inflation risk premium is 1.75 percent and thereal risk-free rate is 3.50 percent. The security’s liquidity risk premium is 0.25 percent and maturityrisk premium is 0.85 percent. The security has no special covenants. Calculate the bond’s defaultrisk premium. (LG6-6)

6-4 Determinants of Interest Rates for Individual Securities A two-year Treasury security currently earns1.94 percent. Over the next two years, the real risk-free rate is expected to be 1.00 percent per year and theinflation premium is expected to be 0.50 percent per year. Calculate the maturity risk premium on the two-year Treasury security. (LG6-6)

6-5 Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expectedone-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, andfour-year-maturity Treasury securities. Plot the resulting yield curve. (LG6-7)

6-6 Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expectedone-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, andfour-year-maturity Treasury securities. Plot the resulting yield curve. (LG6-7)

6-7 Unbiased Expectations Theory One-year Treasury bills currently earn 1.45 percent. You expect that oneyear from now, one-year Treasury bill rates will increase to 1.65 percent. If the unbiased expectationstheory is correct, what should the current rate be on two-year Treasury securities? (LG6-7)

6-8 Unbiased Expectations Theory One-year Treasury bills currently earn 2.15 percent. You expect that oneyear from now, one-year Treasury bill rates will increase to 2.65 percent and that two years from now, one-year Treasury bill rates will increase to 3.05 percent. If the unbiased expectations theory is correct, whatshould the current rate be on three-year Treasury securities? (LG6-7)

6-9 Liquidity Premium Theory One-year Treasury bills currently earn 3.45 percent. You expect that one yearfrom now, one-year Treasury bill rates will increase to 3.65 percent. The liquidity premium on two-yearsecurities is 0.05 percent. If the liquidity premium theory is correct, what should the current rate be on two-year Treasury securities? (LG6-7)

6-10 Liquidity Premium Theory One-year Treasury bills currently earn 2.25 percent. You expect that oneyear from now, one-year Treasury bill rates will increase to 2.45 percent and that two years from now,one-year Treasury bill rates will increase to 2.95 percent. The liquidity premium on two-year securitiesis 0.05 percent and on three-year securities is 0.15 percent. If the liquidity premium theory is correct,what should the current rate be on three-year Treasury securities? (LG6-7)

6-11 Liquidity Premium Theory Based on economists’ forecasts and analysis, one-year Treasury bill ratesand liquidity premiums for the next four years are expected to be as follows:

Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on thegraph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG6-

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7)6-12 Liquidity Premium Theory Based on economists’ forecasts and analysis, one-year Treasury

bill rates and liquidity premiums for the next four years are expected to be as follows:

Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on thegraph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG6-7)

INTERMEDIATE PROBLEMS

6-13 Determinants of Interest Rates for Individual Securities Tom and Sue’s Flowers, Inc.’s, 15-yearbonds are currently yielding a return of 8.25 percent. The expected inflation premium is 2.25 percentannually and the real risk-free rate is expected to be 3.50 percent annually over the next 15 years. Thedefault risk premium on Tom and Sue’s Flowers’ bonds is 0.80 percent. The maturity risk premium is0.75 percent on five-year securities and increases by 0.04 percent for each additional year to maturity.Calculate the liquidity risk premium on Tom and Sue’s Flowers, lnc.’s, 15-year bonds. (LG6-6)

6-14 Determinants of Interest Rates for Individual Securities NikkiG’s Corporation’s 10-year bonds arecurrently yielding a return of 6.05 percent. The expected inflation premium is 1.00 percent annuallyand the real risk-free rate is expected to be 2.10 percent annually over the next 10 years. The liquidityrisk premium on NikkiG’s bonds is 0.25 percent. The maturity risk premium is 0.10 percent on two-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the defaultrisk premium on NikkiG’s 10-year bonds. (LG6-6)

6-15 Unbiased Expectations Theory Suppose we observe the following rates: 1R1 = 8%, 1R2 = 10%. If theunbiased expectations theory of the term structure of interest rates holds, what is the one-year interestrate expected one year from now, E(2r1)? (LG6-7)

6-16 Unbiased Expectations Theory The Wall Street Journal reports that the rate on four-year Treasurysecurities is 1.60 percent and the rate on five-year Treasury securities is 2.15 percent. According to theunbiased expectations theories, what does the market expect the one-year Treasury rate to be fouryears from today, E(5r1)? (LG6-7)

6-17 Liquidity Premium Theory The Wall Street Journal reports that the rate on three-year Treasurysecurities is 5.25 percent and the rate on four-year Treasury securities is 5.50 percent. The one-yearinterest rate expected in three years is, E(4r1), is 6.10 percent. According to the liquidity premiumhypotheses, what is the liquidity premium on the four-year Treasury security, L4? (LG6-7)

6-18 Liquidity Premium Theory Suppose we observe the following rates: 1R1 = 0.75%, 1R2 = 1.20%, andE(2r1) = 0.907%. If the liquidity premium theory of the term structure of interest rates holds, what isthe liquidity premium for year 2, L2? (LG6-7)

6-19 Forecasting Interest Rates You note the following yield curve in The Wall Street Journal. Accordingto the unbiased expectations theory, what is the one-year forward rate for the period beginning oneyear from today, 2f1? (LG6-8)

 Maturity Yield

One day 2.00%

One year 5.50

Two years 6.50

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Three years 9.00

6-20 Forecasting Interest Rates On March 11, 20XX, the existing or current (spot) one-, two-,three-, and four-year zero coupon Treasury security rates were as follows:

Using the unbiased expectations theory, calculate the one-year forward rates on zero coupon Treasurybonds for years 2, 3, and 4 as of March 11, 20XX. (LG6-8)

ADVANCED PROBLEMS

6-21 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that thecurrent rate on 10-year Treasury bonds is 7.25 percent, on 20-year Treasury bonds is 7.85 percent, andon a 20-year corporate bond issued by MHM Corp. is 8.75 percent. Assume that the maturity riskpremium is zero. If the default risk premium and liquidity risk premium on a 10-year corporate bondissued by MHM Corp. are the same as those on the 20-year corporate bond, calculate the current rateon MHM Corp.’s 10-year corporate bond. (LG6-6)

6-22 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that thecurrent rate on 8-year Treasury bonds is 5.85 percent, the rate on 15-year Treasury bonds is 6.25percent, and the rate on a 15-year corporate bond issued by MHM Corp. is 7.35 percent. Assume thatthe maturity risk premium is zero. If the default risk premium and liquidity risk premium on an 8-yearcorporate bond issued by MHM Corp. are the same as those on the 15-year corporate bond, calculatethe current rate on MHM Corp.’s 8-year corporate bond. (LG6-6)

6-23 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that thecurrent rate on 5-year Treasury bonds is 1.85 percent and on 10-year Treasury bonds is 3.35 percent.Assume that the maturity risk premium is zero. Calculate the expected rate on a 5-year Treasury bondpurchased five years from today, E(5r5). (LG6-6)

6-24 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that thecurrent rate on 10-year Treasury bonds is 2.25 percent and the rate on 20-year Treasury bonds is 4.50percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 10-yearTreasury bond purchased 10 years from today, E(10r10). (LG6-6)

6-25 Unbiased Expectations Theory Suppose we observe the three-year Treasury security rate (1R3) to be8 percent, the expected one-year rate next year— E(2r1)—to be 4 percent, and the expected one-yearrate the following year—E(3r1)—to be 6 percent. If the unbiased expectations theory of the termstructure of interest rates holds, what is the one-year Treasury security rate, 1R1? (LG6-7)

6-26 Unbiased Expectations Theory The Wall Street Journal reports that the rate on three-year Treasurysecurities is 1.20 percent and the rate on five-year Treasury securities is 2.15 percent. According to theunbiased expectations theory, what does the market expect the two-year Treasury rate to be three yearsfrom today, E(3r2)? (LG6-7)

6-27 Forecasting Interest Rates Assume the current interest rate on a one-year Treasury bond (1R1) is 4.50percent, the current rate on a two-year Treasury bond (1R2) is 5.25 percent, and the current rate on athree-year Treasury bond (1R3) is 6.50 percent. If the unbiased expectations theory of the termstructure of interest rates is correct, what is the one-year forward rate expected on Treasury billsduring year 3, 3f1? (LG6-8)

6-28 Forecasting Interest Rates A recent edition of The Wall Street Journal reported interest rates of 1.25percent, 1.60 percent, 1.98 percent, and 2.25 percent for three-, four-, five-, and six-year Treasurysecurity yields, respectively. According to the unbiased expectation theory of the term structure ofinterest rates, what are the expected one-year forward rates for years 4, 5, and 6? (LG6-8)

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chapter sixappendix 6A:The Financial Crisis: The Failure of Financial Institution SpecialnessIn the late 2000s, the United States—and indeed the world—experienced the worst financial crisis since the GreatDepression of the 1930s. As of mid-March 2009, in less than a year and a half, the Dow Jones Industrial Average(DJIA) had fallen in value 53.8 percent, compared to 49 percent in the market crash of 1937 and 1938. Homeforeclosures reached record highs in late 2008 and continued to rise through 2009. One in 45 households (2.8million properties) were in default on their home mortgage in 2009. The investment banking industry saw the failure(or acquisition) of all but two of its major firms (Goldman Sachs and Morgan Stanley), and these two firmsconverted to commercial bank holding companies. AIG, one of the largest insurance companies in the U.S., survivedonly because of a federal government bailout. Commercial banking giant Citigroup required a massive governmentguarantee against losses and an injection of cash to prevent failure. The three major U.S. automakers facedbankruptcy without federal money. Even after having received government loans, Chrysler declared Chapter 11bankruptcy in May 2009, while General Motors followed suit a month later. As of October 2009, the U.S.unemployment rate was over 10 percent, the highest level since 1983.

This financial crisis had huge effects on financial institutions and the way they do business today and will dobusiness in the future. In the chapter, we explored the root causes of and changes brought about by the financialcrisis as they apply to specific areas of risk measurement and management within FIs. In this appendix, we reviewthe major events leading up to and throughout the financial crisis so we can see the full economywide impact andimplications for the future.

The Beginning of the CollapseSigns of significant problems in the U.S. economy first arose in late 2006 and the first half of 2007 when homeprices plummeted and mortgage delinquencies began to mount. Mortgage defaults by subprime borrowers surged inthe last quarter of 2006 through 2008 as homeowners, who a half decade earlier had stretched themselves financiallyto buy a home or refinance a mortgage, fell behind on their loan payments. Foreclosure filings jumped 93 percent inJuly 2007 over July 2006. Between August 2007 and October 2008, an additional 936,439 homes were lost toforeclosure. As the mortgage defaults continued, financial institutions that held these mortgages (and mortgage-backed securities) started announcing huge losses on them. These securitized loans, particularly securitizedsubprime mortgage loans, led to the huge financial losses that quite possibly were the root cause of the weakness ofthe U.S. economy during this time. Losses from the falling value of subprime mortgages and securities backed bythese mortgages reached over $400 billion worldwide through 2007.

In 2007, Citigroup, Merrill Lynch, and Morgan Stanley lost a combined $40 billion due mainly to bad mortgageloans. Bank of America took a $3 billion dollar loss for bad loans in just the fourth quarter of 2007, while Wachovialost $1.2 billion. UBS took a loss of $10 billion, Morgan Stanley lost $9.4 billion, Merrill Lynch lost $5 billion, andLehman Brothers took a loss of $52 million, all because of losses on investments in subprime mortgages or assetsbacked by subprime mortgages. Even mortgage-backed security insurers felt the losses. In February 2008,MBIA Inc.—one of the largest insurers of mortgage-backed securities credit risk—reported a $2 billionloss for the fourth quarter of 2007, due mainly to declines in values of mortgage-backed securities it insured.

Early on, some large financial institutions were unable to survive the mortgage crisis. For example, CountrywideFinancial, the country’s largest mortgage issuer, nearly failed in the summer of 2007 due to subprime mortgagedefaults. In an effort to add liquidity, Countrywide drew down its entire $11.5 billion line of credit with otherfinancial institutions. Such an enormous and sudden drawdown sent Countrywide’s shares down from $24.46 to$21.29 (and down 50 percent for the year) and the DJIA down 2.83 percent on fears of an increasing degradation ofthe mortgage markets and potential contagion to other financial markets. Only a $2 billion equity investment byBank of America in 2007 and then an acquisition offer in 2008 kept this financial institution alive. Another earlycasualty of the financial crisis was IndyMac Bank, the ninth-largest mortgage lender in the country in 2007, whichwas seized by the FDIC in July 2008. At that time, IndyMac had more than $32 billion in assets, making it one ofthe largest savings institutions in the U.S. In late 2007 and early 2008, with mounting defaults on its mortgages,

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IndyMac was desperate for more capital, but it could not find investors willing to put new funds into what appearedto be a failing institution. So in the summer of 2008, despite FDIC insurance coverage, depositors withdrew a totalof $1.3 billion, and the FDIC stepped in to rescue the institution. At a cost to the FDIC of between $8.5 billion and$9.4 billion, IndyMac represented the largest depository institution failure in more than 20 years.

The Failure of Bear StearnsIn the early 2000s, investment banks and securities firms were major purchasers of mortgages and mortgage-backedsecurities. Packaging loans as securities allowed them to increase their business. It followed that as mortgagedefaults increased in the mid-2000s, investment banks were particularly hard hit with huge losses on the mortgagesand securities backing them. A prime example of the losses incurred is that of Bear Stearns, at one time the fifthlargest investment bank in the United States. In the summer of 2007, two Bear Stearns funds suffered heavy losseson investments in the subprime mortgage market. The two funds filed for bankruptcy in the fall of 2007. BearStearns’s market value was hurt badly from these losses. The losses became so great that in March 2008 JPMorganChase and the Federal Reserve stepped in to rescue the bank before it failed or was sold piecemeal to variousfinancial institutions. JPMorgan Chase purchased Bear Stearns for $236 million, or $2 per share. Three days prior tothe purchase, Bear Stearns’s stock was selling for $30 per share, and it was selling for $170 less than a year earlier.

Along with brokering the sale of Bear Stearns to JPMorgan Chase, in the spring of 2008, the Federal Reserve Bank(the Fed) took a series of unprecedented steps. First, for the first time the Fed lent directly to Wall Street investmentbanks through the Primary Dealer Credit Facility (PDCF). In the first three days, securities firms borrowed anaverage of $31.3 billion per day from the Fed. Second, the Fed cut interest rates sharply, including one cut on aSunday night in March 2008. The widening regulatory arm of the Fed came amid criticism aimed at the SEC (U.S.Securities and Exchange Commission, traditionally the main regulator of investment banks) and its oversight ofBears Stearns before its collapse. The Fed was now acting as a lender to various financial institutions beyonddepository institutions.

The Crisis HitsSeptember 2008 marked a crucial turning point in the financial crisis. On September 8, the U.S. government seizedFannie Mae and Freddie Mac, taking direct responsibility for these two government-sponsored agencies. Theseagencies provided funding for about three-quarters of new home mortgages written in the United States and weredeeply involved in the market that securitizes subprime mortgages. The two firms recorded approximately $9 billionin losses in the last half of 2007 related to the market for subprime mortgage-backed securities. With theseizure, the two companies were put under a conservatorship. (Today they continue to operate withmanagement under the control of their previous regulator, the Federal Housing Finance Agency.)

On Monday, September 15, Lehman Brothers (the 158-year-old investment bank) filed for bankruptcy. MerrillLynch, rather than face bankruptcy, allowed a sale to Bank of America. AIG (one of the world’s largest insurancecompanies) met with federal regulators to raise desperately needed cash. Washington Mutual (the largest savingsinstitution in the U.S.) sought a buyer to save it from failing. A sense of foreboding gripped Wall Street. As newsspread that Lehman Brothers would not survive, FIs moved to disentangle trades made with Lehman. The Dow fellmore than 500 points, the largest drop in over seven years (see Figure 6A.1).

By Wednesday, September 17, tension had mounted around the world. Stock markets saw huge swings in value asinvestors tried to sort out who might survive (markets throughout Europe were forced to suspend trading as stockprices plunged). Money market mutual fund withdrawals skyrocketed: fund investors pulled out a record $144.5billion through Wednesday (redemptions during the week of September 8 totaled just $7.1 billion) as investorsworried about the safety of even these safest investments. Money market mutual funds participated heavily in the$1.7 trillion commercial paper market, which provided a bulk of the short-term funds to corporations. As investorspulled their money from these funds, the commercial paper market shrank by $52.1 billion for the week (throughWednesday). Without these funds available to meet short-term expenses, factories faced the real possibility ofshutting down and laying off employees. Likewise, without these short-term funds, banks faced the inability to fundshort-term lending units (such as credit card units).

As these events unfolded, financial markets froze, and banks stopped lending to each other at anything butexorbitantly high rates. Banks rely on each other for cash to meet their daily needs. Interest rates on interbankborrowing are generally low because of the confidence that the financial institutions will pay each other back.However, in mid-September, the overnight London Interbank Offered Rate (a benchmark rate that reflects the rate at

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which banks lend to one another) more than doubled (see Figure 6A.2). Confidence had broken down in August of2007 and had not been completely restored. Without funding, banks became reluctant to lend at all and creditmarkets froze further.

FIGURE 6A-1 The Dow Jones Industrial Average, October 2007–January 2010

FIGURE 6A-2  Overnight London Interbank Offered Rate (Libor in USD), 2001–2010

In mid-September 2008, the overnight London Interbank Offered Rate had more than doubled.

The Rescue Plan BeginsWith a financial crisis evident, on Thursday, September 18, the Federal Reserve and central banks around the world

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invested $180 billion in global financial markets in an attempt to unfreeze credit markets. U.S. Treasury SecretaryHenry Paulson met with Congressional leaders to devise a plan to get bad mortgage loans and mortgage-backedsecurities off balance sheets of financial institutions. After two weeks of debate (and one failed vote for passage), a$700 billion rescue plan was passed and signed into law by President George W. Bush on October 3, 2008. The billestablished the Troubled Asset Relief Program (or TARP), which gave the U.S. Treasury funds to buy “toxic”mortgages and other securities from financial institutions. The federal government was mandated to take an equitystake and executive compensation was limited in the companies that took part in the TARP program. The bill alsocalled for the administration to develop a plan to ease the wave of home foreclosures by modifying loans acquiredby the government and increased FDIC deposit insurance to $250,000 from $100,000.

The Crisis Spreads WorldwideAs the U.S. government debated the rescue plan, the financial crisis continued to spread worldwide. During the lastweek of September and first week of October 2008, the German government guaranteed all consumer bank depositsand arranged a bailout of Hypo Real Estate, the country’s second largest commercial property lender. The UnitedKingdom nationalized mortgage lender Bradford & Bingley (the country’s eighth largest mortgage lender) andraised deposit guarantees from $62,220 to $88,890 per account. Ireland guaranteed deposits and debt of its six majorfinancial institutions. Iceland rescued its third largest bank with an $860 million purchase of 75 percent of the bank’sstock, a few days later it seized the country’s entire banking system. Central governments of The Netherlands,Belgium, and Luxembourg together agreed to inject $16.37 billion into Fortis NY (Europe’s first ever cross-borderfinancial services company) to keep it afloat. However, five days later this deal fell apart and the bank was split up.The central bank in India stepped in to stop a run on the country’s second largest bank, ICICI Bank, by promising topump in cash. Central banks in Asia injected cash into their banking systems as banks’ reluctance to lend to eachother, and a run on Bank of East Asia Ltd. led the Hong Kong Monetary Authority to inject liquidity into its bankingsystem. South Korean authorities offered loans and debt guarantees to help small and midsize businesses with short-term funding. All of these actions were a result of the spread of the U.S. financial market crisis to world financialmarkets.

After the Rescue PlanIn the two months after the TARP rescue plan was enacted in the United States, the financial crisis deepened as theworld feared that the initial attempts to rescue the world’s financial system would not be sufficient. Worldwide,stock market values plunged. By mid-October the Dow had dropped 24.7 percent in less than a month, the ShanghaiComposite had dropped 30.4 percent, and the various markets in Europe fell between 20 and 30 percent. By mid-November, the Dow fell to a 5½-year low and the S&P 500 index erased its gains from the previous 10 years. Third-quarter GDP in the United States declined to −2.7 percent. Indeed, some measures of economic activity found theUnited States entered a recession as early as December 2007. The United Kingdom and Germany also saw growthdecline by 0.5 percent in the third quarter of 2008. Countries across the world saw companies scrambling for creditand cutting their growth plans. Additionally, consumers worldwide reduced their spending as the value of theirinvestments shrank. Even China’s booming economy slowed faster than had been predicted, from 10.1 percent in thesecond quarter of 2008 to 9.0 percent in the third quarter. This was the first time since 2002 that China’s growth wasbelow 10 percent and dimmed hopes that Chinese demand could help keep world economies going. In late October,the global crisis hit the Persian Gulf as Kuwait’s central bank intervened to rescue Gulf Bank, the first bank rescuein the oil-rich gulf. Until this time, the area had been relatively immune to the world financial crisis. However,plummeting oil prices (which had dropped over 50 percent between July and October) left the area’s economiessuddenly vulnerable.

Between January and November 2008, 22 U.S. banks failed, up from 3 in all of 2007. The FDIC reported that itadded 54 banks to its list of troubled institutions in the third quarter, a 46 percent increase over the second quarter.Additions to the list reflected the escalating problems in the banking industry. However, it should be noted that the171 banks on the FDIC’s problem list represented only about 2 percent of the nearly 8,500 FDIC-insuredinstitutions. Still, the increase from 117 troubled banks in the second quarter was the largest seen since late 1995. Inwhat came to be known as the “too big to fail” category, commercial banking giant Citigroup required a massivegovernment guarantee against losses (up to $306 billion) and a $20 billion injection of cash to prevent failure. Bythe middle of November it became apparent that the rescue plan enacted in early October actually would not be

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sufficient. Even more distressed financial and nonfinancial companies and consumers called for assistance.

Among the largest companies in need of a bailout were the Big Three automobile manufacturers (General Motors,Ford, and Chrysler). The leaders of these companies painted a grim picture of their financial position during twodays of Congressional hearings, warning that the collapse of the auto industry could lead to the loss of 3 million jobsnationwide. Both General Motors and Chrysler said they could collapse in weeks. However, automakers ran intoresistance from House lawmakers, who chastised the executives for fighting tougher fuel-efficiency standards in thepast and questioned their use of private jets while at the same time seeking government handouts. Fearing that theBig Three would take any bailout money and continue the same “stupid” decisions they had been making for25 years, the U.S. Senate canceled plans for a vote on a bill to take $25 billion in new auto industry loans out of the$700 billion TARP rescue fund. Lawmakers gave the three automakers until mid-December to come back withsubstantial business plans outlining what they would do with any federal funds that might be lent and how theywould restructure and improve the efficiency in their respective companies. After more days of testimony in mid-December, the U.S. Senate again failed to vote on a bailout for the automakers. General Motors and Chrysler statedthat they did not have sufficient funds to continue operations through the end of December. Then on December 19,2008, President Bush announced that $13.4 billion in federal loans would be made immediately available to GeneralMotors and Chrysler.

By the end of December, nearly $7 trillion of loans or commitments had been made (Table 6A.1 outlines the majorcommitments, loans, and investments made by the U.S. government through 2009). The U.S. Treasury had used thefirst $362 billion of TARP money: $250 billion of the $700 billion bailout money to inject capital intobanks ($125 billion of which went to the nine largest banks), another $40 billion to further stabilize insurerAIG, $25 billion to stabilize Citigroup, $20 billion to Bank of America, $20 billion used by the Fed to stabilize otherlending institutions, and $24.9 billion lent to the auto industry. Note that the Treasury had dropped the original plansto use TARP bailout money to buy troubled mortgage assets from financial institutions, stating that it was no longerthe most effective way to restart credit markets. Rather, plans were to take equity stakes in financial institutions.

▼ TABLE 6A.1 Federal Government Rescue Efforts through December 2009

Program Committed Invested Description

TARP $700.0billion$356.2billion

Financial rescue plan aimed atrestoring liquidity to financial markets

AIG 70.0b 69.8b

Auto industry financing 80.1b 77.6b

Capital Purchase Program 218.0b 204.7b

Public–Private Investment Program 100.0b 26.7b

Targeted investments to Citigroup andBank of America

52.5b 45.0b

Amount repaid $118.5billion

Federal Reserve Rescue Efforts $6.4trillion$1.5trillion

Financial rescue plan aimed atrestoring liquidity to financial markets

Asset-backed commercial papermoney market mutual fund liquidityfacility

Unlimited $0.0

Bear Stearns bailout 29.0b 26.3b

Commercial paper funding facility 1.8t 14.3b

Foreign exchange dollar swaps Unlimited 29.1b

GSE (Fannie Mae and Freddie Mac)debt purchases

200.0b 149.7b

GSE mortgage-backed securitiespurchases 1.2t 775.6b

Term asset-backed securities loan

facility 1.0t 43.8b

U.S government bond purchase 300.0b 295.3b

Federal Stimulus Programs $1.2trillion$577.8billion

Programs designed to save or createjobs

Economic Stimulus Act 168.0b 168.0b

Student loan guarantees 195.0b 32.6b

American Recovery and ReinvestmentAct

787.2b 358.2b

American International Group $182.0billion$127.4billion

Bailout to help AIG throughrestructuring, get rid of toxic assets

Asset purchases 52.0b 38.6b

Bridge loan 25.0b 44.0b

TARP investment 70.0b 44.8b

FDIC Bank Takeovers $45.4billion$45.4billion

Cost to FDIC to fund deposit losses onbank failures

2008 failures 17.6b 17.6b

2009 failures 27.8b 27.8b

Other Financial Initiatives $1.7trillion$366.4billion

Other programs designed to rescuethe financial sector

NCUA bailout of U.S.

Central Credit Union 57.0b 57.0b

Temporary Liquidity GuaranteeProgram

1.5t 308.4b

Other Housing Initiatives $745.0billion$130.6billion

Other programs intended to rescue thehousing market and prevent homeforeclosures

Fannie Mae and Freddie Mac bailout 400.0b 110.6b

FHA housing rescue 320.b 20.0b

Overall Total $11.0trillion$3.0trillion

Some Bright SpotsWhile the economy remained in crisis, some positive developments occurred between September and December2008. Oil, which rose to over $142 per barrel in July, had dropped to below $40 in late 2008. As a result, gas prices,which rose to over $4.00 per gallon in the summer of 2008, had fallen to a national average of $1.65 in December.Led by a federal government push, many banks moved to restructure delinquent mortgage loans rather thanforeclose. Fannie Mae and Freddie Mac suspended foreclosures on 16,000 homes over the 2008 holiday periodwhile they evaluated whether the borrowers would qualify for the new loan modification programs. Fannie andFreddie’s modification plan allowed mortgage restructuring, rather than foreclosure, for homeowners whosemortgages were held by one of the two companies, were at least three months behind on their payments, and whosemortgage payments were no more than 38 percent of the homeowner’s pretax monthly income. The FederalReserve’s attempt to stabilize the housing market resulted in a drop in long-term mortgage rates (30-year fixed-ratemortgage rates dipped to below 5.0 percent in late November). In a historic move, on December 17, 2008, the Fedunexpectedly announced that it would drop its target Fed funds rate to a range between 0 and 0.25 percent and lowerits discount window rate to 0.5 percent, the lowest level since the 1940s (see Figure 6A.3). Along with thisannouncement, the Fed announced that it would continue to use all its available tools to promote economic growthand preserve price stability. This was followed by interest rate cuts in many other countries including Japan and theUnited Kingdom, as well as Hong Kong and the European Central Bank.

The Crisis Continues in 2009Despite the many efforts of regulators to stem the tide of the growing recession, the U.S. and world economies

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deteriorated further at the start of 2009. The DJIA and the S&P 500 Index had their worst January ever, falling 8.84percent and 8.57 percent, respectively. Unemployment in January hit 7.6 percent, the highest level since September1992. Also in January, employers cut 589,000 jobs, the highest monthly job losses in over 34 years. Since December2007 (as the recession began) the U.S. economy lost 3.6 million jobs, half of which were lost in the periodNovember 2008 through January 2009. Gross domestic product growth was announced, showing a drop of 5.4percent in the fourth quarter of 2008. New vehicle sales in the United States fell 37 percent in January, the industry’sworst month since 1982 and the worst January since 1963. For the first time ever, more vehicles were sold in Chinathan in the United States. Worldwide, central governments tried to grapple with the building recession. The UnitedKingdom, Belgium, Canada, Italy, and Ireland were just a few of the countries to pass an economic stimulus planand/or bank bailout plan. The Bank of England lowered its target interest rate to a record low of 1 percent, hoping tohelp the British economy out of a recession. The Bank of Canada, Bank of Japan, and Swiss National Bank alsolowered their main interest rate to 1 percent or below.

The U.S. Stimulus Plan With the U.S. economy deteriorating at its swiftest rate in history, President Obamamade good on his pre-election promise to have an economic stimulus plan approved and enacted shortly after hiselection. The House passed its version of an $819 billion stimulus package on January 28, 2009. The Senate passedan $827 billion version of a stimulus plan on February 10, 2009. After more debate and compromise, both arms ofCongress agreed on and passed the economic stimulus plan, called the American Recovery and Reinvestment Act,on February 13, 2009. The plan devoted $308.3 billion to appropriations spending, including $120 billion oninfrastructure and science and more than $30 billion on energy-related infrastructure projects. Another $267 billionwent for direct spending, including increased unemployment benefits and food stamps. Finally, $212 billion was setaside for tax breaks for individuals and businesses (Table 6A.2 lists some of the major items in the stimulus plan).

FIGURE 6A-3 Federal Funds Rate and Discount Window Rate, January 1971–January 2010

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On December 17, 2008, the Fed dropped the target Fed funds rate to a range between 0 and 0.25 percent and the discount window rate to0.5 percent.

Stabilizing the Financial System In addition to the overall economic stimulus plan, the Obama administration,including Treasury Secretary Geithner, announced a separate plan that focused on the stabilization of the financialsystem. Early 2009 saw a plunge in the DJIA (falling to a low of 6,547.05 on March 9, 2009) and, particularly, themarket values of financial institutions. Banks, including Citigroup, Bank of America, and JPMorgan Chase, tradedat less than their book values as investors had little confidence in the value of their assets. Through February 13,2009, 13 U.S. banks had already failed in 2009, while 25 had failed in all of 2008 (the highest annual total since1993). The plan, announced on February 10, 2009, involved a number of initiatives, including

Injecting capital into banks.

Offering federal insurance to banks against losses on bad assets.Buying distressed mortgages from banks.

Helping homeowners avoid foreclosure.Giving the FDIC power to help troubled financial firms other than depository institutions.

▼ TABLE 6A.2 The $787 Billion Stimulus Program as Passed by the U.S. Congress, February 13, 2009

$116.1b Tax cuts and credits to low- and middle-income workers69.8b Middle income taxpayers to get an exemption from the alternative minimum tax87.0b Medicaid provisions27.0b Jobless benefits extension to a total of 20 weeks on top of regular unemployment compensation17.2b Increase in student aid

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40.6b Aid to states30.0b Modernization of electric grid and energy efficiency19.0b Payments to hospitals and physicians who computerize medical record systems29.0b Road and bridge infrastructure construction and modernization18.0b Grants and loans for water infrastructure, flood prevention, and environmental cleanup17.2b Increases in student aid

The plan also proposed expanding the Fed’s Term Asset-Backed Securities Loan Facility (TALF). The TALFcombined capital provided by the TARP with funding from the Federal Reserve in order to promote lending byincreasing investor demand for securitized loans. The TALF significantly expanded the availability and reduced thecost of term financing for investors in derivative securities. The goal of TALF was to stimulate demand for thesesecurities and thereby allow originators of securitized loans to lower the cost and increase the availability of credit toconsumers and businesses. The Fed’s TALF program initially provided financing for investors to purchase securitiesbacked by consumer loans. The Treasury wanted to expand this beyond consumer loans. For homeowners, thebanking plan called for the creation of national standards for loan modifications and for the use of tax dollars to givemortgage companies an incentive to modify mortgage loans. Further, along with the expanded TALF program, theTreasury, working with the Federal Reserve, FDIC, and private investors, created the Public–Private InvestmentFund (PPIF) to acquire real estate–related off-balance-sheet assets. By selling to PPIF, financial institutions couldreduce balance sheet risk, support new lending, and help improve overall market functioning. Finally, in lateFebruary 2009, the Obama administration announced that it would conduct a “stress test” of the 19 largest U.S.banks. This instrument would measure the ability of these banks to withstand a protracted economic slump, with anunemployment rate above 10 percent and home prices dropping another 25 percent. Results of the stress test showedthat 10 of the 19 banks needed to raise a total of $74.6 billion in capital. Within a month of the May 7, 2009, releaseof the results, the banks had raised $149.45 billion of capital.

The Economy Begins to RecoverThroughout the spring of 2009, the federal government continued to take actions to combat the stagnant economy.These included actions such as passage (in May 2009) of the Job Creation through Entrepreneurship Act to helpsmall businesses access capital and credit markets. The Cash for Clunkers Program (in June 2009) to stimulateautomobile sales was wildly popular.

By the summer and fall of 2009 the economy slowly began to recover. Pending home sales and residentialconstruction both posted significant increases in September. September marked the eighth consecutive monthlyincrease in pending home sales, which was the longest such streak since 1991, when this data began to be tracked.Home sales rose at an annual rate of 6.1 percent in September (21.2 percent ahead of their September 2008 level).Meanwhile, the Commerce Department reported that residential construction spending increased at a 3.9 percentannual rate in September. It was the third consecutive monthly increase in residential construction. TheNational Association of Realtors announced that the number of signed contracts increased for the ninthconsecutive month to the biggest year-over-year gain in the history of the index—31.8 percent higher thanSeptember 2008. These signs of life in the construction industry were an indication that the first-time HomebuyerTax Credit, put in place as part of the American Recovery and Reinvestment Act, was working. Indeed, inNovember 2009, President Obama signed into law an expanded Homebuyer Tax Credit that extended the tax creditof up to $8,000 for qualified first-time home buyers and $6,500 for repeat home buyers purchasing a principalresidence.

Third-quarter 2009 GDP increased by 2.2 percent and fourth-quarter GDP rose 5.7 percent. This increase was thefirst since the second quarter of 2008. The increases were the result of consumer spending, which increasedsignificantly. Spending on new cars and trucks was a big contributor (adding 1.45 percent to the third-quarterchange), reflecting the federal Cash for Clunkers program in effect in July and August. The increase in GDP in thefourth quarter primarily reflected increases in private inventory investment, exports, and personal consumptionexpenditures. Automobile output continued to do well, adding 0.61 percent to the fourth-quarter change in GDP.With the positive economic news, on October 14, 2009, the DJIA reached 10,000 for the first time in a year. Still,unemployment lagged, exceeding 10 percent in October 2009. But this rate was short-lived, as the unemploymentrate dropped below 10 percent in November 2009 and job losses began to decline sharply, with only 11,000American jobs lost in November 2009, compared to 741,000 jobs lost in December 2008.

There were 140 failures of banks in 2009, with assets totaling $170.9 billion. The five largest bank failures wereBankUnited ($12.5 billion in assets), Colonial Bank ($25 billion in assets), Guaranty Bank ($13 billion in assets),

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United Commercial Bank ($11.2 billion in assets), and AmTrust Bank ($12 billion in assets). The cost to the FDICfor resolving these failures was $27.5 billion. Compare this with statistics for 2008, when there were 25 bankfailures with assets totaling $373.6 billion.In December 2009, the Obama Administration announced that the long-term cost of the Troubled Asset ReliefProgram would be at least $200 billion less than previously projected, which would help bring down the projectedfederal budget deficit. Throughout 2010 and into 2012, the economy was still fragile and had certainly not recoveredfrom the extreme financial crisis, but it was stabilizing.

Finally, in July 2010, the U.S. Congress passed, and President Obama signed, the 2010 Wall Street Reform andConsumer Protection Act which sought to prevent a repeat of the market meltdown. Touted as the most extensiveproposal for the overhaul of financial rules since the Great Depression, this bill proposed a sweeping overhaul of thenation’s financial system and the rules that govern it. The bill called for the Federal Reserve to receive newoversight powers and to impose conditions designed to discourage any type of financial institution from getting toobig. The proposals put the Federal Reserve in charge of monitoring the country’s biggest financial firms—thoseconsidered critical to the health of the system as a whole. Those firms would also face new, stiffer requirements onhow much capital and liquidity they keep in reserve. The proposed overhaul also provided unprecedented powers tothe Fed to step into any financial institution—such as insurance giant AIG (whose main regulators include the NewYork State Department of Insurance and the Office of Thrift Supervision)—that is facing imminent collapse, inorder to force an orderly bankruptcy that would protect the wider economy.

More specifically, the bill set forth reforms to meet five key objectives:

1. Promote robust supervision and regulation of financial firms by establishing (i) a new Financial ServicesOversight Council of financial regulators (chaired by Treasury and including the heads of the principal federalfinancial regulators as members) to identify emerging systemic risks and improve interagency cooperation; (ii) anew authority for the Federal Reserve to supervise all firms that could pose a threat to financial stability,even those that do not own banks; (iii) stronger capital and other prudential standards for all financialfirms, and even higher standards for large, interconnected firms; (iv) a new National Bank Supervisor to superviseall federally chartered banks; (v) elimination of the federal thrift charter for thrifts not dedicated to mortgage lendingand other loopholes that allowed some depository institutions to avoid bank holding company regulation by theFederal Reserve; and (vi) the registration of advisers of hedge funds and other private pools of capital with the SEC.

2. Establish comprehensive supervision of financial markets by establishing (i) the regulation of securitizationmarkets, including new requirements for market transparency, stronger regulation of credit rating agencies, and arequirement that issuers and originators retain a financial interest in securitized loans; (ii) comprehensive regulationof all over-the-counter derivatives; and (iii) new authority for the Federal Reserve to oversee payment, clearing, andsettlement systems.

3. Protect consumers and investors from financial abuse by establishing (i) a new Consumer Financial ProtectionAgency to protect consumers across the financial sector from unfair, deceptive, and abusive practices; (ii) strongerregulations to improve the transparency, fairness, and appropriateness of consumer and investor products andservices; and (iii) a level playing field and higher standards for providers of consumer financial products andservices, whether or not they are part of a bank.

4. Provide the government with the tools it needs to manage financial crises by establishing (i) a new regime toresolve nonbank financial institutions whose failure could have serious systemic effects and (ii) revisions to theFederal Reserve’s emergency lending authority to improve accountability.

5. Raise international regulatory standards and improve international cooperation by establishing internationalreforms to support our efforts in the United States, including strengthening the capital framework, improvingoversight of global financial markets, coordinating supervision of internationally active firms, and enhancing crisismanagement tools.

NotesCHAPTER 61 Often the Fisher effect formula is written as (1 + i ) = (1 + IP ) × (1 + RFR ), which, when solved for i, becomes: i = Expected IP + RFR +

(Expected IP × RFR), where Expected IP × RFR is the inflation premium for the loss of purchasing power on the promised nominalinterest rate payments due to inflation. For small values of Expected IP and RFR this term is negligible. The approximation formula

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used here assumes these values are small.

2 This section, which contains more technical details, may be included or dropped from the chapter reading, depending on the rigor of thecourse.

3 That is, E (4 r 1) > E (3 r 1) > E (2 r 1) > 1 R 1 .

4 In general, the price and yield on a bond are inversely related. Thus, as the price of a bond falls (become cheaper), the demand for thebond will rise. This is the same as saying that as the yield on a bond rises, it becomes cheaper and the demand for it increases. SeeChapter 7.

5 This section, which contains more technical details, may be included in or dropped from the chapter reading depending on the rigor ofthe course.

chapter sevenValuingBonds

©DNY59/Getty Images

H

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ow important are bonds and the bond market to a capitalist economy? Those unfamiliar with thefinancial markets may have the impression that the stock market dominates capital markets in theUnited States and in other countries. Stock market performance appears constantly on 24-hour TV

news channels and on the evening news. By contrast, we seldom hear any mention of the bond market.While bonds may not generate the same excitement that stocks do, they are an even more importantcapital source for companies, governments, and other organizations. The bond market is actually largerthan the stock market. At the end of 2015, the U.S. bond market represented roughly $39.6 trillion inoutstanding debt obligations. At the same time, the market value of all common stock issues was worthjust over half of the value of the bond market, at roughly $21.0 trillion.

Bonds also trade in great volume and frequency. During 2015, the total average daily trading in alltypes of U.S. bonds reached over $730 billion. Investors are often attracted to the stock market because itoffers the potential for high investor returns—but great risks come with that high potential return. Whilesome bonds offer safer and more stable returns than stocks, other bonds also offer high potential rewardsand, consequently, higher risk.

In this chapter, we will explore bond characteristics and their price dynamics. You will see that bondpricing uses many time value of money principles that we’ve used in the preceding chapters. ■

LEARNING GOALS

LG7-1 Describe bond characteristics.LG7-2 Identify various bond issuers and their motivation for issuing debt.LG7-3 Read and interpret bond quotes.LG7-4 Compute bond prices using present value concepts.LG7-5 Explain the relationship between bond prices and interest rates.LG7-6 Compute bond yields.LG7-7 Find bond ratings and assess credit risk’s effects on bond yields.LG7-8 Assess bond market performance.

viewpointsbusiness APPLICATIONYou are the chief financial officer (CFO) for Beach Sand Resorts. The firm needs $150 million of new capital to renovate a hotelproperty. As you discuss the firm’s plans with a credit rating agency, you learn that if 15-year bonds are used to raise this capital, thebonds will be rated BB and will have to offer a 7 percent return. How many bonds will you have to issue to raise the necessarycapital? What semiannual interest payments will Beach Sand have to make? (See the solution at the end of the book.)

7.1 • BOND MARKET OVERVIEW LG7-1Bond CharacteristicsBonds are debt obligation securities that corporations, the federal government or its agencies, or states and localgovernments issue to fund various projects or operations. All of these organizations periodically need to raise capitalfor various reasons, which was formally discussed in Chapter 6. Bonds are also known as fixed-income securitiesbecause bondholders (investors) know both how much they will receive in interest payments and when theirprincipal will be returned. From the bond issuer’s point of view, the bond is a loan that requires regular interestpayments and an eventual repayment of the borrowed principal. Investors—often pension funds, banks, and mutualfunds—buy bonds to earn investment returns. Most bonds follow a relatively standard structure. A legal contractcalled the indenture agreement outlines the precise terms between the issuer and the bondholders. Any bond’s main

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characteristics include:

bond Publicly traded form of debt.

fixed-income securities Any securities that make fixed payments.

principal Face amount, or par value, of debt.

indenture agreement Legal contract describing the bond characteristics and the bondholder and issuer rights.

The date the principal will be repaid (the maturity date).

maturity date The calendar date on which the bond principal comes due.

The par value, or face value, of each bond, which is the principal loan amount that the borrower must repay.

par value Amount of debt borrowed to be repaid; face value.

The coupon (interest) rate.

A description of any property to be pledged as collateral.Steps that the bondholder can take in the event that the issuer fails to pay the interest or principal.

Table 7.1 describes par value and other bond characteristics. Most bonds have a par value of $1,000. This is theamount of principal the issuer has promised to repay. Bonds have fixed lives. The bond’s life ends when the issuerrepays the par value to the buyer on the bond’s maturity date. Although a bond will mature on a specific calendardate, the bond is usually referenced by its time to maturity, that is, 2 years, 5 years, 20 years, and so on. In fact, themarket groups bonds together by their time to maturity and classifies them as short-term bonds, medium-term bonds,or long-term bonds, regardless of issuer. Long-term bonds carry 20 or 30 years to maturity. Of course, over time, the30-year bond becomes a 20-year bond, 10-year bond, and eventually matures. But other time periods to maturity doexist. For example, in 2011, the railroad company Norfolk Southern Corp. issued $400 million of bonds with 100years to maturity. The bonds have a coupon (interest) rate of 6 percent and mature in 2111.

time to maturity The length of time (in years) until the bond matures and the issuer repays the par value.

personal APPLICATIONYou would like to invest in bonds. Your broker suggests two different bonds. The first, issued by Trust Media, will mature in 2023. Itsprice is quoted at 96.21 and it pays a 5.7 percent coupon. The second bond suggested, issued by Abalon, Inc., also matures in 2023.This bond’s price is 101.94 and pays a 5.375 percent coupon. To help you decide between the bonds, you want to know how muchmoney it will cost to buy 10 bonds, what interest payments you will receive, and what return the bonds offer if purchased today. Also,you want to understand the differences between what the two bonds imply about their risk. (See the solution at the end of thebook.)

How do you even purchase a bond in the first place?

When interest rates economywide fall several percentage points (which often takes several years), homeownerseverywhere seek to refinance their home mortgages. They want to make lower interest payments (and sometimeswant to pay down their mortgage principal) every month. Corporations that have outstanding bond debt will alsowant to refinance those bonds. Sometimes the indenture contract (the legal contract between a bond issuer andbondholders) allows companies to do so; sometimes the indenture prohibits refinancing. Bonds that can berefinanced have a call feature, which means that the issuer can “call” the bonds back and repay the principal beforethe maturity date. To compensate the bondholders for getting the bond called, the issuer pays the principal and a callpremium. The most common call premium is one year’s worth of interest payments. In some indentures, the callpremium declines over time.

call An issuer redeeming the bond before the scheduled maturity date.

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call premium The amount in addition to the par value paid by the issuer when calling a bond.

The bond’s coupon rate determines the dollar amount of interest paid to bondholders. The coupon rate appears on thebond and is listed as a percentage of the par value. So a 5 percent coupon rate means that the issuer will pay 5percent of $1,000, or $50, in interest every year, usually divided into two equal semiannual payments. So a5 percent coupon bond will pay $25 every six months. Companies set the coupon rate as the prevailingmarket interest rate at the time of bond issue. The name coupon is a holdover from the past, when bonds wereactually issued with a coupon book. Every six months a bondholder would tear out a coupon and mail it to theissuer, who would then make the interest payment. These are sometimes referred to as bearer bonds (often a featureof spy or mystery movies), because whoever held the coupon book could receive the payments. Nowadays, issuersregister bond owners and automatically wire interest payments to the owner’s bank or brokerage account.Nevertheless, the term coupon persists today.

coupon rate The annual amount of interest paid expressed as a percentage of the bond’s par value.

▼ TABLE 7.1 Typical Bond Features

Characteristic Description Common Values

Par value The amount of the loan to be repaid. This is often referred to as theprincipal of the bond.

$ 1,000

Time to maturity The number of years left until the maturity date. 1 year to 30 years

Call

The opportunity for the issuer to repay the principal before the maturitydate, usually because interest rates have fallen or issuer’scircumstances have changed. When calling a bond, the issuercommonly pays the principal and one year of interest payments.

Many bonds are not callable. Forthose that are, a common feature isthat the bond can be called any timeafter 10 years of issuance.

Coupon rateThe interest rate used to compute the bond’s interest payment eachyear. Listed as a percentage of par value, the actual payments usuallyare paid twice per year.

2 to 10 percent

Bond price The bond’s market price reported as a percentage of par value. 80 to 120 percent of par value

the Math Coach on…Percent-to-Decimal Conversions

“When discussing interest rates or using them in calculator or spreadsheet time value of money functions,the value should be in percent (%) form, like 2.5%, 7%, and 11%. When using interest rates in formulas, thevalue needs to be in decimal form, like 0.025, 0.07, and 0.11.

To convert between the two forms of representing an interest rate, use

At original issue, bonds typically sell at par value, unless interest rates are very volatile. Bondholders recoup the parvalue on the bond’s maturity date. However, at all times in between these two dates, bonds might trade amonginvestors in the secondary bond market. The bond’s price as it trades in the secondary market will not likely be thepar value. Bonds trade for higher and lower prices than their par values. We’ll thoroughly demonstrate the reasonsfor bond pricing in a later section of this chapter. Bond prices are quoted in terms of percent of par value rather thanin dollar terms. Sources of trading information list a bond that traded at $1,150 as 115, and a bond that traded for$870 as 87.

bond price Current price that the bond sells for in the bond market.

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Bond Issuers LG7-2For many years, bonds were considered stodgy, overly conservative investments. Not anymore! The fixed-incomeindustry has seen tremendous innovation in the past couple of decades. The financial industry has created and issuedmany new types of bonds and fixed-income securities, some with odd-sounding acronyms, like TIGRs, CATS,COUGRs, and PINEs, all of which are securities based on U.S. Treasuries. Even with all the innovation, thetraditional three main bond issuers remain: U.S. Treasury bonds, corporate bonds, and municipal bonds. Figure 7.1shows the amount of money that these bond issuers have raised each year.

EXAMPLE 7-1 Bond Characteristics LG7-1

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Consider a bond issued 10 years ago with an at-issue time to maturityof 30 years. The bond’s coupon rate is 8 percent and it currently tradesin the bond market for 109. Assuming a par value of $1,000, what is thebond’s current time to maturity, semiannual interest payment, and bondprice in dollars?

SOLUTION:

Time to maturity = 30 years − 10 years = 20 years

Annual payment = 0.08 × $1,000 = $80, so semiannual payment is $40

Bond price = 1.09 × 1,000 = $1,090

Similar to Problems 7-1, 7-2, 7-3, 7-4, Self-Test Problem 1

FIGURE 7-1 Amount of Capital Raised Yearly from Bonds Issued by Local and Federal Government and Corporations

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Local or municipal governments, the U.S. Treasury, and corporations have issued many new types of bonds and fixed-income securities overthe past two decades.Source: Securities Industry and Financial Markets Association.

Treasury Bonds Treasury bonds carry the “full-faith-and-credit” backing of the U.S. government and investorshave long considered them among the safest fixed-income investments in the world. The federal government sellsTreasury securities through public auctions to finance the federal deficit. When the deficit is large, more bonds cometo auction. In addition, the Federal Reserve System (the Fed) uses Treasury securities to implement monetary policy.Technically, Treasury securities issued with 1 to 10 years until maturity are Treasury notes. Securities issued with 10to 30 years until maturity are Treasury bonds. Figure 7.1 shows that the number of new Treasuries being offeredactually declined in the late 1990s as the federal budget deficit declined. However, this reversed in 2002 and thendramatically accelerated in 2009 after the global financial crisis and during the years of the Fed’s quantitative easingprograms.

Corporate Bonds Corporations raise capital to finance investments in inventory, plant and equipment, researchand development, and general business expansion. As managers decide how to raise capital, corporations can issuedebt, equity (stocks), or a mixture of both. The driving force behind a corporation’s financing strategy is the desireto minimize its total capital costs. Through much of the 1990s, corporations tended to issue equity (stocks) to raisecapital. Beginning in 1998 and through 2015, corporations switched to raising capital by issuing bonds to takeadvantage of low interest rates and issued $17.1 trillion in new bonds. You can see this rise in capital reflected inFigure 7.1.

Municipal Bonds State and local governments borrow money to build, repair, or improve streets, highways,hospitals, schools, sewer systems, and so on. The interest and principal on these municipal bonds are repaid in twoways. Projects that benefit the entire community, such as courthouses, schools, and municipal office buildings, aretypically funded by general obligation bonds and repaid using tax revenues. Projects that benefit only certain groupsof people, such as toll roads and airports, are typically funded by revenue bonds and repaid from user fees. Interestpayments paid to municipal bondholders are not taxed at the federal level, or by the state for which the bond isissued.

Other Bonds and Bond-Based SecuritiesTreasury Inflation-Protected Securities (TIPS) have proved one of the most successful recent innovations in the bondmarket. The U.S. Treasury began issuing this new type of Treasury bond, which is indexed to inflation, in 1997.TIPS have fixed coupon rates like traditional Treasuries. The new aspect is that the federal government adjusts thepar value of the TIPS bond for inflation. Specifically, it increases at the rate of inflation (measured by the consumerprice index, CPI). As the bond’s par value changes over time, interest payments also change. At maturity, investorsreceive an inflation-adjusted principal amount. If inflation has been high, investors will expect that the adjustedprincipal amount will be substantially higher than the original $1,000. Consider a 10-year TIPS issued on January15, 2009, that pays a 2⅛ percent coupon. The reference CPI for these bonds is 214.69971. Four years later (onJanuary 15, 2013) the reference CPI was 230.22100. So the par value of the TIPS in early 2013 was $1,072.29 (=$1,000 × 230.22100 ÷ 214.69971). Therefore, the 2⅛ percent coupon (paid semiannually) would be $11.39 =(0.02125 × $1,072.29 ÷ 2). A TIPS total return comes from both the interest payments and the inflation adjustmentto the par value.

Treasury Inflation-Protected Securities TIPS are U.S. government bonds where the par value changes with inflation.

U.S. government agency securities are debt securities issued to provide low-cost financing for desirable private-sector activities such as home ownership, education, and farming. Fannie Mae, Freddie Mac, Student LoanMarketing Association (Sallie Mae), Federal Farm Credit System, Federal Home Loan Banks, and the SmallBusiness Administration, among others, issue these agency bonds to support particular sectors of the economy.Agency securities do not carry the federal government’s full-faith-and-credit guarantee, but the government hasnever let one of its agencies fail. Because investors believe that the federal government will continue in thiswatchdog role, agency bonds are thought to be very safe and may provide a slightly higher return than Treasurysecurities do.

agency bonds Bonds issued by U.S. government agencies.

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EXAMPLE 7-2 TIPS Payments LG7-2

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

A TIPS bond was issued on July 15, 2006, that pays a 2½ percentcoupon. The reference CPI at issue was 201.95. The reference CPI forthe following interest payments were

January 2009 214.70

July 2009 213.52

January 2010 216.25

Given these numbers, what is the par value and interest payment of theTIPS on the three interest-payment dates? What is the total return fromJanuary 2009 to January 2010?

SOLUTION:

Compute the TIPS index ratio for each period as current CPI divided bythe at-issue CPI: The par value for January 2009 is $1,000 × 214.70 ÷201.95 = $1,063.13, so the interest payment is 0.025 × $1,063.13 ÷ 2 =$13.29. The answers for the next two dates are:

July 2009 Par value = $1,057.29 Interest payment = $13.22

January 2010 Par value = $1,070.81 Interest payment = $13.39

The capital gain between January 2009 and January 2010 is $1,070.81− $1,063.13 = $7.68. Adding the two interest payments together resultsin $26.61 (= $13.22 + $13.39). Thus, the total return is 3.23% = ($7.68+ $26.61 )/$ 1,063.13.

Similar to Problems 7-7, 7-8, 7-19, 7-20, 7-33, 7-34

finance at work //: personal financeBuy Treasuries Direct!

©Comstock Images/Jupiter Images

Treasury bonds are U.S. government-issued debt securities that investors trade on secondary markets. The government also issuesnonmarketable debt, called “savings bonds,” directly to investors. The common EE savings bonds, introduced in 1980, do not payregular interest payments. Instead, interest accrues and adds to the bond’s value. After a one-year holding period, they can beredeemed at many banks or credit unions. You can also purchase savings bonds and other Treasury securities (bills, notes, bonds, andTIPS) electronically through the U.S. Treasury’s website, treasurydirect.gov. You can set up an account in minutes and buy savingsbonds with cash from your bank account. You can also redeem your bonds and transfer the proceeds back to your bank account. Bondscan be purchased 24 hours a day, 7 days a week at no cost.

When bondholders redeem savings bonds, they receive the original value paid plus the accrued interest. Paper bonds sell at half ofthe face value; if investors hold them for the full 30 years, they receive the par value. Investors buy electronic bonds at face value andearn interest in addition to the par value. Unlike other bonds, savers need not report income from these interest payments to the IRSuntil they actually redeem the bonds. So savings bonds count as tax-deferred investments.

About one in six Americans owns savings bonds. Savings bonds are used for a variety of purposes, such as personal savingsinstruments or gifts from grandparents to grandchildren. After the September 11, 2001, terrorist attacks, many Americans wanted toshow support for the government. In December 2001, banks selling government EE savings bonds began printing “Patriot bond” onthem. So EE savings bonds are now often called Patriot Bonds.

Want to know more?Key Words to Search for Updates: TreasuryDirect (go to www.treasurydirect.gov)

U.S. government agencies invented one popular type of debt security: mortgage-backed securities (MBSs). Fannie Maeand Freddie Mac offer subsidies or mortgage guarantees for people who wouldn’t otherwise qualify for mortgages,especially first-time homeowners. Fannie Mae started out as a government-owned enterprise in 1938 and became apublicly held corporation in 1968. Freddie Mac was chartered as a publicly held corporation at its inception in 1970.Since 2008, both have been in government conservatorship and run by the Federal Housing Finance Agency. Toincrease the amount of money available (liquidity) for the home mortgage market, Fannie Mae and Freddie Macpurchase home mortgages from banks, credit unions, and other lenders. They combine the mortgages into diversifiedportfolios of such loans and then issue mortgage-backed securities, which represent a share in the mortgage debt, toinvestors. As homeowners pay off or refinance the underlying portfolio of mortgage loans, MBS investors receiveinterest and principal payments. After selling mortgages to Fannie Mae or Freddie Mac, mortgage lenders have“new” cash to provide more mortgage loans. This process worked well for decades until the late 2000s, whensubprime mortgages were given to people who couldn’t afford them. As you know, defaults on these loans were theunderpinnings of the financial crisis.

mortgage-backed securities Securities that represent a claim against the cash flows from a pool of mortgage loans.

We could apply the same concept to any type of loan; indeed, the financial markets have already invented manysuch pooled-debt securities. Typical examples include credit card debt, auto loans, home equity loans, andequipment leases. Like mortgage-backed securities, investors receive interest and principal from asset-backed

page 206securities as borrowers pay off their consumer loans. The asset-backed securities market is one of thefastest-growing areas in the financial services sector.

asset-backed securities Debt securities whose payments originate from other loans, such as credit card debt, auto loans, and homeequity loans.

On the bond’s maturity date, the bondholder receives the par value, which is typically $1,000. However, somecorporate bonds give the bondholder a choice between the par value and a specified number of shares of stock. Thistype of bond is referred to as a convertible bond because it can be converted to company stock. The number of sharesof stock for which the bond can be converted is specified when the bond is originally issued. Thus, the bondholderwill want to receive the shares when the stock price has risen since bond issuance, and they will want the $1,000when the stock has declined in value. Although the bondholder can convert to the stock shares anytime, investorstend to wait until the maturity date when the interest payments from the bond exceed the dividends that would bepaid from the stock shares.

convertible bond A debt security that can be converted to shares of stock or another type of security.

finance at work //: marketsMortgage-Backed Securities and Financial Crisis

©Andy Dean Photography/Alamy

In the old days, a bank with $100,000 to lend would fund a mortgage and charge a fee for originating the loan. The bank would thencollect interest on the loan over time. In the past few decades, the process changed to where that bank could sell that mortgage toinvestment banks and get the $100,000 back. The bank could then originate another mortgage and collect another fee. Bank revenuetransitioned from interest earnings to fee earnings. This worked pretty well for several decades because the bank made more profits andmore money was funneled into the community for home buyers. It is the securitization of debt that makes this possible. Financialinstitutions like Fannie Mae and investment banks bought up these mortgages, pooled them, and issued bonds against them (calledmortgage-backed securities, or MBSs) to sell to investors. In effect, buyers of the MBSs are the actual lenders of the mortgage andbanks simply earned fees for servicing the loans.

Note that this lending model gives banks and mortgage brokers the incentive to initiate as many mortgage loans as they can resell tomaximize fee income. Then in 2000 to early 2004, the Federal Reserve kept adjusting interest rates on federal funds downward and keptthem low. This both made home ownership more affordable, sparking a housing bubble, and drove investors to look for bonds that paidhigher yields. Consequently, many loans were granted to individuals with poor creditworthiness (subprime borrowers). These subprimeborrowers were charged higher interest rates. When these subprime mortgages were packed into the pool of mortgages, the MBSsoffered higher yields. Thus, there was a high demand from investors for these MBSs, which fostered more poor credit quality loanoriginations.

Then from July 2004 to July 2006, the Federal Reserve started increasing interest rates. This placed some downward pressure onhousing prices because it made homes less affordable. At the same time, most subprime mortgages originating from 2005 and 2006were written on adjustable rates, and those interest rates adjusted upward too, making the payments too high for many borrowers. Thesubprime borrowers soon began to fall behind on their monthly payments leading to foreclosures and additional downward pressure onhousing prices. The devaluation of housing prices eroded the home equity of homeowners and led to further foreclosures and furtherprice decreases. The MBSs also devalued quickly.

Who owned MBSs? It turns out that the owners of these securities were financial firms, such as investment banks, commercial

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banks, insurance companies, mutual funds, and pension funds all over the world. Their weakened financial strength led to bank failures,bailouts, and a global credit crisis.

Want to know more?Key Words to Search for Updates: subprime, MBS, financial crisis

Further Reading: John W. Schoen, “7 years on from crisis, $150 billion in bank fines and penalties,” CNBC, April 30, 2015.http://www.cnbc.com/2015/04/30/7-years-on-from-crisis-150-billion-in-bank-fines-and-penalties.html

Reading Bond Quotes LG7-3To those familiar with bond terminology, bond quotes provide all of the information needed to make informedinvestment decisions. The volume of Treasury securities traded each day is substantial. Treasury bonds and notesaverage more than a half billion dollars in trading daily. Investors exhibit much less enthusiasm for corporate ormunicipal bonds, perhaps because the markets for each particular bond or bonds with the same maturity, couponrate, and credit ratings are much thinner and, therefore, less liquid. Most bond quote tables report only a smallfraction of the outstanding bonds on any given day. Bond quotes and data can be found in The Wall Street Journaland online at places like Yahoo! Finance (finance.yahoo.com). Table 7.2 shows three bond quote examples.

A typical listing for Treasury bonds appears first. Here, this Treasury bond pays bondholders a coupon of 2.750percent. On a $1,000 par value bond, this interest income would be $27.50 annually, paid as $13.750 every sixmonths per bond. The bond will mature in February of 2018—since this is fairly soon, the bond is considered ashort-term bond. Both the bid and the ask quotes for the bond appear, expressed as percentages of the bond’s parvalue of $1,000. The bid price is the price at which investors can sell the bond. A bid of 104.0156 means that aninvestor could sell for $1,040.156. Investors can buy this bond at the ask price of 104.0313, or $1,040.313. Since theprice is higher than the par value of the bond, the bond is selling at a premium to par because its coupon rate ishigher than current rates. Thus, investors call this kind of security a premium bond.

premium bond A bond selling for greater than its par value.

Notice that the ask price is higher than the bid price. The difference is known as the bid-ask spread. Investors buy atthe higher price and sell at the lower price. The bid-ask spread is thus the cost of actively trading bonds. Investorsbuy and sell with a bond dealer. Since the bond dealer takes the opposite side of the transaction, the dealer buys atthe low price and sells at the higher price. The bid-ask spread is part of the dealer’s compensation for taking on risk.An investor who bought this bond and held it to maturity would experience a $40.31 (= $1,040.31 − $1,000) capitalloss (−3.87 percent = −$40.31/$1,040.31]). The bond lost 0.0234 percent of its value during the day’s trading—achange of −$0.23 for a $1,000 par value bond. Last, the bond is offering investors who purchase it at the ask priceand hold it to maturity a 0.771 percent annual return.

Corporate bond quotes provide similar information. The table shows the quote for a Boeing bond that offersbondholders a coupon of 2.60 percent, or $13.00 semiannually (= $1,000 × 0.026 ÷ 2). The bond would beconsidered a mid-term bond (usually five years to maturity), since it matures in the year 2025. Corporate bonds arealso quoted in percentage of par value. The price quote of 98.400 indicates that the last trade occurred at a price of$984.00 per bond. Since the bond is selling for a price lower than its $1,000 par value, it’s called a discount bond. Aninvestor who bought this bond would reap a $16.00 (= $1,000 − $984.00) capital gain if the bond were held tomaturity. The Boeing bond represents an annual return of 2.79 percent for the investor who purchases the bond at$984.00.

discount bond A bond selling for lower than its par value.

▼ TABLE 7.2 Bond Quote Examples

Treasury Securities

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COUPON RATE MO/YR BID ASKED CHG ASK YLD

2.750 Feb 18 104.0156 104.0313 −0.0234 0.771

Corporate Bond

COMPANY COUPON MATURITY LAST PRICE YIELD

Boeing Co 2.60 October 2025 98.400 2.79

Municipal Bond

ISSUE COUPON MATURITY PRICE BID YLD

NYC Muni Wtr Fin Auth 4.500 06-15-37 97.570 4.66

Companies set a bond’s coupon rate when they originally issue the bond. A number of factors determine that couponrate:

The amount of uncertainty about whether the company will be able to make all the payments.

The term of the loan.The level of interest rates in the overall economy at the time.

Bonds from different companies carry different coupon rates because some, or all, of these determining factorsdiffer. Even a single company that has raised capital through bond issues many times may carry very differentcoupon rates on its various issues, because the bond issues would be offered in different years when the overalleconomic condition and interest rates differ.

Table 7.2 also shows a quote for a municipal bond issued by the New York City Municipal Water FinanceAuthority. This city government agency has raised capital by issuing municipal bonds to build reservoir facilities toprovide water to New York City. The bond pays a 4.500 percent coupon, and since it matures in 2037, it’sconsidered a long-term bond. According to Table 7.2, the bond is trading at a price just below par value—97.57percent. Most municipal bonds, unlike other bonds, feature a $5,000 face value rather than the typical par value of$1,000. So, the 97.57 percent price quote represents a dollar amount of $4,878.50 (= 0.9757 × $5,000). Thelow rate of return relative to Treasury bonds with similar maturities also has an explanation. Municipalbondholders do not have to pay federal income taxes on the interest payments that they receive from those securities.We explore this (sometimes) substantial advantage further in a later section of this chapter.

EXAMPLE7-3 Bond Quotes LG7-3

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

You note the following bond quotes and wish to determine each bond’s price, term, and interestpayments.

Treasury Securities

MATURITYRATE MO/YR BID ASKED CHG

9.00 Nov 20 137.5938 137.6250 −0.1563

Corporate Bond

COMPANY COUPON MATURITYLASTPRICE

LASTYIELD

Kohls Corp 7.375 Oct 15,2023

110.01 4.991

Municipal Bond

ISSUE COUPON MATURITY PRICEYLD TO

MAT

Florida StAquis &BridgeConstr

5.00 July 1,2025

106.78 4.458

SOLUTION:

The Treasury bond matures in November of 2020 and pays 9 percent interest. Investors receive cashinterest payment of $45 (= 0.09 × $1,000 ÷ 2) semiannually. Since the bond matures in less than 10years but more than 1 year, we would consider it a mid-term bond. Since no “n” appears next to thematurity date, we can also tell that the security was issued as a bond that would mature in 30 years.Investors could sell this bond for $1,375.94 (= 137.594 × $1,000) and buy it for $1,376.25 (= 1.37625× $1,000). The price fell on this particular day by $1.56 (= −0.001 5625 × $1,000). The dealer earned$0.31 (× $1,376.25 − $1,375.94) on each trade of these premium bonds.

The Kohls corporate bond pays a semiannual interest payment of $36.88 (= 0.07375 × $1,000 ÷ 2)and its price is $1,100.10 (= 1.1001 × $1,000). This premium bond’s 7.375 percent rate is likely wellabove market rates, which is why an investor would be willing to pay a premium for it.

The state of Florida issued the muni bond to fund bridge construction. With a $5,000 par value, theinterest payments are $125 (= 0.05 × $5,000 ÷ 2) every six months. The bonds are priced at$5,339.00 (= 1.0678 × $5,000).

Similar to Problems 7-9, 7-10, Self-Test Problem 1

time out!7-1 Describe the different reasons that the U.S. government, local governments, and corporations would issue bonds.7-2 What is the following bond’s price and what dollar amount will the bond pay for its semiannual interest payment?

COMPANY COUPON MATURITY PRICE YIELD

Home Depot Inc. 5.40 Mar 1, 2020 100.06 5.391

7.2 • BOND VALUATION LG7-4Present Value of Bond Cash FlowsAny bond’s value computation directly applies time value of money concepts. Bondholders know the interestpayments that they are scheduled to receive and the repayment of the par value at maturity. The current price of abond is, therefore, the present value of these future cash flows discounted at the prevailing market interest rate. Theprevailing market interest rate will depend on the bond’s term to maturity, credit quality, and tax status.

The simplest type of bond for time value of money calculations is a zero coupon bond. As you might guess from itsname, a zero coupon bond makes no interest payments. Instead, the bond pays only the par value payment at itsmaturity date. So a zero coupon bond sells at a substantial discount from its par value. For example, a bond with apar value of $1,000, maturing in 20 years, and priced to yield 6 percent, might be purchased for about $306.56. Atthe end of 20 years, the bond investor will receive $1,000. The difference between $1,000 and $306.56 (which is$693.44) represents the interest income received over the 20 years based upon the discount rate of 6 percent. Thetime line for this zero coupon bond valuation appears as

zero coupon bond A bond that does not make interest payments but generally sells at a deep discount and then pays the par value atthe maturity date.

We compute the zero’s price by finding the present value of the $1,000 cash flow received in 20 years. However, tobe consistent with regular coupon-paying bonds, zero coupon bonds are priced using semiannual compounding. Sothe formula and calculator valuation would use 40 semiannual periods at a 3 percent interest rate rather than 20periods at 6 percent. Using the present value equation of Chapter 4 results in

So the zero coupon bond’s price is indeed a steep discount to its par value. This makes sense because investorswould only buy a security that pays $1,000 in many years for a price that is much lower to make enough profit tomake up for the forgone semiannual interest payments. For comparison’s sake, instead of the 20-year zero, considera 20-year bond with a 7 percent coupon. So this 20-year maturity bond pays $35 in interest payments every sixmonths. We can think of these interest payments as an annuity stream. If the market discount rate is 6 percentannually, the time line appears as

page 210The time line shows the 40 semiannual payments (with the accompanying semiannual interest rate at 3 percent) of$35 and the par value payment at the bond’s maturity. Think through this: When bonds pay semiannualpayments, the discount rate must be a semiannual rate. Thus, the 6 percent annual rate becomes a 3 percentsemiannual rate. So we then compute the price of this bond by adding the present value of the interest paymentannuity cash flow to the present value of the future par value. A combination of the present value equations for theannuity cash flows and the value of the par redemption appear in the bond valuation equation 7-1:

(7-1)

where PMT is the interest payment, N is the number of periods until maturity, and i is the market interest rate perperiod on securities with the same bond characteristics. If this bond paid interest annually, then these variableswould take yearly period values. Since this bond pays semiannually, PMT, N, and i are all denoted in semiannualperiods. The price of this coupon bond should be

Of the $1,115.57 bond price, most of the value comes from the semiannual $35 coupon payments ($809.017) andnot the value from the future par value payment ($306.557).

Because equation 7-1 is quite complex, we usually compute bond prices using a financial calculator or computerprogram. An investor would compute the bond value using a financial calculator by entering N = 40, I = 3, PMT =35, FV = 1000, and computing the present value (PV). The calculator solution is $1,115.57.1

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EXAMPLE 7-4 Consider a 15-year bond that has a 5.5 percent coupon, paidsemiannually. If the current market interest rate is 6.5 percent, and thebond is priced at $940, should you buy this bond?

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

SOLUTION:

Compute the value of the bond using equation 7-1. Use semiannualcompounding (N = 2 × 15 = 30, i = 6.5 ÷ 2 = 3.25, and PMT = 0.055 ×$1,000 ÷ 2 = $27.50) as

So this bond’s value is $905.09, which is less than the $940 price. Thebond is overvalued in the market and you should not buy it.

Similar to Problems 7-21, 7-22, 7-23, 7-24, Self-Test Problem 1

the Math Coach on…Bond Pricing and Periods

“Since most bonds have semiannual interest payments, we must use semiannual periods to discount thecash flows. Most errors in computing a bond price occur in the adjustment for semiannual periods. The errorshappen whether you are using either the bond pricing equation or a financial calculator. To convert tosemiannual periods, be sure to adjust the three variables: number of periods, interest rate, and payments.

The number of years needs to be multiplied by 2 for the number of semiannual periods. The interest rateshould be divided by 2 for a six-month rate. Divide the annual coupon payment by 2 for the six-monthpayment. Remember to adjust all three inputs for the semiannual periods.

A coupon-paying bond’s price should hover reasonably around the par value of the bond. For a $1,000 parvalue bond, we could expect a price in the range of $700 to $1,300. If you compute a price outside this range,check to see whether you made the semiannual period adjustments correctly.„

Bond Prices and Interest Rate Risk LG7-5At the time of purchase, the bond’s interest payments and par value expected at maturity are fixed and known. Overtime, economywide interest rates change, but the bond’s coupon rate remains fixed. A rise in prevailing interest rates(also called increasing the discount rate) reduces all bonds’ values. If interest rates fall, all bonds will enjoy risingvalues. Consider that when interest rates rise, newly issued bonds offer to pay higher interest rates than the ratesoffered on existing bonds. So to sell an existing bond with its lower coupon rate, its market price must fall so thatthe buyer can expect a profit similar to that offered by newly issued bonds. Similarly, when prevailing interest ratesfall, market prices for outstanding bonds rise to bring the offered return on older bonds with higher coupon rates intoline with new issues. So market interest rates and bond prices are inversely related. That is, they move in oppositedirections.

Figure 7.2 demonstrates how the price of a 30-year Treasury bond may change over time. The 7.47 percent coupon

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exactly matched prevailing interest rates when the bond was issued in 1986. Consequently, the bond sells for its parvalue of $1,000. Shortly thereafter, interest rates quickly rose to over 9 percent. As interest rates rose, bond priceshad to decline. Then in 1988, interest rates started a prolonged descent to lows not seen for decades. Note that whilea bond is issued at $1,000 and returns $1,000 at maturity, its price can vary a great deal in between. Bond investorsmust be aware that bond prices fluctuate on a day-to-day basis as interest rates fluctuate. Note that since the bondwill only pay $1,000 when it matures, the price must converge to $1,000 at the end. The determinants of marketinterest rate levels and changes are discussed in Chapter 6. Bondholders can incur large capital gains or capitallosses.The fact that, as prevailing interest rates change, the prices of existing bonds will change has a specific name in thefinancial industry—interest rate risk. Interest rate risk means that during periods when interest rates changesubstantially (and quickly), bondholders experience distinct gains and losses in their bond inventories. But interestrate risk does not affect all bonds exactly the same. Very short-term bonds experience little or no fluctuation in theirprices, and thus expose the bondholder to little interest rate risk. Long-term bondholders experience substantialinterest rate risk. Table 7.3 illustrates the impact of interest rate risk on bonds with different coupons and times tomaturity.

interest rate risk The chance of a capital loss due to interest rate fluctuations.

The first four rows show the prices and price changes for 30-year bonds with different coupon rates. Notice that thebonds with higher coupon rates also have higher prices. Bondholders as a rule find it more valuable to receive thelarge annuity payments. Also notice that a 1 percent increase in interest rates from 6 percent to 7 percent causesbond prices to fall. Bondholders with higher coupon bonds are not affected as much by interest rate increasesbecause they can take the large coupon payments and reinvest those cash flows in new bonds that offer higherreturns.

FIGURE 7-2 A Demonstration of the Price and Market Interest Rate over Time of a 30-Year Treasury Bond Issued in 1986 with a Couponof 7.47 Percent

As interest rates rise, bond prices fall. Here you can see great variance in the economy over 30 years. Long-term bondholders experiencesubstantial interest rate risk.Source: Yahoo! Finance, finance.yahoo.com.

▼ TABLE 7.3 Interest Rate Risk

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The price decline is greater for bonds with lower coupons because of reinvestment rate risk. When interest ratesincrease, bondholders’ cash flows—both periodic payments and final payoff at maturity—are discounted at a higherrate, decreasing a bond’s value. Because the cash flows from low-coupon bonds are smaller, the holder of suchbonds will have less money available from interest payments to buy the new, higher coupon bonds. Thusbondholders of lower coupon bonds have their capital tied up in assets that are not making them as much money.They face a bad dilemma: They can sell their lower coupon bonds and take a greater capital loss, using the (smaller)proceeds to buy new bonds with higher coupon rates. Or they can continue to receive the small income paymentsand hold their lower coupon bonds to maturity to avoid locking in the capital loss. Either way, they lose moneyrelative to those bondholders with higher coupon rates. You can see this illustrated in the 30-year bonds shown inTable 7.3. Reinvestment rates tend to help partially offset changing discount rates for higher coupon paying bonds.

reinvestment rate risk The chance that future interest payments will have to be reinvested at a lower interest rate.

EXAMPLE 7-5Capital Gains in the BondMarket LG7-5

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Say that you anticipate falling long-term interest rates from 6 percent to5.5 percent during the next year. If this occurs, what will be the totalreturn for a 20-year, 6.5 percent coupon bond through the interest ratedecline?

SOLUTION:

To determine the total return, compute the capital gain or loss and theinterest paid over the year. The capital gain or loss is determined fromthe change in price. The current bond price is

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The price in one year would be

So, the capital gain is $59.18 (= $1,116.97 − $1,057.79). The interestpayment during the year is $65 (= 0.065 × $1,000). If interest rates fallto 5.5 percent, then this bond should provide a total return of $124.18,which would be an 11.74 percent return (= $124.18 ÷ $1,057.79). Ofcourse, this is only an anticipated interest rate change and it may notoccur.

Similar to Problems 7-25, 7-26, 7-35, 7-36, Self-Test Problem 5

Another factor that influences the amount of reinvestment risk bondholders face is their bonds’ time to maturity. Thelast four bonds in the table all have a 5 percent coupon but have different times to maturity. Note that when interestrates increase, the bond prices of longer-term bonds decline more than shorter-term bonds. This shows that bondswith longer maturities and lower coupons have the highest interest rate risk. Short-term bonds with high couponshave the lowest interest rate risk. High interest rate risk bonds experience considerable price declines when interestrates are rising. However, these bonds also experience dramatic capital gains when interest rates are falling. While a1 percent change in market interest rates is not commonly seen on a daily or monthly basis, such a change is notunusual over the course of several months or a year.

time out!7-3 Show the time line and compute the present value for an 8.5 percent coupon bond (paid semiannually) with 12 years left

to maturity and a market interest rate of 7.5 percent.7-4 Describe the relationship between interest rate changes and bond prices.

7.3 • BOND YIELDS LG7-6Current YieldAlthough we speak about “the prevailing interest rate,” bond relationships reflect many interest rates (also calledyields). Some rates are difficult to calculate but accurately reflect the return the bond is offering. Others, like thecurrent yield, are easy to compute but only approximate the bond’s true return. A bond’s current yield is defined asthe bond’s annual coupon rate divided by the bond’s current market price. Current yield measures the rateof return a bondholder would earn annually from the coupon interest payments alone if the bond werepurchased at a stated price. Current yield does not measure the total expected return because it does not account forany capital gains or losses that will occur from purchasing the bond at a discount or premium to par.

current yield Return from interest payments; computed as the annual interest payment divided by the current bond price.

Yield to MaturityYield to maturity is a more meaningful equation for investors than the simple current yield calculation. The yield to

maturity calculation tells bond investors the total rate of return that they might expect if the bond were bought at aparticular price and held to maturity. While the yield to maturity calculation provides more information than thecurrent yield calculation, it’s also more difficult to compute, because we must compute the bond’s cash flows’internal rate of return. This calculation seeks to equate the bond’s current market price with the value of allanticipated future interest and par value payments. In other words, it is the discount rate that equates the presentvalue of all future cash flows with the current price of the bond. To calculate yield to maturity, investors must solvefor the interest rate, i, in equation 7-2, or solve for i in

yield to maturity The total return the bond offers if purchased at the current price and held to maturity.

(7-2)

Investors commonly compute the yield to maturity using financial calculators. For example, consider a 7 percentcoupon bond (paid semiannually) with eight years to maturity and a current price of $1,150. The return that the bondoffers investors, the yield to maturity, is computed as N = 16, PV = −1150, PMT = 35, and FV = 1000. Computingthe interest rate (i) gives us 2.363 percent. We must remember, however, that 2.363 percent is only the return for sixmonths because the bond pays semiannually. Yield to maturity always means an annual return. So, this bond’s yieldto maturity is 4.73 percent (2 × 2.363 percent).

Notice the link between a bond’s yield to maturity and the prevailing market interest rates used to determine abond’s price as we discussed in the previous section. We use the market interest rate to compute the bond’s value.We use the actual bond price to compute its yield to maturity. If the bond is correctly priced at its economic value,then the market interest rate will equal the yield to maturity. Thus, the relationship that we previously identifiedbetween bond prices and market interest rates applies to yields as well. This shows the inverse relationship betweenbond prices and bond yields. As a bond’s price falls, its yield to maturity increases and a rising bond priceaccompanies a falling yield. Look back at Figure 7.2 and you will see this relationship clearly.

EXAMPLE 7-6Computing Current Yield andYield to Maturity LG7-6

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

You have identified a 3.5 percent Treasury bond with four years left tomaturity and a quoted price of 96.281. Calculate the bond’s currentyield and yield to maturity.

SOLUTION:(1) First, identify that the bond’s price is $962.81 (= 96.281% × $1,000 =

0.96281 × $1,000).(2) The annual $35 in interest payments is paid in two $17.50 semiannual

payments. Therefore, the current yield of the bond is 3.64 percent (=$35 ÷ $962.81).

(3) The yield to maturity is computed using equation 7-2 and the financialcalculator as N = 8, PV = −962.81, PMT = 17.50, and FV = 1,000.Computing the interest rate (/) results in 2.263 percent and multiplyingby 2 gives the yield to maturity of 4.53 percent.

(4) Note that the current yield is less than the yield to maturity because itdoes not account for the capital gain to be earned if held to maturity.

Similar to Problems 7-13, 7-14, 7-27, 7-28, Self-Test Problem 2

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the Math Coach on…Bond Yields and Financial Calculators

“People computing a bond’s yield to maturity make three common mistakes. To avoid the first mistake,ensure that the bond price (PV) is a different sign than the interest and par value cash flows (PMT and FV).The second mistake: People forget to make the number of periods (N) and the per-period interest payment(PMT) consistent. Both should be in semiannual terms if the coupon payment is paid semiannually. Last,many people forget to multiply the resulting calculator interest rate (I) output by 2 to convert the semiannualrate back to an annual rate.„

Yield to CallThe yield to maturity computation assumes that the bondholder will hold the bond to its maturity. But remember thatsome bonds have call provisions that allow the issuers to repay the bondholder’s par value prior to its scheduledmaturity. Issuers often call bonds after large drops in market interest rates. In such cases, issuers commonly paybondholders the bond’s par value plus one year of interest payments. The reasons behind early bond redemptions areobvious. When interest rates fall, issuers can sell new bonds at lower interest rates. Companies want to refinancetheir debt—just as homeowners do—to reduce their interest payments.

Issuers gain important advantages with call provisions because they allow refinancing opportunities. Of course, thesame provisions are disadvantages for bond investors. When bonds are called, investors receive the par value andcall premium, but then investors must seek equally profitable bonds to buy with the proceeds. You will recall thatinvestors can face reinvestment risk—the available bonds aren’t as profitable because interest rates have declined.Bonds are called away at the worst time for investors. In addition, bond prices will rise as market interest rates fall,which could provide issuers opportunities to sell the bonds at a profit. But the price increases will be limited by thefact that the bond will likely be called early. As partial compensation, bond investors receive the call price, which isthe par value of the bond plus the call premium (typically one year of interest payments). The possibility that bondscan be called early dampens their upside price potential. We can even compute the price of a bond that’s likely to becalled from the equation

(7-3)

In this case, N is the number of periods until the bond can be called and i is the prevailing market rate. Theprevailing market interest rate will probably differ from the rate for a noncallable bond. The previous sectiondemonstrated via the yield curve that bonds with different maturities have different yields. A bond that matures in 20years, but is likely to be called in 5 years, will carry a yield appropriate for a five-year bond.

Now, reconsider the 20-year bond with a 7 percent coupon that we discussed previously. If the bond can be called infive years with a call price of $1,070, the appropriate discount rate happens to be 5.75 percent annually atthat time (instead of the 6 percent in the original problem). This time line would be

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The changes in this time line are only 10 semiannual payments of $35 (rather than 40 such semiannual payments), a2.875 percent semiannual discount rate, and the call price payment of $1,070. The price of this callable bond wouldbe

the Math Coach on…Spreadsheets and Bond Pricing

“Common spreadsheet programs have functions that can compute the price or yield to maturity of a bond.The functions are

Compute a bond price = PRICE(settlement,maturity,rate,yld,redemption,frequency,basis)

Compute a yield to maturity = YIELD(settlement,maturity,rate,pr,redemption,frequency,basis)

Settlement is the bond’s settlement date. This is the purchase date of the bond; typically it is today. Maturity isthe bond’s maturity date. Rate is the bond’s annual coupon rate. Pr is the bond’s price per $100 face value.Note that the par value of a bond is typically $1,000, so an adjustment is needed for this input. Redemption isthe bond’s redemption value per $100 face value. Frequency is the number of coupon payments per year. Forsemiannual, frequency = 2. Basis is the type of day count basis to use.

Consider the bond valuation problem of Example 7-4. The spreadsheet solution is the same as the TVMcalculator solution and the pricing equation.

Also consider the yield to maturity problem in Example 7-6. This spreadsheet solves for the yield to maturity.

See this textbook’s online student center to watch instructional videos on using spreadsheets. Also note thatthe solutions for all the examples in the book are illustrated using spreadsheets in videos that are alsoavailable on the textbook website.„

In this example, the callable bond would be priced at $1,106.38, which is slightly lower than an identical bond that

was not callable, priced at $1,115.57.

If a bond is likely to be called, then the yield to maturity calculation does not give investors a good estimate of theirreturn. Bondholders can use instead a yield to call calculation, which differs from the yield to maturity only in that itscalculation assumes that the investor will receive the par value and call premium at the earliest call date. Forexample, reconsider the 7 percent coupon bond (paid semiannually) with eight years to maturity, which weexamined previously. The current bond price is $1,130 (which is slightly lower than the yield to maturity bond priceof $1,150). If the bond can be called in three years at a specific call price of the par value plus one annual coupon,then what is the yield to call? The yield to call is computed as N = 6, PV = −1130, PMT = 35, and FV = 1070. Theresulting interest rate (i) is 2.26 percent. The yield to call for this bond is thus 4.52 percent (= 2 × 2.26%).

yield to call The total return that the bond offers if purchased at the current price and held until the bond is called.

Municipal Bonds and YieldMunicipal bonds (munis) seem to offer low yields to maturity compared to the return that corporate bonds andTreasury securities offer. Munis offer lower rates because the interest income they generate for investors is tax-exempt—at least at the federal level.2 Specifically, income from municipal bonds is not subject to taxation by thefederal government or the state government where the bonds are issued. As a result, municipal bond investorswillingly accept lower yields than those they can obtain from taxable bonds. Generally speaking, investors comparethe after-tax interest income earned on taxable bonds against the return earned on municipal bonds. For example,suppose an investor in the 35 percent marginal income tax bracket has $100,000 to invest in either corporate ormunicipal bonds. The $100,000 investment would earn a taxable $7,000 annually from 7 percent corporate bonds or$5,000 from tax-exempt 5 percent municipal bonds. After taxes, the corporate bond leaves the investor with $4,550[=(1 − 0.35) × $7,000]. Obviously, this is less than the tax-free income of $5,000 generated by the muni bond.

A common way to compare yields from muni bonds versus those from taxable bonds is to convert the yield tomaturity of the muni to a taxable equivalent yield, as shown in equation 7-4.

(7-4)

taxable equivalent yield Modification of a municipal bond’s yield to maturity used to compare muni bond yields to taxable bond yields.

EXAMPLE 7-7Which Bond Has a Better After-Tax Yield? LG7-6

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Imagine a time when you have a high income, placing you in the 31percent marginal tax bracket. You are interested in investing somemoney in a bond issue and have three alternatives. The first is acorporate bond with a 6.4 percent yield to maturity. The second bond isa Treasury that offers a 5.7 percent yield. The third choice is amunicipal bond priced at a yield to maturity of 4.0 percent. Which bondgives you the highest after-tax yield?

SOLUTION:

The Treasury and corporate bonds are both taxable, so we cancompare them directly with each other. The yield of 6.4 percent on thecorporate is clearly higher than the 5.7 percent yield offered by theTreasury bond. To include a comparison with the nontaxable municipalbond, compute its equivalent taxable yield as in equation 7-4:

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The municipal bond’s equivalent taxable yield of 5.80 percent is higherthan the Treasury but lower than the corporate bond.

Similar to Problems 7-15, 7-16, 7-31, 7-32, 7-37, 7-38, Self-TestProblem 3

For high-income investors (in the 35 percent marginal tax bracket) a 5 percent muni bond has an equivalent taxableyield of 7.69 percent = 0.05 ÷ (1 − 0.35)]. The 5 percent muni is more attractive for this investor than a 7 percentcorporate bond. However, for an investor with lower income (in the 28 percent marginal tax bracket) the equivalenttaxable yield is only 6.94 percent. The corporate bond provides more after-tax profit than the muni for this investor.It’s easy to see why muni bonds are popular among high-income investors (those with substantial marginal taxrates).

Summarizing YieldsIn this section, we have presented several different types of interest rates, or yields, associated with bonds. See asummary in Table 7.4. Many of these yields relate to one another. Consider the bonds and associated yields reportedin Table 7.5. Treasury bonds (1) to (3) show how coupon rates, current yield, and yield to maturity relate. When abond trades at its par value (usually $1,000), then the coupon rate, current yield, and yield to maturity are all thesame. When that bond is priced at a premium (bond 2), then both the current yield and the yield to maturity will belower than the coupon rate. They are both higher than the coupon rate when the bond trades at a discount. Noticethat yield to maturity is higher than current yield for discount bonds, and that yield to maturity is lower than currentyield for premium bonds. In other words, the current yield always lies between the coupon rate and the yield tomaturity. Both the current yield and the yield to maturity move in the opposite direction to the bond’s price.

Bonds (4) to (6) are callable corporate bonds. Recall that all the yields (current yield, yield to maturity, and yield tocall) are identical when the bond trades at par value. When interest rates fall and bond prices increase, as with bond(5), the issuing corporation has a strong incentive to call the bond after five years, as allowed in the indentureagreement. So investors should base their purchase decisions on the yield to call. When interest rates increase, bondprices decline (as bond (6) shows). In this case, investors could compute the yield to call (as shown), but theinformation isn’t useful because the company will not likely call the bond while interest rates are high.

▼ TABLE 7.4 Summary of Interest Rates

InterestRate Purpose Description

Couponrate

Computebond cashinterestpayments

The coupon rate is reported as a bond characteristic. It is reported as a percentageand is multiplied by the par value of the bond to determine the annual cash interestpayment. The coupon rate will not change through the life of the bond.

Currentyield

Quickassessmentof the interestrate a bond isoffering

Computed as the annual interest payment divided by the current price of the bond. Itmeasures the return to be expected from just the interest payments if the bond waspurchased at the current price. Since the bond price may change daily, the currentyield will change daily.

Yield tomaturity

Accuratemeasurementof the interestrate a bond isoffering

The return offered by the bond if purchased at the current price. This return includesboth the expected income and capital gain/loss if held to the maturity date. The yieldto maturity will change daily as the bond price changes.

Interest rate

Yield tocall

obtained if thebond is called

Same as the yield to maturity except that it is assumed that the bond will be called atthe earliest date it can be called.

Taxableequivalentyield

Comparisonof nontaxablebond yields totaxable bondyields

Investors must pay taxes on most types of bonds. However, municipal bonds are taxfree. To compare the muni’s nontaxable yield to maturity to that of taxable bonds,divide the yield by one minus the investor’s marginal tax rate.

Marketinterestrate

Comparisonof prices of allbonds

The interest rate determined by the bond prices of actual trades between buyers andsellers. The market interest rate will be different for bonds of different times tomaturity and different levels of risk.

Totalreturn

Determinerealizedperformanceof aninvestment

Realized return that includes both income and capital gain/loss profits.

▼ TABLE 7.5 Price, Coupon, and Yield Relationships of a 10-Year Bond

Call price = Par value + One year’s interest

The last three bonds shown in the table are municipal bonds. Recall that these bonds typically offer lower yieldsbecause the income from munis is tax exempt. It is easier to compare municipal bonds with Treasuries and corporatebonds if you compute the municipal bond’s taxable equivalent yield first. Here, we use a marginal tax rate of 35percent in the calculation. The last column of the table shows that the taxable equivalent yield of the municipalbonds is really quite competitive with corporate bond yields. Any investor with income taxed at the 35 percentmarginal tax bracket would prefer the municipal bond over the corporate bond if the muni’s taxable equivalent yieldis higher than the yield to maturity (or yield to call) of the corporate bond.

The table also shows that Treasury securities offer lower yields than corporate bonds with similar terms to maturity.The difference (or spread) between Treasury and corporate yields gives rise to a discussion of bond credit risk,which follows.

time out!7-5 Calculate the yield to maturity for a zero coupon bond with a price of $525 and 10 years left to maturity.7-6 Which is higher for a discount bond, the yield to maturity or the coupon rate? Why?

7.4 • CREDIT RISK LG7-7

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Bond RatingsWill a bond issuer make the promised interest and par value payments over the next 10, 20, or even 30 years? Creditquality risk is the chance that the bond issuer will not be able to make timely payments. To assess this risk,independent bond rating agencies, such as Moody’s and Standard & Poor’s, monitor corporate, U.S. agency, ormunicipal developments during the bond’s lifetime and report their findings as a grade or rating. The U.S.government issues the highest credit quality debt, though that consensus has recently come into doubt as the U.S.debt and budget deficit have ballooned.

credit quality risk The chance that the issuer will not make timely interest payments or even default.

bond rating A grade of credit quality as reported by credit rating agencies.

The primary “big three” bond credit rating agencies in the United States include Moody’s Investors Service,Standard & Poor’s Corporation, and Fitch IBCA Inc. Each of these credit analysis firms assigns similar ratingsbased on detailed analyses of issuers’ financial condition, general economic and credit market conditions, and theeconomic value of any underlying collateral. The Standard & Poor’s ratings are shown in Table 7.6. Theirhighest credit quality rating is AAA. Bonds rated AAA, AA, A, or BBB are considered investment gradebonds. The issuers of these securities have the highest chance of making all interest and par value paymentspromised in the indenture agreement.

investment grade High credit quality corporate bonds.

▼ TABLE 7.6 Standard & Poor’s Bond Credit Ratings

Credit RiskCreditRating Description

Investment Grade

Highestquality

AAA The obligor’s (issuer’s) capacity to meet its financial commitment on the obligation isextremely strong.

Highquality

AA The obligor’s capacity to meet its financial commitment on the obligation is very strong.

Uppermediumgrade

AThe obligor’s capacity to meet its financial commitment on the obligation is still strong,though somewhat susceptible to the adverse effects of changes in circumstances andeconomic conditions.

Mediumgrade BBB

The obligor exhibits adequate protection. However, adverse economic conditions orchanging circumstances are more likely to lead to a weakened capacity to meet its financialcommitment.

Below Investment Grade

Somewhatspeculative BB

Faces major ongoing uncertainties or exposure to adverse business, financial, or economicconditions which could lead to the obligor’s inadequate capacity to meet its financialcommitment.

Speculative B Adverse business, financial, or economic conditions will likely impair the obligor’s capacity orwillingness to meet its financial commitment.

Highlyspeculative

CCC Currently vulnerable to nonpayment, and is dependent upon favorable business, financial,and economic conditions for the obligor to meet its financial commitment.

Mostspeculative

CC Currently highly vulnerable to nonpayment.

Imminentdefault

C Bankruptcy petition has been filed or similar action taken, but payments on this obligationare being continued.

Default D Obligations are in default or the filing of a bankruptcy petition has occurred and paymentsare jeopardized.

Source: Standard & Poor’s.

The investment community considers bonds rated BB and below to be below-investment grade bonds, and someinvestors, such as pension funds or other fiduciaries, cannot purchase these securities for their portfolios. These

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bonds are considered to be speculative because they carry a significant risk that the issuer will not make current orfuture payments. Speculative bonds are sometimes called junk bonds because of this risk. In order to attract buyers,issuers sell these bonds at a considerable discount from par and a high associated yield to maturity. Agencies oftenenhance ratings from “AA” to “CCC” with the addition of a plus (+) or minus (−) sign to show relative standingwithin the major rating categories. For example, the Greek government saw its bonds upgraded from CCC+ to B−by Standard & Poor’s on January 22, 2016. The next week, Standard and Poor’s downgraded Dutch Shell Plc fromAA− to A+. These rating changes impact not only the current prices of these bonds, but also the interest rate Greeceand Royal Dutch Shell would have to pay if they issued new bonds.

junk bonds Low credit quality corporate bonds, also called speculative bonds or high-yield bonds.

Standard & Poor’s signals that it’s considering a rating change by placing an individual bond, or all of a givenissuer’s bonds, on CreditWatch (S&P). Rating agencies make their ratings information available to the publicthrough their ratings information desks. In addition to published reports, ratings are made available in many publiclibraries and over the Internet.

Credit rating agencies conduct general economic analyses of companies’ business and analyze firms’ specificfinancial situations. A single company may carry several outstanding bond issues. If these issues featurefundamental differences, then they may have different credit level risks. For example, unsecured corporate bonds, ordebentures, are backed only by the reputation and financial stability of the corporation. A senior bond has a priorityclaim over junior (more recently issued) securities in the event of default or bankruptcy. So, senior bondscarry less credit risk than junior bonds. Some bonds are secured with collateral. When you buy a car usinga loan, the car is collateral for that loan. If you don’t make the loan payments, the bank will repossess the car.Companies can also offer collateral when issuing bonds. When a firm uses collateral such as real estate or factoryequipment, the bonds are called mortgage bonds or equipment trust certificates, respectively. Bonds issued with nocollateral generally carry higher credit risk.

unsecured corporate bonds Corporate debt not secured by collateral such as land, buildings, or equipment.

debentures Unsecured bonds.

senior bonds Older bonds that carry a higher claim to the issuer’s assets.

mortgage bonds Bonds secured with real estate as collateral.

equipment trust certificates Bonds secured with factory and equipment as collateral.

Credit Risk and YieldInvestors will only purchase higher risk bonds if those securities offer higher returns. Therefore, issuers price bondswith high credit risk to offer high yields to maturity. So another common name for junk bonds is high-yield bonds.Differences in credit risk are a prime source of differences in yields between government and various corporatebonds. Figure 7.3 shows the historical average annual yields for long-term Treasury bonds and corporate bonds withcredit ratings of Aaa and Baa since 1980. Riskier low-quality bonds always offer a higher yield than the higherquality bonds. However, the yield spread between high- and low-quality bonds varies substantially over time. Theyield difference between Baa bonds and Treasuries was as high as 3.7 percent and 3.3 percent in 1982 and 2003,respectively. The spread has been as narrow as 1.3 percent and 1.4 percent in 1994 and 2006, respectively.

high-yield bonds Bonds with low credit quality that offer a high yield to maturity, also called junk bonds.

How do some corporations’ debt obligations become junk bonds? Some companies that aren’t economically soundor those that use a high degree of financial leverage issue junk bonds. In other cases, financially strong companiesissue investment grade bonds and then, over time, begin to have trouble. Eventually a company’s bonds can bedowngraded to junk status. For example, General Motors (GM) bonds were considered of the highest quality fromthe 1950s through the 1980s and much of the 1990s. On May 9, 2005, Standard & Poor’s downgraded GM bonds tojunk status. Junk bonds that were originally issued at investment grade status are called fallen angels. GM eventuallyfiled for bankruptcy protection in June 2009. By 2016, its credit rating was at the lowest end of investment grade(BBB−).

FIGURE 7-3 Yield to Maturity on Long-Term Bonds of Different Credit Risk, 1980–2015

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Looking at the historical yields for long-term Treasury and corporate bonds, notice how the yield spread between high- and low-quality bondsvaries substantially over time.

finance at work //: marketsA Greek Tragedy: Debt Crisis

©Max Shen/Getty Images

Greece joined the European monetary union in 2000, which means the euro replaced drachmas as the national currency. The euro wasa much stronger currency than the drachma because it was backed by the economic prosperity of the whole European Union. Hence,the Greek government was able to borrow from foreign investors at much lower interest rates. This contributed to the ensuing economicboom and expansion of government spending in Greece.

The Greek government has long been operating on high budget deficits and borrowing. But the problems really began in the Fall of2009 when the new elected government found that it had inherited a financial burden that was much larger than previously reported. Thebudget deficit was revised to be larger than 13 percent of the size of the economy. The revelation of these huge government deficits anddebts cast enormous doubt on the ability of the Greek government to pay its debts.

This increase in risk was reflected on December 8, 2009, by the downgrade to BBB (lowest in the Euro Zone) of the Sovereign bondof Greece by the Fitch credit rating firm. Standard & Poor’s and Moody’s both downgraded Greece Sovereigns to junk bond status inMay and June of 2010. As a consequence, Greece found that it was difficult to borrow more money and had to offer lenders yields of asmuch as 12 percent and a financial crisis developed.

In order to restore investor confidence, the Greek government has pledged to an austerity plan that cuts spending and reduces thebudget deficit. However, the success of the plans has been undermined by strong domestic opposition as illustrated by strikes and even

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riots. As a temporary solution, the European Union and the International Monetary Fund together offered a large loan package to helpout Greece. This calmed the bond market and Greek bond yields fell, but they are still high. Unfortunately, the severe economicdepression in Greece has caused further problems with its ability to pay its debt. In 2011 and 2012, Greece enacted several bondrestructurings which mandated changes in the terms. They are considered selective bond defaults. In June of 2015, Greece became thefirst developed country to miss an International Monetary Fund loan repayment.

Want to know more?Key Words to Search for Updates: Greek bonds, Greek debt crisis

time out!7-7 Explain why a change in a bond’s credit rating will cause its price to change.7-8 One company has issued two bond classes. One issue is a mortgage bond and the other is a debenture. Which issue will

have a higher bond rating and which will offer a higher yield?

Bonds that experience credit-rating downgrades must offer a higher yield. As all the future cash flows are fixed, thebond price must fall to create a higher yield to maturity. Alternatively, bonds that are upgraded experience priceincreases and yield decreases. Bond upgrades often occur during strong economic periods because corporate issuerstend to perform better financially at these times. In a weak economy, high-yield bonds lose their luster because thedefault risk rises. More credit downgrades occur during economic recessions. In general, any event that impacts thelikelihood of a firm paying back the interest payments and principle it owes will impact its credit risk. Credit risk isa determinant of the discount rate. The discount rate is also influenced by macroeconomic factors, like decisions bythe Federal Reserve Board. A change in the discount rate directly changes the value of the bond. Therefore,company performance, strength of the economy, and monetary policy all affect bond values.

7.5 • BOND MARKETS LG7-8The majority of trading volume in the bond market occurs in a decentralized, over-the-counter market. Most tradesoccur between bond dealers and large institutions (like mutual funds, pension funds, and insurance companies).Dealers bid for bonds that investors seek to sell and offer bonds from their own inventory when investorswant to buy. This is especially true for the very active Treasury securities market. However, a smallnumber of corporate bonds are listed on centralized exchanges.

FIGURE 7-4 Most Active Investment Grade Bonds, February 5, 2016

This is an example of the most actively traded investment bonds for a given day.

Source: The New York Times, http://markets.on.nytimes.com/research/markets/bonds/bonds.asp

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The NYSE operates the largest centralized U.S. bond market. The majority of bond volume at the NYSE is incorporate debt. The most actively traded investment grade bonds for the day are shown in Figure 7.4. Even the mostactive corporate bonds experience relatively low trading volume. Note that some of the bonds traded are short-term,like Anadarko Pete Corp and JPMorgan Chase & Co. Other bonds have many years to maturity, like the Anheuser-busch Inbev bond that matures in February 2046. Most of the ones shown are premium bonds (price greater than parvalue), while one is a discount bond.

Following the Bond MarketThe entire bond market encompasses a wide variety of securities with varying credit quality from different issuers.Large differences also arise among bonds in terms of their characteristics such as term to maturity and size of thecoupon. The biggest factor associated with changes in bond prices is changes in interest rates. So, one common wayto describe the direction of bond prices is simply to report the change in interest rates, since we know that interestrate changes will affect all bonds the same way. The interest rate referenced is the yield to maturity and daily yieldchange for the 10-year Treasury. Knowing how this interest rate changed today gives bond investors a good idea ofthe general price movement of all types of bonds.

Bond indexes track specific segments of the bond market. Various securities firms, such as Barclays Capital orMerrill Lynch, maintain these indexes that capture bond price and yield changes in particular segments. You canfind information about major bond indexes on the Internet and in publications like The Wall Street Journal (both inprint and online). Figure 7.5 shows indexes that track bonds by type of issuer (federal government, corporation, localgovernment, etc.) and time to maturity (short, intermediate, and long).

time out!7-9 Why can we use various interest rates to describe the performance of the entire bond market?7-10 What bond segments are measured by which bond indexes?

FIGURE 7-5 Major Bond Indexes as Reported in The Wall Street Journal and on the Internet, February 5, 2016

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Here are indexes that track bonds by type of issuer (federal government, corporation, local government, etc.) and time to maturity (short,intermediate, and long).

Source: The Wall Street Journal Online. Tracking Bond Benchmarks web page.

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Your Turn…Questions

1. What does a call provision allow issuers to do, and why would they do it? (LG7-1)

2. List the differences between the new TIPS and traditional Treasury bonds. (LG7-2)

3. Explain how mortgage-backed securities work. (LG7-2)

4. Provide the definitions of a discount bond and a premium bond. Give examples. (LG7-3)

5. Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zerocoupon bond. (LG7-4)

6. All else equal, which bond’s price is more affected by a change in interest rates, a short-term bond or a longer-term bond? Why? (LG7-5)

7. All else equal, which bond’s price is more affected by a change in interest rates, a bond with a large coupon ora small coupon? Why? (LG7-5)?

8. Explain how a bond’s interest rate can change over time even if interest rates in the economy do not change.(LG7-5)

9. Compare and contrast the advantages and disadvantages of the current yield computation versus yield tomaturity calculations. (LG7-6)

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10. What is the yield to call and why is it important to a bond investor? (LG7-6)

11. What is the purpose of computing the equivalent taxable yield of a municipal bond? (LG7-6)

12. Explain why high-income and wealthy people are more likely to buy a municipal bond than a corporate bond.(LG7-6)

13. Why does a Treasury bond offer a lower yield than a corporate bond with the same time to maturity?Could a corporate bond with a different time to maturity offer a lower yield? Explain. (LG7-7)

14. Describe the difference between a bond issued as a high-yield bond and one that has become a “fallen angel.”(LG7-7)

15. What is the difference in the trading volume between Treasury bonds and corporate bonds? Give examplesand/or evidence. (LG7-8)

ProblemsBASIC PROBLEMS

7-1 Interest Payments Determine the interest payment for the following three bonds: 3½ percent couponcorporate bond (paid semiannually), 4.25 percent coupon Treasury note, and a corporate zero coupon bondmaturing in 10 years. (Assume a $1,000 par value.) (LG7-1)

7-2 Interest Payments Determine the interest payment for the following three bonds: 4½ percent couponcorporate bond (paid semiannually), 5.15 percent coupon Treasury note, and a corporate zero coupon bondmaturing in 15 years. (Assume a $1,000 par value.) (LG7-1)

7-3 Time to Maturity A bond issued by Ford on May 15, 1997, is scheduled to mature on May 15, 2097. Iftoday is November 16, 2014, what is this bond’s time to maturity? (LG7-1)

7-4 Time to Maturity A bond issued by IBM on December 1, 1996, is scheduled to mature on December 1,2096. If today is December 2, 2015, what is this bond’s time to maturity? (LG7-1)

7-5 Call Premium A 6 percent corporate coupon bond is callable in five years for a call premium of one yearof coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuercalls the bond? (LG7-1)

7-6 Call Premium A 5.5 percent corporate coupon bond is callable in 10 years for a call premium of one yearof coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuercalls the bond? (LG7-1)

7-7 TIPS Interest and Par Value A 2¾ percent TIPS has an original reference CPI of 185.4. If the currentCPI is 210.7, what is the current interest payment and par value of the TIPS? (LG7-2)

7-8 TIPS Interest and Par Value A 3⅛ percent TIPS has an original reference CPI of 180.5. If the currentCPI is 206.8, what is the current interest payment and par value of the TIPS? (LG7-2)

7-9 Bond Quotes Consider the following three bond quotes: a Treasury note quoted at 97.844, a corporatebond quoted at 103.25, and a municipal bond quoted at 101.90. If the Treasury and corporate bonds have apar value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these threebonds in dollars? (LG7-3)

7-10 Bond Quotes Consider the following three bond quotes: a Treasury bond quoted at 106.438, acorporate bond quoted at 96.55, and a municipal bond quoted at 100.95. If the Treasury and corporatebonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the priceof these three bonds in dollars? (LG7-3)

7-11 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 20 years if themarket interest rate is 3.8 percent. (LG7-4)

7-12 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 15 years if the

market interest rate is 5.75 percent. (LG7-4)7-13 Current Yield What’s the current yield of a 3.8 percent coupon corporate bond quoted at a price of

102.08? (LG7-6)

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7-14 Current Yield What’s the current yield of a 5.2 percent coupon corporate bond quoted at a price of96.78? (LG7-6)

7-15 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield tomaturity of 3.5 percent for an investor in the 33 percent marginal tax bracket? (LG7-6)

7-16 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield tomaturity of 2.9 percent for an investor in the 28 percent marginal tax bracket? (LG7-6)

7-17 Credit Risk and Yield Rank from highest credit risk to lowest risk the following bonds, with thesame time to maturity, by their yield to maturity: Treasury bond with yield of 5.55 percent, IBM bondwith yield of 7.49 percent, Trump Casino bond with yield of 8.76 percent, and Banc One bond with ayield of 5.99 percent. (LG7-7)

7-18 Credit Risk and Yield Rank the following bonds in order from lowest credit risk to highest risk allwith the same time to maturity, by their yield to maturity: Treasury bond with yield of 4.65 percent,United Airlines bond with yield of 9.07 percent, Bank of America bond with a yield of 6.25 percent,and Hewlett-Packard bond with yield of 6.78 percent. (LG7-7)

INTERMEDIATE PROBLEMS

7-19 TIPS Capital Return Consider a 3.5 percent TIPS with an issue CPI reference of 185.6. At thebeginning of this year, the CPI was 193.5 and was at 199.6 at the end of the year. What was the capitalgain of the TIPS in dollars and in percentage terms? (LG7-2)

7-20 TIPS Capital Return Consider a 2.25 percent TIPS with an issue CPI reference of 187.2. At thebeginning of this year, the CPI was 197.1 and was at 203.8 at the end of the year. What was the capitalgain of the TIPS in dollars and in percentage terms? (LG7-2)

7-21 Compute Bond Price Compute the price of a 3.8 percent coupon bond with 15 years left to maturityand a market interest rate of 6.8 percent. (Assume interest payments are semiannual.) Is this a discountor premium bond? (LG7-4)

7-22 Compute Bond Price Compute the price of a 5.6 percent coupon bond with 10 years left to maturityand a market interest rate of 7.0 percent. (Assume interest payments are semiannual.) Is this a discountor premium bond? (LG7-4)

7-23 Compute Bond Price Calculate the price of a 5.2 percent coupon bond with 18 years left to maturityand a market interest rate of 4.6 percent. (Assume interest payments are semiannual.) Is this a discountor premium bond? (LG7-4)

7-24 Compute Bond Price Calculate the price of a 5.7 percent coupon bond with 22 years left to maturityand a market interest rate of 6.5 percent. (Assume interest payments are semiannual.) Is this a discountor premium bond? (LG7-4)

7-25 Bond Prices and Interest Rate Changes A 5.75 percent coupon bond with 10 years left to maturity ispriced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity willbe 5.8 percent. What is the change in price the bond will experience in dollars? (LG7-5)

7-26 Bond Prices and Interest Rate Changes A 6.5 percent coupon bond with 14 years left to maturity ispriced to offer a 7.2 percent yield to maturity. You believe that in one year, the yield to maturity willbe 6.8 percent. What is the change in price the bond will experience in dollars? (LG7-5)

7-27 Yield to Maturity A 5.65 percent coupon bond with 18 years left to maturity is offered for sale at

$1,035.25. What yield to maturity is the bond offering? (Assume interest payments are semiannual.)(LG7-6)

7-28 Yield to Maturity A 4.30 percent coupon bond with 14 years left to maturity is offered for sale at$943.22. What yield to maturity is the bond offering? (Assume interest payments are semiannual.)(LG7-6)

7-29 Yield to Call A 6.75 percent coupon bond with 26 years left to maturity can be called in 6 years. Thecall premium is one year of coupon payments. It is offered for sale at $1,135.25. What is the yield tocall of the bond? (Assume interest payments are semiannual.) (LG7-6)

7-30 Yield to Call A 5.25 percent coupon bond with 14 years left to maturity can be called in 4 years. Thecall premium is one year of coupon payments. It is offered for sale at $1,075.50. What is the yield to

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call of the bond? (Assume interest payments are semiannual.) (LG7-6)7-31 Comparing Bond Yields A client in the 39 percent marginal tax bracket is comparing a municipal

bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45percent yield. Which bond will give the client more profit after taxes? (LG7-6)

7-32 Comparing Bond Yields A client in the 28 percent marginal tax bracket is comparing a municipalbond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45percent yield. Which bond will give the client more profit after taxes? (LG7-6)

ADVANCED PROBLEMS

7-33 TIPS Total Return Reconsider the 3.5 percent TIPS discussed in problem 7-19. It was issued withCPI reference of 185.6. The bond is purchased at the beginning of the year (after the interest payment),when the CPI was 193.5. For the interest payment in the middle of the year, the CPI was 195.1. Now,at the end of the year, the CPI is 199.6 and the interest payment has been made. What is the totalreturn of the TIPS in dollars and in percentage terms for the year? (LG7-2)

7-34 TIPS Total Return Reconsider the 2.25 percent TIPS discussed in problem 7-20. It was issued withCPI reference of 187.2. The bond is purchased at the beginning of the year (after the interest payment),when the CPI was 197.1. For the interest payment in the middle of the year, the CPI was 200.1. Now,at the end of the year, the CPI is 203.8 and the interest payment has been made. What is the totalreturn of the TIPS in dollars and in percentage terms for the year? (LG7-2)

7-35 Bond Prices and Interest Rate Changes A 6.25 percent coupon bond with 22 years left to maturity ispriced to offer a 5.5 percent yield to maturity. You believe that in one year, the yield to maturity willbe 6.0 percent. If this occurs, what would be the total return of the bond in dollars and percent? (LG7-5)

7-36 Bond Prices and Interest Rate Changes A 7.5 percent coupon bond with 13 years left to maturity ispriced to offer a 6.25 percent yield to maturity. You believe that in one year, the yield to maturity willbe 7.0 percent. If this occurs, what would be the total return of the bond in dollars and percentageterms? (LG7-5)

7-37 Yields of a Bond A 2.50 percent coupon municipal bond has 12 years left to maturity and has a pricequote of 98.45. The bond can be called in four years. The call premium is one year of couponpayments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield(for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest paymentsare semiannual and a par value of $5,000.) (LG7-6)

7-38 Yields of a Bond A 3.85 percent coupon municipal bond has 18 years left to maturity and has a pricequote of 103.20. The bond can be called in eight years. The call premium is one year of couponpayments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield(for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest paymentsare semiannual and a par value of $5,000.) (LG7-6)

7-39 Bond Ratings and Prices A corporate bond with a 6.5 percent coupon has 15 years left to maturity. It

has had a credit rating of BBB and a yield to maturity of 7.2 percent. The firm has recently gotten intosome trouble and the rating agency is downgrading the bonds to BB. The new appropriate discountrate will be 8.5 percent. What will be the change in the bond’s price in dollars and percentage terms?(Assume interest payments are semiannual.) (LG7-7)

7-40 Bond Ratings and Prices A corporate bond with a 6.75 percent coupon has 10 years left to maturity.It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm has recently becomemore financially stable and the rating agency is upgrading the bonds to BBB. The new appropriatediscount rate will be 7.1 percent. What will be the change in the bond’s price in dollars and percentageterms? (Assume interest payments are semiannual.) (LG7-7)

7-41 Spreadsheet Problem Say that in June of this year, a company issued bonds that are scheduled tomature three years from now in June. The coupon rate is 5.75 percent and is semiannually. The bondissue was rated AAA.a. Build a spreadsheet that shows how much money the firm pays for each interest rate payment and

when those payments will occur if the bond issue sells 50,000 bonds.

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b. If the bond issue rating would have been BBB, then the coupon rate would have been 6.30 percent.Show the interest payments with this rating. Explain why bond ratings are important to firms issuingcapital debt.

c. Consider that interest rates in the economy increased in the first half of this year. If the firm wouldhave issued the bonds in January of this year, then the coupon rate would have only been 5.40percent. How much extra money per year is the firm paying because it issued the bonds in Juneinstead of January?

7-42 Spreadsheet Problem You have a portfolio of three bonds. The long bond will mature in 19 yearsand has a 5.5% coupon rate. The midterm bond matures in 9 years and has a 6.6% coupon rate. Theshort bond matures in only 2 years and has a 4% coupon rate.a. Construct a spreadsheet that shows the value of these three bonds and the portfolio when the

discount rate is 5%. The spreadsheet can look something like this:b. Illustrate what happens when the discount rate increases by 0.5%. What do you notice about the

changes in price between the three bonds?c. Show the bond prices when the discount rate decreases by 0.5% from the discount rate in part a.

What do you notice about the price change between parts b and c?

A B C D E

1 Now Change to

2 Interest rate = 5.00% 5.50%

3 Bonds Bond Price Now Price After Change Change in $ Change in %

4 Long bond

5 Midterm bond

6 Short bond

7 Total = $0.00 $0.00

NotesCHAPTER 71. In order to focus on the valuation concepts, we present these examples with the full six months until the bond’s next interest payment.

However, bonds can be sold anytime between interest payments. When this occurs, we simply add the interest accrued since the lastpayment to the price.

2. States have differing rules about whether they tax the income from a particular municipal bond—they will generally tax income frommunis issued out of state. Further, capital gains arising from municipal bond sales may be taxed, and the income from municipal bondsmust be added to overall income when determining the Alternative Minimum Tax consesquences.

chapter eightValuing Stocks

©Benny Marty/Shutterstock

B

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usinesses need capital to start up operations, expand product lines and services, and serve newmarkets. In the last chapter, we discussed debt, which is one source of financial capital upon whichbusinesses can draw. Their other source of capital is called equity, or business ownership. Public

corporations share business ownership and raise money by issuing stocks to investors. When thecompany sells this form of equity ownership to raise money, it gives up some ownership—and thus somecontrol—over the business. Investors buy stock to receive the benefits of business ownership. Mostcitizens do not have the time or expertise to operate their own businesses. Buying stock allows them toparticipate in the profits of economic activities. Access to equity capital has allowed entrepreneurs like BillGates of Microsoft and Larry Page of Google to take their companies public so that their businesses canbecome large corporations. Both the company founders and the new owners (stock investors) haveamassed much wealth over the years under this arrangement. One very important reason that investorsare willing to buy company stock as an investment is that they know that they can sell the stockduring any trading day. Investors buy and sell stocks among themselves in stock markets. Well-functioning stock markets are critical to any capitalistic economy. In this chapter, we’ll discuss stockmarket operations and stock valuation.■

LEARNING GOALS

LG8-1 Understand the rights and returns that come with common stock ownership.LG8-2 Know how stock exchanges function.LG8-3 Track the wider stock market with stock indexes and differentiate among the kinds of information each index provides.LG8-4 Know the terminology of stock trading.LG8-5 Compute stock values using dividend discount and constant-growth models.LG8-6 Calculate the stock value of a variable-growth-rate company.LG8-7 Assess relative stock values using the P/E ratio model.

viewpointsbusiness APPLICATIONAs CEO of your firm, Dawa Tech, which makes computer components, you have been able to grow its dividends by 8 percent peryear to a recent $2 per share. You expect this growth to continue. As a result, the stock price has risen to $65 and has a P/E ratio of16.25.

Tomorrow, you are scheduled to meet with some stockholders and financial analysts. To prepare for the meeting, you should knowwhat return the shareholders seem to expect and estimate where the Dawa stock price may be in three years. How will you go aboutpreparing for this meeting? (See the solution at the end of the book.)

8.1 • COMMON STOCK LG8-1Equity securities (stocks) represent ownership shares in a corporation. Common stock offers buyers the potential forcurrent income from dividends and capital appreciation from any stock price increases. Over time, some corporateprofits are reinvested in the firm, which increases the value of each shareholder’s stake in the business. At any pointin time, the market value of a firm’s common stock depends on many factors, including

common stock An ownership stake in a corporation.

The company’s profitability.Growth prospects for the future.

Current market interest rates.Conditions in the overall stock market.

Over periods of 30 to 40 years, stocks have offered investors the best opportunities to increase wealth. Since stocks

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are also susceptible to price declines and stock price fluctuations can be very volatile over short periods of time,stock investing requires a longer-term outlook.

Virtually any business firm that is organized as a corporation (see Chapter 1) may choose to issue publicly tradedstock. Common stockholders vote to elect the board of directors; they also vote on various other proposals requestedby other shareholders or the management team. As owners of the firm, common stockholders are considered to beresidual claimants. This means that common stockholders have the right to claim any cash flows or value after allother claimants have received what they are owed. As a company earns cash flows, it must pay suppliers,employees, expenses, taxes, and debt interest payments. Stockholders claim the leftover (or residual) cash flow.These profits can be used to reinvest in the firm to foster growth, pay dividends to shareholders, or a combination ofthe two.

residual claimants Ownership of cash flows and value after other claimants are paid.

Stocks of growing firms are valuable. Stocks in firms that pay dividends to shareholders are also valuable. Stocksissued by firms that have greater amounts of residual cash flow are more valuable. The value is reflected in the stockprice. Therefore, stock price values arise from the company’s underlying business success. Many different investorsand analysts may estimate a stock’s fundamental value based upon some outlook or theory. But the actualstock price is determined on stock exchanges when investors seek to trade with one another. Let’s discussthis trading process and then explore how stocks are valued.

personal APPLICATIONYou are impressed with the news and entertainment firm CBC Newscorp. The per-share dividends have increased from $1.25 peryear three years ago to the recent $1.68 annual dividend. Then you discover that 15 analysts are following the firm and that theirmean growth estimate for the future is 10.1 percent. Now you want to know if the current selling price of $54 seems like a good deal ifthe appropriate required return for the stock is 13.5 percent. (See the solution at the end of the book.)

Who are these “analysts,” and where can you find their opinions?

8.2 • STOCK MARKETS LG8-2In general, people will invest significant amounts of their wealth in stocks only if they know that they can converttheir shares into cash at any time. Stock exchanges provide this liquidity, allowing buyers and sellers the means totransact stock trades with each other. This liquidity gives many people the confidence to invest in the first place andmakes stocks (as well as bonds) attractive investments relative to less-liquid assets like real estate or fine collectibles—which can be difficult to sell quickly at full value.

The most well-known stock exchange in the world is the New York Stock Exchange (NYSE). The New York StockExchange, located in New York City on the corner of Wall Street and Broad Street, is the largest U.S. stockexchange as measured by the value of companies listed and the dollar value of trading activity. The NYSE is thelargest equities marketplace in the world and is home to approximately 2,800 companies (many with multiplesecurities listed). While other exchanges may boast more companies listed, the largest companies in the world tendto list in New York. The holding company that owns the NYSE, Intercontinental Exchange, also operates Euronext,a Europe-based electronic exchange market. For decades, the American Stock Exchange, located just down thestreet, competed with the NYSE. However, in 2008, the NYSE acquired this exchange. Now, smaller companiestrade at this location, which is referred to as AMEX.

New York Stock Exchange (NYSE) Large and prestigious stock exchange with a trading floor.

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The NYSE trades millions upon millions of stock shares in a given day.©Tetra Images/Getty Images

Much of the stock buying and selling at the NYSE occurs at 17 stations, called trading posts, on the trading floor.Each post is staffed by a designated market maker (formerly known as specialists), who oversees the orderly tradingof the specific stocks assigned to that post. Brokers, located around the perimeter of the floor, act as agents for thosebuying and selling stocks. Brokers execute orders by matching buy and sell orders. Once the buy and sell ordersmatch, the transaction is completed and the trade appears on trading screens viewed by people all over the world.

trading posts Trading location on the floor of a stock exchange.

brokers Floor traders who execute orders for others and themselves.

Consider this scenario. You decide to buy shares of McDonald’s stock because of new menu items and otherinitiatives. You place a buy order for 100 shares with your broker—either with a simple phone call or through anonline brokerage service. The broker then sends the order to the NYSE electronically to the trading post assigned forMcDonald’s stock. At the trading post, the specialist makes sure the transaction is executed in a fair and orderlymanner. Your buy order competes with other orders at the point of sale for the best price and an on-floor brokerexecutes your purchase. You will receive a trade confirmation from your broker describing the trade and noting theexact amount you owe for the 100 shares of McDonald’s plus any applicable commissions. The NYSE reports thetransaction and it appears within seconds on displays across the country and around the world. Note that buy and sellorders are electronically routed from all over the world to the NYSE, which then routes trade results back. Sincemost of the trade orders are already in electronic form, why not electronically match buy and sell orders and bypassany human intervention in floor trading? Indeed, the NYSE has joined many other exchanges in becomingincreasingly electronic. Some floor market-maker firms can see a time when no human intervention will be a part offloor trading at the NYSE.

The NYSE will trade millions of McDonald’s stock shares in a given day. A stock quote for McDonald’s stock,ticker symbol MCD, is shown in Figure 8.1. On February 10, 2016, more than 5.7 million McDonald’s shares traded.The stock closed at $117.54 per share, which was $0.53 higher than the closing price of the previous day. At thisprice, McDonald’s stock is currently closer to its 52-week high of $124.83 than to its 52-week low of $87.50.

ticker symbol Unique code for a company consisting of one to five letters.

FIGURE 8-1 Read a Stock Quote, February 10, 2016, Yahoo! Finance

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If you know what to look for, reading a stock quote is not as complicated as it first may appear.Source: Yahoo! Finance.

To list its stock on the NYSE, a company must meet minimum requirements for itsTotal number of stockholders.

Level of trading volume.Corporate earnings.

Firm size.

The exchange also charges an initial list fee and an annual fee. Listing standards and fees are higher for the NYSEthan for other stock exchanges, so many firms cannot (or choose not to) list their stocks there.

Another popular stock trading system is the NASDAQ Stock Market, an electronic stock market without a physicaltrading floor. Today, NASDAQ features many of the big-name high-tech companies investors have come to know,like Apple Computer (ticker: AAPL), Intel (ticker: INTC), Microsoft (ticker: MSFT), and Qualcomm (ticker:QCOM). Many newer high-tech companies like Google (ticker: GOOG), Netflix (ticker: NFLX), and AdobeSystems Inc. (ticker: ADBE), are also listed on NASDAQ. In 2007, NASDAQ purchased OMX, which owned sevenNordic and Baltic stock exchanges, and became NASDAQ OMX. NASDAQ ranks second, behind the NYSE,among the world’s equity markets in terms of total dollar volume. NASDAQ lists approximately 3,100 domestic andforeign companies.

NASDAQ Stock Market Large electronic stock exchange.

Instead of having a trading floor, NASDAQ uses a vast electronic trading system that executes trades via computerrather than in person. Instead of one designated market maker overseeing the process for an individual stock on atrading floor, Nasdaq’s system uses multiple market makers, or dealers. Market makers use their own stock inventoryand capital to compete with other dealers to buy and sell the stocks they represent. When an investor places an orderthrough a stockbroker for a NASDAQ-listed stock, the electronic system routes the order and the investor buysshares from the dealer offering the best (lowest) price. Typical NASDAQ stocks support 10 market makers activelycompeting with one another for investor trades.

market makers Dealers and specialists who oversee an orderly trading process.

dealers NASDAQ market makers who use their own capital to trade with investors

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time out!8-1 What are three primary stock exchanges in the United States and where are they located? For which of the exchanges does

physical location matter? Why?8-2 Describe differences in trading procedures on the NYSE versus the NASDAQ. Which do you think is most fair to investors?

Why?

Table 8.1 shows trading activity on the three main stock exchanges for one day in February 2016. Note that all threeexchanges traded more than 1 billion shares during the day.

The business of providing platforms or forums for investors and speculators to trade stocks and other financial assetshas been changing rapidly. Many exchanges that previously used physical floor trading systems with specialists andopen outcry to establish stock prices are shifting to electronic systems with no trading floors. Long-standing,traditional exchanges are also merging with other domestic and international exchanges to create fewer, but larger,forums that focus not just on U.S. securities but on many more internationally focused financial assets. The widerrange of represented securities allows traders new opportunities to explore trading relationships among securitiestraded across the world. This worldwide trading will establish economically sound prices and additional financialstability around the world.

▼ TABLE 8.1 Trading on the NYSE, NASDAQ, and AMEX, February 10, 2016

NYSE AMEX NASDAQ

Advancing issues 1,624 (52%) 744 (53%) 1,269 (48%)

Declining issues 1,426 (46%) 607 (44%) 1,298 (49%)

Unchanged issues    78 (2%)  42 (3%)    94 (4%)

New highs 44 20 6

New lows 156 67 201

Total volume 4,428,773,681 1,042,526,864 2,388,659,663

Source: Yahoo! Finance.

Tracking the Stock Market LG8-3With thousands of stocks trading every minute, many stock prices rise while others fall. Table 8.1 also shows that,throughout the trading day, 1,624 stocks increased in price on the NYSE while 1,426 stocks decreased in price.While the AMEX also experienced more stocks with increases in price than declines, the NASDAQ saw moredeclines. In addition to the number of stocks advancing and declining, the table also shows the number of stocks thathit new 52-week price highs (44 listed on the NYSE) and new lows (156 on the NYSE) on that day. So, was this agood day or a bad day in the stock market?

To say anything about the general direction of the stock market, stock indexes are useful. Dozens of stock indexes aredesigned to track the overall market; many more track different market segments. The three most recognized indexesare the Dow Jones Industrial Average (DJIA), the Standard & Poor’s 500 Index (S&P 500), and the NASDAQ Composite Index.

stock index Index of market prices of a particular group of stocks. The index is used to measure those stocks’ performance.

Dow Jones Industrial Average (DJIA) A popular index of 30 large, industry-leading firms.

Standard & Poor’s 500 Index (S&P 500) A stock index of 500 large companies.

NASDAQ Composite Index A technology-firm weighted index of stocks listed on the NASDAQ Stock Exchange.

Charles H. Dow invented the first stock average in 1884. At the turn of the 20th century, railroads were the firstmajor corporations. So he began with 11 stocks, mostly railroads. Dow created a price average by simply adding up11 stock prices and dividing by the number 11. Two years later, Dow began tracking a 12-stock industrial average.This industrial average would eventually evolve into the modern DJIA, which is a price average of 30 large,industry-leading stocks that together represent roughly 30 percent of the total stock value of all U.S. equities. DJIAlevel changes describe how the largest companies that participate in the stock market performed over a given period.The DJIA was at 15,914.74, a change of −99.64 (or −0.62 percent), on the day illustrated in Table 8.1.

The Standard & Poor’s Corp. introduced its 500-stock index in 1957. Standard & Poor’s chooses companies toinclude in the S&P 500 Index to represent the 10 sectors of the economy:

1. Financial

2. Information technology3. Health care

4. Industrials5. Consumer discretionary

6. Consumer staples7. Energy

8. Telecom services9. Utilities

10. Materials

S&P uses market capitalization (a measure of company size using stock price times shares outstanding), not just stockprices, of the largest 500 U.S. firms to compute the index. These 500 firms represent roughly 80 percent of theoverall stock market capitalization (number of shares times share price). Although the DJIA is a long-time favoritewith the media and individual investors, the S&P 500 is much preferred in the investment industry because of itsbroader representation of the market as a whole. S&P 500 performance provides a standard against which most U.S.money managers and pension plan sponsors can compare their investment performance. During trading on February10, 2016, the S&P 500 lost 0.35 (-0.02 percent) to close at 1,851.86.

market capitalization The size of the firm measured as the current stock price multiplied by the number of shares outstanding.

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Investors consider the NASDAQ to be a reflection of the tech sector’s general performance.©TongRo Image Stock/Alamy

The NASDAQ Composite Index measures the market capitalization of all common stocks listed on the NASDAQstock exchange. Since the NASDAQ lists so many large, technology-oriented companies, many investors andanalysts consider this index to reflect the tech sector performance more than that of the overall stockmarket. The NASDAQ Composite gained 14.83 to 4,283.59 on February 10, 2016, a gain of 0.35 percent.It was a bit of an unusual trading day because the DJIA was down, the S&P 500 was flat, and the NASDAQ was up.

Figure 8.2 shows the levels of all these stock indexes since 1980. The DJIA (maroon line) level appears on the left-hand axis. Both the S&P 500 (green line) and the NASDAQ Composite (orange line) run from the right-hand axis.The rapid price appreciation for NASDAQ stocks during the late 1990s—the tech boom years—is unprecedented forsuch a large and widely followed market index. The NASDAQ Composite soared from 817 in March 1995 to peakon March 10, 2000, at 5,048.62, for a 518 percent total return in only five years—a 43.9 percent annual rate ofshare-price appreciation for NASDAQ stocks. The NASDAQ index performed much better than did the DJIA (19.0percent per year) or the S&P 500 (22.7 percent per year). The NASDAQ “price bubble” set the stage for one of themost dramatic stock price declines in history: The NASDAQ Composite Index plunged to 1,114.11 on October 9,2002, losing 78 percent of its value. The other index values also fell during this period, albeit not as sharply. Notethat the DJIA didn’t climb back to its 2000 high until March 2006. The S&P 500 Index finally recovered in May2007. The NASDAQ Composite did not exceed its 2000 high until April 22, 2015. The stock market has been veryvolatile during the past two decades.

time out!8-3 Discuss why the day’s market return may be different when measured by the DJIA, S&P 500 Index, and NASDAQ

Composite taken separately.8-4 Why might the “market bubble” phenomenon appear more dramatic because it occurred in the NASDAQ Composite rather

than by the DJIA or S&P 500 Index?

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8-5 If you followed the market regularly, to which index would you give the most credence? Why?

The figure also shows the stock market reaction to the financial crisis that began in 2008. There were sharp declinesin all three indexes. After closing at a new high of 14,093.08 on October 12, 2007, the DJIA then fell to close at only6,547.05 on March 9, 2009. The DJIA fully recovered in early 2013 and closed above 15,000 for the first time onMay 7, 2013, and above 18,000 on February 13, 2015. This massive stock market rise coincides with thequantitative easing programs implemented by the U.S. Federal Reserve.

FIGURE 8-2 Stock Market Index Levels since 1980

This graph comparing the DJIA, S&P 500, and NASDAQ Composite indexes gives you a picture of their magnitude, as well as their patterns.

Trading Stocks LG8-4People who wish to buy and sell stocks need to open stock brokerage accounts. Traditional, full-service stockbrokers(e.g., Morgan Stanley Smith Barney, Merrill Lynch, UBS, Edward Jones) provide clients with research and advicein addition to executing trades. Their clients pay for this research and advice: Commission fees for these servicesmay run well over $100 per trade. Discount brokerage firms (e.g., Charles Schwab, E-trade, Scottrade, TDAmeritrade) charge a much lower commission, $5 to $30 per trade, but do not provide the additional services.Investors at discount brokerages usually place trades through the brokerage’s Internet sites.

finance at work //: behavioralInvestor PsychologyTo us today, it may seem ludicrous that in the years 1634 to 1636, the people of Holland were in the midst of “Tulip Mania,” and the pricefor a single rare tulip bulb approached the equivalent of $35,000. Then the bubble burst and tulip prices quickly plunged to less than theequivalent of $1. We may call those people who invested in a $35,000 tulip bulb irrational or even “crazy.”

But this type of story seems to repeat itself throughout history. Investors paid extremely high prices for the new computer stocks inthe 1960s, the “nifty fifty” companies in the 1970s, Japanese stocks during the 1980s, and Internet stocks during the late 1990s. Themania for stocks like Iomega drove its price from an equivalent of $1 per share in January of 1995 to over $75 in just 16 months. Whenthe bubble burst, the price fell hard. Many years later, in 2008, the company was purchased by EMC Corporation for dollars per share.

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But that’s just one company. A portfolio full of Internet stocks experienced a similar price mania followed by a severe fall. Investorscreated a stock index (TheStreet.com Internet Index) designed to track Internet stocks in late 1998, but by that time, part-time investorsand veterans alike were already well into the craze. The Internet index started at 250, quickly rose to 1,270 by March of 2000, andsubsequently fell to a low of 63 in October of 2002. Of course, the tech stock bubble was followed by the real estate bubble. Inretrospect, irrational bubble-like prices are not confined to tulips and the 17th century in Holland.

Seemingly irrational behavior may not occur only during highly emotional periods of a price bubble. Recently, a growing recognitionhas arisen that “normal” investors often behave in a way that might not be described as fully rational. Investors, being human, aresubject to cognitive biases and emotions. Studies of investor behavior have discovered that investors commonly succumb topsychological biases and

Source: USDA Natural Resources Conservation Service

Trade too much.

Sell winners too soon.Refuse to realize losses.

Become overconfident—especially when trading online.Seek stocks that have already increased in price—perhaps up to their full potential price.

Consider and react to what’s happening with each stock in isolation, rather than remembering the purpose for forming an overallportfolio.

Investors who succeed in the long run are those who learn to avoid these psychological biases.

Want to know more?Key Words to Search for Updates: irrational exuberance, price bubble, mania

Buy and sell orders go through the brokerage firm to a market maker (a dealer or a specialist) at a stock exchange.The quoted bid is the highest price at which the market maker offers to pay for the stock. Investors have little choicebut to accept this selling price, because regardless of the broker used, the market maker offers the only place to sellthe stock. The quoted ask price is the lowest price at which a market maker will sell a stock—so investorsbuy at the ask price. The difference between the bid and the ask price may be only $0.01 for high-volumestocks and can be as high as $0.20 for less-often traded companies. The spread between the bid and the ask price is acost to the investor and a profit for the market maker. This profit compensates the market maker for providing amarket and liquidity for that stock.

bid The quoted price investors are likely to receive when they sell stock.

ask The quoted price investors are likely to pay when they buy stock.

Investors can place a buy or sell market order. A market order to buy stock will be filled immediately at the currentask price when routed to the stock exchange. A sell market order will be filled at the current bid price. Theadvantage of a market order is that it executes immediately at the best available price. The disadvantage of a marketorder is that the investor does not know in advance what that fill price will be. Investors can name their own pricesby using limit orders, in which investors specify the price at which they are willing to execute the buy or sell order.With a buy limit order, a trade is executed if the ask quote is at or below the price target. For a sell limit order, a

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trade is executed if the bid quote moves through the specified price. If the current quote does not meet the price citedin the limit order, the trade is not executed. The advantage of a limit order is that the investor makes the trade at thedesired price; the disadvantage is that the trade might not be executed at all.

market order A stock buy or sell order to be immediately executed at the current market price.

limit order A stock buy or sell order at a specific price. It will only be executed if the market price meets the specified price.

Consider a quote of McDonald’s stock with a bid price of $117.00 and an ask price of $117.05. An investor placinga market buy order would purchase the stock at $117.05. A market sell order would execute as the price risesthrough $117.00. Note that an investor who simultaneously bought and sold 100 shares would pay $11,705 andreceive $11,700—losing $5. An investor who places a buy limit order at $116.75 will only purchase the shares if theask price falls to $117.75 or lower. If the ask does not fall, the order will not execute. Bid and ask prices tellinvestors at what prices the stock can currently be traded in general. But being able to buy at the ask price does notguarantee that the stock should be valued at that price. We’ll discuss various ways to arrive at reasonable per-sharestock values in the next section.

time out!8-6 Explain how the difference in the bid and ask prices might be considered a hidden cost to the investor.8-7 The bid and ask prices for Amazon.com are $37.79 and $37.85. If these quotes occur when a trade order is made, at what

price would a market buy order execute? Would a limit sell order execute with a target price of $37.75?

8.3 • BASIC STOCK VALUATION LG8-5Cash FlowsIn the previous chapter, we showed how we value bonds by finding the present value of the future interest paymentsand the future par value. Stock valuation uses the same concept of finding the present value of future dividends andthe future selling price. But of course uncertainty about both price appreciation and future dividend payment streamscomplicate stock valuation. Consider the simple case of valuing a stock to be held for one year shown in the timeline.

The value of such a stock today, P0, is the present value of the dividend to be received in the first year, D1, plus thepresent value of the expected sales price in one year, P1. The interest rate used to discount the cash flows is shownas i. Using the present value equation from Chapter 4 results in

(8-1)

Whenever investors deal with future stock prices and future dividend payments, they must use expected values, notcertain ones. Companies rarely decrease their dividends; most companies’ dividends either remain constantor slowly grow. Examining a firm’s dividend history over the past few years will give clues to thatcompany’s future dividend policy. For example, The Coca-Cola Company (ticker: KO) paid a $0.155 per sharedividend for each quarter in 2006. The firm then raised the quarterly dividend to $0.17 for each quarterly dividend in2007. The company paid quarterly dividends in 2008, 2009, 2010, 2011, and 2012 of $0.19, $0.205, $0.22, $0.235,and $0.255, respectively. For 2013 through 2015, Coca-Cola raised its quarterly dividend 2.5 cents every year. So

the quarterly dividend was $0.33 in 2015, for an annual dividend of $1.32. This dividend growth seems fairly stableand predictable.

Coca-Cola increased its dividend by 3 cents per year over a five-year span.©McGraw-Hill Education/Jill Braaten, photographer

Stock prices, though, show much more volatility than dividend histories do. We face much uncertainty in trying topredict stock prices in the short term. Using a longer holding period to estimate stock value reduces some, but by nomeans all, of the uncertainty. A 2-year holding period appears like this:

The present value of the cash flows in years 1 and 2 is today’s stock value:

(8-2)

Notice that the divisor for the second term on the right-hand side of equation 8-2 is raised to the second power. Thisreflects the two years over which those cash flows must be discounted. You can do this analysis over any holdingperiod. For a holding period of n years, the value of a stock is measured by the present value of dividends over the n

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years, and the eventual sale price, Pn.

(8-3)

This formula incorporates both dividend income and capital appreciation or capital loss. It fully includes both majorcomponents of the investor’s total return from investment.

McDonald’s pays an annual dividend instead of quarterly dividends.©McGraw-Hill Education/John Flournoy, photographer

As is often the case in finance, implementing equation 8-3 presents problems for some firms in practical terms.What will the future dividends of the firm be? What will the stock price be in 3, 5, or 10 years? While it seems thatthe dividend growth of Coca-Cola will be constant, consider the actual dividends and stock price of McDonald’sCorp. since 2000 shown in Figure 8.3.

McDonald’s paid an annual dividend from 2000 to 2007. Some increases were small, like the $0.01 increase from2000 to 2001 and again to 2002. Other increases were quite large, like the $0.50 increase between 2006 and 2007.Then McDonald’s changed to the more common quarterly dividend in 2008. Since the change to quarterlypayments, McDonald’s dividend growth has been more stable and predictable through 2015. The figure also showsthat McDonald’s stock price has been very volatile. The price fell from a split adjusted $25 in 2000 to$9.50 in 2003 and then steadily climbed to $45 in 2007. The stock went sideways during the financialcrisis and then shot up to $88 in late 2011. The stock again went mostly sideways from 2012 to 2014 and then shotup again in 2015. An investor in 2000 would have had a very difficult time accurately forecasting these futuredividends and stock prices. Indeed, short-term stock price changes seem almost random. Stock valuation can reallyonly be viewed from a long-term perspective. Because predicting future dividends is uncertain at best, it’s better toproject valuation as a likely range of prices under reasonable assumptions rather than as a single price. After all, thiscomputed price is an estimate of the firm’s intrinsic value. This intrinsic value may differ from the stock pricetrading in the market. This possibility is discussed as a market efficiency topic in Chapter 10.

EXAMPLE8-1 Valuing Coca-Cola Stock LG8-5

For interactive

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versions of thisexample, log in

to Connect or go tomhhe.com/CornettM4e.

In February 2016, you are valuing Coca-Cola stock to compare its value to itsmarket price. The current market price is $43.01. Given the history of Coca-Cola’s dividends, you believe that the company will pay total dividends in2016 of $1.42 (= 4 ×$0.355). Your analysis indicates that the total dividends in2017 and 2018 will be $1.54 and $1.66, respectively. In addition, you believethat the price of Coca-Cola stock at the end of 2015 will be $54.10 per share.If the appropriate discount rate is 11.0 percent, what is the value of Coca-Colastock?

SOLUTION:

To organize your data, you first create the following timeline:

Using equation 8-3, you compute the stock value as

Since your analysis shows that Coca-Cola’s stock should be valued at $43.30while it’s selling for only $43.01, the stock appears to be slightly undervalued.You believe that this might be a good time to buy some Coca-Cola stock.

Similar to Problems 8-15, 8-16, 8-27, 8-28, Self-Test Problem 1

Dividend Discount ModelsWe can extend the discounted cash flow approach in equation 8-3 for an infinite stream of dividends, n→∞, and nofinal future selling price. If stockholders receive all future cash flows as future dividends, the stock’s value to theinvestor is the present value of all these future dividends. In other words, embedded in any stock price is the value ofall future dividends. We can demonstrate this value as

(8-4)

This equation shows the general case of the dividend discount model. The dividend discount model providesa useful theoretical basis because it illustrates the importance of dividends as a fundamental stock pricedeterminant.

dividend discount model A valuation approach based on future dividend income.

FIGURE 8-3 Dividends and Stock Price of McDonald’s since 2000

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Dividends rarely decline, but stock prices often do!

But, again, finance professionals find it difficult to apply the dividend discount model because it requires that theyestimate an infinite number of future dividends. To use the model in practice, analysts make simplifyingassumptions to make the model workable. One common assumption: The firm has a constant dividend growth rate,g. If this is the case, next year’s dividend is simply this year’s dividend that grew one year at the growth rate, that is,D1 = D0 × (1 + g). In fact, we can express each dividend as a function of D0 and we can rewrite equation 8-4 as

(8-5)

So, with this version of the model, we need not forecast an infinite string of dividends; D0 and g take care of that.However, we must still compute an infinite sum of numbers. Luckily, mathematicians know equations like these;they are known as power series. This power series can be simplified to the constant-growth model, and it assumes thatthe growth rate is smaller than the discount rate (i.e., for g < i):

constant-growth model A valuation method based on constantly growing dividends.

Stock value = Next year’s dividend ÷ (Discount rate − Growth rate)

(8-6)

If g ≥ i, then the denominator would be zero or negative. Economically and mathematically, this is a nonsensicalresult. In the short run, a firm can grow very quickly. In the long run, no company can grow faster than the overalleconomic growth rate forever. You may hear the constant-growth model referred to as the Gordon growth model,after financial economist Myron J. Gordon.

EXAMPLE Constant Growth and Coca-Cola

8-2 Stock LG8-3

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

Assume that you are valuing Coca-Cola stock again. This time you are usingthe constant growth model, assuming a discount rate of 11.0 percent.

SOLUTION:

You have a choice of three growth rates to use. The implied projecteddividend growth rate is 7.94 percent. Past dividend growth has been 7.63percent and analysts forecast an 8.95 percent growth. Compute the stockvalue using all three growth rates.

Using a dividend growth rate of 7.94 percent and equation 8-6, the stockvalue is $47.27:

Using a dividend growth rate of 8.95 percent, the stock value is $71.22:

Using a dividend growth rate of 7.63 percent, the stock value is $42.80:

Notice how a small change in the growth rate has a large impact on the stockvalue in this model. At a current price of $43.01 per share, Coca-Cola couldbe considered undervalued or overvalued depending on the growth rate used.

Similar to Problems 8-19, 8-20, 8-29, 8-30, 8-31, 8-32, Self-Test Problem 2

Investors use several methods to estimate a firm’s growth rate for this model. They can project the dividend trendinto the future and determine the implied growth rate, compute the past growth rate, or even consider a financialanalyst’s growth rate predictions. Consider Coca-Cola’s dividend behavior. If the 2015 dividend was $1.34 and theprojected dividends will grow to $1.66 in 2018, the implied projected dividend growth rate is therefore 7.94 percent(N = 3, PV = −1.34, PMT = 0, FV = 1.66, CPT I = 7.94) annually. The growth rate in dividend changes from 2008to 2012 was 7.63 percent (N = 4, PV = −0.76, PMT = 0, FV = 1.02, CPT I = 7.63) per year. You can find analystforecasts many places online. The Yahoo! Finance web page for Coca-Cola has an Analyst Estimates link, whichshows the average analysts’ forecast for the firm’s growth in the next five years at 8.95 percent.

Preferred StockA special case of the constant-growth model occurs when the dividend does not grow but is the same every year.This zero-growth rate case describes a preferred stock. The term preferred comes from the fact that this type of stocktakes preference over common stock in bankruptcy proceedings. Preferred stockholders have a higher priority forreceiving proceeds from bankruptcy proceedings than do common stockholders. Preferred stock is largely owned byother companies, rather than by individual investors, because its dividends are mostly nontaxable income (70percent of the income is exempt from taxes) to other corporations. Preferred stockholders do not have voting rights

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like common stockholders, though, which prevents one company from controlling another through preferred stockownership.

preferred stock A hybrid security that has characteristics of both long-term debt and common stock.

An interesting characteristic of preferred stock is that it pays a constant dividend. Because the dividend does notchange, the preferred stock can be valued using the constant-growth-rate model with a zero growth rate expressed asP = D/i. What would Coca-Cola’s stock be worth if its dividend stayed at $1.34 and never grew? Using thesame 11.0 percent discount rate, the stock would be valued at $12.18 (= $1.34 ÷ 0.110). Given Coca-Cola’s current stock price of $43.01, over 71.6 percent [= ($43.01 − $12.18)/$43.01] of its stock value comes fromthe expectation that Coca-Cola’s dividend will grow. In other words, investors highly value a growing firm.

Most companies issue only common stock, but nearly 1,000 preferred stock issues still exist. Table 8.2 compares thecommon stock and preferred stock for 10 firms. Many of the preferred stocks come from the finance, energy, andreal estate sectors. Notice that the dividend yield for preferred stock is higher than for the common stock, becausepreferred stock investors should expect a return from dividend payments only. Common stockholders will alsoexpect a return from capital appreciation over time. Common stocks also trade much more frequently than preferredstocks do.

dividend yield Last four quarters of dividend income expressed as a percentage of the current stock price.

the Math Coach on…Using the Constant-Growth-Rate Model

“The distinction between the recent year’s dividends, D0, and next year’sdividends, D1, can be confusing in the constant growth-rate model. The model’sequation presents two different numerators. If you are given information aboutdividends last year or just paid, use the D0(1 + g) version of the equation. If youhave information about expected dividends or next year’s dividend, use the D1version of the equation.„

The zero-growth-rate version of the constant-growth valuation model shows that, since dividends are fixed, apreferred stock’s price changes because of changes in the discount rate, i. When interest rates throughout theeconomy change, the discount rate also changes. Preferred stock prices thus tend to act like bond prices. Wheninterest rates rise, preferred stock prices fall. When interest rates decline, preferred stock prices rise. Preferred stockis usually categorized with bonds in the fixed-income security group because it acts so much like debt securities,even though a preferred stock represents equity ownership, like common stock.

Expected ReturnStock valuation models require a discount rate, i, in order to compute the present value of the future cash flows. Thediscount rate used should reflect the investment risk level. Higher risk investments should be evaluated using higherinterest rates. For example, the previous chapter on bonds demonstrated that higher risk bonds, such as junk bonds,offer higher rates of return. Similarly, investors demand higher returns from higher risk stocks than they do fromlower risk stocks. We discuss stock risk measurement and appropriate expected returns in the next section of thisbook.

▼ TABLE 8.2 Common and Preferred Stock, February 12, 2016

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COMMON STOCK PREFERRED STOCK

Company Ticker Price

AnnualDividend(Yield%) Volume Ticker Price

AnnualDividend(Yield%) Volume

Alcoa Inc. AA $ 7.69 $0.12(1.2) 26,021,380 AAPRB $26.74 $2.69(8.1) 49,122

El Du Pont deNemours & Co.

DD $ 58.48 $1.72(2.6) 5,397,520 DDPRA $79.75 $3.50(4.5)

Ford Motor Co. F $ 11.55 $0.60(4.3) 28,080,850 FPRA $25.55 $1.88(7.3) 97,959

NationalHealthcare

NHC $ 61.29 $1.54(2.5) 23,484 NHCA $15.52 $0.80(5.1)

PG&E Corp. PCG $ 55.21 $1.82(3.4) 2,877,339 PCG.PRA $30.57 $0.75(2.6) 3,247

Public StorageInc.

PSA $233.61 $6.50(2.6) 1,040,665 PSAPRW $24.74 $1.30(5.7) 51,329

Source: New York Stock Exchange (www.nyse.com).

finance at work //: investmentsFinancial Analysts’ Predictions and Opinions

©bunhill/Getty Images

Financial analysts examine a firm’s business and financial success and assess long-term prospects and management effectiveness.They combine this microeconomic analysis with a macroeconomic view of the conditions of the economy, financial markets, and industryoutlooks. Their evaluation results in earnings predictions, stock price targets, and opinions about whether investors should buy the stock.Such recommendations can help investors decide whether to buy, hold, or sell the stock.

Analysts hired by brokerage firms and investment banks are called sell-side analysts because their firms make money by sellingstocks and bonds. These analysts publicize their predictions and opinions publicly and in company “tip sheets” that are passed along toclients. Keep in mind that sell-side analysts often have incentives to be optimistic. Pension funds and mutual funds often hire analysts togive fund managers private opinions about securities. These analysts are referred to as buy-side analysts because they are hired byinvestment firms looking for advice on what stocks to buy for their portfolios. Because this is private, little buy-side research is madepublic.

Consider the 26 sell-side analysts’ predictions reported for Coca-Cola on the Yahoo! Finance website. The average five-year shareprice growth prediction from these analysts is 8.95 percent. This is lower than the growth prediction for the industry (12.96 percent) andsector (12.79 percent). Last, analysts give opinions on whether investors should buy, sell, or hold Coca-Cola stock. Recommendationscome in five levels: Strong Buy, Buy, Hold, Underperform, and Sell. Of the 26 analysts, 4 recommend a Strong Buy, 9 recommend aBuy, and 10 recommend a Hold. Note that even though the analysts predict lower than average growth for the industry and sector, andthat the analysts provide meager price targets, only three of the analysts recommend an Underperform and none a Sell. This optimism inanalysts’ opinions is common. Knowledgeable investors know that a “hold” recommendation is as negative as most public or sell-side

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analysts get, and therefore a “hold” may actually represent a signal to sell.

Want to know more?Key Words to Search for Updates: analyst opinion, financial analyst bias

However, one method for determining what return stock investors require from a stock is to use the constant-growth-rate model. If the current stock price fairly reflects its value, then the discount rate, i, in equation 8-6 shouldbe the expected return for the stock. Solving for this expected return results in equation 8-7:

(8-7)

Note that the expected return comes again from two sources: dividend yield and expected appreciation of the stockprice, or capital gain. For example, consider that Coca-Cola’s dividend in 2016, D1, is expected to be $1.42 pershare. At a current price of $43.01, Coca-Cola offers a dividend yield of 3.30 percent (= $1.42 ÷ $43.01). Sinceanalysts believe that the firm’s stock price will grow at 8.95% percent in the future, investors expect a total return of12.25 percent (= 3.30% + 8.95%). Dividend yield can represent a substantial portion of the profits for an investor.Many people get too enamored of high growth stocks that do not pay dividends and therefore miss out on animportant source of stable returns.

growth stocks Companies expected to have above-average rates of growth in revenue, earnings, and/or dividends.

time out!8-8 Explain how valuable a firm’s (and therefore its stock’s) growth is. Demonstrate this with growth and no-growth examples.8-9 What proportion of the 12.25 percent of Coca-Cola’s expected return above comes from dividend yield?

Corporate managers conduct an important application of the expected return concept to determine the return thattheir shareholders expect of them. We will discuss this application in detail in Part Six: Capital Budgeting.

8.4 • ADDITIONAL VALUATION METHODS LG8-6Variable-Growth TechniquesSome companies grow at such a high rate that we cannot use the constant-growth-rate model to forecast their value.High growth rates might be sustainable for several years, but cannot continue forever. Consider what happens to ahigh-growth firm. Other companies will surely notice the market potential for high-growth rates and will enter thoseproduct markets to compete with the high-growth firm. The competition will soon drive down the growth rates forall companies in that product market. Companies that experience unusually high-growth tend to see that growthbecome only average in the future unless they possess some kind of entry barrier such as a patent or governmentregulation due to economies of scale.

Remember that the constant-growth-rate model does not work for companies where g > i. And of course, we do notreally expect the growth rate for these fast-growing firms to remain constant. To value these firms, we must use avariable-growth-rate technique. The variable-growth-rate method combines the present-value cash flow from equation8-3 and the constant-growth-rate model from equation 8-6.

variable growth rate A valuation technique used when a firm’s current growth rate is expected to change some time in the future.

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First, the investor chooses two different growth rates for two stages of the analysis. The first and higher growth rate,g1, is the current growth rate, which we expect to last only a few years. A few years from now, we expect the firm togrow at a slower but more sustainable rate of growth, g2. Figure 8.4 shows the cash flow time line when the firstgrowth rate applies for the first n years, followed by the second growth rate, which applies forever.

When we analyze a variable-growth-rate stock like the one in the figure, we know the recent dividend, D0, and thetwo expected growth rates. Therefore, we can calculate each of the dividends shown in general terms (i.e., D1). Forexample, the dividend in the first year (D1) is the year zero dividend that grows at g1, specifically D1 = D0 × (1 +g1). The dividend then grows at g1 again for the second year dividend, D2 = D0 × (1 + g1)

2. The dividend continuesto grow through the first stage to year n at Dn = D0 × (1 + g1)

n. Figure 8.5 shows the first-stage dividends.

At this point, the company starts to move into stage 2 at the more modest growth rate, g2, and the dividends reflectthat slower growth rate. So Dn+1 is the dividend Dn that grew at the rate g2, or Dn+1 = D0 × (1 + g1)

n × (1 + g2).Similarly, the dividend in year n + 2 is Dn+2 = D0 × (1 + g1)

n × (1 + g2)2. We can now substitute the known

dividends as presented in Figure 8.5 into Figure 8.6.

Once we have calculated all of the dividends, we can begin finding the value of the variable-growth stock byfocusing on Stage 2 of the problem. Assume that the dividends in Stage 2 are growing at a modest rate, g2, forever.As long as g2 < i, Stage 2 can use the constant-growth model, equation 8-6. Remember that the constant-growthmodel, P0 = D1/(i − g), replaces all future dividends with one value in the previous period. In previousapplications, the growth began in year 1, so the value used for all future dividends came from the year 0 dividend. Inthis case, the change in the dividend rate occurs in year n + 1, so we will use the value from year n. So, using theconstant-growth model, we can replace all the cash flows in Stage 2 with one value from year n, as

The cash flows from Figure 8.6 now appear as shown in Figure 8.7.

FIGURE 8-4 Variable Dividend Growth

Divide into two stages at the first year of the new growth rate.

FIGURE 8-5 Stage 1 Dividends

Calculate the dividends in the first stage.

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FIGURE 8-6 Details of the Variable Growth Dividends

Compute the dividends in the second stage.

By replacing all the Stage 2 cash flows that continued indefinitely with one terminal price in year n, we reduce theproblem to a fixed number of cash flows. The value of this variable-growth stock is finally computed as the presentvalue of these cash flows, as solved with equation 8-3. Substituting the cash flows shown in Figure 8.7 into equation8-3 gives us the general formula for finding the value of a variable-growth stock:

General two-stage growth valuation model:

(8-8)

The practical application of the variable-growth valuation technique requires the investor to decide how long thecurrent high-growth rate will last before declining to a more stable rate.

FIGURE 8-7 New Stage 1 of the Variable Growth Dividend Technique

Replace all of the dividends to infinity with the price (terminal value) in year n. Stage 2 disappears.

The constant-growth-rate model is most useful for large, mature companies that grow in a stable manner. Thevariable-growth-rate model works well for dividend-paying companies that have an unusually fast rate of growth inthe near future but are expected to enter a more stable growth rate environment soon. But there are still many firmsthat do not fit these two descriptions of firm growth. For example, many firms pay no dividends. To value firms withno dividends, replace the dividends in the models with cash flows. When you do this, you are valuing the entirefirm, not just the stock value, because cash flows go to both stockholders and debt holders. In the case where a firmhas low or even negative cash flows, the valuation techniques in the next section can be employed.

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time out!8-10 Explain how the variable-growth-rate technique could be used for a firm whose dividend is not expected to grow for three

years and then will grow at 5 percent indefinitely.8-11 Set up and solve the McDonald’s valuation problem assuming that the first stage growth will last only two years.

EXAMPLE8-3

Variable Growth and StockValue LG8-6

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

The dividend has grown from $1.00 per share on November 13, 2009, to$2.80 during 2015. This represents an annual growth rate of 18.7 percent (N= 6, PV = −1.00, PMT = 0, FV = 2.80, CPT I = 18.7). You think this growthrate will continue for three years and then fall to the long-term growth rate of9.29 percent predicted by analysts. You assume a 13 percent discount rate.

SOLUTION:

Figure 8.3 shows a $2.80 (= 4 × $0.70) per share recent annual dividend.Modify equation 8-8 for a Stage 1 length of three years and then substitute i =0.13, g1 = 0.187, g2 = 0.0929, and D0 = $2.80. The valuation equation andsolution becomes

Given these parameters, the company’s stock is worth nearly $105 per share.

Similar to Problems 8-33, 8-34, Self-Test Problem 3

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The P/E Model LG8-7The valuation models that we’ve presented thus far help investors attempt to compute a stock’s fundamental valuebased upon its cash flows to the investor. Another common approach is to assess a stock’s relative value. Thisapproach compares one company’s stock valuation to other firms’ stock values to evaluate whether your targetcompany’s stock is appropriately priced. The price of a stock taken in isolation doesn’t give us a good measure ofhow expensive it is. Let’s use an analogy: At the grocery store, we are less concerned with the total price of a bag ofsugar than we are with the price per pound. Similarly, the price of the stock matters less than its price per one dollarof earnings.

relative value A stock’s priceyness measured relative to other stocks.

Consider one company that earned $5 per share in profits for the year. Its stock sells for $100. Another companyearned $2 per share and its stock price is $50 per share. At first glance, the first stock appears to be more expensivebecause its price is a high $100 compared to the lower $50 price of the second stock. However, the first companygenerated higher per-share profits than did the second company. Buying the first stock means that you purchase $5in earnings. The $100 stock price implies a cost of $20 for every $1 in earnings (= $100 ÷ $5) generated. The $50price of the second stock implies a cost of $25 for every $1 in earnings (= $50 ÷ $2). So in this regard, the secondcompany becomes more expensive. The price-earnings (P/E) ratio represents the most common valuation yardstick inthe investment industry; it allows investors to quickly compare the cost of earnings. The P/E ratio is simply thecurrent price of the stock divided by the last four quarters of earnings per share:

(8-9)

price-earnings (P/E) ratio Current stock price divided by four quarters of earnings per share.

More accurately, this figure is the trailing P/E ratio and it is often denoted as P/E0, where the 0 subscript denotes thepast (or trailing) earnings.

trailing P/E ratio The P/E ratio computed using the past four quarters of earnings per share.

Figure 8.8 shows two companies’ trailing P/E ratios: Coca-Cola and McDonald’s, as well as the Dow JonesIndustrial Average’s trailing P/E ratio over a 16-year period. The P/E ratio for the DJIA changes slowly and mostlystays in the 18 to 27 range until the recent drop to 15. Historically, the DJIA’s P/E ratio has fallen as low as singledigits and climbed to over 30. The figure also shows that the P/E ratio for McDonald’s has varied morethan has the index’s P/E ratio. The P/E ratio for Coca-Cola has experienced wild changes—as high as 63and as low as 18. Figure 8.8 shows that investors valued Coca-Cola more than McDonald’s in the late 1990s, butvalued them nearly the same by the beginning of 2008.

FIGURE 8-8 Historical P/E Ratio of the DJIA, Coca-Cola, and McDonald’s

P/E ratios of large, successful companies can vary considerably over time. Here, you see that investors valued Coca-Cola over McDonald’sfor much of the period, but there were periods when McDonald’s was valued higher.Source: Dow Jones and Company.

Variations in P/E ratios between popular companies can be quite large. For example, in February of 2016, the P/Eratio for Alphabet (the parent company of Google) was 28.7, while the ratio for Boeing Company was only 14.6.Alphabet stock is much more expensive than Boeing. But this does not mean that Boeing stock is a better deal thanAlphabet stock. Investors are willing to pay much more in relative terms for Alphabet because they expect Alphabetwill grow much faster than Boeing. Indeed, analysts predict an annual growth rate of 16.7 percent per year forAlphabet over the next five years, while they expect a growth rate of only 11.9 percent for Boeing. Remember thatExample 8-2 shows how small changes in growth can result in large stock value changes. The large difference inexpected growth between Alphabet and Boeing causes a large difference in their relative value.

We can more directly see the impact that growth can have on the P/E ratio by modifying the constant-growth model.Begin with the model, P0 = D1 ÷ (i − g). Dividing both sides by the firm’s earnings results in P0/E0 = (D1/E0) ÷ (i −g). Note that the dividend payout ratio of the firm (D/E), the discount rate (i), and the growth rate (g), taken together,determine the P/E ratio. All else held equal, larger growth rates will lead to larger P/E ratios. Also, firms that havehigher payout ratios will have higher P/E ratios. Of course, if a firm pays out a high portion of its earnings asdividends, then it may not have the cash to fund high growth. Thus, high dividend payout firms tend not to be pricedthe same as high growth firms.

The value of a stock, and thus its price, relates directly to its future success. Note that valuation models use estimatesof future dividends and growth rates. Because of this focus on the future, many people prefer to use a P/E ratio thatalso looks forward rather than trailing. A forward P/E ratio uses analyst estimates of the earnings in the next 12 monthsinstead of the past 12 months and can be denoted as P/E. The forward P/E ratio has the advantage over the trailingP/E ratio in that it incorporates investors’ expectations of the firm’s upcoming profits. A disadvantage is thatexpected earnings are harder to estimate and thus less accurate than past earnings. The media uses the trailing P/Eratio, while financial managers and investors use the forward P/E ratio more.

forward P/E ratio The P/E ratio computed using the estimated next four quarters of earnings per share.

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Investors consider Home Depot an appropriately priced stock.

Knowledgeable investors who use the P/E ratio as a relative measure of value compare it to the firm’s expectedgrowth rate. Table 8.3 shows the forward P/E ratio and analysts’ expected growth rates for the 30 Dow JonesIndustrial Average firms. Investors consider companies with high P/E ratios and high growth rates to beappropriately priced. Companies with low P/E ratios and low growth also seem to be appropriately priced. Investorsshould be concerned about firms with high P/E ratios and only single-digit growth rates. As such, Procter & Gamble,Coca-Cola, McDonald’s, and Chevron, among others, may be too expensive for their expected growth rates. Manyinvestors like to buy growth stocks. They seek companies with high growth rates. But growth stock investors arealso concerned about paying too much for a stock. While examining growth stocks, they can use the P/E ratio toassess how expensive the stock is. On the other hand, investors consider companies with low P/E ratios and highexpected growth to be undervalued, and they are often referred to as value stocks. Apple and Boeing wouldqualify as value stocks. Many investors like to buy value stocks because they feel they are getting abargain price for a stable company.

value stocks Companies considered to be temporarily undervalued.

▼ TABLE 8.3 P/E Ratios and Analyst Growth Estimates of DJIA Firms, February 12, 2016

A B C D E

1 Ticker Company Name Stock Price Forward P/E Ratio Next 5 Year’s Growth (%)

2 HD Home Depot $116.32 18.88 14.39

3 PG Procter & Gamble 80.99 20.00 6.95

4 KO Coca-Cola Company 43.11 20.83 8.95

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5 MCD McDonald’s Corporation 117.93 19.56 9.50

6 VZ Verizon Communication 50.11 12.31 4.51

7 DIS Walt Disney 91.15 14.68 11.85

8 MMM 3M Company 153.96 17.26 8.10

9 JNJ Johnson & Johnson 101.82 14.76 5.32

10 AAPL Apple, Inc. 93.99 9.39 11.93

11 UTX United Technologies 85.95 12.24 9.07

12 GE General Electric 28.26 15.96 7.97

13 WMT Walmart Stores 66.18 15.87 0.87

14 AXP American Express 52.66 9.37 8.10

15 PFE Pfizer 29.36 11.65 5.44

16 MRK Merck & Company 49.03 12.87 4.24

17 XOM Exxon Mobil 81.03 18.58 26.40

18 IBM International Business Machines 121.04 8.55 7.25

19 TRV The Travelers Company 107.49 10.79 2.94

20 DD E.I. du Pont de Nemours 58.40 16.88 9.00

21 BA Boeing Company 108.63 11.53 11.92

22 NKE Nike, Inc. 56.42 22.84 12.62

23 CSCO Cisco Systems 25.11 10.51 8.24

24 INTC Intel Corporation 28.64 10.77 10.00

25 CAT Caterpillar 63.15 17.21 0.43

26 CVX Chevron Corporation 85.43 18.18 −23.86

27 UNH UnitedHealth Group 111.82 12.74 14.03

28 MSFT Microsoft Corporation 50.50 16.45 9.51

29 GS Goldman Sachs Group 146.13 7.54 4.31

30 JPM JPMorgan Chase 57.49 8.59 7.89

31 V Visa, Inc. 70.42 21.67 16.62

Source: Yahoo! Finance Screener.

There are some cases when a P/E ratio is not useful for relative valuation. For example, sometimes, a firm will losemoney. That is, the earnings are negative. In other cases, a firm will take a large “write-off” that will temporarilysuppress earnings. In these cases, the P/E ratio would be negative or temporarily large. Therefore, other commonrelative value techniques are to utilize cash flow (CF) or book value (B) instead of earnings. The P/CF ratio is usefulwhen firms take accounting write-offs that temporarily and dramatically impact earnings. The P/B ratio is useful inall cases but is particularly useful when a firm loses money and has negative cash flows. The book value of a firm isa very stable measure of accounting value, and it is therefore useful when earnings are volatile.

EXAMPLE8-4

The P/E Ratio Model forCaterpillar LG8-7

page 255

For interactiveversions of this

example, log in toConnect or go tomhhe.com/CornettM4e.

For interactive versions of this example, log in to Connect or go tomhhe.com/CornettM4e. Look at Table 8.3 and notice that the P/E ratio forCaterpillar seems high at 17.21 relative to the growth (0.43 percent) thatanalysts expect. Caterpillar earned $3.50 per share and paid a $3.08 dividendlast year. You decide to explore this apparent anomaly and figure out whatCaterpillar’s stock price might reach in five years.

SOLUTION:

Compute the expected future price in five years under two different scenarios.The first assumption is that Caterpillar’s P/E ratio will be the same in fiveyears as it is today. But since this P/E ratio seems a bit high, the secondscenario allows for a decline in the P/E ratio to 13. Under these two scenarios,the future price estimates are

Note that if the P/E ratio decreases from 17.21 to 13 in five years, the futureprice could be much lower than analysts expect without the change.

Similar to Problems 8-25, 8-26, 8-35, 8-36

time out!8-12 Consider two firms with the same P/E ratio. Explain how one could be described as expensive compared to the other.8-13 Compute the stock price for Goldman Sachs in five years if you expect the P/E ratio to decline to 6 and the earnings per

share is $18.58.

Estimating Future Stock PricesWe can often find it useful to estimate a stock’s future price. Consider equation 8-3’s cash flow discount valuationmodel. The model requires estimates of future dividends and a future price. How can investors estimate this futureprice? They can use the P/E ratio model for this purpose. Upon reflection, you will see that multiplying the P/E ratioby earnings results in a stock price. So, in order to estimate a future price, simply multiply the expected P/E ratio bythe expected earnings. This concept is captured in the following equation:

Future price = Future P / E ratio × Future earnings per share

(8-10)

As the formula shows, we can use assumptions about the earnings growth rate to estimate earnings in year n. Manyinvestors believe the firm’s P/E ratio in year n is best estimated using today’s P/E ratio. However, if today’s P/Eratio seems unusual compared with similar firms or even compared with a stock index, then adjustments might bewise.

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Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. As owners, what rights and advantages do shareholders obtain? (LG8-1)

2. Describe how being a residual claimant can be very valuable. (LG8-1)

3. Obtain a current quote of McDonald’s (MCD) from the Internet. Describe what has changed since the quote inFigure 8.1. (LG8-2)

4. Get the trading statistics for the three main U.S. stock exchanges. Compare the trading activity to that of Table8.1. (LG8-2)

5. Why might the Standard & Poor’s 500 Index be a better measure of stock market performance than the DowJones Industrial Average? Why is the DJIA more popular than the S&P 500? (LG8-3)

6. Explain how it is possible for the DJIA to increase one day while the NASDAQ Composite decreases duringthe same day. (LG8-3)

7. Which is higher, the ask quote or the bid quote? Why? (LG8-4)

8. Illustrate through examples how trading commission costs impact an investor’s return. (LG8-4)

9. Describe the difference in the timing of trade execution and the certainty of trade price between market ordersand limit orders. (LG8-4)

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10. What are the differences between common stock and preferred stock? (LG8-5)

11. How important is growth to a stock’s value? Illustrate with examples. (LG8-5)

12. Under what conditions would the constant-growth model not be appropriate? (LG8-5)

13. The expected return derived from the constant-growth-rate model relies on dividend yield and capitalgain. Where do these two parts of the return come from? (LG8-5)

14. Describe, in words, how to use the variable-growth-rate technique to value a stock. (LG8-6)

15. Can the variable-growth-rate model be used to value a firm that has a negative growth rate in Stage 1 and astable and positive growth in Stage 2? Explain. (LG8-6)

16. Explain why using the P/E relative value approach may be useful for companies that do not pay dividends.(LG8-7)

17. How is a firm’s changing P/E ratio reflected in the stock price? Give examples. (LG8-7)

18. Differentiate the characteristics of growth stocks and value stocks. (LG8-7)

19. What’s the relationship between the P/E ratio and a firm’s growth rate? (LG8-7)

20. Describe the process for using the P/E ratio to estimate a future stock price. (LG8-7)

ProblemsBASIC PROBLEMS

8-1 Stock Index Performance On March 5, 2013, the Dow Jones Industrial Average set a new high. Theindex closed at 14,253.77, which was up 125.95 that day. What was the return (in percent) of the stockmarket that day? (LG8-3)

8-2 Stock Index Performance On March 9, 2009, the Dow Jones Industrial Average reached a new low. Theindex closed at 6,547.05, which was down 79.89 that day. What was the return (in percent) of the stockmarket that day? (LG8-3)

8-3 Buying Stock with Commissions Your discount brokerage firm charges $7.95 per stock trade. Howmuch money do you need to buy 200 shares of Pfizer, Inc. (PFE), which trades at $31.40? (LG8-4)

8-4 Buying Stock with Commissions Your discount brokerage firm charges $9.50 per stock trade. Howmuch money do you need to buy 300 shares of Time Warner, Inc. (TWX), which trades at $22.62? (LG8-4)

8-5 Selling Stock with Commissions Your full-service brokerage firm charges $140 per stock trade. Howmuch money do you receive after selling 200 shares of Nokia Corporation (NOK), which trades at $20.13?(LG8-4)

8-6 Selling Stock with Commissions Your full-service brokerage firm charges $135 per stock trade. Howmuch money do you receive after selling 250 shares of International Business Machines (IBM), whichtrades at $96.17? (LG8-4)

8-7 Buying Stock with a Market Order You would like to buy shares of Sirius Satellite Radio (SIRI). Thecurrent ask and bid quotes are $3.96 and $3.93, respectively. You place a market buy order for 500 sharesthat executes at these quoted prices. How much money did it cost to buy these shares? (LG8-4)

8-8 Buying Stock with a Market Order You would like to buy shares of Coldwater Creek, Inc. (CWTR).The current ask and bid quotes are $20.70 and $20.66, respectively. You place a market buy order for 200shares that executes at these quoted prices. How much money did it cost to buy these shares? (LG8-4)

8-9 Selling Stock with a Limit Order You would like to sell 200 shares of Xenith Bankshares, Inc. (XBKS).The current ask and bid quotes are $4.66 and $4.62, respectively. You place a limit sell order at $4.65. Ifthe trade executes, how much money do you receive from the buyer? (LG8-4)

8-10 Selling Stock with a Limit Order You would like to sell 100 shares of Echo Global Logistics, Inc.

(ECHO). The current ask and bid quotes are $15.33 and $15.28, respectively. You place a limit sell orderat $15.31. If the trade executes, how much money do you receive from the buyer? (LG8-4)

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8-11 Value of a Preferred Stock A preferred stock from Duquesne Light Company (DQUPRA) pays $3.55in annual dividends. If the required return on the preferred stock is 6.7 percent, what’s the value of thestock? (LG8-5)

8-12 Value of a Preferred Stock A preferred stock from Hecla Mining Co. (HLPRB) pays $3.50 in annualdividends. If the required return on the preferred stock is 6.8 percent, what is the value of the stock? (LG8-5)

8-13 P/E Ratio and Stock Price Ultra Petroleum (UPL) has earnings per share of $1.56 and a P/E ratio of32.48. What’s the stock price? (LG8-7)

8-14 P/E Ratio and Stock Price JPMorgan Chase Co. (JPM) has earnings per share of $3.53 and a P/E ratioof 13.81. What is the price of the stock? (LG8-7)

INTERMEDIATE PROBLEMS

8-15 Value of Dividends and Future Price A firm is expected to pay a dividend of $1.35 next year and$1.50 the following year. Financial analysts believe the stock will be at their price target of $68 in twoyears. Compute the value of this stock with a required return of 10 percent. (LG8-5)

8-16 Value of Dividends and Future Price A firm is expected to pay a dividend of $2.05 next year and$2.35 the following year. Financial analysts believe the stock will be at their price target of $110 intwo years. Compute the value of this stock with a required return of 12 percent. (LG8-5)

8-17 Dividend Growth Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. Whatwas the annual growth rate? (LG8-5)

8-18 Dividend Growth Annual dividends of Generic Electrical grew from $0.66 in 2012 to $1.03 in 2017.What was the annual growth rate? (LG8-5)

8-19 Value a Constant Growth Stock Financial analysts forecast Safeco Corp.’s (SAF) growth rate forthe future to be 8 percent. Safeco’s recent dividend was $0.88. What is the value of Safeco stock whenthe required return is 12 percent? (LG8-5)

8-20 Value a Constant Growth Stock Financial analysts forecast Limited Brands (LTD) growth rate forthe future to be 12.5 percent. LTD’s recent dividend was $0.60. What is the value of Limited Brandsstock when the required return is 14.5 percent? (LG8-5)

8-21 Expected Return Ecolap Inc. (ECL) recently paid a $0.46 dividend. The dividend is expected togrow at a 14.5 percent rate. At a current stock price of $44.12, what is the return shareholders areexpecting? (LG8-5)

8-22 Expected Return Paychex Inc. (PAYX) recently paid an $0.84 dividend. The dividend is expected togrow at a 15 percent rate. At a current stock price of $40.11, what is the return shareholders areexpecting? (LG8-5)

8-23 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its firstdividend of $0.20 per share in three years. This dividend will grow at 11 percent indefinitely. Using a12 percent discount rate, compute the value of this stock. (LG8-6)

8-24 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its firstdividend of $0.25 per share in two years. This dividend will grow at 10 percent indefinitely. Using an11.5 percent discount rate, compute the value of this stock. (LG8-6)

8-25 P/E Ratio Model and Future Price Kellogg Co. (K) recently earned a profit of $2.52 earnings pershare and has a P/E ratio of 13.5. The dividend has been growing at a 5 percent rate over the past fewyears. If this growth rate continues, what would be the stock price in five years if the P/E ratioremained unchanged? What would the price be if the P/E ratio declined to 12 in five years? (LG8-7)

8-26 P/E Ratio Model and Future Price New York Times Co. (NYT) recently earned a profit of $1.21

per share and has a P/E ratio of 19.59. The dividend has been growing at a 7.25 percent rate over thepast six years. If this growth rate continues, what would be the stock price in five years if the P/E ratioremained unchanged? What would the price be if the P/E ratio increased to 22 in five years? (LG8-7)

ADVANCED PROBLEMS

8-27 Value of Future Cash Flows A firm recently paid a $0.45 annual dividend. The dividend is expected

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to increase by 10 percent in each of the next four years. In the fourth year, the stock price is expectedto be $80. If the required return for this stock is 13.5 percent, what is its value? (LG8-5)

8-28 Value of Future Cash Flows A firm recently paid a $0.60 annual dividend. The dividend is expectedto increase by 12 percent in each of the next four years. In the fourth year, the stock price is expectedto be $110. If the required return for this stock is 14.5 percent, what is its value? (LG8-5)

8-29 Constant Growth Stock Valuation Waller Co. paid a $0.137 dividend per share in 2000, whichgrew to $0.55 in 2012. This growth is expected to continue. What is the value of this stock at thebeginning of 2013 when the required return is 13.7 percent? (LG8-5)

8-30 Constant Growth Stock Valuation Campbell Supper Co. paid a $0.632 dividend per share in 2013,which grew to $0.76 in 2016. This growth is expected to continue. What is the value of this stock atthe beginning of 2017 when the required return is 8.7 percent? (LG8-5)

8-31 Changes in Growth and Stock Valuation Consider a firm that had been priced using a 10 percentgrowth rate and a 12 percent required return. The firm recently paid a $1.20 dividend. The firm justannounced that because of a new joint venture, it will likely grow at a 10.5 percent rate. How muchshould the stock price change (in dollars and percentage)? (LG8-5)

8-32 Changes in Growth and Stock Valuation Consider a firm that had been priced using an 11.5percent growth rate and a 13.5 percent required return. The firm recently paid a $1.50 dividend. Thefirm has just announced that because of a new joint venture, it will likely grow at a 12 percent rate.How much should the stock price change (in dollars and percentage)? (LG8-5)

8-33 Variable Growth A fast-growing firm recently paid a dividend of $0.35 per share. The dividend isexpected to increase at a 20 percent rate for the next three years. Afterwards, a more stable 12 percentgrowth rate can be assumed. If a 13 percent discount rate is appropriate for this stock, what is itsvalue? (LG8-6)

8-34 Variable Growth A fast-growing firm recently paid a dividend of $0.40 per share. The dividend isexpected to increase at a 25 percent rate for the next four years. Afterwards, a more stable 11 percentgrowth rate can be assumed. If a 12.5 percent discount rate is appropriate for this stock, what is itsvalue? (LG8-6)

8-35 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per share and dividendper share are $2.50 and $1.30, respectively. Both are expected to grow at 8 percent. However, thefirm’s current P/E ratio of 22 seems high for this growth rate. The P/E ratio is expected to fall to 18within five years. Compute a value for this stock by first estimating the dividends over the next fiveyears and the stock price in five years. Then discount these cash flows using a 10 percent required rate.(LG8-5, LG8-7)

8-36 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per share and dividendper share are $2.75 and $1.60, respectively. Both are expected to grow at 9 percent. However, thefirm’s current P/E ratio of 23 seems high for this growth rate. The P/E ratio is expected to fall to 19within five years. Compute a value for this stock by first estimating the dividends over the next fiveyears and the stock price in five years. Then discount these cash flows using an 11 percent requiredrate. (LG8-5, LG8-7)

8-37 Spreadsheet Problem Spreadsheets are especially useful for computing stock value under

different assumptions. Consider a firm that is expected to pay the following dividends:

Year1 2 3 4 5 6

$1.20 $1.20 $1.50 $1.50 $1.75 $1.90 and grow at5% thereafter

a. Using an 11 percent discount rate, what would be the value of this stock?b. What is the value of the stock using a 10 percent discount rate? A 12 percent discount rate?c. What would the value be using a 6 percent growth rate after year 6 instead of the 5 percent rate

using each of these three discount rates?d. What do you conclude about stock valuation and its assumptions?

8-38 Spreadsheet Problem Design a spreadsheet similar to the one below to compute the value of avariable growth rate firm over a five-year horizon.

a. What is the value of the stock if the current dividend is $1.30, the first stage growth is 18 percent,the second stage growth is 9 percent, and the discount rate is 11 percent?

b. What is the value of the stock if the current dividend is $1.30, the first stage growth is 2 percent, thesecond stage growth is 8 percent, and the discount rate is 9.5 percent?

c. What is the value of the stock if the current dividend is $2.50, the first stage growth is 15 percent,the second stage growth is 7 percent, and the discount rate is 10 percent?

A B C D E F

1 Inputs

2 Current dividend =

3 First-stage growth =

4 Second-stage growth =

5 Discount rate =

6

7 Year 1 2 3 4 5

8 Projected dividend

9 Terminal price =

10 Present value =

chapter ninecharacterizing risk and return

©Brand X/JupiterImages

Y

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ou can invest your money very safely by opening a savings account at a bank or by buying Treasurybills. So why would you invest your money in risky stocks and bonds if you can take advantage oflow-risk opportunities? The answer: Very low risk investments also provide a very low return.

Investors take on higher risk investments in expectation of earning higher returns. Likewise, businessesalso take on risky capital investments only if they expect to earn higher returns that at least cover theircosts, including investors’ required return. Both investor and business sentiments create a positiverelationship between risk and expected return. Of course, taking risk means that you get no guaranteethat you will recoup your investment. In the short run, higher risk investments often significantlyunderperform lower risk investments. In addition, not all forms of risk are rewarded. In this chapter, you’llsee how the risk-return relationship fundamentally affects finance theory. We focus on using historicalinformation to characterize past returns and risks. We show how you can diversify to eliminate some riskand expect the highest return possible for your desired risk level. In Chapter 10, we’ll turn to estimatingthe risks and returns you should expect in the future. ■

LEARNING GOALS

LG9-1 Compute an investment’s dollar and percentage return.LG9-2 Find information about the historical returns and volatility for the stock, bond, and cash markets.LG9-3 Measure and evaluate the total risk of an investment using several methods.LG9-4 Recognize the risk-return relationship and its implications.LG9-5 Plan investments that take advantage of diversification and its impact on total risk.LG9-6 Find efficient and optimal portfolios.LG9-7 Compute a portfolio’s return.

viewpointsbusiness APPLICATIONManagers from the production and marketing departments have proposed some risky new business projects for your firm. These newideas appear to be riskier than the firm’s current business operations.

You know that diversifying the firm’s product offerings could reduce the firm’s overall risk. However, you are concerned that takingon these new projects will make the firm’s stock too risky. How can you determine whether these project ideas would make the firm’sstock riskier or less risky? (See the solution at the end of the book.)

9.1 • HISTORICAL RETURNS LG9-1Let’s begin our discussion of risk and return by characterizing the concept of return. First, we need a method forcalculating returns. After computing a return, investors need to assess whether it was a good, average, or badinvestment return. Examining returns from the past gives us a general idea of what we might expect to see in thefuture. We should think in terms of return for the long run because a return for any one year can be quite differentfrom the average returns from the past couple of decades.

Computing ReturnsHow much have you earned on each of your investments? Two ways to determine this are to compute the actualdollar return or compute the dollar return as a percentage of the money invested.

Dollar Return The dollar return earned includes any capital gain (or loss) that occurred as well as any income thatyou received over the period. Equation 9-1 illustrates the dollar return calculation:

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(9-1)

dollar return The amount of profit or loss from an investment denoted in dollars.

For example, say you held 50 shares of Alphabet (GOOG), the parent company of Google. The stock price had amarket price of $526.40 per share at the end of 2014. Alphabet paid no dividends during 2015. At the end of 2015,Alphabet’s stock price was $758.88. For the whole of 2015, you earned a capital gain of ($758.88 − $526.40) × 50shares, or $11,624.

In Alphabet’s case, the stock price increased, so you experienced a capital gain. On the other hand, the toy and gameproducer Mattel, Inc. (MAT) started the year at $30.95 per share, paid $1.52 in dividends, and ended 2015 at $27.17.If you owned 200 shares of Mattel, you would have experienced a capital loss of −$756 (= [$27.17 − $30.95] × 200shares). This loss would have been partially offset by the $304 of dividends received. However, the total dollarreturn would still have been −$452 (= −$756 + $304). Stock prices can fluctuate substantially and cause largepositive or negative dollar returns.

personal APPLICATIONSuppose an investor owns a portfolio invested 100 percent in long-term Treasury bonds because the owner prefers low risk. Theinvestor has avoided owning stocks because of their high volatility.

The investor’s stockbroker claims that putting 10 percent of the portfolio in stocks would actually reduce total risk and increase theportfolio’s expected return. The investor knows that stocks are riskier than bonds. How can adding the risky stocks to the bondportfolio reduce the risk level? (See the solution at the end of the book.)

Is there such a thing as a high-reward, zero-risk investment?

Does your dollar return depend on whether you continue to hold the Alphabet and Mattel stock or sell it? No. Ingeneral, finance deals with market values. Alphabet stock was worth $758.88 at the end of 2015 regardless ofwhether you held the stock or sold it. If you sell it, then we refer to your gains as “realized” gains. If you continue tohold the stock, the gains are “unrealized” gains.

Percentage Return We usually find it more useful to characterize investment earnings as percentage returns sothat we can easily compare one investment’s return to other alternatives’ returns. We calculate percentage return bydividing the dollar return by the investment’s value at the beginning of the time period.

(9-2)

Because it’s standardized, we can use percentage returns for almost any type of investment. We can use beginningand ending values for stock positions, bond prices, real estate values, and so on. Investment income may be stockdividends, bond interest payments, or other receipts. The percentage return for holding the Mattel stock duringcalendar year 2015 was −7.3 percent, computed as

The return for the Alphabet position during the same period was a whopping 44.16 percent:

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Both firms belong to the S&P 500 Index, which earned 1.38 percent in 2015.

Are one-year returns typical for expectations in the long run? We look to average returns to examine performanceover time. The arithmetic average return provides an estimate for how the investment has performed over longerperiods of time. The formula for the average return is

(9-3)

where the return for each subperiod is summed up and divided by the number of subperiods. You can statethe returns in either percentage or decimal format.

percentage return The dollar return characterized as a percentage of money invested.

average returns A measure summarizing the past performance of an investment.

EXAMPLE 9-1 Computing Returns LG9-1

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

You are evaluating a stock’s short-term performance. On August 16,2010, technology firm 3PAR saw its stock price surge on news of atakeover battle between Dell and Hewlett-Packard. 3PAR stock hadclosed the previous trading day at $9.65 and was up to $18.00 by theend of the day. 3PAR had ended 2009 at $11.85 and does not pay adividend. What is the dollar return and percentage return of 300 sharesof 3PAR for the day and year to date?

SOLUTION:

For the day, realize that no income is paid. Therefore, the dollar returnis $2,505 = 300 × ($18.00 − $9.65) + 0 and the percent return is86.53% = $2,505 ÷ (300 × $9.65). The year to date (YTD) return alsodoes not include dividend income. So the dollar YTD return is $1,845 =300 × ($18.00 − $11.85). The 3PAR YTD percentage return is

Hewlett-Packard eventually won the bidding war and purchased 3PARfor $33 per share!

Similar to Problems 9-1, 9-2, 9-3, 9-4, Self-Test Problem 1

Alphabet has only been a public company for a relatively brief period, so it will not have a long history of returns.Thus, Table 9.1 shows the annual returns for Mattel and office supply store Staples, Inc., from 1991 to 2015. First,notice that over time, the returns are quite varied for both firms. The stock return for Mattel has ranged from a lowof −52.4 percent in 1999 to a high of 82.6 percent in 1991. Staples’ stock return varied between −45.7 percent(2015) to 171.6 percent (1991). Also note that the returns appear unpredictable or random. Sometimes a large

negative return is followed by another bad year, like Mattel’s returns in 2007 and 2008. Other times, a poor year isfollowed by a very good year, like 2008 and 2009 for Staples. The table also reports average annual returns forMattel and Staples of 14.8 percent and 19.4 percent, respectively. Over the years, the annual returns for these stockshave been quite different from their average returns.

▼ TABLE 9.1 Annual and Average Returns for Mattel and Staples, 1991 to 2015

A B C D E F

1 Mattel Staples Mattel Staples

2 1991 82.6% 171.6% 2004 5.4% 24.0%

3 1992 33.0% 14.9% 2005 −12.6% 9.5%

4 1993 6.9% 13.5% 2006 52.1% 9.4%

5 1994 15.5% 30.0% 2007 −10.5% −5.9%

6 1995 59.8% 46.3% 2008 −28.5% −32.5%

7 1996 10.5% 24.9% 2009 44.3% 49.5%

8 1997 46.6% 32.9% 2010 24.0% −3.3%

9 1998 −43.0% 136.4% 2011 35.6% −32.7%

10 1999 −52.4% −16.8% 2012 25.9% −4.6%

11 2000 47.4% −30.5% 2013 34.3% 0.8%

12 2001 28.8% 10.0% 2014 −32.1% 34.5%

13 2002 5.5% −5.8% 2015 −5.2% −45.7%

14 2003 −3.5% 55.0%

15 Average = 14.8% 19.4%

Note the range of returns. Few annual returns are close to the average return.

Source: Yahoo! Finance.

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Mattel’s stock returns have ranged from -52.4 percent to 82.6 percent.©McGraw-Hill Education/Mark Steinmetz, photographer

The average returns shown in this chapter are more precisely called arithmetic average returns. These averagereturns are appropriate for statistical analysis. However, they do not accurately illustrate the historical performanceof a stock or portfolio. To see this, consider the $100 stock that earned a 50 percent return one year (to $150) andthen earned a −50 percent return the next year (to $75). The arithmetic average return is therefore (50% + −50%) ÷ 2= 0%. Do you believe the average return was zero percent per year? If you started with a $100 stock and ended witha $75 stock, did you earn zero percent? No, you lost money. A measure of that performance should illustrate anegative return. The accurate measure to be used in performance analysis is called the geometric mean return,or the mean return computed by finding the equivalent return that is compounded for N periods. In thisexample, the mean return is [(1 + 0.50) × (1 + −0.50)]1/2 − 1 = −0.134, or −13.4 percent. Given the loss of $25 overtwo years, this −13.4 percent per year mean return seems more reasonable than the zero percent average return.

The general formula for the geometric mean return is

(9-4)

geometric mean return The mean return computed by finding the equivalent return that is compounded for N periods.

Performance of Asset Classes LG9-2During any given year, the stock market may perform better than the bond market, or it may perform worse. Overlonger time periods, how do stocks, bonds, or cash securities perform? Historically, stocks have performed betterthan either bonds or cash. Table 9.2 shows the average returns for these three asset classes over the period 1950 to2015, as well as over various subperiods. Over the entire period, stocks (as measured by the S&P 500 Index) earnedan average 12.6 percent return per year. This is nearly double the 6.6 percent return earned by long-term Treasurybonds. Cash securities, measured by U.S. Treasury bills, earned an average 4.4 percent return.

▼ TABLE 9.2 Annual and Average Returns for Stocks, Bonds, and T-Bills, 1950 to 2015

A B C D E

1 Stocks Long-Term Treasury Bonds T-Bills

2 1950 to 2015 Average 12.6% 6.6% 4.4%

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3 1950 to 1959 Average 20.9% 0.0% 2.0%

4 1960 to 1969 Average 8.7% 1.6% 4.0%

5 1970 to 1979 Average 7.5% 5.7% 6.3%

6 1980 to 1989 Average 18.2% 13.5% 8.9%

7 1990 to 1999 Average 19.0% 9.5% 4.9%

8 2000 to 2009 Average 0.9% 8.0% 2.7%

9 2010 Annual Return 15.1% 9.4% 0.01%

10 2011 Annual Return 2.1% 29.9% 0.02%

11 2012 Annual Return 16.0% 3.6% 0.02%

12 2013 Annual Return 32.4% −12.7% 0.07%

13 2014 Annual Return 13.7% 25.1% 0.05%

14 2015 Annual Return 1.4% −1.2% 0.21%

15 2010 to 2015 Average 13.4% 9.0% 0.06%

Returns have been very different among decades.

The table also shows each asset class’s average return for each decade since 1950. The best decade for the stockmarket was the 1950s, when stocks earned an average 20.9 percent per year. The 1990s ran a close second with a 19percent per year return. The best decade for the bond market was the 1980s, when it earned an average 13.5 percentper year return due to capital gains as interest rates fell. Stocks have outperformed bonds in every decade since 1950except the recent 2000s. Notice that the average return in the stock and bond markets has not been negative duringany decade since 1950. But average stock returns do not really paint a very accurate picture of annualreturns. Individual annual returns can vary strongly and be quite negative in any particular year. Indeed,this annual variability defines risk. The stock market return in 2008 was particularly poor because of the financialcrisis. However, not all stocks fell the same amount. Notice that Mattel and Staples declined by only 28.5 and 32.5percent while the stock market in general declined 35.5 percent. Financial company stocks fell the most during thecrisis.

time out!9-1 How important were dividend payments to the total returns that Mattel and Staples offered investors?9-2 Using the average returns shown in Table 9.2, compute how much a $10,000 investment made in each asset class at the

beginning of each decade would become at the end of each decade.

9.2 • HISTORICAL RISKS LG9-3

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When you purchase a U.S. Treasury bill, you know exactly what your dollar and percentage return are going to be.Many people find comfort in the certainty from this safe investment. On the other hand, when you purchase a stock,you do not know what your return is going to be—either in the short term or in the long run. This uncertainty isprecisely what makes stock investing risky. It’s useful to evaluate this uncertainty quantitatively so that we cancompare risk among different stocks and asset classes.

Computing VolatilityFinancial theory suggests that investors should look at an investment’s historical returns to assess how muchuncertainty to expect in the future. If you see high variability in historical returns, you should expect a high degreeof future uncertainty. Table 9.2 shows that between 2010 and 2015, the stock market experienced a range of 1.4percent return in 2015 to a 32.4 percent return in 2013. Bonds also experienced variability: −12.7 percent return in2013 to 29.9 percent return in 2011. Examining the range of historical returns provides just one way to express thereturn volatility that we can expect. In practical terms, the finance industry uses a statistical return volatility measureknown as the standard deviation of percentage returns. We calculate standard deviation as the square root of thevariance, and this figure represents the security’s or portfolio’s total risk. We’ll discuss other risk measurements inthe next chapter.

standard deviation A measure of past return volatility, or risk, of an investment.

total risk The volatility of an investment, which includes current portions of firm-specific risk and market risk.

Our process of computing standard deviation starts with the average return over the period. The average annualreturn for the stock market since 1950 is 12.6 percent. How much can the return in any given year deviate from thisaverage? We compute the actual annual deviation by subtracting the return each year from this averagereturn: Return(1950) − Average return; Return(1951) − Average return; Return(1952) − Average return, and soon. Note that many of these deviations will be negative (from a lower-than-average return that year) and others willbe positive (from a higher-than-average return). If we computed the average of these return deviations, our resultwould be zero. Large positive deviations cancel out large negative deviations and hide the variability. To really seethe size of the variations without the distractions that come with including a positive or negative sign, we squareeach deviation before adding them up. Dividing by the number of returns in the sample minus one provides thereturn variance.1 The square root of the return variance is the standard deviation:

(9-5)

Note that this equation provides an estimate of the true population standard deviation using a specific historicalsample. A large standard deviation indicates greater return volatility—or high risk. Table 9.3 shows the standarddeviations of Mattel stock returns over 25 years. The Deviation column shows the annual return minus Mattel’saverage return of 14.8 percent. The last column squares each deviation. Then we sum up these squared deviationsand divide the result by the number of observations less one (24) to compute the return variance. If wewant to use a measure that makes sense in the real world (how would you interpret a squared percentage,anyway?), we take the square root of the variance to get the standard deviation. Mattel’s standard deviation ofreturns during this sample period comes to 33.4 percent. In comparison, the standard deviation of Staples stockreturns for this same period is 48.7 percent. Since Staples’ standard deviation is higher, its stock features more totalrisk than Mattel’s stock does.

▼ TABLE 9.3 Computation of Mattel Stock Return Standard Deviation

Investors use standard deviation as a measure of risk; the higher the standard deviation, the riskier the asset.

Source: Yahoo! Finance.

EXAMPLE 9-2 Risk and Return LG9-1, LG9-3

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For interactive versions of thisexample, log in to Connect or goto mhhe.com/CornettM4e.

Find the average return and risk (as measured by standard deviation) for Mattel since 2006.Table 9.3 shows the annual returns for years 2006 to 2015.

SOLUTION:

First, compute the average annual return for the period. Using equation 9-3

Mattel has averaged a 14.0 percent return per year since 2006. To compute the risk, use thestandard deviation equation 9-5. First, find the deviations of return for each year:

Year2006 2007 2008 2009 2010 2011 2012 2013 2014

52.1%−14.0%

−10.5%−14.0%

−28.5%−14.0%

44.3%−14.0%

24.0%−14.0%

35.6%−14.0%

25.9%−14.0%

34.3%−14.0%

−32.1%−14.0%

Square those deviations:

Year 2006 2007 2008 2009 2010 2011 2012 2013

(52.1%−14.0%)2

(−10.5%−14.0%)2

(−28.5%−14.0%)2

(44.3%−14.0%)2

(24.0%−14.0%)2

(35.6%−14.0%)2

(25.9%−14.0%)2

(34.3%−14.0%)

Then add them up, divide by n − 1, and take the square root:

Mattel stock has averaged a 14.0 percent return with a standard deviation of 30.5 percent since2006.

Similar to Problems 9-15, 9-16, 9-17, 9-18, 9-33, 9-34, Self-Test Problem 2

Although analysts and investors use a stock return’s standard deviation as an important and commonmeasure of risk, it’s laborious to compute by hand. Most people use a spreadsheet or statistical software tocalculate stock return standard deviations.

Risk of Asset Classes LG9-2

Because RadioShack’s standard deviation is higher, it’s stock features more total risk.©Juice Images/Getty Images

We report the standard deviations of return for stocks, bonds, and T-bills in Table 9.4 for 1950 to 2015 and for eachdecade since 1950. Over the entire sample, the stock market returns’ standard deviation is 17.3 percent. As wewould expect, stock market volatility is higher than bond market volatility (11.1 percent) or for T-bills (3.0 percent).These volatility estimates are consistent with our previously stated position that the stock market carries more riskthan the bond or cash markets do. Every decade since 1950 has seen a lot of stock market volatility. The bondmarket has experienced the most volatility since the 1980s as interest rates varied dramatically.

▼ TABLE 9.4 Annual Standard Deviation of Returns for Stocks, Bonds, and T-Bills, 1950 to 2015

Stocks Long-Term Treasury Bonds T-Bills

1950 to 2015 17.3% 11.1% 3.0%1950 to 1959 19.8 4.9 0.81960 to 1969 14.4 6.2 1.31970 to 1979 19.2 6.8 1.81980 to 1989 12.7 15.1  2.61990 to 1999 14.2 12.8  1.22000 to 2009 20.4 10.3  1.92010 to 2015 11.3 16.1  0.1

Some decades experience higher risk than others in each asset class.

You will recall from Chapter 7 that since any bond’s par value and coupon rate are fixed, bond prices must fluctuateto adjust for changes in interest rates. Bond prices respond inversely to interest rate changes: As interest rates rise,bond prices fall, and if interest rates fall, bond prices rise. T-bill returns have experienced very low volatility overeach decade. Indeed, T-bills are commonly considered to be one of the only risk-free assets. Higher-risk investmentsoffer higher returns over time. But short-term fluctuations in the value of higher risk investments can be substantial.The stock market is risky—while it has offered a good annual return of 12.6 percent, that return comes withvolatility of 17.3 percent standard deviation. Many investors may intellectually understand that this high risk meansthat they may receive very poor returns in the short term. Investors really felt the full force of this risk when thestock market declined three years in a row (2000 to 2002). Some investors even decided that this was too much riskfor them and they sold out of the stock market before the 2003 rally. Other investors got out of the stock market afterit plunged to lows in March 2009. Market volatility can cause investors to make emotionally based decisions—selling at low prices.

The stock market returns’ standard deviations that appear in Table 9.4 are all considerably lower than the standarddeviations of Mattel and of Staples stocks (33.4 percent and 48.7 percent, respectively). In this case, we measure

page 270stock market return and standard deviation using the S&P 500 Index. Mattel and Staples are both included in theS&P 500 Index. Why do these two large firms have measures of total risk—standard deviations—that areat least twice as large as the standard deviations on the stock market returns? Are Mattel and Staples justtwo of the most risky firms in the Index? Actually, no. The differences in standard deviations between theseindividual companies and the entire market have much more to do with diversification. Owning 500 companies,such as all of those included in the S&P 500 Index, generates much less risk than owning just one company. Thisphenomenon appears in the standard deviation measure. We’ll discuss the effects of diversification in detail later inthis chapter.

Risk versus Return LG9-4Investors can buy very safe T-bills. Or they can take some risk to seek higher returns. How much extra return canyou expect for taking more risk? This is known as the trade-off between risk and return. The coefficient of variation(CoV) is a common relative measure of this risk-vs-reward relationship. The equation for the coefficient of variationis simply the standard deviation divided by average return. It is interpreted as the amount of risk (measured byvolatility) per unit of return:

(9-6)

As an investor, you would want to receive a very high return (the denominator in the equation) with a very low risk(the numerator). So, a smaller CoV indicates a better risk-reward relationship. Since the average return and standarddeviation for Mattel stock are 14.8 percent and 33.4 percent, its CoV is 2.26 (= 33.4 ÷ 14.8). This is better thanStaples’ CoV of 2.51 (= 48.7 ÷ 19.4). For all asset classes for the period 1950 to 2015, the stock market earned ahigher return than bonds and was also riskier. But which one had a better risk-return relationship? The CoV forcommon stock is 1.37 (= 17.3 ÷ 12.6). For Treasury bonds, the coefficient of variation is 1.68 (= 11.1 ÷ 6.6). Eventhough stocks are riskier than bonds, they involve a somewhat better risk-reward trade-off.

coefficient of variation A measure of risk to reward (standard deviation divided by average return) earned by an investment over aspecific period of time.

EXAMPLE 9-3 Risk versus Return LG9-4

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

You are interested in the risk-return relationship of stocks in eachdecade since 1950. Obtain the average returns and risks in Table 9.2and Table 9.4.

SOLUTION:

Using the coefficient of variation, the average returns, and standarddeviation of return, compute the following risk-return relationships:

Note that over short time periods, the stock risk-return relationshipvaries significantly.

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Similar to Problems 9-7, 9-8, 9-19, 9-20, 9-33, and 9-34, Self-TestProblem 3

time out!9-3 What volatility measure can we use to evaluate and compare risk among different investment alternatives?9-4 Explain why the coefficients of variation for Mattel and Staples are so much higher than the CoV for the stock market as a

whole.

9.3 • FORMING PORTFOLIOS LG9-5As we noted previously, Mattel and Staples stocks’ risk as measured by their standard deviations appear quite highcompared to the standard deviation of the S&P 500 Index. This is by no means a coincidence. Combining stocks intoportfolios can reduce many sources of stock risk. Diversification reduces risk. The S&P 500 Index, for example, tracks500 companies, which allows for a great deal of diversification.

Diversifying to Reduce RiskThink about a stock’s total risk as having two components. The first component includes risks that are both specificto that company and common to other companies in the same industry. We call this risk firm-specific risk. The stock’sother risk component is general risk that all firms—and all individuals, for that matter—face based upon economicstrength both domestically and globally. We call this type of risk market risk. These risks appear in the equation

(9-7)

Standard deviations measure total risk. Individual stocks are subject to many firm-specific risks. We can reducefirm-specific risk by combining stocks into a portfolio. Since we can reduce firm-specific risk by diversifying, thisrisk is sometimes referred to as diversifiable risk. If Staples announces lower-than-expected profits, its stock price willdecline. However, since this news is specific to Staples, the news should not affect Mattel stock’s price. On the otherhand, if the government announces a change in unemployment, both stocks’ prices will change to some degree.Macroeconomic events represent market risks because such events—unemployment claims, interest rate changes,national budget deficits or surpluses—affect all companies.

portfolio A combination of investment assets held by an investor.

diversification The process of putting money in different types of investments for the purpose of reducing the overall risk of the portfolio.

firm-specific risk The portion of total risk that is attributable to firm or industry factors. Firm-specific risk can be reduced throughdiversification.

market risk The portion of total risk that is attributable to over-all economic factors.

diversifiable risk Another term for firm-specific risk.

Diversification reduces risk.©Dimitri Vervitsiotis/Getty Images

Suppose that you own only Mattel stock and have earned the annual returns shown in Table 9.5. Then someonesuggests that you add Staples to your Mattel stock to form a two-stock portfolio. Both Mattel and Staples stockscarry a lot of total risk. But look at the risk and return characteristics of a portfolio consisting of 50 percent Staplesstock and 50 percent Mattel stock. You start with Mattel stock, which provided an average return of 14.8 percentwith a risk of 33.4 percent. The Staples stock you are adding has more risk than Mattel. The two-stock portfolioearns an average 17.1 percent return with a standard deviation of only 32.1 percent. You added a high-risk stock to ahigh-risk stock and you ended up with a portfolio with lower risk and a higher return! This is a hallmark of mostportfolios, which pool market risk but often provide offsetting, reduced firm-specific risks overall.

▼ TABLE 9.5 Combining Stocks Can Greatly Reduce Risk

The risk-reducing power of diversification! Note that the risk of the portfolio is lower than the risk of the two stocks individually.

Source: Yahoo! Finance.

Next, add IBM stock to your Mattel and Staples stock portfolio. Figure 9.1 shows that the total risk of this three-stock portfolio declines to 25.7 percent. Note that adding Newmont Mining, Disney, and General Electric alsoreduces the total risk of the stock portfolio. As you add more stocks, the firm-specific risk portion of the totalportfolio risk declines. The total risk falls rapidly as we add the first few stocks. Diversification’s power to reduce

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firm-specific risk weakens for the later stocks added to the portfolio, because we have already eliminatedmuch of the firm-specific risk. We could continue to add stocks until the portfolio comprises all S&P 500Index firms, in which case the standard deviation of the portfolio would be 17.3 percent. At this point, virtually allof the firm-specific risk has been purged and the portfolio carries only market risk, which is sometimes callednondiversifiable risk.

nondiversifiable risk Another term for market risk.

FIGURE 9.1 Adding Stocks to a Portfolio Reduces Risk

The total portfolio risk is greatly reduced by adding the first few stocks to a portfolio.

finance at work //: personalInvestor Diversification ProblemsExperts have examined investor behavior using detailed datasets of stock brokerage accounts, employee pension plans, and the Surveyof Consumer Finances. Studies have identified many investor behaviors that are inconsistent with the principle of full diversification:

Many households own relatively few individual stocks—they held a median number of two stocks until 2001, when it rose to three. Ofcourse, many households own equity indirectly, through mutual funds or retirement accounts, and these indirect holdings tend to bemuch better diversified.

Ten to 15 percent of households with between $100,000 and $1 million in financial asset wealth own no stocks (neither directly norindirectly through funds).Investors seem to prefer securities of local firms. Many geographic regions feature companies that are heavily concentrated in fewindustries. Thus, a local preference could reduce diversification opportunities.

Many employees hold mostly their employers’ stocks (more than 50 percent of employee holdings), particularly within their 401(k)retirement savings accounts. Holding a lot of a single stock creates a “portfolio” with high total risk.

Finance professionals and the investment industry have established diversification concepts for many decades and can helpinvestors maximize their returns with appropriate risk levels. But many investors do not consult professionals; they fail to diversify andthus take unnecessary diversifiable risk.

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Ten to fifteen percent of households with between $100,00 and $1 million in financial asset wealth own no stocks.

©Photodisc/Punchstock

Want to know more?Key Words to Search for Updates: diversification, pension plan choices, asset allocation

Sources: Dimmock, Stephen G., Roy Kouwenberg, Olivia S. Mitchell, and Kim Peijnenburg, “Ambiguity Aversion and HouseholdPortfolio Choice Puzzles: Empirical Evidence,” Journal of Financial Economics; in press (2016); and Hans-Martin Von Gaudecker, “HowDoes Household Portfolio Diversification Vary with Financial Literacy and Financial Advice?,” Journal of Finance 70 (2015): 489–507.

Modern Portfolio Theory LG9-6The concept that diversification reduces risk was formalized in the early 1950s by Harry Markowitz, who eventuallywon the Nobel Prize in Economics for his work. Markowitz’s modern portfolio theory shows how risk reduction occurswhen securities are combined. The theory also describes how to combine stocks to achieve the lowest total riskpossible for a given expected return. Or, said differently, it describes how to achieve the highest expected return forthe desired risk level. The combination of securities that achieves the highest expected return for a person’s desiredlevel of risk is called the investor’s optimal portfolio.

In our Mattel and Staples portfolio example, we allocated 50 percent of the portfolio to Mattel and 50 percent toStaples. Is this the best allocation for the portfolio? Consider the different allocations shown in Figure 9.2 for thetwo stocks. The graph shows the expected return (computed as average return) and risk (computed as standarddeviation) of various portfolios. It would be terrific if you could find a portfolio located in the upper left-handcorner. That is, investors would like a high expected return with low risk. One large dot shows the risk-return pointfor owning only Mattel. The other large dot shows owning only Staples. The smaller diamonds show 10/90, 25/75,40/60, 50/50, 60/40, 75/25, and 90/10 allocations of Mattel/Staples stocks.

FIGURE 9.2 Risk and Return Ramifications of Portfolio Allocations to Mattel and Staples

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Investors only value the portfolios at the top of the graph because they offer the same risk as the lower portfolios but with higher expectedreturn!

While all these portfolios are possible, not all are desirable. For example, the portfolio of 75 percent Mattel and 25percent Staples is not desirable. Other portfolios provide both higher return and lower risk. We say that one portfoliodominates the other if it has higher expected return for the same (or less) risk, or the same (or higher) expectedreturn with lower risk. The dominating portfolios appear higher and to the left in the figure. One such portfolioconsists of 25 percent Mattel stock and 75 percent Staples stock. The 50/50 portfolio (circled in the figure) is alsobetter than the 75/25 portfolio. Portfolios with the highest return possible for each risk level are called efficientportfolios. Notice that if you drew a line connecting the dots, the figure would appear like the end of a bullet. Theportfolios on the top of the bullet dominate the portfolios on the bottom; the top portfolio dots show the efficientportfolios for these two stocks.

modern portfolio theory A concept and procedure for combining securities into a portfolio to minimize risk.

optimal portfolio The best portfolio of securities for the investor’s level of risk aversion.

efficient portfolios The set of portfolios that have the maximum expected return for each level of risk.

Figure 9.3 shows efficient portfolios for combining the four stocks: Staples, Mattel, IBM, and NewmontMining. We used this portfolio to demonstrate how diversification reduces risk in Figure 9.1. Theseportfolios appear as diamonds in the figure with each diamond representing a different allocation of the four stocks.The single square represents the portfolio that consists of 25 percent in each of the four stocks. Notice that other,efficient portfolios dominate this portfolio.

FIGURE 9.3 Efficient Portfolios from Four Stocks

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The efficient portfolios dominate all of the individual stocks.

If we showed all efficient portfolios, they would appear as a line that connects the upper side of the bullet shape. Ifwe added all available securities to the graph, then all of the efficient portfolios of those securities form the efficientfrontier. Efficient frontier portfolios dominate all other possible stock portfolios. The shape of the efficient frontierimplies that diminishing returns apply to risk-taking in the investment world. To gain ever-higher expected rates ofreturn, investors must be willing to take on ever-increasing amounts of risk. The optimal portfolio for you is one onthe efficient frontier that reflects the amount of risk that you’re willing to take. Clearly, optimal portfolio choicedepends on individual risk preferences. Highly risk-averse investors will select low-risk portfolios on the efficientfrontier, while more adventuresome investors will select higher-risk portfolios. Any choice may be appropriate,given differences in individual risk preferences.

Investors can further diversify by adding foreign stocks and commodities to their portfolio. For example, a U.S.investor can lower total risk by adding stocks from emerging market countries and gold.

efficient frontier The combination of all efficient portfolios.

How Does Diversification Work? LG9-5 Will combining any two stocks greatly reduce total risk as much ascombining Staples and Mattel did? The answer is no. If two stocks are subject to exactly the same kinds of eventssuch that their returns always behave the same way over time, then we have no need to own both stocks—simplypick the one that performs better. Diversification comes when two stocks are subject to different kinds of eventssuch that their returns differ over time.

Consider the illustration in Figure 9.4. You own Stock A in Panel A of the figure. The stock features risk,as demonstrated by its price volatility over time. You would like to reduce the risk by combining yourposition in Stock A with an equal position in Stock B. In this case, the alternative stock, Stock B, moves the sameway over time as Stock A does. When Stock A goes up, so does Stock B. They also decline together. A portfolio ofboth stocks is illustrated. Notice how the portfolio has the same volatility of Stocks A and B separately. Combiningthese two stocks did not reduce volatility, or total risk.

FIGURE 9.4 Efficient Portfolios from Four Stocks

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Combining stocks that move together over time does not offer much risk reduction. Combining stocks that do not move together provides alot of risk reduction.Correlation shows that some stocks move together and some do not.

Now consider Stock C, shown in Panel B. Stock C has the same volatility as Stock A, but its price moves indifferent directions than does the price of Stock A. When Stock A’s price increases, Stock C’s price increasessometimes and decreases sometimes. As shown, a portfolio of Stock A and Stock C features much lower volatilitythan either Stock A or Stock C alone. Combining Stocks A and C reduces risk because their price movements oftencounteract one another. In short, combining stocks with similar characteristics does not provide muchdiversification and thus risk reduction. Combining stocks with many differences does providediversification and thus lowers risk.

The ways that stocks co-move over time determines how much diversification and thus risk reduction we canachieve by combining them. So what we need is some measure of co-movement to help investors form diversifiedportfolios. That measure, called correlation, is denoted by the Greek letter ρ (rho). Correlation is a statistical measurewith some very useful characteristics that makes it easy to interpret. Its value is bounded between −1 and +1. Acorrelation value of +1 means that returns from two different securities move perfectly in sync. They change lock-step up and down together. A value of −1 means that returns from two securities are perfectly inversely correlated—they move exactly opposite. A value of 0 means that the movements of the two returns over time are unrelated toone another. Investors seeking diversification look for stocks where the returns have low or negative correlationswith each other.

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correlation A measurement of the co-movement between two variables that ranges between −1 and +1.

What return correlations are common between stocks? Panel A of Table 9.6 shows the correlations between manycompanies. One high correlation shown is the 0.690 correlation between Citigroup and the Bank of New York. Thisshouldn’t be surprising, because these are two similar firms in the same industry. Combining these two stockswouldn’t reduce risk very much in a portfolio. The largest negative correlation is the correlation of −0.212 betweenNewmont Mining and the Bank of New York. These firms practice in very different industries and provide large riskreduction possibilities. Note that the correlation between Staples and Mattel is 0.198. This low correlation gives usan answer to the question of why total risk (in the form of standard deviations) fell so much when we combined thetwo stocks relative to their individual standard deviations as shown in Figure 9.2. Most of the correlations in Table9.6 are positive. Because most stocks are positively correlated, we typically add many stocks together to fullyeliminate all the firm-specific risk in the portfolio, as we showed in Figure 9.1.

▼ TABLE 9.6 Correlation between Various Stocks and Asset Classes

PANEL A: COMPANY ANNUAL RETURNS, 1991 TO 2015

Staples Mattel IBMNewmont

Mining DisneyGeneralElectric Citigroup

Staples 1Mattel 0.198 1IBM 0.314 −0.029 1NewmontMining

−0.036 −0.117 −0.087 1

Disney 0.163 0.440 0.076 −0.171 1General Electric 0.380 0.134 0.396 −0.038 0.517 1Citigroup 0.297 0.328 0.056 0.139 0.414 0.773 1Bank of NewYork

0.584 0.459 0.045 −0.212 0.606 0.671 0.690

PANEL B: ASSET CLASS ANNUAL RETURNS,1950 TO 2015

StocksLong-Term Treasury

Bonds T-Bills

Stocks 1Long-termTreasury bonds

−0.035 1

T-bills −0.063 0.137 1

LG9-2Panel B of Table 9.6 shows correlations between stocks, bonds, and T-bills. At −0.035, the correlation betweenstocks and bonds is small. The small correlation allows for the possibility of good risk reduction by adding bonds toa stock portfolio. Therefore, a well-diversified portfolio will contain both stocks and bonds.

finance at work //: marketsInternational Opportunities for DiversificationThe U.S. stock market represents nearly 47 percent of all stock value worldwide. Japanese and U.K. stock markets represent 11 percentand 8 percent of the worldwide stock market value, respectively. Many investment and diversification opportunities present themselvesinternationally! However, most people allocate very little or none of their portfolios to international securities. If worldwide opportunitiescan create greater diversification, then those who don’t invest in international stocks miss out on an important opportunity to reduce riskin their portfolios.

MSCI Barra is the leading provider of global stock market indexes. Some MSCI Barra indexes follow individual countries. In addition,MSCI Barra compiles composite indexes for groups of companies in developed markets, emerging markets, frontier markets, and bygeographic regions. Investment managers use the MSCI World Index, the MSCI EAFE (Europe, Australasia, Far East) Index, and theMSCI Emerging Markets Index as premier benchmarks to measure global stock market performance.

The following table shows the average annual returns and standard deviations for the U.S. stock market, Treasury bonds, and the

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MSCI EAFE and MSCI Emerging Markets indexes for the period 1988 to 2015. Note that both the EAFE and the Emerging Marketsindexes feature higher risk than the S&P 500 Index. The Emerging Markets return has been high, but the EAFE return has been lowcompared to the U.S. stock and bond markets.

S&P 500 Bonds EAFE Emerging Markets

Average 11.7%  9.2%  5.6% 13.3%Std. Deviation 17.6 11.9 19.4 33.7

The correlations among these markets appear as follows:

S&P 500 Bonds EAFE Emerging Markets

S&P 500  1Bonds −0.15  1EAFE  0.74 −0.41 1Emerging Markets  0.48 −0.31 0.73 1

The correlation between the S&P 500 Index and the MSCI EAFE is 0.74 and between the Emerging Markets is 0.48. These correlationsindicate that diversification might work. Even better diversification appears to be possible between the U.S. Treasury Bond Market andthe EAFE and Emerging Markets indexes—look at the negative correlations!

Source: www.msci.com.

Want to know more?Key Words to Search for Updates: international diversification, global asset allocation

Portfolio Return LG9-7 A portfolio’s return calculation is straightforward. A portfolio’s return comes directlyfrom the returns of the portfolio securities and the proportion of the portfolio invested in each security. For example,General Electric stock earned −1.9 percent. The Newmont Mining earned 17.3 percent over the same period. If youhad invested a quarter of your money in General Electric stock and three quarters of it in Newmont Miningstock, then your portfolio return would be

the Math Coach on…

“When computing portfolio returns, use the decimal format for the portfolioweights and the percentage format for the security returns. The result of equation9-8 will then be in percentage format.„

To calculate the return on a three-stock portfolio, you will need the proportion of each stock in the portfolio andeach stock’s return. We typically call these proportions weights, signified by w. So, a portfolio with n securities willhave a return of

(9-8)

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where the sum of the weights, w, must equal one.

The portfolio’s rate of return is a simple weighted sum of the returns of each stock in the portfolio. Investors chooseportfolio weights by determining how much of each stock they want in their portfolios. Ideally, investors will chooseweights for their portfolios located on the efficient frontier (shown in Figure 9.3).

EXAMPLE 9-4Computing PortfolioReturns LG9-7

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

At the beginning of the year, you owned $5,000 of Disney stock,$10,000 of Bank of New York stock, and $15,000 of IBM stock. Duringthe year, Disney, Bank of New York, and IBM returned −4.8 percent,19.4 percent, and 12.8 percent, respectively. What is your portfolio’sreturn?

SOLUTION:

First determine your portfolio weights. The three stocks make up a$30,000 portfolio. Disney makes up a 16.67 percent (= $5,000 ÷$30,000) portion of the portfolio. Bank of New York stock makes up a33.33 percent (=$10,000 ÷ $30,000) portion, and IBM a 50.0 percent(=$15,000 ÷ $30,000) portion.

The portfolio return can now be computed as

Similar to Problems 9-11, 9-12, 9-13, 9-14, 9-23, 9-24, 9-25, 9-26, 9-29, 9-30, 9-31, 9-32, Self-Test Problem 1

time out!9-5 Describe characteristics of companies that would be good to combine into a portfolio.9-6 Explain why one portfolio made up of the same companies (but not in the same proportions) as another portfolio can be

undesirable in comparison.

9-7 Combining which two companies in Table 9.6 would reduce risk the most? Combining which two would create the leastdiversification?

Get Online

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©JGI/Jamie Grill/Blend Images LLC.

Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. Why is the percentage return a more useful measure than the dollar return? (LG9-1)

2. Characterize the historical return, risk, and risk-return relationship of the stock, bond, and cash markets. (LG9-2)

3. How do we define risk in this chapter and how do we measure it? (LG9-3)

4. What are the two components of total risk? Which component is part of the risk-return relationship? Why?(LG9-3)

5. What’s the source of firm-specific risk? What’s the source of market risk? (LG9-3)

6. Which company is likely to have lower total risk, General Electric or Coca-Cola? Why? (LG9-3)

7. Can a company change its total risk level over time? How? (LG9-3)

8. What does the coefficient of variation measure? Why is a lower value better for the investor? (LG9-4)

9. You receive an investment newsletter advertisement in the mail. The letter claims that you should invest in astock that has doubled the return of the S&P 500 Index over the last three months. It also claims that this stockis a surefire safe bet for the future. Explain how these two claims are inconsistent with finance theory. (LG9-4)

10. What does diversification do to the risk and return characteristics of a portfolio? (LG9-5)

11. Describe the diversification potential of two assets with a −0.8 correlation. What’s the potential if thecorrelation is +0.8? (LG9-5)

12. You are a risk-averse investor with a low-risk portfolio of bonds. How is it possible that adding some

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stocks (which are riskier than bonds) to the portfolio can lower the total risk of the portfolio? (LG9-5)

13. You own only two stocks in your portfolio but want to add more. When you add a third stock, the total risk ofyour portfolio declines. When you add a tenth stock to the portfolio, the total risk declines. Adding whichstock, the third or the tenth, likely reduced the total risk more? Why? (LG9-5)

14. Many employees believe that their employer’s stock is less likely to lose half of its value than a well-diversifiedportfolio of stocks. Explain why this belief is erroneous. (LG9-5)

15. Explain what we mean when we say that one portfolio dominates another portfolio. (LG9-6)

16. Explain what the efficient frontier is and why it is important to investors. (LG9-6)

17. If an investor’s desired risk level changes over time, should the investor change the composition of his or herportfolio? How? (LG9-6)

18. Say you own 200 shares of Mattel and 100 shares of Staples. Would your portfolio return be different if youinstead owned 100 shares of Mattel and 200 shares of Staples? Why? (LG9-7)

ProblemsBASIC PROBLEMS

9-1 Investment Return FedEx Corp. stock ended the previous year at $103.39 per share. It paid a $0.35 pershare dividend last year. It ended last year at $106.69. If you owned 200 shares of FedEx, what was yourdollar return and percent return? (LG9-1)

9-2 Investment Return Sprint Nextel Corp. stock ended the previous year at $23.36 per share. It paid a $2.37per share dividend last year. It ended last year at $18.89. If you owned 500 shares of Sprint, what was yourdollar return and percent return? (LG9-1)

9-3 Investment Return A corporate bond that you own at the beginning of the year is worth $975. During theyear, it pays $35 in interest payments and ends the year valued at $965. What was your dollar return andpercent return? (LG9-1)

9-4 Investment Return A Treasury bond that you own at the beginning of the year is worth $1,055. Duringthe year, it pays $35 in interest payments and ends the year valued at $1,065. What was your dollar returnand percent return? (LG9-1)

9-5 Total Risk Rank the following three stocks by their level of total risk, highest to lowest. Rail Haul has anaverage return of 12 percent and standard deviation of 25 percent. The average return and standarddeviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent.(LG9-3)

9-6 Total Risk Rank the following three stocks by their total risk level, highest to lowest. Night Ryder has anaverage return of 12 percent and standard deviation of 32 percent. The average return and standarddeviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent.(LG9-3)

9-7 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. RailHaul has an average return of 12 percent and standard deviation of 25 percent. The average return andstandard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20percent. (LG9-4)

9-8 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. NightRyder has an average return of 13 percent and standard deviation of 29 percent. The average returnand standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percentand 40 percent. (LG9-4)

9-9 Dominant Portfolios Determine which one of these three portfolios dominates another. Name thedominated portfolio and the portfolio that dominates it. Portfolio Blue has an expected return of 12 percentand risk of 18 percent. The expected return and risk of portfolio Yellow are 15 percent and 17 percent, andfor the Purple portfolio are 14 percent and 21 percent. (LG9-6)

9-10 Dominant Portfolios Determine which one of the three portfolios dominates another. Name thedominated portfolio and the portfolio that dominates it. Portfolio Green has an expected return of 15

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percent and risk of 21 percent. The expected return and risk of portfolio Red are 13 percent and 17percent, and for the Orange portfolio are 13 percent and 16 percent. (LG9-6)

9-11 Portfolio Weights An investor owns $6,000 of Adobe Systems stock, $5,000 of Dow Chemical, and$5,000 of Office Depot. What are the portfolio weights of each stock? (LG9-7)

9-12 Portfolio Weights An investor owns $3,000 of Adobe Systems stock, $6,000 of Dow Chemical, and$7,000 of Office Depot. What are the portfolio weights of each stock? (LG9-7)

9-13 Portfolio Return Year-to-date, Oracle had earned a –1.34 percent return. During the same timeperiod, Valero Energy earned 7.96 percent and McDonald’s earned 0.88 percent. If you have aportfolio made up of 30 percent Oracle, 25 percent Valero Energy, and 45 percent McDonald’s, whatis your portfolio return? (LG9-7)

9-14 Portfolio Return Year-to-date, Yum Brands had earned a 3.80 percent return. During the same timeperiod, Raytheon earned 4.26 percent and Coca-Cola earned −0.46 percent. If you have a portfoliomade up of 30 percent Yum Brands, 30 percent Raytheon, and 40 percent Coca-Cola, what is yourportfolio return? (LG9-7)?

INTERMEDIATE PROBLEMS

9-15 Average Return The past five monthly returns for Kohls are 4.11 percent, 3.62 percent, −1.68percent, 9.25 percent, and −2.56 percent. What is the average monthly return? (LG9-1)

9-16 Average Return The past five monthly returns for PG&E are −3.17 percent, 3.88 percent, 3.77percent, 6.47 percent, and 3.58 percent. What is the average monthly return? (LG9-1)

9-17 Standard Deviation Compute the standard deviation of Kohls’ monthly returns shown in problem 9-15. (LG9-3)

9-18 Standard Deviation Compute the standard deviation of PG&E’s monthly returns shown in problem9-16. (LG9-3)

9-19 Risk versus Return in Bonds Assess the risk-return relationship of the bond market (see Tables 9.2and 9.4) during each decade since 1950. (LG9-2, LG9-4)

9-20 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see Tables 9.2 and 9.4)during each decade since 1950. (LG9-2, LG9-4)

9-21 Diversifying Consider the characteristics of the following three stocks:The correlation between Thumb Devices and Air Comfort is −0.12. The correlation between ThumbDevices and Sport Garb is −0.21. The correlation between Air Comfort and Sport Garb is 0.77. If youcan pick only two stocks for your portfolio, which would you pick? Why? (LG9-4, LG9-5)

Expected Return Standard Deviation

Thumb Devices 13% 23%

Air Comfort 10  19 

Sport Garb 10  17 

9-22 Diversifying Consider the characteristics of the following three stocks:The correlation between Pic Image and Tax Help is 0.88. The correlation between Pic Imageand Warm Wear is −0.21. The correlation between Tax Help and Warm Wear is −0.19. If you can pickonly two stocks for your portfolio, which would you pick? Why? (LG9-4, LG9-5)

Expected Return Standard Deviation

Pic Image 11% 19%

Tax Help 9  19 

Warm Wear 14  25 

9-23 Portfolio Weights If you own 200 shares of Alaska Air at $42.88, 350 shares of Best Buy at $51.32,and 250 shares of Ford Motor at $8.51, what are the portfolio weights of each stock? (LG9-7)

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9-24 Portfolio Weights If you own 400 shares of Xerox at $17.34, 500 shares of Qwest at $8.15, and 350shares of Liz Claiborne at $44.73, what are the portfolio weights of each stock? (LG9-7)

9-25 Portfolio Return At the beginning of the month, you owned $5,500 of General Dynamics, $7,500 ofStarbucks, and $8,000 of Nike. The monthly returns for General Dynamics, Starbucks, and Nike were7.44 percent, −1.36 percent, and −0.54 percent. What is your portfolio return? (LG9-7)

9-26 Portfolio Return At the beginning of the month, you owned $6,000 of News Corp, $5,000 of FirstData, and $8,500 of Whirlpool. The monthly returns for News Corp, First Data, and Whirlpool were8.24 percent, −2.59 percent, and 10.13 percent. What’s your portfolio return? (LG9-7)

ADVANCED PROBLEMS

9-27 Asset Allocation You have a portfolio with an asset allocation of 50 percent stocks, 40 percent long-term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 tocompute the return of the portfolio in the year 2010 and each year since. Then compute the averageannual return and standard deviation of the portfolio and compare them with the risk and return profileof each individual asset class. (LG9-2, LG9-5)

9-28 Asset Allocation You have a portfolio with an asset allocation of 35 percent stocks, 55 percent long-term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 tocompute the return of the portfolio in the year 2010 and each year since. Then compute the averageannual return and standard deviation of the portfolio and compare them with the risk and return profileof each individual asset class. (LG9-2, LG9-5)

9-29 Portfolio Weights You have $15,000 to invest. You want to purchase shares of Alaska Air at $42.88,Best Buy at $51.32, and Ford Motor at $8.51. How many shares of each company should you purchaseso that your portfolio consists of 30 percent Alaska Air, 40 percent Best Buy, and 30 percent FordMotor? Report only whole stock shares. (LG9-7)

9-30 Portfolio Weights You have $20,000 to invest. You want to purchase shares of Xerox at $17.34,Qwest at $8.15, and Liz Claiborne at $44.73. How many shares of each company should you purchaseso that your portfolio consists of 25 percent Xerox, 40 percent Qwest, and 35 percent Liz Claiborne?Report only whole stock shares. (LG9-7)

9-31 Portfolio Return The following table shows your stock positions at the beginning of the year, thedividends that each stock paid during the year, and the stock prices at the end of the year. What is yourportfolio dollar return and percentage return? (LG9-7)

Company Shares Beginning of Year Price Dividend Per Share End of Year Price

US Bank 300 $43.50 $2.06 $43.43

PepsiCo 200 59.08 1.16 62.55

JDS Uniphase 500 18.88 16.66

Duke Energy 250 27.45 1.26 33.21

9-32 Portfolio Return The following table shows your stock positions at the beginning of the year, thedividends that each stock paid during the year, and the stock prices at the end of the year. What is yourportfolio dollar return and percentage return? (LG9-7)

Company Shares Beginning of Year Price Dividend Per Share End of Year Price

Johnson Controls 350 $72.91 $1.17 $85.92

Medtronic 200 57.57 0.41 53.51

Direct TV 500 24.94 24.39

Qualcomm 250 43.08 0.45 38.92

9-33 Risk, Return, and Their Relationship Consider the following annual returns of Estee Lauder and

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Lowe’s Companies:Compute each stock’s average return, standard deviation, and coefficient of variation. Which stockappears better? Why? (LG9-3, LG9-4)

Estee Lauder Lowe’s Companies

Year 1 23.4% −6.0%

Year 2 −26.0  16.1 

Year 3 17.6  4.2 

Year 4 49.9  48.0 

Year 5 −16.8  −19.0 

9-34 Risk, Return, and Their Relationship Consider the following annual returns of Molson Coors andInternational Paper:Compute each stock’s average return, standard deviation, and coefficient of variation. Which stockappears better? Why? (LG9-3, LG9-4)

Molson Coors International Paper

Year 1 16.3% 4.5%

Year 2 −9.7  −17.5  

Year 3 36.5  −0.2 

Year 4 −6.9  26.6 

Year 5 16.2  −11.1 

9-35 Spreadsheet Problem Following are the monthly returns for March 2011 to February 2016 of threeinternational stock indices: All Ordinaries of Australia, Nikkei 225 of Japan, and FTSE 100 ofEngland.

a. Compute and compare each index’s monthly average return and standard deviation.b. Compute the correlation between (1) All Ordinaries and Nikkei 225,(2) All Ordinaries and FTSE

100, and (3) Nikkei 225 and FTSE 100, and compare them.c. Form a portfolio consisting of one-third of each of the indexes and show the portfolio return each

year, and the portfolio’s return and standard deviation.

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9-36 Spreadsheet Problema. Create a spreadsheet like the one shown below. The spreadsheet should use the returns for assets A

and B to form a portfolio return using the weights for each asset shown in cells E1 and E2. Theaverage portfolio return and standard deviation should compute at the bottom of the column ofportfolio returns. When you change the weights, the portfolio returns, average, and standarddeviation should recalculate.

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b. Use the Solver function to find the weights that provide the highest return for a standard deviationof 6 percent, 7.5 percent, 9 percent, 10.5 percent, 12 percent, and 13.5 percent. Report the weightsand the return for each of these portfolio standard deviations. The Solver function is found in theData tab. (You may have to enable the function through the File tab, then Options, then Add-ins.)The solver image illustrates the maximizing of the average return for the specific constraints. Theconstraints are that the weights must be between 0 and 1, inclusive, and must sum to 1. Lastly, setthe standard deviation constraint to the desired level.

NotesCHAPTER 91. We use the denominator of N – 1 to compute a sample’s standard deviation, which is the most common for finance applications. We

would divide the standard deviation of a population simply by N.

I

chapter tenestimatingrisk and return

©Ingram Publishing

s it possible for investors to know the exact risk they have to take? In Chapters 9 and 10, we exploremethods to find the return that individual or institutional investors require to make a particularinvestment attractive. In the previous chapter, we established a positive relationship between risk and

return using historical data. Risk and return play an undeniable role as investors seek the best return forthe least risk. But until there’s some way to forecast the future, financial managers and investors mustmake investment decisions armed only with their expectations about future risk and return. We need anexact specification that shows directly the amount of reward required for investors to take the level of riskin a given firm’s stock or portfolio of securities. In this chapter we will also see how investors get theinformation they need to make risk-reward decisions.

Investors need to know how much risk they have to take to confidently expect a 10 percent return.Managers also want to know what return shareholders require so that they can decide how to meet thoseexpectations. In Chapter 11, we’ll explore how managers conduct financial analysis to find theshareholders’ required return. If we want to specify the exact risk–return relationship, we need to developa better measure of risk for individuals and institutional investors. As we saw in Chapter 9, any firm’s totalrisk is specific to that particular firm. But the market doesn’t reward firm-specific risk because investorscan easily diversify away any single firm’s specific risks by owning other offsetting firms’ stocks to createa portfolio subject only to market or undiversifiable risk. So, we need to find just the market risk portion of

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total risk for investors. The theory to find the market risk portion of stock ownership extends modernportfolio theory. Our search to find market risk will lead us to the capital asset pricing model (CAPM),which utilizes a measure of market risk called beta. CAPM’s risk–return specification provides us apowerful tool to make better investment decisions.

LEARNING GOALS

LG10-1 Compute forward-looking expected return and risk.LG10-2 Understand risk premiums.LG10-3 Know and apply the capital asset pricing model (CAPM).LG10-4 Calculate and apply beta, a measure of market risk.LG10-5 Differentiate the levels of market efficiency and their implications.LG10-6 Calculate and explain investors’ required return and risk.LG10-7 Use the constant-growth model to compute required return.

viewpointsbusiness APPLICATIONConsider that you work in the finance department of a large corporation. Your team is analyzing several new projects the firm canpursue. To complete the analysis, the team needs to know what return stockholders require from the firm.

You are to estimate this required return. Shareholders’ expected return will depend on your company’s risk level. What informationdo you need to gather and how might you compute this return? (See the solution at the end of the book.)

Corporate finance managers and investment professionals commonly use the beta measure. But likeany theory, CAPM has its limitations. We’ll discuss the CAPM’s limitations and concerns about beta andpropose an alternate required return measure. Whether beta or any other risk–return specification isuseful relies in part on whether a stock’s price represents a fair estimate of the true company value. Stockprice validity and reliability—their general correctness— are vitally important both to investors andcorporate managers.

10.1 • EXPECTED RETURNS LG10-1In the previous chapter, we characterized risk and return in historical terms. We defined a stock’s return as the actualprofit realized while holding the stock or the average return over a longer period. We described risk simply as thestandard deviation of those returns—a term already familiar to you from your statistics classes. So, we did a goodjob describing the risk and return that the stock experienced in the past. But do those risk and return figures holdinto the future? Firms can quite possibly change their stocks’ risk level by substantially changing their business. If afirm takes on riskier new projects over time, or changes the nature of its business, the firm itself will become riskier.Similarly, firms can reduce their risk level—and hence, their stock’s riskiness—by choosing low-risk new projects.Both investors and firms find expected return, a forward-looking return calculation that includes risk measures, veryuseful to estimate future stock performance.

Expected Return and RiskWe can attribute a company’s business success over a year partly to its management talent, strategies, and otherfirm-specific activities, but overall economic conditions will also affect a firm’s level of success or failure. Considera steel manufacturer—Nucor Corp. The steel business closely follows economic trends. In a good economy, demandfor steel is strong as builders and manufacturers step up building and production. During economic

recessions, demand for steel falls off quickly. So, if we want to assess Nucor’s probabilities for success next year,we know that we must look partly at Nucor’s managerial ability and partly at the economic outlook.

personal APPLICATIONYou have just started your first job in the corporate world and need to make some retirement plan decisions. The company’s 401(k)retirement plan offers three investment choices: a stock portfolio with a beta of 1, a bond portfolio with a beta of 0.18, and a moneymarket account. For your allocation, you decide to contribute $200 per month to the stock portfolio, $100 to the bond portfolio, and$50 to the money market account.

If the expected return to the market portfolio is 11 percent, what risk level are you taking in your retirement portfolio and what returnshould you expect over the long run? (See the solution at the end of the book.)

Investing mainly in my own company’s stock is safer, right? Maybe not . . .

Unfortunately, we cannot accurately predict what the economy will be like next year. Predicting economic activity islike predicting the weather—forecasts give the probability of rain or sunshine. Economists cannot say for surewhether the economy will be good or bad next year. Instead, they may forecast a 70 percent chance that theeconomy will be good and a 30 percent chance of a recession. Similarly, analysts might say that given Nucor’smanagerial talent, if the economy is good, Nucor will perform well and the stock will increase 20 percent. If theeconomy goes into a recession, then Nucor’s stock will fall 10 percent. So what return do you expect from Nucor?The return still depends on the state of the economy.

A company’s success depends partly on management talent, strategies, and other activities.©Robert Nicholas/AGE Fotostock

This leads us directly to a key concept: expected return. We compute expected return by multiplying each possiblereturn by the probability, p, of that return occurring. We then sum them (recall that all probabilities must add toone). Let’s place Nucor in an economy with only two states: good and recession. In this scenario, Nucor’s expectedreturn would be 11 percent [= (0.7 × 20%) + (0.3 × −10%)]. Of course, nothing is quite that simple. Economistsseldom predict simple two-state views of the economy as in the previous example. Rather, economists give muchmore detailed forecasts (such as three states: red-hot economy, average expansion, and recession). So our generalequation for a stock’s expected return with S different conditions of the economy is

(10-1)

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The result of this expected return calculation has some interesting properties. First, the expected return figureexpresses what the average return would be over time if the probabilistic states of the economy occur as predicted.For example, the 70/30 probability distribution for good/recession economic states suggests that the economy will begood in 7 of the next 10 years, earning Nucor shareholders a 20 percent return in each of those years.Shareholders would lose 10 percent in each of the three recession years. So the average return over those10 years would be 11 percent, the same as the expected return. The second interesting property: The expected returnitself will not likely occur during any one year. Remember that Nucor will earn either a return of 20 percent or −10percent. Yet its expected return is 11 percent, a value that it cannot earn because we have no economic condition forwhich the return is 11 percent. Again, this illustration seems extreme because we used only two economic states.Any real economic forecast would instead include a probability distribution of many potential economic conditions.

probability The likelihood of occurrence.

expected return The average of the possible returns weighted by the likelihood of those returns occurring.

probability distribution The set of probabilities for all possible occurrences.

We can also characterize risk via this expected return figure. The expected return procedure shows potential returnpossibilities, but we don’t know which one will actually occur, so we face uncertainty. In the last chapter, wemeasured risk using the standard deviation of returns over time. We can use the same principle to measure risk forexpected returns. What range of different expected returns will Nucor exhibit from the expected return of 11percent? In our two-state description of the economy, the deviation could be either 9 percent (= 20% − 11%) or −21percent (= −10% − 11%). We compute the standard deviation of expected returns the same way we did for historicalreturns. We square the deviations, then multiply by the probability of that deviation occurring, and then sum them allup. So Nucor’s return variance is 189.0 As a final step, we take the square root of our result toput the figure back into sensible terms. The standard deviation for Nucor is 13.75 percent (= ). The generalequation for the standard deviation of S different economic states is

(10-2)

the Math Coach on…Expected Return and StandardDeviation

“When you compute expected return and standard deviation, you’ll find it helpfulto use the decimal format for the probability of the economic state andpercentages to state the return in each state.„

Risk Premiums LG10-2Throughout the book, we have mentioned the positive relationship between expected return and risk. Consider thiskey question: You have a riskless investment available to you. The short-term government debt security, the T-bill,

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offers you a low return with no risk. Why would you invest in anything risky, when you could simply buy T-bills?The answer, of course, is that some investors want a higher return and are willing to take some risk to raise theirreturns. Investors who take on a little risk should expect a slightly higher return than the T-bill rate. People who takeon higher risk levels should expect higher returns. Indeed, it’s only logical that investors require this extra return towillingly take the added risk.The expected return of an investment is often expressed in two parts, a risk-free return and a risky contribution. Thereturn investors require for the risk level they take is called the required return:

(10-3)

required return The level of total return needed to be compensated for the risk taken. It is made up of a risk-free rate and a riskpremium.

The risk-free rate is typically considered the return on U.S. government bonds and bills and equals the real interestrate and the expected inflation premium that we discussed in Chapter 6. The risk premium is the reward investorsrequire for taking risk. How large are the rewards for taking risk? As we discussed in the previous chapter, themarket doesn’t reward all risks. The firm-specific portion of total risk for any stock can be diversified away, andsince the investor takes on such risk out of ignorance or by mistake, an efficient market will not reward anyone fortaking on this “superfluous” risk. So as we examine historical risk premiums, we do so with a diversified portfoliothat contains no firm-specific risk.

risk premium The portion of the required return that represents the reward for taking risk.

EXAMPLE 10-1 Expected Return and Risk LG10-1

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Bailey has a probability distribution for four possible states of theeconomy, as shown below. She has also calculated the return thatMotor Music stock would earn in each state. Given this information,what’s Motor Music’s expected return and risk?

Economic State Probability Return

Fast growth 0.15 25%

Slow growth 0.60 15

Recession 0.20 −5

Depression 0.05 −20

SOLUTION:

Bailey can compute the expected return using equation 10-1:

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Then Bailey can compute the expected return by computing thestandard deviation using equation 10-2:

The expected return and standard deviation are 10.75 percent and11.76 percent, respectively. We could also show these equations in atable, such as

Similar to Problems 10-1, 10-2, 10-17, 10-18, 10-23, 10-24, Self-TestProblem 1

▼ TABLE 10.1 The Realized Average Annual Risk Premium for Stocks

1950to

2015

1950to

1959

1960to

1969

1970to

1979

1980to

1989

1990to

1999

2000to

2009

2010to

2015

Riskpremium

8.2% 18.8% 4.7% 1.2% 9.3% 14.1% −1.8% 13.4%

Realized risk premiums were very different in each decade. The recent decade even had a negative risk premium!

Source: S&P 500 Index and T-bill rate data.

Table 10.1 shows the average annual return on the S&P 500 Index minus the T-bill rate for different timeperiods. The remainder after we subtract the T-bill rate is the risk premium; in this case, it’s the market riskpremium—the reward for taking general (unsystematic) stock market risk. Since 1950, the average market riskpremium has been 8.3 percent per year. Over the long run, this is the reward for taking stock market risk. The actual,realized risk premium during particular decades has varied. The average risk premium has been as high as 18.8percent for the 1950s and as low as −1.8 percent during the 2000s. The performance in the 2000s is unusual; thestock market return has been so poor that it has not beaten the risk-free rate. Investors require a risk premium fortaking on market risk. But taking that risk also means that they will periodically experience poor returns.

time out!10-1 Describe the similarities between computing average return and expected return. Also, describe the similarities between

expected return risk and historical risk.10-2 Why would people take risks by investing their hard-earned money?

10.2 • MARKET RISK LG10-3

How much risk should you take to achieve the return you want over time? In the previous chapter, we demonstratedthat individual stocks and different portfolios exhibit different levels of total risk. Recall that the rewards forcarrying risk apply only to the market risk (or undiversifiable) portion of total risk. But how do investors know howmuch of the 33.4 percent standard deviation of returns for Mattel Inc. is firm-specific risk and how much of thatdeviation is market risk? The answer to this important question will determine how much of a risk premiuminvestors should require for Mattel. The attempt to specify an equation that relates a stock’s required return to anappropriate risk premium is known as asset pricing.

The Market PortfolioThe best-known asset pricing equation is the capital asset pricing model, typically referred to as CAPM. Though manytheorists formulated theories that, in the end, supported the CAPM’s effectiveness, credit for the model goes toWilliam Sharpe and John Lintner. Sharpe eventually won a Nobel Prize for his work in 1990. (Lintner died in 1983,and Nobel Prizes are not awarded posthumously.) Today, both investors and corporate finance professionals useCAPM widely. In developing the CAPM, Lintner and Sharpe sought to emphasize the individual investor’s beststrategy to maximize returns for a given amount of market risk.

CAPM starts with modern portfolio theory. Remember from the previous chapter that when you combine securitiesinto a portfolio, you can find a set of portfolios that dominate all others. The best combinations possible use all therisky securities available (but not the risk-free asset) to create efficient frontier portfolios, which would lie along acurved line in risk/return space, as shown in Figure 10.1, panel A. These portfolios represent combinations ofvarious risky securities that give the highest expected return for each potential level of risk (i.e., they lie the furthest“up and to-the-left” that we can achieve when considering all possible combinations of the available riskysecurities).

FIGURE 10.1 Maximizing Expected Return

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In MPT, investors want to be on the efficient frontier (Panel A) because it gives them the highest expected return for each level of risk.However, after adding a riskless asset (Panel B), investors can then get portfolios on the straight line (shown), which offers a higher expectedreturn for each level of risk than the efficient frontier.

The idea of a risk premium in equation 10-3 implies a risk-free investment, like T-bills. Panel B shows where therisk-free asset would appear on the capital market line (CML). The risk-free asset must lie on the y-axis preciselybecause it carries no risk. Now we draw a line from the risk-free security to a point tangent to the efficient frontier.The CML relationship appears as a line because investments show a direct risk–reward relationship. You may recallfrom your economics classes that only one tangency point will be possible between this kind of curve and a straightline. The spot where the tangency occurs is called the market portfolio, which has a special significance. The marketportfolio represents ownership in all traded assets in the economy, so this portfolio provides maximumdiversification. You can locate your optimal portfolio on this line by owning various combinations of the risk-freesecurity and the market portfolio. If most of your money is invested in the market portfolio, then you will have aportfolio on the line that lies just to the left of the market portfolio dot in the graph. If you own just a little of themarket portfolio and hold mostly risk-free securities, then your portfolio will lie on the line near the risk-free security dot. For your investments to lie on the line to the right of the market portfolio, you wouldhave to invest all your money in the market portfolio, then borrow more money at the risk-free rate and invest theseadditional funds in the market portfolio. Borrowing money to invest is known as using financial leverage. Usingfinancial leverage increases the overall risk of the portfolio, which is illustrated in this figure as a higher standarddeviation.

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market risk premium The return on the market portfolio minus the risk-free rate. Risk premiums for specific firms are based on themarket risk premium.

asset pricing The process of directly specifying the relationship between required return and risk.

capital asset pricing model (CAPM) An asset pricing theory based on a beta, a measure of market risk.

capital market line (CML) The line on a graph of return and risk (standard deviation) from the risk-free rate through the market portfolio.

market portfolio In theory, the market portfolio is the combination of securities that places the portfolio on the efficient frontier and on aline tangent from the risk-free rate. In practice, the S&P 500 Index is used to proxy for the market portfolio.

financial leverage The extent to which debt securities are used by a firm.

Notice that if you had a portfolio on the efficient frontier (labeled “old portfolio”), you could do better. Instead ofowning the old portfolio, you can put some of your money in the market portfolio and some in the risk-free securityto obtain the “new portfolio.” See how the new portfolio dominates that old one? It carries the same risk level, butoffers a higher return. In fact, notice that the line drawn between the risk-free investment and the market portfoliodominates all of the efficient frontier portfolios (except the market portfolio itself). All portfolio allocations betweenthe risk-free security and the market portfolio constitute the capital market line. All investors should want to locatetheir portfolios on the CML, rather than the efficient frontier. Portfolios on the CML offer the highest expectedreturn for any level of desired risk, which the investor controls by deciding how much of the market portfolio andhow much of the risk-free asset to hold. Risk-averse investors can put more of their money in T-bills and less intothe market portfolio. Investors willing to take on higher risk for larger returns can put more of their money in themarket portfolio.

Beta, a Measure of Market Risk LG10-4The CML demonstrates that the market portfolio is crucial. Indeed, its return less the risk-free rate represents theexpected average market risk premium. The market portfolio features no firm-specific risk; all such risk isdiversified away. So the market portfolio carries only market risk. Thus the market portfolio’s risk factor allows usto compute a measure of firm-specific risk for any individual stock or portfolio. We can now examine the questionposed at the beginning of this section: “How much of Mattel’s total risk is attributable to market risk?” The standarddeviation of returns includes all of Mattel stock’s risk—it quantifies how much the stock price rises and falls. Themarket risk portion will rise and fall along with the market portfolio. If we subtract the market risk portion from thetotal risk measure, we’re left with firm-specific risk. This part of risk rises and falls in ways unrelated to marketchanges.

Remember that portfolio theory describes a measure—correlation—that measures how two stocks move togetherthrough time. Instead of measuring how any two stocks or portfolios move together, we now want to know how astock or portfolio moves relative to market portfolio movements. This measure is known as beta ( β). Beta measuresthe comovement between a stock and the market portfolio.

beta (β) A measure of the sensitivity of a stock or portfolio to market risk.

If Mattel’s total risk level is measured by its standard deviation, σMattel, then we can find the portion of this risk thatis attributable to the market in general by multiplying Mattel’s total risk by its correlation with the marketportfolio, σMattel × ρMattel, Market. The beta computation is scaled so that the market portfolio itself has abeta of one. The scaling is done by dividing by standard deviation of the market portfolio: σMattel × ρMattel, Market ÷σMarket.

1 Stocks with betas larger than one are considered riskier than the market portfolio, while betas of less thenone indicate lower risk. Mattel has a beta of 0.65, meaning that Mattel has low sensitivity to market risk. When themarket portfolio moves, you can expect Mattel stock to move in the same direction. Technically, you should expectMattel’s realized risk premium to be 35 percent less than the realized market risk premium.

Table 10.2 shows the beta for each of the 30 companies in the Dow Jones Industrial Average. Investors considermany of these companies high risk, like Du Pont (β = 2.01) and Disney (1.56). These firms’ stocks carry highmarket risk because the demand for their products is very sensitive to the overall economy’s strength. Investorsconsider other companies safe bets with low risk, like Walmart (0.19), Verizon (0.47), and McDonald’s (0.56).Many lower-beta firms sell consumer goods that we consider the necessities of life, which we will buy whether theeconomy is in recession or expansion. The demand for these products is price inelastic and not sensitive to economicconditions. Some companies have nearly the same risk as the market portfolio, like Pfizer (1.02), Microsoft (1.02),

and Intel (1.02).

▼ TABLE 10.2 Dow Jones Industrial Average Stock Betas

Company Beta Company Beta

3M Company 1.08 Intel 1.02

American Express 1.21 Johnson & Johnson 0.89

Apple 1.35 JPMorgan Chase 1.20

Boeing 1.36 McDonald’s 0.56

Caterpillar 1.09 Merck 0.75

Cisco Systems 1.18 Microsoft 1.02

Chevron 1.17 Nike 0.63

Coca-Cola 0.77 Pfizer 1.02

Disney 1.56 Procter & Gamble 0.66

Du Pont de Nemours 2.01 Travelers 1.22

Exxon Mobil 0.92 United Technologies 1.18

General Electric 1.22 UnitedHealth Group 0.62

Goldman Sachs 1.35 Verizon Communications 0.47

Home Depot 0.96 Visa 1.06

IBM 0.66 Walmart Stores 0.19

Source: Yahoo! Finance, March 2, 2016.

The Security Market Line LG10-3Beta indicates the market risk that each stock represents to investors. So the higher the beta, the higher the riskpremium investors will demand to undertake that security’s market risk. Since beta sums up precisely what investorswant to know about risk, we often replace the standard deviation risk measure shown in Figure 10.1 with beta.Figure 10.2 shows required return versus beta risk. We call the line in this figure the security market line (SML),which illustrates how required return relates to risk at any particular time, all else held equal. The SML also showsthe market portfolio’s risk premium or any stock’s risk premium.

FIGURE 10.2 The Security Market Line Uses Beta as the Risk Measure

General Electric has higher risk than the overall stock market, so it should require a higher return.

security market line Similar to the capital market line except risk is characterized by beta instead of standard deviation.

When a stock like General Electric carries a beta greater than one, then its risk premium must be larger than themarket risk premium. A stock like Johnson & Johnson carries a lower beta than does the overall market; thereforeJohnson & Johnson would offer a lower risk premium to investors.

We can use the SML to show the relationship between risk and return for any stock or portfolio. To preciselyquantify this relationship, we need the equation for the SML. The equation of any line can be defined as y = b + mx,where b is the intercept and m is the slope. In this case, the y-axis is required return and the x-axis is beta. Theintercept is Rf. You may remember that the slope is the “rise over run” between two points on the line. The risebetween the risk-free security and the market portfolio is RM − Rf and the run is 1−0. Substituting into the lineequation results in the CAPM:

(10-4)

So, we have determined a way to estimate any stock’s required return once we have determined its beta. Considerthis: We expect the market portfolio to earn 12 percent and T-bill yields are 5 percent. Then General Electric’srequired return, with a β = 1.22, is 5% + 1.22 × (12%−5%) = 13.54 percent. Table 10.3 shows the 30 Dow JonesIndustrial Average stocks’ required return, using these same market and risk-free rate assumptions. Higher-riskcompanies have higher betas, and thus require higher returns.

▼ TABLE 10.3 Required Returns for DJIA Stocks

Company Required Return Company Required Return

3M Company 12.56% Intel 12.14%

American Express 13.47  Johnson & Johnson 11.23 

Apple 14.45  JPMorgan Chase 13.40 

Boeing 14.52  McDonald’s 8.92 

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Caterpillar 12.63  Merck 10.25 

Cisco Systems 13.26  Microsoft 12.14 

Chevron 13.19  Nike 9.41 

Coca-Cola 10.39  Pfizer 12.14 

Disney 15.92  Proctor & Gamble 9.62 

Du Pont de Nemours 19.07  Travelers 13.54 

Exxon Mobil 11.44  United Technologies 13.26 

General Electric 13.54  UnitedHealth Group 9.34 

Goldman Sachs 14.45  Verizon Communications 8.29 

Home Depot 11.72  Visa 12.42 

IBM 9.62  Walmart Stores 6.33 

Higher beta stocks require higher expected returns.

Assumptions: market return = 12% and risk-free rate = 5%.

Source: Yahoo! Finance, March 2, 2016.

Portfolio Beta As you might expect, a stock portfolio’s beta is the weighted average of the portfoliostocks’ betas.The portfolio beta equation resembles equation 9-7, which gives the return of a portfolio:

(10-5)

portfolio beta The combination of the individual company betas in an investor’s portfolio.

EXAMPLE 10-2

CAPM and Under- or OvervaluedStock LG10-3

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Say that you are a corporate CFO. You know that the risk-free rate iscurrently 4.5 percent and you expect the market to earn 11 percent thisyear. Through your own analysis of the firm, you think it will earn a 13.5percent return this year. If the beta of the company is 1.2, should youconsider the firm undervalued or overvalued?

SOLUTION:

You can compute shareholders’ required return with CAPM as 4.5% +1.2 × (11% − 4.5%) = 12.3%. Since you think the firm will actually earnmore than this required return, the firm appears to be currentlyundervalued. That is, its price must rise more then predicted by CAPMto obtain the return you estimated in your original analysis.

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Similar to Problems 10-7, 10-8, 10-19, 10-20, Self-Test Problem 3

With this equation, you can easily determine whether adding a particular stock to the portfolio will increase ordecrease the portfolio’s total market risk. If you add a stock with a higher beta than the existing portfolio, then thenew portfolio will carry higher market risk than the old one did. Although we can find the effects on total portfoliorisk of adding particular stocks using beta, the same is not necessarily true if we use standard deviations as our riskmeasure. The new stock, however risky, might have low correlations with the other stocks in the portfolio—offsetting (negative) correlations would reduce total risk.

Finding Beta LG10-4The CAPM is an elegant explanation that relates the return you should require for taking on various levels of marketrisk. Although CAPM provides many practical applications, you need a company’s beta to use those applications.Where or how can you obtain a beta? You have two ways. First, given the returns of the company and the marketportfolio, you can compute the beta yourself. Second, you can find the beta that others have computed throughfinancial information data providers.

Many financial outlets publish company betas. Websites that provide company betas for free include MSN Moneyand Yahoo! Finance, to name just a couple. For example, in March 2016, the beta these websites listed for Disneywere: MSN Money (1.41) and Yahoo! Finance (1.56). Note that these reported betas have some differences. Toknow why differences might arise, consider how you would go about gathering information and computing betayourself.

EXAMPLE 10-3 Portfolio Beta LG10-4

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

You have a portfolio consisting of 20 percent Boeing stock (β = 1.04),40 percent Hewlett- Packard stock (β = 1.54), and 40 percentMcDonald’s stock (β = 0.34). How much market risk does the portfoliohave?

SOLUTION:

Compute a beta for the portfolio. Using equation 10-5, the portfolio betais 0.2 × 1.04 + 0.4 × 1.54 + 0.4 × 0.34 = 0.96. Note that this portfoliocarries 4 percent less market risk than the general market does.

Similar to Problems 10-11, 10-12, 10-21, 10-22, 10-27, 10-28, Self-TestProblem 2

To compute your own beta, first obtain historical returns for the company of interest and of the marketportfolio. Then run a regression of the company return as the dependent variable and the market portfolioreturn as the independent variable. The resulting market portfolio return coefficient is beta. Many importantquestions may come to mind. First, what do you use as the market portfolio? People typically use a major stockindex like the S&P 500 Index to proxy for the market portfolio. Second, what time frame should you use? You canuse daily, weekly, monthly, or even annual returns. Using monthly returns is the most common. How long a timeseries is needed? As you will recall, statistical estimates become more reliable and valid as more data are used. Butyou will have to weigh those statistical advantages against the fact that companies change their business enterprisesand thus their risk levels over time. Using data from too long ago reflects risks that may no longer apply. Generallyspeaking, using time series data of three to five years is common. Whatever decisions you make to address thesequestions, be consistent by making the same decisions for all the company betas you compute. Table 10.4 shows thespreadsheet of a stock’s beta calculation. In this case, monthly returns from five years are used for the stock returnand a market index. The SLOPE() function of the spreadsheet directly computes the regression coefficient of

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interest. The beta estimation using the spreadsheet function is 0.83.

▼ TABLE 10.4 Compute Beta Using a Spreadsheet

The spreadsheet function SLOPE() finds the statistical relationship between a stock’s return and the market return. Considering thesemonthly returns for a stock and a market index, the beta of this stock is 0.83.

finance at work //: marketsAre Stocks Really Good or Bad?One of the basic financial theories tells us how we should view the relationship between risk and expected returns. In a nutshell, risk andexpected return are positively related. A high-risk investment needs to have a high expected return, or no one would want to buy thatinvestment. With this lack of demand, the investment’s price would drop until it offers new buyers a high expected return for the future.The higher return is the reward for taking the extra risk. Similarly, low-risk investments offer low expected returns.

To quantify risk, the finance industry tends to use two measures; volatility of returns and beta. The volatility, measured by variance orstandard deviation, tells us how much a return can deviate from the average return. Beta tells us how much market risk an investmenthas. These measures are very useful in assessing the risk of an investment or portfolio and what return premium should be expected fortaking risk.

However, people do not naturally think of risk within this financial theory framework. First, investors care less about how aninvestment’s return deviates from expectations and more about how the return may be lower than expected. In other words, a higherreturn than expected is not considered risky, only a lower return, or even, gulp, a loss, is viewed as risk.

Also, real people do not think in terms of the high risk/return versus the low risk/return scale. Instead, people think in terms of betteror worse. For example, three financial economists ran an experiment in which they asked high net worth individuals for either theirexpected return predictions or their risk assessment (both on a 0 to 10 scale) of over 200 of the Fortune 500 companies. When theycompiled all the responses, they found the relationship in the figure shown below. Notice anything odd? This shows that firms with lowrisk are expected to earn a high return. People act as if expected return and risk are negatively related! This is the opposite of financialtheory. Instead of evaluating firms within the framework that high expected return goes with high risk and low return goes with low risk,people seem to think in terms of good versus bad stocks. What are the characteristics of a “good” stock? Characteristics that seem goodare high expected return and low risk. When an investor feels a stock is good, then it is attributed with high return and low risk. When aninvestor feels the stock is bad, then it is attributed with low return and high risk. Psychologists call this perception or belief an “affect.”

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Unfortunately, thinking about risk and return from the affect framework causes investors to misunderstand the underlying dynamics ofactual expected return and risk. Thus, they may make poor decisions regarding risk and return.

Want to know more?Key Words to Search for Updates: affect, measuring investment risk, risk and behavioral finance

Source: Statman, Meir, Kenneth L. Fisher, and Deniz Anginer, “Affect in a Behavioral Asset-Pricing Model,” Financial Analysts Journal,March/April 2008, Figure 3: Relationship between Expected Return Scores and Risk Scores.

Concerns about BetaConsider the estimation choices just mentioned. Say you estimate a firm’s beta using monthly data for five years andthe Dow Jones Industrial Average return as the market portfolio. Suppose that the result is a beta of 1.3. Then youtry again using weekly returns for three years and the return from the S&P 500 Index as the market portfolio’s yield,resulting in a beta of 0.9. These estimates are quite different and would create a large variation in required return ifyou plugged them into the CAPM. So, which is the more accurate estimate? Unfortunately, we may not be able todetermine which is most representative, or “true.” In general, you may estimate a little different beta using differentmarket portfolio proxies, different return intervals (like monthly returns versus annual returns), and different timeperiods. Problem 10-31 at the end of this chapter explores these differences.

In addition to these estimation problems, a company can change its risk level, and thus its beta, bychanging the way it operates within its business, by expanding into new businesses, and/or by changing itsdebt load. So even if beta is an accurate measure of what the firm’s risk level was in the past, does it apply to thefuture? Beta’s applicability will depend on the firm’s future plans.

Both financial managers and investors share these concerns about beta. In the end, beta’s usefulness depends on itsreliability. Unfortunately, beta’s empirical record is not as good as we would like. We should expect that companieswith high betas yield higher returns than companies with low betas. On average, though, this does not turn out to bethe case. A company’s beta does not appear to predict its future return very well. Since characterizing the risk–returnrelationship is so important, finance researchers have introduced other asset pricing models. One promising modeladds more risk factors to the predictive relationship other than just market risk. Firm size and book-to-market ratiohave had some success predicting returns, so new models often include factors derived from these characteristicsalong with beta as a measure of market risk.

time out!10-3 Explain why portfolios that lie on the capital market line offer better risk–return trade-offs than those that lie on the efficient

frontier.

10-4 Examine the betas in Table 10.2. Which seem about right to you and which seem to indicate too much or too little risk forthat firm?

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10.3 • CAPITAL MARKET EFFICIENCY LG10-5The risk and return relationship rests on an underlying assumption that stock prices are generally “correct”—theyare not predictably too high or too low. Imagine having a system that identified undervalued stocks with low risks(i.e., relatively high returns with a low beta). Because those stocks are undervalued, they will earn you a high return,on average, as their stock prices rise to their correct value. Note that the CAPM’s risk-return relationship would beincorrect. You would be consistently getting high returns with low risk. On the other hand, if you consistentlypicked overvalued stocks, you wouldn’t be earning enough return to compensate you for the risks you are taking.Investors move their money to the best alternatives by selling overvalued stocks and buying undervalued stocks.This causes the prices of the overvalued stocks to drop and the prices of the undervalued stocks to rise until bothstocks’ returns stand more in line with their riskiness. Thus, the risk–return relationship relies on the idea that pricesare generally accurate.

What conditions are necessary for an efficient market? Efficient, or perfectly competitive, markets featureMany buyers and sellers.

No prohibitively high barriers to entry.Free and readily available information available to all participants.

Low trading or transaction costs.

Are these conditions met for the U.S. stock market? Certainly millions of stock investors trade every day, buyingand selling securities. With discount brokers and online traders, the costs to trade are fairly minimal and present noreal barriers to enter the market. Information is increasingly accessible from many sources and trading philosophies,and commission costs and bid–ask spreads have steadily declined. With millions of the larger companies’ shares(say the S&P 500) of stock trading every day, the U.S. stock exchanges appear to meet efficiency conditions. Butother segments of the market, like those exchanges that trade in penny stocks, feature very thin trading. The prices ofthese very small companies’ stock may not be fair and these equities may be manipulated in fraudulent scams. In the1970s and 1980s, penny stock king Meyer Blinder and his firm Blinder-Robinson was known as “blind ’em and rob’em” as they practiced penny stock price manipulation to rob many small investors of their entire investments inthese small markets. These days, penny stock price manipulation is typically conducted through e-mail and Webposting scams.

efficient market A securities market in which prices fully reflect available information on each security.

penny stocks The stocks of small companies that are priced below $1 per share.

Efficient Market HypothesisOur concept of market efficiency provides a good framework for understanding how stock prices change over time.This theory is described in the efficient market hypothesis (EMH), which states that security prices fully reflect allavailable information. At any point in time, the price for any stock or bond reflects the collective wisdom of marketparticipants about the company’s future prospects. Security prices change as new information becomes available.Since we cannot predict whether new information about a company will be good news or bad news, we cannotpredict whether its stock price will go up or go down. This makes short-term stock-price movements unpredictable.But in the longer run, stock prices will adjust to their proper level as market participants gather and digest allavailable information.

The EMH brings us to the question of what type of information is embedded within current stock prices. Segmentinginformation into three categories leads to the three basic levels of market efficiency, described as:

1. Weak-form efficiency—current prices reflect all information derived from trading. This stock market information generally includescurrent and past stock prices and trading volume.

2. Semistrong-form efficiency—current prices reflect all public information. This includes all information that has already been revealedto the public, like financial statements, news, analyst opinions, and so on.

3. Strong-form efficiency—current prices reflect all information. In addition to public information, prices reflect the privately heldinformation that has not yet been released to the public, but may be known to some people, like managers, accountants, auditors,and so on.

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efficient market hypothesis (EMH) A theory that describes what types of information are reflected in current stock prices.

public information The set of information that has been publicly released. Public information includes data on past stock prices andvolume, financial statements, corporate news, analyst opinions, etc.

privately held information The set of information that has not been released to the public but is known by few individuals, likelycompany insiders.

Each of the EMH’s three forms rests on different assumptions regarding the extent of information that isincorporated into stock prices at any point in time. A fourth possibility—that markets may not be efficient and pricesmay not reflect all the information known about a company—also arises.

The weak-form efficiency level involves the lowest information hurdle, stating that stock prices reflect all past priceand trading volume activity. If true, this level of efficiency would have important ramifications. A segment of theinvestment industry uses price and volume charts to make investment timing decisions. Technical analysis has alarge following and its own vocabulary of patterns and trends (resistance, support, breakout, momentum, etc.). If themarket is at least weak-form efficient, then prices already reflect this information and these activities would notresult in useful predictions about future price changes, and thus would be a waste of time. Indeed, the people whomake the most money from price charting services are the people who sell the services, not the investors who buyand use those services.

The semistrong-form efficiency level assumes that stock prices include all public information. Notice that past stockprices and volumes are publicly available information, so this level includes the weak form as a subset. Importantinvestment implications arise if markets are efficient to public information. Many investors conduct security analysisin which they obtain financial data and other public information to assess whether a company’s stock is undervaluedor overvalued. But in a semistrong-form efficient market, stock prices already reflect this information and are thus“correct.” Using only public information, you would not be able to determine whether a stock is misvalued becausethat information is already reflected in the price.

If prices reflect all public information, then those prices will react as traders hear new (or private) information.Consider a company that announces surprisingly good quarterly profits. Traders and investors will have factored theold profit expectations into the stock price. As they incorporate the new information, the stock price will quickly riseto a new and accurate price as shown in the solid black line in Figure 10.3. Note that the stock price was$35 before the announcement and $40 immediately following. If you tried to buy the stock after hearingthe news, then you would have bought at $40 and not received any benefit of the good quarterly profit news. On theother hand, if the market is not semistrong-form efficient, then the price might react quickly, but not accurately. Thedashed red line shows a reaction in a non-semistrong efficient market where the price continues to drift up well afterthe announcement. This gradual drift to the “correct” price indicates that the market initially underreacted to thenews. In this case, you could have bought the stock after the announcement and still earned a profit. The dashed blueline shows an overreaction to the firm’s better-than-expected profits announcement. If markets either consistentlyunderreact or consistently overreact to announcements that would change stock prices (earnings, stock split,dividend, etc.), then we would believe that the market is not semistrong efficient.

FIGURE 10-3 Potential Price Reaction to a Good News Announcement

Stock prices react quickly to news, but do they react accurately?

The strong-form market efficiency level presents the highest hurdle to test market reaction to information. Thestrong-form level includes information considered by the weak-form, the semistrong-form, as well as privatelyknown information. People within firms, like CEOs and CFOs, know information that has not yet been released tothe public. They may trade on this privately held, or insider, information and their trading may cause stock prices tochange as it reflects that private information. In this way, stock prices could reflect even privately knowninformation. Note that the firm managers, accountants, and auditors know several days in advance that a firm hasearned unexpectedly high quarterly profits. If the stock price already incorporated this closely held privateknowledge, then the big price reaction shown in Figure 10.3 would not occur.

So, is the stock market efficient? If it is, at what level? This has been a hotly debated topic for decades and continuesto be. It is not likely that the market is strong-form efficient. Since insider trading is punished, insider informationmust be valuable. However, much evidence suggests that the market could be weak-form or semistrong-formefficient. Of course, we also have evidence that the market is not efficient at any of the three levels. We will explorethis more in the following section.

Behavioral FinanceThe argument for the market being efficient works as follows: Many individual and professional investors constantlylook for mispriced stocks. If they find a stock that is undervalued, they will buy it and drive up its price until it’scorrectly priced. Likewise, investors would sell an overpriced stock, driving down its price until it’s correctlyvalued. With so many investors looking for market “mistakes,” it’s unlikely that any mispriced stock opportunitieswill be left in the market.

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The technology sector fell victim to a stock market bubble in 2000.©Ingram Publishing/SuperStock

The argument against the market being efficient is equally convincing. The market comprises many peopletransacting with one another. When someone makes trading decisions influenced by emotion or psychological bias,those decisions may not seem rational. When many people fall under such influences, their trading decisions mayactually drive stock prices away from the correct price as emotion carries the traders away from rationality. Forexample, many people believe that investors were “irrationally exuberant” about technology stocks in the late 1990s—and that their buying excitement drove prices to an artificially high level. In 2000, the excitement wore off andtech stock prices plummeted. Whenever a set of stock prices go unnaturally high and subsequently crashdown, the market experiences what we call a stock market bubble.

In the past couple of decades, finance researchers have studied behavioral finance and found that people often behavein ways that are very likely “irrational.” At times, investors appear to be too optimistic, as though they are lookingthrough rose-colored glasses. At other times they appear to be too pessimistic. Common investment decisions aren’tnecessarily optimal ones, which flies in the face of the economist’s expectation of rational economic actors. Perhaps,then, capital markets don’t represent perfectly competitive or efficient markets if buyers and sellers do not alwaysmake rational choices.

It may take many biased investors to move a stock’s price enough that it would be considered a pricing mistake.However, the important decisions in a company are typically made by just one CEO or a management team. Thus,their biases can have a direct impact on decisions involving hundreds of millions, or even billions of dollars. In otherwords, the contribution of behavioral finance to economic decision making is likely to be even more important incorporate behavior than market behavior. For example, consider the psychological concept of overconfidence. One ofthe most pervasive biases, overconfidence describes a tendency for people to overestimate the accuracy of theirknowledge and underestimate the risks of a decision. These problems can adversely affect important decisions ofinvestment (i.e., acquiring other firms) and financing (i.e., issuing new stock or bonds).

stock market bubble Investor enthusiasm causes an inflated bull market that drives prices too high, ending in a dramatic collapse inprices.

behavioral finance The study of the cognitive processes and biases associated with making financial and economic decisions.

overconfidence Overconfidence is used to describe three psychological observations. First, people are miscalibrated on understandingthe precision of their knowledge. Second, people have a tendency to underestimate risks, and third, people tend to believe that they arebetter than average at tasks they are familiar with.

time out!10-5 Can the market be semistrong-form efficient but not weak-form efficient? Explain.10-6 If the market usually overreacts to bad news announcements, what would your return be like if you bought after you heard

the bad news?

10.4 • IMPLICATIONS FOR FINANCIAL MANAGERS LG10-6Financial managers must understand the crucial relationship between risk and return for several reasons. First, whilethe relationship between risk and return is demonstrated here using the capital markets, it equally applies to manybusiness decisions. A firm’s product mix, marketing campaign combination, and research and developmentprograms all entail risk and potential rewards. Being able to understand and characterize these decisions within arisk and return framework can help managers make better decisions. In addition, managers must understand whatreturn their stockholders require at various times of firm operations. After all, a firm must receive enough revenuefrom its variously risky activities to pay its business and debt costs and reward the owners (the stockholders).Managers must thus include the return to shareholders when they analyze new business opportunities.

Firms and capital markets also interact directly. For example, a good understanding of market efficiency helpsmanagers understand how their stock prices will react to different types of decisions (like dividend changes) and

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news announcements (like unexpectedly high or low profitability). In fact, many managers own company stock andare thus compensated through programs that rely on the stock price, like restricted stock and executive stock options.Companies also periodically issue (sell) additional shares of stock to raise more capital, and these sales depend uponmarket efficiency assumptions. The firm would not want to sell additional shares if the stock price is too low (i.e.,undervalued). They would want to sell more shares at any time that they thought their shares are overvalued. Othertimes, firms repurchase (buy back) shares of stock. The firm might want to do this if its shares were undervalued,but not if its shares were overvalued. Of course, valuation is not an issue if security markets are efficient.

restricted stock A special type of stock that is not transferable from the current holder to others until specific conditions are satisfied.

executive stock options Special rights given to corporate executives to buy a specific number of shares of the company stock at afixed price during a specific period of time.

Using the Constant-Growth Model for Required Return LG10-7For decades, financial managers have used the CAPM to compute shareholders’ required return. Given recentconcerns about beta’s limitations, many see the CAPM as a less useful model for calculating appropriate returns.Some have turned instead to another model useful for computing required return—the constant-growth modeldiscussed in Chapter 8. We can arrange the terms of that model as

(10-6)

finance at work //: marketsBubble TroubleMany professionals criticize the EMH because the overall market sometimes seems too high or too low. A very dramatic example of themarket level being artificially high is the market bubble. During a market bubble, the market quickly inflates on rampant speculation andsubsequently crashes. Investors who buy near the peak of the bubble risk losing nearly all their investment.

One of the United States’ earliest stock market bubbles was the bubble and crash of 1929. Note from the figure that the DJIA startedin 1927 at around 160. By October 1929, the DJIA had reached nearly 400 and then crashed. By mid-1932, the DJIA had fallen to the40s. The sustained fall coincided with an economic depression. Panel A of the figure also shows a price bubble in gold. The price of goldwas $230 per ounce in January 1979. The late 1970s and early 1980s saw double-digit inflation throughout the economy, and manyinvestors felt that gold represented a safe and inflation-proof investment. Just one year later, the price had skyrocketed to $870. It thenfell below $300 in less than two and a half years. Could gold be in another bubble? In late 2008, gold’s price was $750; it shot to $1,500in late 2011.

See the spectacular tech bubble during the 1990s? The NASDAQ 100, which started in 1985 at 250, soared to a peak of 4,816.35 onMarch 24, 2000. It then fell to less than 1,000 in two and a half years. The rise and fall of the NASDAQ 100 seems much morepronounced than the Japanese stock bubble of the 1980s. From a January 2, 1985, start at 11,543, the Nikkei 225 soared to a closinghigh of 38,916 on December 29, 1989. The bubble then burst and the Japanese stock market plummeted. The Nikkei has yet to fullyrecover, trading today at around the 16,500 level.

EMH critics do not believe that the entire stock market, or a substantial segment of it, can be correctly valued before, during, or aftera bubble. It certainly appears to be overvalued during the time the bubble is inflating.

Want to know more?Key Words to Search for Updates: stock bubble, irrational exuberance

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Of course, this model assumes that the stock is efficiently priced. This model holds an advantage in that it usescurrent firm data (dividend, D1, and price, P0) and a simple forward estimate (growth, g) to assess what investorscurrently expect the stock to return, i. For example, Table 10.2 shows McDonald’s beta as 0.56. Using this beta,Table 10.3 shows that shareholders require only 8.92 percent return to hold McDonald’s stock, given itslow risk profile. You may find it hard to believe that McDonald’s owners (the shareholders) expect such alow return from one of the world’s most profitable firms. So perhaps this is a case in which the CAPM result isn’tvery useful. Applying the constant-growth model looks something like this: McDonald’s is expected to pay a $3.56dividend this year and the stock price currently stands at $117 per share. Financial analysts believe McDonald’s willgrow at 9.50 percent per year for the next five years. The constant growth rate model suggests that McDonald’sshareholders expect a 12.54 percent return [= ($3.56 ÷ $117) + 0.095]. So, which required return seems more likely,the 8.92 percent computed from CAPM or the 12.54 percent suggested by the constant-growth model? It is likelythat McDonald’s investors are expecting closer to the 13 percent return than the 9 percent estimate.

Financial managers need an estimate of their shareholders’ required return in order to make appropriate decisionsabout their companies’ future growth. Good financial managers will compute shareholders’ required return using asmany methods as they can to determine the most realistic value possible.

EXAMPLE 10-4 Required Return LG10-7

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Consider that the required returns for 3M, Home Depot, and Hewlett-Packard are 12.56 percent, 12.07 percent, and 15.78 percent,respectively. These expectations may seem quite far apart, consideringthat all three firms are in the DJIA and are leaders in their marketsectors. Use the following information to compute the constant-growthmodel estimate of the required return:

ExpectedDividend

CurrentPrice

Analyst GrowthEstimate

3MCompany

$2.54 $105.70 10.4%

HomeDepot

1.56  70.10 14.5 

Hewlett- 0.53  22.00 0.25 

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Hewlett-Packard

0.53  22.00 0.25 

SOLUTION:

You can now use equation 10-6 to find each company’s required returnas

The 3M estimates using CAPM and the constant-growth rate model aresimilar. The constant-growth rate model estimate is more than 4percent higher than the CAPM estimate for Home Depot, but far lowerfor Hewlett-Packard.

Similar to Problems 10-15, 10-16, 10-29, 10-30, Self-Test Problem 3

time out!10-7 Why is the shareholders’ required return important to corporate managers?

Get Online

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Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. Consider an asset that provides the same return no matter what economic state occurs. What would be thestandard deviation (or risk) of this asset? Explain. (LG10-1)

2. Why is expected return considered “forward-looking”? What are the challenges for practitioners to utilizeexpected return? (LG10-1)

3. In 2000, the S&P 500 Index earned −9.1 percent while the T-bill yield was 5.9 percent. Does this mean themarket risk premium was negative? Explain. (LG10-2)

4. How might the magnitude of the market risk premium impact people’s desire to buy stocks? (LG10-2)

5. Describe how adding a risk-free security to modern portfolio theory allows investors to do better than theefficient frontier. (LG10-3)

6. Show on a graph like Figure 10.2 where a stock with a beta of 1.3 would be located on the security market line.Then show where that stock would be located if it is undervalued. (LG10-3)

7. Consider that you have three stocks in your portfolio and wish to add a fourth. You want to know if the fourthstock will make the portfolio riskier or less risky. Compare and contrast how this would be assessed usingstandard deviation versus market risk (beta) as the measure of risk. (LG10-3)

8. Describe how different allocations between the risk-free security and the market portfolio can achieveany level of market risk desired. Give examples of a portfolio from a person who is very risk averseand a portfolio for someone who is not so averse to taking risk. (LG10-3)

9. Cisco Systems has a beta of 1.25. Does this mean that you should expect Cisco to earn a return 25 percent

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higher than the S&P 500 Index return? Explain. (LG10-4)

10. Note from Table 10.2 that some technology-oriented firms (Apple) in the Dow Jones Industrial Average havehigh market risk while others (Intel and Verizon) have low market risk. How do you explain this? (LG10-4)

11. Find a beta estimate from three different sources for General Electric (GE). Compare these three values. Whymight they be different? (LG10-4)

12. If you were to compute beta yourself, what choices would you make regarding the market portfolio, the holdingperiod for the returns (daily, weekly, etc.), and the number of returns? Justify your choices. (LG10-4)

13. Explain how the concept of a positive risk–return relationship breaks down if you can systematically findstocks that are overvalued and undervalued. (LG10-5)

14. Determine what level of market efficiency each event is consistent with the following: (LG10-5)

a. Immediately after an earnings announcement the stock price jumps and then stays at the new level.b. The CEO buys 50,000 shares of his company and the stock price does not change.c. The stock price immediately jumps when a stock split is announced, but then retraces half of the gain over the

next day.d. An investor analyzes company quarterly and annual balance sheets and income statements looking for

undervalued stocks. The investor earns about the same return as the S&P 500 Index.

15. Why do most investment scams conducted over the Internet and e-mail involve penny stocks instead of S&P500 Index stocks? (LG10-5)

16. Describe a stock market bubble. Can a bubble occur in a single stock? (LG10-5)

17. If stock prices are not strong-form efficient, what might be the price reaction to a firm announcing a stockbuyback? Explain. (LG10-6)

18. Compare and contrast the assumptions that need to be made to compute a required return using CAPM and theconstant-growth model. (LG10-7)

19. How should you handle a case where required return computations from CAPM and the constant-growth modelare very different? (LG10-7)

ProblemsBASIC PROBLEMS

10-1 Expected Return Compute the expected return given these three economic states, their likelihoods, andthe potential returns: (LG10-1)

Economic State Probability Return

Fast growth 0.3 40%

Slow growth 0.4 10 

Recession 0.3 −25 

10-2 Expected Return Compute the expected return given these three economic states, their likelihoods,and the potential returns: (LG10-1)

Economic State Probability Return

Fast growth 0.2 35%

Slow growth 0.6 10 

Recession 0.2 −30 

10-3 Required Return If the risk-free rate is 3 percent and the risk premium is 5 percent, what is the required

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return? (LG10-2)10-4 Required Return If the risk-free rate is 4 percent and the risk premium is 6 percent, what is the required

return? (LG10-2)10-5 Risk Premium The average annual return on the S&P 500 Index from 1986 to 1995 was 15.8 percent. The

average annual T-bill yield during the same period was 5.6 percent. What was the market risk premiumduring these 10 years? (LG10-2)

10-6 Risk Premium The average annual return on the S&P 500 Index from 1996 to 2005 was 10.8 percent. Theaverage annual T-bill yield during the same period was 3.6 percent. What was the market risk premiumduring these 10 years? (LG10-2)

10-7 CAPM Required Return Hastings Entertainment has a beta of 0.65. If the market return is expected to be11 percent and the risk-free rate is 4 percent, what is Hastings’ required return? (LG10-3)

10-8 CAPM Required Return Nanometrics, Inc., has a beta of 3.15. If the market return is expected to be 10percent and the risk-free rate is 3.5 percent, what is Nanometrics’ required return? (LG10-3)

10-9 Company Risk Premium Netflix, Inc., has a beta of 3.61. If the market return is expected to be 13 percentand the risk-free rate is 3 percent, what is Netflix’s risk premium? (LG10-3)

10-10 Company Risk Premium Paycheck, Inc., has a beta of 0.94. If the market return is expected to be 11percent and the risk-free rate is 3 percent, what is Paycheck’s risk premium? (LG10-3)

10-11 Portfolio Beta You have a portfolio with a beta of 1.35. What will be the new portfolio beta if youkeep 85 percent of your money in the old portfolio and 5 percent in a stock with a beta of 0.78?(LG10-3)

10-12 Portfolio Beta You have a portfolio with a beta of 1.1. What will be the new portfolio beta if youkeep 85 percent of your money in the old portfolio and 15 percent in a stock with a beta of 0.5?(LG10-3)

10-13 Stock Market Bubble The NASDAQ stock market bubble peaked at 4,816 in 2000. Two and a halfyears later it had fallen to 1,000. What was the percentage decline? (LG10-5)

10-14 Stock Market Bubble The Japanese stock market bubble peaked at 38,916 in 1989. Two and a halfyears later it had fallen to 15,900. What was the percentage decline? (LG10-5)

10-15 Required Return Paccar’s current stock price is $48.20 and it is likely to pay a $0.80 dividend nextyear. Since analysts estimate Paccar will have an 8.8 percent growth rate, what is its required return?(LG10-7)

10-16 Required Return Universal Forest’s current stock price is $57.50 and it is likely to pay a $0.26dividend next year. Since analysts estimate Universal Forest will have a 9.5 percent growth rate, whatis its required return? (LG10-7)

INTERMEDIATE PROBLEMS

10-17 Expected Return Risk For the same economic state probability distribution in problem 10-1,determine the standard deviation of the expected return. (LG10-1)

Economic State Probability Return

Fast growth 0.3 40%

Slow growth 0.4 10 

Recession 0.3 −25 

10-18 Expected Return Risk For the same economic state probability distribution in problem 10-2,determine the standard deviation of the expected return. (LG10-1)

Economic State Probability Return

Fast growth 0.2 35%

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Slow growth 0.6 10 

Recession 0.2 −30 

10-19 Undervalued/Overvalued Stock A manager believes his firm will earn a 14 percent return next year.His firm has a beta of 1.5, the expected return on the market is 12 percent, and the risk-free rate is 4percent. Compute the return the firm should earn given its level of risk and determine whether themanager is saying the firm is undervalued or overvalued. (LG10-3)

10-20 Undervalued/Overvalued Stock A manager believes his firm will earn a 14 percent return next year.His firm has a beta of 1.2, the expected return on the market is 11 percent, and the risk-free rate is 5percent. Compute the return the firm should earn given its level of risk and determine whether themanager is saying the firm is undervalued or overvalued. (LG10-3)

10-21 Portfolio Beta You own $10,000 of Olympic Steel stock that has a beta of 2.2. You also own $7,000of Rent-a-Center (beta = 1.5) and $8,000 of Lincoln Educational (beta = 0.5). What is the beta of yourportfolio? (LG10-3)

10-22 Portfolio Beta You own $7,000 of Human Genome stock that has a beta of 3.5. You also own $8,000of Frozen Food Express (beta = 1.6) and $10,000 of Molecular Devices (beta = 0.4). What is the betaof your portfolio? (LG10-3)

ADVANCED PROBLEMS

10-23 Expected Return and Risk Compute the expected return and standard deviation given these foureconomic states, their likelihoods, and the potential returns: (LG10-1)

Economic State Probability Return

Fast growth 0.30 60%

Slow growth 0.50 13 

Recession 0.15 −15 

Depression 0.05 −45 

10-24 Expected Return and Risk Compute the expected return and standard deviation given these foureconomic states, their likelihoods, and the potential returns: (LG10-1)

Economic State Probability Return

Fast growth 0.25 50%

Slow growth 0.55 11 

Recession 0.15 −15 

Depression 0.05 −50 

10-25 Risk Premiums You own $10,000 of Denny’s Corp. stock that has a beta of 2.9. You also own$15,000 of Qwest Communications (beta = 1.5) and $5,000 of Southwest Airlines (beta = 0.7).Assume that the market return will be 11.5 percent and the risk-free rate is 4.5 percent. What is themarket risk premium? What is the risk premium of each stock? What is the risk premium of theportfolio? (LG10-3)

10-26 Risk Premiums You own $15,000 of Opsware, Inc., stock that has a beta of 3.8. You also own$10,000 of Lowe’s Companies (beta = 1.6) and $10,000 of New York Times (beta = 0.8). Assume thatthe market return will be 12 percent and the risk-free rate is 6 percent. What is the market riskpremium? What is the risk premium of each stock? What is the risk premium of the portfolio? (LG10-3)

10-27 Portfolio Beta and Required Return You hold the positions in the following table. What is the betaof your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, whatis the required return of the portfolio? (LG10-3)

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Price Shares Beta

Amazon.com $40.80 100 3.8

Family Dollar Stores 30.10 150 1.2

McKesson Corp. 57.40 75 0.4

Schering-Plough Corp. 23.80 200 0.5

10-28 Portfolio Beta and Required Return You hold the positions in the following table. What is the betaof your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, whatis the required return of the portfolio? (LG10-3)

Price Shares Beta

Advanced Micro Devices $ 14.70 300 4.2

FedEx Corp. 120.00 50 1.1

Microsoft 28.90 100 0.7

Sara Lee Corp. 17.25 150 0.5

10-29 Required Return Using the information in the table, compute the required return for each companyusing both CAPM and the constant-growth model. Compare and discuss the results. Assume that themarket portfolio will earn 12 percent and the risk-free rate is 3.5 percent. (LG10-3, LG10-7)

Price Upcoming Dividend Growth Beta

US Bancorp $36.55 $1.60 10.0% 1.8

Praxair  64.75  1.12 11.0  2.4

Eastman Kodak  24.95  1.00 4.5  0.5

10-30 Required Return Using the information in the table, compute the required return for each companyusing both CAPM and the constant-growth model. Compare and discuss the results. Assume that themarket portfolio will earn 11 percent and the risk-free rate is 4 percent. (LG10-3, LG10-7)

Price Upcoming Dividend Growth Beta

Estee Lauder $47.40 $0.60 11.7% 0.75

Kimco Realty  52.10  1.54 8.0  1.3 

Nordstrom  5.25  0.50 14.6  2.2 

10-31 Spreadsheet Problem As discussed in the text, beta estimates for one firm will vary depending onvarious factors such as the time over which the estimation is conducted, the market portfolio proxy,and the return intervals. You will demonstrate this variation using returns for Microsoft.

a. Using all 45 monthly returns for Microsoft and the two stock market indexes, compute Microsoft’sbeta using the S&P 500 Index as the market proxy. Then compute the beta using the NASDAQindex as the market portfolio proxy. Compare the two beta estimates.

b. Now estimate the beta using only the most recent 30 monthly returns and the S&P 500 Index.Compare the beta estimate to the estimate in part (a) when using the S&P 500 Index and all 45monthly returns.

c. Estimate Microsoft’s beta using the following quarterly returns. Compare the estimate to the onesfrom parts (a) and (b).

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10-32 Spreadsheet Problem Build a spreadsheet that automatically computes the expected market returnand risk for different assumptions about the state of the economy.

a. First, create a spreadsheet like the one shown below and compute the expected return and standarddeviation.

b. Compute the expected return and risk for the following two scenarios:

NotesCHAPTER 10

1. A mathematically equivalent equation for beta is , where cov() is the covariance between the stock andmarket portfolio returns, and var() is the variance of the market portfolio.

I

chapter elevenCalculating the cost of capital

©Photodisc/Getty Images

n the previous two chapters, we discussed investors’ required return given a particular risk profile. Inthis chapter, we examine the question from the firm’s point of view: How much must the firm pay tofinance its operations and expansions using debt and equity sources? Firms use a combination of debt

and equity sources to fund their operations, projects, and any expansions they may undertake. In Chapter14, we’ll explore the factors that managers consider as they choose the optimal capital structure mix. Fornow, we’ll assume that management has chosen the optimal mix for us, and that it’s our job to implementit.

LG11-1

As we’ve seen in previous chapters, investors face different kinds of risks associated with debt,preferred stock, and equity. As a result, their required rates of return for each debt or equity source differas well. So, as the firm uses a combination of different financing sources, we must calculate the investors’average required rate of return to use as the cost of capital for evaluating decisions about investing thefirm’s capital. Since firms seldom use equal amounts of debt and equity capital sources, we will need tocalculate this as a weighted average, with weights based on the proportion of debt and equity capitalused.

As we’ll see, we can measure such a weighted-average cost of capital (WACC) in a variety of situations and

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for a number of purposes. For example, if we’re interested in determining the average rate of return thatthe firm must earn from existing operations when we don’t expect the firm’s capital structure to change,we can calculate the WACC using the firm’s current capital structure and existing component costs; however,if we’re trying to determine the average rate of return that we would need to earn from a new project inorder for it to add value to the firm, we would want to use the project’s proposed capital structure and itscomponent costs.

weighted-average cost of capital (WACC) The weighted-average after-tax cost of the capital used by a firm, with weights set equal tothe relative percentage of each type of capital used.

component costs The individual costs of each type of capital—bonds, preferred stock, and common stock.

LEARNING GOALS

LG11-1 Understand the relationship of cost of capital to the investor’s required return.LG11-2 Use the weighted-average cost of capital (WACC) formula to calculate a project’s cost of capital.LG11-3 Explain how the firm chooses among estimating costs of equity, preferred stock, and debt.LG11-4 Calculate the weights used for WACC projections.LG11-5 Identify which elements of WACC are used to calculate a project-specific WACC.LG11-6 Evaluate trade-offs between a firmwide WACC and a divisional cost of capital approach.LG11-7 Distinguish subjective and objective approaches to divisional cost of capital.LG11-8 Demonstrate how to adjust the WACC to reflect flotation costs.

viewpointsbusiness APPLICATIONMP3 Devices, Inc., is about to launch a new project to create and market a combination MP3 player-video projector. MP3 Devicescurrently uses a particular mixture of debt, common stock, and preferred shares in its capital structure, but the firm is thinking of usingthe launch of the new project as an opportunity to change that capital structure.

The new project will be funded with 40 percent debt, 10 percent preferred stock, and 50 percent common stock. MP3 Devicescurrently has 10 million shares of common stock outstanding, selling at $18.75 per share, and expects to pay an annual dividend of$1.35 one year from now, after which future dividends are expected to grow at a constant 6 percent rate. MP3’s debt consists of 20-year, 10 percent annual coupon bonds with a face value of $150 million and a market value of $165 million, and the company’s capitalmix also includes 100,000 shares of 10 percent preferred stock selling at par.

If MP3 Devices faces a marginal tax rate of 34 percent, what weighted average cost of capital should it use as it evaluates thisproject? (See the solution at the end of the book.)

One important point about the component costs to be used in the firm’s computation of the averagerequired rate of return is that dividends paid to either common or preferred stockholders are not taxdeductible, but interest paid to debt holders is. Therefore, paying a certain rate of return to stockholderscosts the firm that same rate, but paying the same interest rate to debt holders actually costs the firm lessthan the rate paid. The reason is that, since interest on debt is tax deductible, paying rate iD to debtholders is, for all intents and purposes, subsidized by the government: If the firm hadn’t paid out thatinterest rate to the debt holders, it would have had to have paid out taxes to the government on themoney it used to pay the interest. So, effectively, the firm’s effective after-tax interest cost will be equal tothe interest rate paid on debt multiplied by one minus the firm’s relevant tax rate.

For example, if a firm pays a 10 percent coupon on $1 million in debt while it is subject to a 35 percenttax rate, then each coupon payment will be equal to 0.10 × $1,000,000 = $100,000, but that $100,000 ininterest, being tax deductible, will reduce the firm’s tax bill by 0.35 × $100,000 = $35,000. So paying$100,000 in interest saves the firm $35,000 in taxes, making the effective after-tax cost of debt equal to$100,000 − $35,000 = $65,000 and the effective after-tax interest rate equal to 10% × (1 − 0.35) = 6.5%.

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11.1 • THE WACC FORMULA LG11-2The average cost per dollar of capital raised is called the weighted-average cost of capital (WACC). We calculateWACC using equation 11-1:

(11-1)

personal APPLICATIONMackenzie is currently finishing up her bachelor’s degree and is considering going back to grad school for a master’s degree. Shecurrently has $17,125 in student loans carrying an 8 percent interest rate from her bachelor’s degree and estimates that she will needto take out an additional $29,000 in student loans (at the same interest rate) to make it through the master’s program she’d like toattend. The IRS allows taxpayers with student loans to deduct the interest on those loans, but only up to a maximum amount of$2,500 per year. Assuming that Mackenzie will face a marginal personal tax rate of 25 percent when she graduates, what will be theaverage after-tax interest rate that she will be paying on the student loans immediately after she graduates with her master’s? (Seethe solution at the end of the book.)

How else can Mackenzie finance her graduate degree? What will happen to her after-tax interest rate?

where

Notice that we use weights based on market values rather than book values because market values reflect investors’assessment of what they would be willing to pay for the various types of securities, while book values would reflectwhat was paid for such securities at varying times in the past. Since we’re interested in coming up with the cost ofcapital for new investments in the firm or its projects, using market values here makes more sense.

Calculating the Component Cost of Equity LG11-3

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We could calculate iE using the capital asset pricing model, as discussed in Chapter 10:

(11-2)

Or, we can assume that the equity in question is a constant-growth stock such as the ones we modeled in Chapter 8.Under this assumption, we can solve the constant-growth model for iE:

(11-3)

Which way is better? Well, theoretically, both should give us the same answer, but depending on the situation, somepragmatic reasons may dictate your choice.

1. In situations where you do not have sufficient historic observations to estimate β (i.e., when the stock is fairly new), or when yoususpect that the past level of the stock’s systematic (or market) risk might not be a good indicator of the future risk, youdo not want to use the CAPM. Using calculated historic systematic risk when it is not a good estimate of βE, estimatedfuture systematic risk, will not work too well.

2. In situations where you can expect constant dividend growth, the constant-growth model is appropriate. But although you can try toadjust the model for stocks without constant dividend growth, doing so may introduce potentially sizable errors, so it is not the bestchoice for stocks that increase their dividends irregularly.

EXAMPLE 11-1 Cost of Equity LG11-2

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

ADK Industries’ common shares sell for $32.75 per share. ADKexpects to set its next annual dividend at $1.54 per share. If ADKexpects future dividends to grow by 6 percent per year, indefinitely, thecurrent risk-free rate is 3 percent, the expected return on the market is9 percent, and the stock has a beta of 1.3, what should be firm’s cost ofequity?

SOLUTION:

The cost of equity using the CAPM will be

The cost of equity using the constant-growth model will be

Similar to Problems 11-1, 11-2

Overall, we should expect that the CAPM approach to estimating iE will apply more accurately in most cases.However, if you do encounter a situation in which the constant-growth model applies, then you can certainly use it.

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If we are really fortunate and happen to have enough information to use both approaches, then we should probablyuse both, taking an average of the resulting estimates of iE.

1

Calculating the Component Cost of Preferred StockAs we discussed in Chapter 8, preferred stock represents a special case of the constant-growth model, wherein gequals zero. So we can estimate preferred stocks’ component cost using a simplified version of equation 11-3:

(11-4)

Calculating the Component Cost of DebtBecause of the tax deductibility of debt for the firm, computing the component cost of debt actually has two parts.We must estimate the before-tax cost of debt, iD, and then adjust this figure to convert it to the after-tax rate ofreturn, iD × (1 − TC).

To estimate iD, we need to solve for the yield to maturity (YTM) on the firm’s existing debt

(11-5)

EXAMPLE 11-2 Cost of Preferred Stock LG11-3

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Suppose that ADK also has one million shares of 7 percent preferredstock outstanding, trading at $72 per share. What is ADK’s componentcost for preferred equity?

SOLUTION:

The cost of the preferred stock will equal

Similar to Problems 11-7, 11-8

Solve for the interest rate that makes the price equal to the sum of the present values of the coupons and the facevalue of the bond, as discussed in Chapter 7.

Intuitively, by using the price on the firm’s existing debt in equation 11-5, we are calculating the rate of returnexpected by investors currently buying the firm’s existing bonds. As discussed later when we cover how to calculateproject-specific WACCs, the fact that all of the firms’ bonds get their interest paid out of all the firm’s cash flowsbefore any of the firm’s shareholders get anything implies that this expected rate of return on existing firm debtshould also be a good proxy for the rate of return that potential investors would demand on any new debt issued bythe firm, as well.

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Finally, if we think of the YTM as the rate that bond investors expect to get for investing in the bond, then we needto adjust it for the tax deductibility of debt interest to convert this to a measure of how much it actually costs thefirm to pay that YTM. We do so by multiplying the YTM by (1 − TC).

Choosing Tax RatesThe interest paid on debt is tax deductible, but the benefit to each dollar of interest will vary based on the marginaltax rate that the firm would have had to have paid on that dollar if it was not paid out as interest. Therefore, theappropriate, overall average marginal tax rate to be used in the WACC will be the weighted average of the marginaltax rates that would have been paid on the taxable income shielded by the interest deduction, where the weights willbe equal to the proportion of the taxable income that would have been taxed at each marginal rate.

the Math Coach on…Preferred Stock Dividends

“The assumed par value of preferred stock is $100. So, a 7 percent preferredstock pays $7 a year in dividends.„

For example, if a firm had earnings before interest and taxes (EBIT) of $400,000, taxable interest deductions of$100,000, and faced the corporate tax schedule shown in Table 11.1, then the $100,000 in taxable interestdeductions would reduce the firm’s taxable income from $400,000 to $400,000 − $100,000 = $300,000,meaning that the taxes saved by the interest deduction would have been from dollars that would have been taxed inthe fourth (i.e., $100,001 to $335,000) and fifth ($335,001 to $10,000,000) rows (or “brackets”) in Table 11.1. Sothe appropriate tax rate to use in the WACC would be a weighted average of the marginal tax rates from the fourth(i.e., 39%) and fifth (34%) tax brackets, where the weights would be determined by how much of the $100,000 intaxable interest deductions would have been taxed at 39 percent and how much would have been taxed at 34 percentif the $100,000 had not been paid out as interest:

▼ TABLE 11.1 Corporate Tax Rates

Taxable Income Tax Rate

$    0 − $  50,000 15%50,001 − 75,000 25 75,001 − 100,000 34 

100,001 − 335,000 39 335,001 − 10,000,000 34 

10,000,001 − 15,000,000 35 15,000,001 − 18,333,333 38 18,333,334 + 35 

EXAMPLE 11-3 Cost of Debt LG11-3

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For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

ADK has 30,000 20-year, 8 percent annual coupon bonds outstanding.If the bonds currently sell for 97.5 percent of par and the firm pays anaverage tax rate of 35.92 percent, what will be the before-tax and after-tax component cost for debt?

SOLUTION:

The before-tax cost of debt will be the solution to

which will equal 8.26 percent. Multiplying this by one minus the tax ratewill yield the after-tax cost of debt: 0.0826 × (1 − 0.3592) = 0.0529, or5.29%.

Similar to Problems 11-3, 11-4

EXAMPLE 11-4 Tax Rate LG11-3

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to Connect or go tomhhe.com/CornettM4e.

Suppose that ADK expects EBIT to be approximately $20 million peryear for the foreseeable future. Given the 30,000 20-year, 8 percentannual coupon bonds discussed in the previous example, what wouldthe appropriate tax rate be for use in the calculation of the debtcomponent of ADK’s WACC?

SOLUTION:

The interest payments on the bonds would total 30,000 × $1,000 × 0.08= $2,400,000 per year, resulting in earnings before tax (EBT) of$20,000,000 − $2,400,000 = $17,600,000.

As taxable income falls from $20,000,000 to $17,600,000 after the firmpays the interest on the bonds, $1,666,667, or 69.44 percent, of the$2,400,000 reduction would fall in the highest 35 percent bracket, whilethe remaining $733,333, or 30.56 percent ($733,333/$2,400,000),would occur in the 38 percent tax bracket, making the weightedaverage applicable tax rate equal to

Similar to Problems 11-5, 11-6

Calculating the Weights LG11-4

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Calculating the weights to be used in the WACC formula is mathematically very simple: We just calculate thepercentages of the funding that come from equity, preferred stock, and debt, respectively.

Sounds easy, right? Well, the tricky part to this lies in determining what we mean by “the funding”: If we arecalculating WACC for a firm, then “the funding” encompasses all the capital in the firm, and E, P, and Dwill be determined by computing the total market value of the firm’s common stock, preferred stock, anddebt, respectively. However, if we are computing WACC for a project, then “the funding” will only include thefinancing for that project, and E, P, and D will be equal to the amount of each used in the financing of that project.2

EXAMPLE 11-5

Capital Structure Weights andWACC LG11-4

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For interactive versions of this example, log in to Connect or go tomhhe.com/CornettM4e.

Let us continue the previous examples. Suppose that ADK has issued3 million shares of common stock, 1 million shares of preferred stock,and the previously mentioned 30,000 bonds outstanding. What willADK’s WACC be, considering ADK as a firm?

SOLUTION:

Using the securities’ prices given in previous examples, ADK’s equity,preferred stock, and debt will have the following total market values:

Equity: 3m × $32.75 = $98.25m

Preferred stock: 1m × $72 = $72m

Debt: 30,000 × $975 = $29.25m

The total combined market value for all three capital sources is $199.5million. The applicable weights for each capital source will therefore be

Tying this all together with the answers from the previous examples,ADK will have a WACC of

Similar to Problems 11-9 to 11-14, 11-21, 11-22, Self-Test Problem 1

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If you think about this for a second, you will realize that this means that projects can wind up having differentWACCs than their firm. That is not just OK, it is also exactly right because, as we will see in a later chapter, the firmis like a diversified portfolio of different projects, all with different risks and returns. And one of the things that cancontribute to the risk of a project is the choice of how much common stock, preferred stock, and debt is used tofinance it.

time out!11-1 Explain why we multiply the component cost of debt by the marginal tax rate, TD, but don’t do so for the component costs

of equity or preferred stock.11-2 How would we compute iD if a company had multiple bond issues outstanding?

11.2 • FIRM WACC VERSUS PROJECT WACC LG11-5So far, we have been defining the WACC as a weighted-average cost across the firm’s different financing sources. Ifwe think of the firm as a portfolio of different projects and products, we see that the WACC will be a weighted-average cost of capital across the items in that portfolio, too. This way it represents the cost of capital for the“typical” project that the firm is currently undertaking. However, firms grow by taking on new projects. So now thequestion is: Can managers use our firm-wide WACC, calculated previously, to evaluate the firm’s newly proposedprojects?

The answer is: It depends. If a new project is similar enough to existing projects, then yes, managers can use thefirm’s WACC as the new project’s cost of capital. But say that your firm is contemplating undertaking asignificantly different project—one far different from any project that the firm is already engaged in. What then?Then we cannot expect the firm’s overall WACC to appropriately measure the new project’s cost of capital.

Let your intuition work on this for a second: If the new project is riskier than the firm’s existing projects, then itshould be “charged” a higher cost of capital; if it’s safer, then the firm should assign the new project a lower cost ofcapital. That seems only fair, right?

Consider a U.S. firm—let’s call it GassUp—that currently owns a chain of gas stations. Firm management isconsidering a new project: opening up a series of gourmet coffee shops inside their existing gas stations. Given thedemand for upscale coffee in the United States, as well as the historically volatile oil markets, it’s probably difficultto say exactly whether the coffee shops will be more or less risky than gas stations. We can probably say, though,that the two enterprises will face different risks. For example, one could argue that at least a certain amount of gas isa necessity, while gourmet coffee is more of a luxury good, so it makes sense that the two “parts” of the new,expanded product line for GassUp will perform differently in boom or bust periods. Likewise, what if the coffeeshops are located within the busiest and most stable gas stations—say the ones that lie along freeways? Then thefirm faces remodeling existing buildings, rather than starting from scratch, and can pick and choose to put gourmetcoffee facilities in the gas stations that have the volume to support them, which likely means that the risks of addingthe facilities for gourmet coffee to those stations will be lower than building new facilities from scratch.

So, this means that GassUp probably should not use the same WACC for the new line of gourmet coffee expansionsto its gas stations as it does for the gas stations themselves; that is, the WACC for the new expansion projects shouldnot be equal to the WACC of the firm as it currently exists.

©Ingram Publishing/Superstock

Even if GassUp’s coffee venture fails, the firm’s creditors would likely still collect payments from gas station operations.©Tetra Images/Alamy

However, does this mean that all the components of WACC for each new gourmet coffee expansion should bedifferent for every store? Well, not exactly. As we’ll discuss, some inputs to WACC should be project-specific, butothers should be consistent with the firmwide values used in calculating a firmwide WACC.

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Project Cost Numbers to Take from the FirmIt is tempting to argue that all component inputs for a project-specific WACC should be based on the specific projectattributes, but if we created all project-specific numbers, what fundamental issue related to bonds and preferredstock would we be ignoring? That both bonds and preferred stocks create claims on the firm, not on any particulargroup of projects within that firm. Furthermore, debt claims are superior to those of common stockholders. So if thenew project does significantly increase the firm’s overall risk, the increased risk will be borne disproportionately bycommon stockholders. Debt holders and preferred stockholders will likely face minimal impact on the risk andreturn that their investments give them, no matter what new project the firm undertakes—even if those claimantsown bonds or preferred shares that the firm issued to fund the new project.

For example, suppose GassUp decides to build entirely separate facilities for its coffee shops, which it will name“Bottoms Up.” Furthermore, suppose GassUp partially finances its expansion into coffee shops with debt, and thatthe project turns out to be more like “Bottoms Down”—far less successful than the firm had hoped. Though thiswould be an unfortunate turn of events for GassUp’s common shareholders, the firm’s creditors and preferredshareholders would likely still collect their usual interest and dividend payments from GassUp’s gross revenuesfrom gas station operations.

Creditors understand that their repayment probably comes from continuing operations and take current cash flowsinto account when a firm comes seeking funds. For example, if a small firm approaches a bank for a loan to financean expansion, the bank will normally spend more time analyzing current cash flows to determine theprobability that they will recoup their loan than it will analyzing the potential new cash flows from theproposed expansion.

Note that this situation holds true only as long as the new projects represent fairly small investments compared toongoing operations. As new projects become large relative to ongoing cash-flow producing activities, creditors willhave to examine the likelihood of being repaid from the new projects much more closely. New projects, howevergreat their potential, inherently carry more risk than do established current operations. Changes in the proportion ofnew projects relative to ongoing operations will thus translate into increased risk for the creditor, who will ask for ahigher rate of return to offset the risk.

Since most firms tend to grow incrementally, we will assume (unless otherwise indicated) that we’re examiningsituations in which the number of new projects is small relative to ongoing operations. We can therefore also assumethat using the firm’s existing, pre-project component costs of debt and preferred stock to calculate WACC isappropriate.

Project Cost Numbers to Find Elsewhere: The Pure-Play ApproachSince we have decided not to adjust the firmwide costs of debt or preferred stock for the risk of a project, whereshould we account for the new project risk brought to the firm overall? As with several other questions associatedwith risk-and profit-sharing that we’ll discuss in Chapter 16, the answer lies with equity.

The firm’s risk changes when it takes on a project that is noticeably different from its existing lines of business.Debt holders and preferred stockholders will not bear much of this change in risk; rather, when it takes on a newproject, the firm instead creates risk for its common stockholders that is disproportionately large compared to theamount of stockholder capital used to finance the project.

In response to such a change in the firm’s risk profile, stockholders adjust their required rate of return to adjust forthe new risk level. Absent any alteration to the firm’s capital structure,3 changes in the firm’s risk profile are due todifferences in the firm’s business risks based on the mix of the new and existing product lines. The stock’s betareflects those differences in each product line.

Obviously, no proposed new project will have a history of previous returns. Without such data, neither analysts norinvestors can calculate a project-specific beta. So what data can we use? To the extent that we can find other firmsengaged in the proposed new line of business, we can use their betas as proxies to estimate the project’s risk. Ideally,the other firms would be engaged only in the proposed new line of business; such monothemed firms are usuallyreferred to as pure plays, with this term also in turn being applied to this approach to estimating a project’s beta.

An average of n such proxy betas will give us a fairly accurate estimate of what the new project’s beta will be.4

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where

(11-6)

business risk The risk of a project arising from the line of business it is in; the variability of a firm’s or division’s cash flows.

proxy beta The beta (a measure of the riskiness) of a firm in a similar line of business as a proposed new project.

This average will be an estimate, in the strictest statistical sense of the word. You might recall from your statisticsclasses that we will need to be careful to get as large a sample as possible if we want to get as much statistical powerfor our estimate as possible. Ideally, we would like to find at least three or four companies from which todraw proxy betas, called pure-play proxies, to ensure that we have a large enough sample size to safelymake meaningful inferences. In reality, however, two proxies (or even one) might represent a suitable sample if theirbusiness line resembles the proposed new project closely enough. In particular, we may want to use betas fromindustry front-runners, and rely less on betas of any firms that the company really doesn’t want to emulate.

EXAMPLE 11-6

Calculation of ProjectWACC LG11-5

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Suppose that Evita’s Subs, a local shipyard, is considering opening upa chain of sandwich shops. Evita’s capital structure currently consistsof 2 million outstanding shares of common stock, selling for $83 pershare, and a $50 million bond issue, selling at 103 percent of par.Evita’s stock has a beta of 0.72, the expected market risk premium is 7percent, and the current risk-free rate is 4.5 percent. The bonds pay a 9percent annual coupon and mature in 20 years. The current operationsof the firm produce EBIT of $100 million per year, and the newsandwich operations would add only an expected $12 million per yearto that. Also, suppose that Evita’s management has done someresearch on the sandwich shop industry, and discovered that suchfirms have an average beta of 1.23. If the new project will be fundedwith 50 percent debt and 50 percent equity, what should be the WACCfor this new project?

SOLUTION:

First, note that Evita’s currently doesn’t have any outstanding preferredstock and doesn’t plan on using any to finance the new project, so thatmakes our job a little simpler. Also note that, though we are givenenough information to calculate the firm’s current capital structureweights and component cost of equity, we won’t need those figures, asthis new project’s capital structure differs from the firm’s existingstructure. We already know the capital structure weights for the newproject (50 percent debt and 50 percent equity), so we just need tocalculate the appropriate component costs.

For equity, the appropriate cost will be based upon the average risk ofsandwich shops:

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Since the new sandwich project appears to be small relative to thefirm’s existing line of business, we will assume that the newbondholders will expect to be repaid out of cash flows to the existingshipyards, and the YTM on the new bonds issued to finance this projectwill be the same as the YTM on the existing bonds:

which gives us an iD of 8.68 percent.

Finally, the current EBIT already puts the firm in the top 35 percent taxbracket, so the additional EBIT generated by the project will also betaxed at this same marginal 35 percent tax rate. Therefore, the WACCof the new project will be

Similar to Problems 11-16 to 11-21, Self-Test Problem 2

What shall we do if we cannot find any pure-play proxies? Well, in that case, we may want to use firms that, whilenot solely in the same business as the proposed project’s venture, have a sizable proportion of revenuesfrom that line. We may then be able to “back out” the impact of their other lines of business from theirfirm’s beta to leave us with a good enough estimate of what the new project’s beta might be.

Be sure to use weights based on the project’s sources of capital, and not necessarily the firm’s capital structure. Ifthe new project is going to use more or less debt than the firm’s existing projects do, then the risk- and reward-sharing are going to vary across the different types of capital (as discussed in Chapter 16), and we will want torecognize this in our WACC computation.

Finally, we need to consider the appropriate corporate tax rate to use in calculating the WACC for a project. Thatmarginal corporate tax rate will be the average marginal tax rate to which the project’s cash flows will be subject.Assume a firm with $400,000 of EBIT from current operations is considering a new project that will increase EBITby $200,000. Since this $200,000 increase will keep the firm’s marginal tax in the fifth bracket of Table 11.1, theappropriate tax rate to compute the project’s WACC will simply be 34 percent.

To summarize, the component costs and weights to compute a project-specific WACC should be as shown inequation 11-7, with the source of each part indicated by the appropriate subscript:

(11-7)

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time out!11-3 For computing a project WACC, why do we take some component costs from the firm but compute others that are specific

for the project being considered?11-4 It is usually much easier to find proxy firms that are engaged in multiple lines of business than it is to find pure-play

proxies. Explain how such firms can be used to estimate the beta for a new project.

11.3 • DIVISIONAL WACC LG11-6Do firms calculate risk-appropriate WACC for every new project they consider? While this would be ideal,pragmatically it just is not always feasible. In large corporations, managers evaluate dozens or even hundreds ofproposed new projects each year. The costs in terms of time and effort of estimating project-specific WACCsindividually for each project are simply prohibitive. Instead, large firms often take a middle-of-the-road approachthat can achieve many of the results of using project-specific WACC calculations with much less time andresources. The key to this approach is to calculate divisional WACCs for each product line of the company based onthat line’s, but not each individual product’s, risk profile.

divisional WACC An estimated WACC computed using some sort of proxy for the average equity risk of the projects in a particulardivision.

Pros and Cons of a Divisional WACCAs with most choices in life as well as finance, there are pros and cons to using the divisional WACC approach.Let’s first consider the disadvantage of using a firm’s WACC to evaluate new, risk-heterogeneous projects. To makethings simple, let’s assume that we are looking at a firm that uses only equity finance, so that WACC is simply equalto iE, and let’s further assume that all the proposed new projects are in the same product line as each other and as thefirm’s existing projects, so that the divisional WACC would be equal to the firm’s existing WACC.

Take a look at Figure 11.1. Similar to our discussion of the security market line in Chapter 10, required rates ofreturn for projects with varying degrees of risk would lie along the sloped line shown in the figure. We could thenevaluate projects with various degrees of risk based on the relationship between their expected rate of return and therequired rate of return for that risk level. Turning to Figure 11.2, you can see that using risk-appropriate WACCs,projects A and B would be accepted, since their expected rates of return would be higher than their respectiverequired rates of return. Projects C and D would be rejected because our simple scheme shows that theseprojects are not expected to return enough to cover market-required returns, given the projects’ riskiness.

FIGURE 11.1 Risk-Appropriate WACCs

In an all-equity firm, WACC is theoretically equal to iE for each proposed project, which will increase as the risk (i.e., β ) of the projectincreases.

FIGURE 11.2 Sample Projects versus Risk-Sensitive WACC

Projects A and B have expected returns greater than their risk-appropriate WACCs. Projects C and D have expected returns less than theirrisk-appropriate WACCs.

However, using a firmwide WACC would result in a comparison of the project’s expected rates of return to a single,flat, firmwide cost of capital as Figure 11.3 shows. Using a simple firmwide WACC to evaluate new projects wouldgive an unfair advantage to projects that present more risk than the firm’s average beta. Using a firmwide WACCwould also work against projects that involved less risk than the firm’s average beta. Looking at the same sampleprojects as before, we see that Project A would now be rejected, while Project C would be accepted.

FIGURE 11.3 Sample Project versus Firmwide WACC

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If we were to mistakenly compare projects bearing different risks to this single firmwide WACC, we would conclude that projects A and Dhave expected rates of return less than the firmwide WACC and Projects B and C have expected returns greater than the firmwide WACC.

Using a firmwide WACC in this way, as an inappropriate benchmark for projects of differing risk from the firm’scurrent operations, will result in quite a few incorrect decisions. In fact, the use of a firmwide WACC to evaluateany projects with risk-return coordinates lying in the two shaded triangles shown in Figure 11.4 will result in anincorrect accept/reject decision.

FIGURE 11.4 Incorrect Decisions Caused by Inappropriate Use of Firmwide WACC

The gold-shaded triangle on the lower left contains projects such as Project A, which is incorrectly rejected by a firm. It has risk less than theaverage risk of the firm. Its expected rate of return is greater than its correctly calculated risk-appropriate WACC but less than aninappropriately calculated firmwide WACC. The pink-shaded triangle on the upper right contains projects such as Project C, which isincorrectly accepted by a firm. It has risk greater than the average risk of the firm. Its expected rate of return is less than a correctlycalculated risk-appropriate WACC but greater than an inappropriately calculated firmwide WACC.

Computing a few“risk aware” divisional WACCs instead of just one“risk insensitive” firmwide WACCcan greatly reduce the number of projects that get incorrectly accepted or rejected this way. To do so, wedivide the firm’s existing projects into divisions, where the different divisions proxy for systematically differentaverage project risk levels. Calculating WACCs for each division separately, as Figure 11.5 shows, greatly reducesthe problem of basing decisions on inaccurate results from using firmwide WACC for all projects.

FIGURE 11.5 Divisional WACCs

Instead of calculating a single firmwide WACC based on the average risk of all projects in the firm, assume that the firm calculates division-specific WACCs based on the average risk of the projects in each respective division.

Using divisional WACCs like this will not eliminate problems of incorrect acceptance and incorrect rejection, but itwill greatly reduce their frequency. Instead of making errors corresponding to the two large triangular areasindicated in Figure 11.4, we will instead have six smaller areas of error shown in Figure 11.6. Moreacceptance/rejection regions will result in fewer errors.

FIGURE 11.6 Divisional WACC Errors

Total incorrect acceptances/rejections turn out to be less when divisional WACCs are used.

For example, let’s consider our four sample projects from before. Suppose that, instead of assigning the proposednew projects to the same firmwide division we had previously assumed, the firm divides its operations into “low-risk,” “mid-risk,” and “high-risk” product lines and decides that, based on their associated products and risk profiles,Project A should be assigned to the “low-risk” division, Project D to the “mid-risk” division, and Projects B and Cto the “high-risk” division. If we were to now evaluate them using divisional WACCs as shown in Figure 11.7, wewould correctly accept both projects A and B and correctly reject projects C and D.

FIGURE 11.7 Example Decisions Using Divisional WACCs

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Projects A and B here are correctly accepted, while projects C and D are correctly rejected.

Subjective versus Objective Approaches LG11-7We can form divisional WACCs subjectively by simply considering the project’s risk relative to the firm’s existinglines of business and then, if the project is riskier (safer) than the firm average, adjust the firm WACC upward(downward) to account for our subjective opinion of project riskiness. The biggest disadvantage to this approach isthat the adjustments are pretty much picked out of thin air and created just for the project at hand. For example,consider the sample subjective divisional WACCs in Table 11.2. Both the project assignments to the divisions andthen the WACC adjustments for the very low risk, low risk, high risk, and very high risk are fairly arbitrary.

▼ TABLE 11.2 Subjective Divisional WACCs

Risk Level Discount Rate

Very low risk Firm WACC − 5%Low risk Firm WACC − 2%Same risk as firm Firm WACCHigh risk Firm WACC + 3%Very high risk Firm WACC + 7%

EXAMPLE 11-7

Divisional Costs of Capital LG11-7

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Assume that BF, Inc., an all-equity firm, has a firmwide WACC of 10percent, and that the firm is broken into three divisions: Textiles,Accessories, and Miscellaneous. The average Textiles project has abeta of 0.7; the average Accessories project has a beta of 1.3; and theaverage Miscellaneous project has a beta of 1.1.

The firm is currently considering the projects shown in the table below.The current approach is to use the firm’s WACC to evaluate allprojects, but management sees the wisdom in adopting a subjectivedivisional cost of capital approach. Firm management is thusconsidering a divisional cost of capital scheme in which they will usethe firm’s WACC for Miscellaneous projects, the firm’s WACC minus 1

percent for Textiles projects, and the firm’s WACC plus 3 percent forAccessories projects. The current expected return to the market is 12percent, and the current risk-free rate is 5.75 percent.

For this group of projects, how much better would their accept/rejectdecisions be if they used this approach rather than if they continued touse the firm’s WACC to evaluate all projects? Would switching to anobjective divisional cost of capital approach, where the WACC for eachdivision is based on that division’s average beta, improve theiraccept/reject criteria any further?

Project Division Expected iE Beta

A βAccessories 17.00% 1.3

B βAccessories 15.00  1.2

C βMiscellaneous 13.00  1.3

D βMiscellaneous 11.00  0.7

E βTextiles 9.00  0.8

F βTextiles 7.00  0.5

SOLUTION:

Determine the required rates of return for each project assuming thatthe firm uses the firmwide WACC and adds the subjective adjustmentsto construct divisional WACCs. The objective computation of divisionalWACCs using each division’s average beta and the iE computed usingeach project’s specific beta is indicated in the table on the next page. Ineach case, project acceptances appear in blue print, and projectrejections appear in red print.

Using the “Specific iE” yields the“correct” accept/reject decision; that is,these accept/reject decisions would be generated exactly the same ifthe firm had the time and resources to compute the iE on a project-by-project basis. In this particular situation, using the firm WACC as abenchmark for all the projects would result in projects E and F beingrejected, since they both will return expected rates less than the firm’s10 percent required rate of return. By comparison to the results usingthe Specific iE, both of these rejections are appropriate. We wouldprefer that the accept/reject criteria took account of risk; that is, both

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projects would be rejected because their expected returns (9 percentand 7 percent, respectively) are less than the required returns (10.75and 8.88 percent, respectively) based on their specific levels of projectrisk rather than assuming that both projects carry the same risk as thefirm’s overall risk. However, using the firm’s WACC incorrectly acceptsproject C.

Using the subjectively adjusted approach to calculating iEresults in required rates of return of 13 percent forAccessories projects, 10 percent for Miscellaneous projects, and 9percent for Textiles projects. The associated accept/reject decisionsactually incorrectly accepts projects C and E, making the subjectivelyadjusted WACC approach worse (in this specific example) than simplyusing the firmwide WACC.

Finally, using the objective approach to constructing divisional costs ofcapital, along with the three divisions’ average betas given above,results in required rates of return for the three divisions of

As these solutions show, using these divisional costs of capital figuresas required rates of return for each project results in correct rejectionsof projects E and F, but also results in an incorrect rejection of projectD and an incorrect acceptance of project C relative to computing iE ona project-by-project basis.

Overall, using either the objective or subjective approaches tocalculating divisional costs of capital will not be as precise as usingproject-specific WACCs: We will wind up incorrectly accepting and/orrejecting some projects. Making incorrect decisions on some of ourproject choices may be worth it if the projects in question aren’t largeenough for project-specific calculations to be cost-effective.

Similar to Problems 11-25 to 11-28

An objective approach would be to compute the average beta per division, use these figures in the CAPM formula tocalculate iE for each division, and then, in turn, use divisional estimates of iE to construct divisional WACCs.Though the objective approach would usually be more precise, resulting in fewer incorrect accept/reject decisions,the subjective approach is more frequently used because it is easier to implement.

time out!11-5 Divisions of a corporation are not usually formed based explicitly on differences in risk between the projects in different

divisions. Rather, they are normally formed along product-type or geographic differences. Explain how this division schememay still result in divisions that do differ among themselves by average risk. Also explain why calculating divisional WACCsin such a situation will still improve decision making over simply using a firmwide WACC for project acceptance orrejection.

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11-6 Explain why, in Example 11-7, using objectively computed divisional WACCs still resulted in an incorrect accept/rejectdecision for project D.

11.4 • FLOTATION COSTS LG11-8We know that firms use varied sources of funding. Until now, our calculations have been assuming that we wereusing retained earnings to fund projects. What if a firm funds a project by issuing externally generated new capital—additional stock, bonds, and so on? Then the firm has to pay the costs of printing the new stock or bond certificates,commissions to the underwriters helping the firm to sell the stocks and bonds, government registration fees, andother associated costs. So to figure project WACCs, we must integrate these flotation costs into our component costsas well.

flotation costs Fees paid by firms to investment banks for issuing new securities.

We can approach the commission costs in two basic ways. We can either increase the project’s WACC toincorporate the flotation costs’ impact as a percentage of WACC, or we can leave the WACC alone andadjust the project’s initial investment upward to reflect the “true” cost of the project. Both approaches haveadvantages and disadvantages. The first approach tends to understate the component cost of new equity, and thelatter approach violates the separation principle of capital budgeting, which states that the calculations of cash flowsshould remain independent of financing. We will discuss the separation principle and the second approach in thenext chapter.

separation principle Theory maintaining that the sources and uses of capital should be decided upon independently.

Adjusting the WACCThe first approach to adjusting for flotation costs is to adjust the issue price of new securities by subtracting flotationcost, F, to reflect the net security price. Then use this net price to calculate the component cost of capital. For equity,this approach is most commonly applied to the constant-growth model:

(11-8)

If we instead want to apply this approach to the cost of equity obtained from the CAPM formula, we would adjust itupward by an equivalent amount.

EXAMPLE 11-8

Flotation-Adjusted Cost ofEquity LG11-8

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Suppose that, as in Example 11-1, ADK Industries’ common shares areselling for $32.75 per share, and the company expects to set its nextannual dividend at $1.54 per share. All future dividends are expected togrow by 6 percent per year indefinitely. In addition, let us suppose thatADK faces a flotation cost of 20 percent on new equity issues.Calculate the flotation-adjusted cost of equity.

SOLUTION:

Twenty percent of $32.75 will be $6.55, so the flotation-adjusted cost ofequity will be

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Notice that the result is 1.18 percent above the non-flotation-adjustedcost of equity, 10.70 percent, computed using the constant-growthmodel in Example 11-1. If we instead wanted to use the CAPMestimate, we would take the non-flotation-adjusted CAPM estimatefrom the same example, 10.80 percent, and add the same differentialof 1.18 percent to it to get the flotation-adjusted value:

The adjustments for the component costs of preferred stock and debtwill be similar:

(11-9)

(11-10)

Similar to Problems 11-23, 11-24

time out!11-7 Why should we expect the flotation costs for debt to be significantly lower than those for equity?11-8 Explain how we should go about computing the WACC for a project that uses both retained earnings and a new equity

issue.

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Log in to your Connect course for study materials including self-test problems with solutions, answers tothe Time Out quizzes, guided example videos, and more.

Your Turn…Questions

1. How would you handle calculating the cost of capital if a firm were planning to issue two different classes ofcommon stock? (LG11-1)

2. Expressing WACC in terms of iE, iP, and iD, what is the theoretical minimum for the WACC? (LG11-2)

3. Under what situations would you want to use the CAPM approach for estimating the component cost of equity?The constant-growth model? (LG11-3)

4. Could you calculate the component cost of equity for a stock with nonconstant expected growth rates individends if you didn’t have the information necessary to compute the component cost using the CAPM? Whyor why not? (LG11-3)

5. Why do we use market-based weights instead of book-value-based weights when computing the WACC?(LG11-4)

6. Suppose your firm wanted to expand into a new line of business quickly, and that management anticipated thatthe new line of business would constitute over 80 percent of your firm’s operations within three years. If theexpansion was going to be financed partially with debt, would it still make sense to use the firm’s existing costof debt, or should you compute a new rate of return for debt based on the new line of business? (LG11-5)

7. Explain why the divisional cost of capital approach may cause problems if new projects are assigned to thewrong division. (LG11-6)

8. When will the subjective approach to forming divisional WACCs be better than using the firmwideWACC to evaluate all projects? (LG11-7)

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9. Suppose a new project was going to be financed partially with retained earnings. What flotation costs shouldyou use for retained earnings? (LG11-8)

ProblemsBASIC PROBLEMS

11-1 Cost of Equity Diddy Corp. stock has a beta of 1.2, the current risk-free rate is 5 percent, and the expectedreturn on the market is 13.5 percent. What is Diddy’s cost of equity? (LG11-3)

11-2 Cost of Equity JaiLai Cos. stock has a beta of 0.9, the current risk-free rate is 6.2 percent, and theexpected return on the market is 12 percent. What is JaiLai’s cost of equity? (LG11-3)

11-3 Cost of Debt Oberon, Inc., has a $20 million (face value) 10-year bond issue selling for 97 percent of parthat pays an annual coupon of 8.25 percent. What would be Oberon’s before-tax component cost of debt?(LG11-3)

11-4 Cost of Debt KatyDid Clothes has a $150 million (face value) 30-year bond issue selling for 104 percentof par that carries a coupon rate of 11 percent, paid semiannually. What would be Katydid’s before-taxcomponent cost of debt? (LG11-3)

11-5 Tax Rate Suppose that LilyMac Photography expects EBIT to be approximately $200,000 per year for theforeseeable future, and that it has 1,000 10-year, 9 percent annual coupon bonds outstanding. What wouldthe appropriate tax rate be for use in the calculation of the debt component of LilyMac’s WACC? (LG11-3)

11-6 Tax Rate PDQ, Inc., expects EBIT to be approximately $11 million per year for the foreseeable future,and that it has 25,000 20-year, 8 percent annual coupon bonds outstanding. What would the appropriate taxrate be for use in the calculation of the debt component of PDQ’s WACC? (LG11-3)

11-7 Cost of Preferred Stock ILK has preferred stock selling for 97 percent of par that pays an 8 percentannual coupon. What would be ILK’s component cost of preferred stock? (LG11-3)

11-8 Cost of Preferred Stock Marme, Inc., has preferred stock selling for 96 percent of par that pays an 11percent annual coupon. What would be Marme’s component cost of preferred stock? (LG11-3)

11-9 Weight of Equity FarCry Industries, a maker of telecommunications equipment, has 2 million shares ofcommon stock outstanding, 1 million shares of preferred stock outstanding, and 10,000 bonds. If thecommon shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, and thebonds are selling for 98 percent of par, what would be the weight used for equity in the computation ofFarCry’s WACC? (LG11-4)

11-10 Weight of Equity OMG Inc. has 4 million shares of common stock outstanding, 3 millionshares of preferred stock outstanding, and 5,000 bonds. If the common shares are selling for $17per share, the preferred shares are selling for $26 per share, and the bonds are selling for 108 percentof par, what would be the weight used for equity in the computation of OMG’s WACC? (LG11-4)

11-11 Weight of Debt FarCry Industries, a maker of telecommunications equipment, has 2 million shares ofcommon stock outstanding, 1 million shares of preferred stock outstanding, and 10,000 bonds. If thecommon shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, andthe bonds are selling for 98 percent of par, what weight should you use for debt in the computation ofFarCry’s WACC? (LG11-4)

11-12 Weight of Debt OMG Inc. has 4 million shares of common stock outstanding, 3 million shares ofpreferred stock outstanding, and 5,000 bonds. If the common shares are selling for $27 per share, thepreferred shares are selling for $26 per share, and the bonds are selling for 108 percent of par, whatweight should you use for debt in the computation of OMG’s WACC? (LG11-4)

11-13 Weight of Preferred Stock FarCry Industries, a maker of telecommunications equipment, has 2million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and10,000 bonds. If the common shares sell for $27 per share, the preferred shares sell for $14.50 pershare, and the bonds sell for 98 percent of par, what weight should you use for preferred stock in thecomputation of FarCry’s WACC? (LG11-4)

11-14 Weight of Preferred Stock OMG Inc. has 4 million shares of common stock outstanding, 3 millionshares of preferred stock outstanding, and 5,000 bonds. If the common shares sell for $17 per share,

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the preferred shares sell for $16 per share, and the bonds sell for 108 percent of par, what weightshould you use for preferred stock in the computation of OMG’s WACC? (LG11-4)

INTERMEDIATE PROBLEMS

11-15 WACC Suppose that TapDance, Inc.’s, capital structure features 65 percent equity, 35 percent debt,and that its before-tax cost of debt is 8 percent, while its cost of equity is 13 percent. If the appropriateweighted average tax rate is 34 percent, what will be TapDance’s WACC? (LG11-2)

11-16 WACC Suppose that JB Cos. has a capital structure of 78 percent equity, 22 percent debt, and that itsbefore-tax cost of debt is 11 percent while its cost of equity is 15 percent. If the appropriate weighted-average tax rate is 25 percent, what will be JB’s WACC? (LG11-2)

11-17 WACC Suppose that B2B, Inc., has a capital structure of 37 percent equity, 17 percent preferredstock, and 46 percent debt. If the before-tax component costs of equity, preferred stock, and debt are14.5 percent, 11 percent, and 9.5 percent, respectively, what is B2B’s WACC if the firm faces anaverage tax rate of 30 percent? (LG11-2)

11-18 WACC Suppose that MNINK Industries’ capital structure features 63 percent equity, 7 percentpreferred stock, and 30 percent debt. If the before-tax component costs of equity, preferred stock, anddebt are 11.60 percent, 9.5 percent, and 9 percent, respectively, what is MNINK’s WACC if the firmfaces an average tax rate of 34 percent? (LG11-2)

11-19 WACC TAFKAP Industries has 3 million shares of stock outstanding selling at $17 per share, and anissue of $20 million in 7.5 percent annual coupon bonds with a maturity of 15 years, selling at 106percent of par. If TAFKAP’s weighted-average tax rate is 34 percent and its cost of equity is 14.5percent, what is TAFKAP’s WACC? (LG11-3)

11-20 WACC Johnny Cake Ltd. has 10 million shares of stock outstanding selling at $23 per share and anissue of $50 million in 9 percent annual coupon bonds with a maturity of 17 years, selling at 93.5percent of par. If Johnny Cake’s weighted-average tax rate is 34 percent, its next dividend is expectedto be $3 per share, and all future dividends are expected to grow at 6 percent per year, indefinitely,what is its WACC? (LG11-3)

11-21 WACC Weights BetterPie Industries has 3 million shares of common stock outstanding, 2 millionshares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $47 pershare, the preferred shares are selling for $24.50 per share, and the bonds are selling for 99 percent ofpar, what would be the weights used in the calculation of BetterPie’s WACC? (LG11-4)

11-22 WACC Weights WhackAmOle has 2 million shares of common stock outstanding, 1.5 millionshares of preferred stock outstanding, and 50,000 bonds. If the common shares are selling for$63 per share, the preferred shares are selling for $52 per share, and the bonds are selling for 103percent of par, what would be the weights used in the calculation of WhackAmOle’s WACC? (LG11-4)

11-23 Flotation Cost Suppose that Brown-Murphies’ common shares sell for $19.50 per share, that the firmis expected to set their next annual dividend at $0.57 per share, and that all future dividends areexpected to grow by 4 percent per year, indefinitely. If Brown-Murphies faces a flotation cost of 13percent on new equity issues, what will be the flotation-adjusted cost of equity? (LG11-8)

ADVANCED PROBLEMS

11-24 Flotation Cost A firm is considering a project that will generate perpetual after-tax cash flows of$15,000 per year beginning next year. The project has the same risk as the firm’s overall operationsand must be financed externally. Equity flotation costs 14 percent and debt issues cost 4 percent on anafter-tax basis. The firm’s D/E ratio is 0.8. What is the most the firm can pay for the project and stillearn its required return? (LG11-2)

11-25 Firmwide versus Project-Specific WACCs An all-equity firm is considering the projects shownbelow. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its currentWACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly rejected?(LG11-6)

Project Expected Return Beta

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A 8.0% 0.5

B 19.0  1.2

C 13.0  1.4

D 17.0  1.6

11-26 Firmwide versus Project-Specific WACCs An all-equity firm is considering the projects shownbelow. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its currentWACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly accepted?(LG11-6)

Project Expected Return Beta

A 8.0% 0.5

B 19.0  1.2

C 13.0  1.4

D 17.0  1.6

11-27 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyzeprojects. The firm currently has four divisions, A through D, with average betas for each division of0.6, 1.0, 1.3, and 1.6, respectively. If all current and future projects will be financed with half debt andhalf equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 7 percent) is 13 percent and the after-tax yield on the company’s bonds is 8 percent, whatwill the WACCs be for each division? (LG11-7)

11-28 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyzeprojects. The firm currently has four divisions, A through D, with average betas for each division of0.9, 1.1, 1.3, and 1.5, respectively. If all current and future projects will be financed with 25 percentdebt and 75 percent equity, and if the current cost of equity (based on an average firm beta of 1.2 and acurrent risk-free rate of 4 percent) is 12 percent and the after-tax yield on the company’s bonds is 9percent, what will the WACCs be for each division? (LG11-7)

NotesCHAPTER 111. Think of taking such an average as being intuitively the same as diversifying our “portfolio” of data across the two different estimation

techniques, thereby reducing the average amount of estimation error. Taking this average is intuitively the same as diversifying yourportfolio of data across two different estimation techniques. These options allow you to reduce your average amount of estimation error.

2. We’ll discuss more about calculating WACC for a project later in the chapter.3. In reality, new projects are often financed with different proportions of equity, debt, and preferred stock than were used to fund the

firm’s existing operations. As we will discuss in Chapter 16, such a change in capital structure will result in a change in financial riskwith increased leverage magnifying β.

4. As we will also discuss in Chapter 16, we will be able to take a straight average of the proxy firm’s betas as the estimate of our betaonly if the capital structures of all the proxies are identical to each other and to that of our proposed new project. If not, we will need toadjust the proxies’ estimated betas for differences in capital structures before averaging them. Then we will need to readjust theaverage beta for our project’s capital structure before using the estimate.

T

chapter twelveestimating cash flows oncapital budgeting projects

©Stockbyte/Getty Images

o evaluate capital budgeting projects, we have to estimate how much cash outflow each project willneed and how much cash inflow it will generate, as well as exactly when such outflows and inflowswill occur. Estimating these cash flows isn’t difficult, but it is complicated, as there are lots of little

details to keep track of. Accordingly, as you look through this chapter’s examples, questions, andproblems, you’ll notice that these types of problems involve a lot more information than those you’ve seenelsewhere in the text, such as

The particular new product or service’s costs and revenues.

The likely impact that the new service or product will have on the firm’s existing products’ costs and revenues.The impact of using existing assets or employees already employed elsewhere in the firm.

How to handle charges such as the research and development costs incurred to develop the new product.

One of the keys to this chapter will be making sure that we have a systematic approach to handlingand arranging details. In the next few sections, we’re going to construct a process which, if we follow itfaithfully, will guide us in considering factors such as those listed.

LEARNING GOALS

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LG12-1 Explain why we use pro forma statements to analyze project cash flows.LG12-2 Identify which cash flows we can incrementally apply to a project and which ones we cannot.LG12-3 Calculate a project’s expected cash flows using the free cash flow approach.LG12-4 Explain how accelerated depreciation affects project cash flows.LG12-5 Calculate free cash flows for replacement equipment.LG12-6 Calculate cash flows associated with cost-cutting proposals.LG12-7 Demonstrate the EAC approach to choosing among alternative cash streams for recurring projects.LG12-8 Adjust initial project investments to account for flotation costs.

viewpointsbusiness APPLICATIONSuppose that McDonald’s is considering introducing the McTurkey Dinner (MTD). The company anticipates that the MTD will haveunit sales, prices, and cost figures as shown in the following table for the next five years, after which the firm will retire the MTD.Introducing the MTD will require $7 million in new assets, which will fall into the MACRS five-year class life. McDonald’s expects thenecessary assets to be worth $2 million in market value at the end of the project life. In addition, the company expects that NWCrequirements at the beginning of each year will be approximately 13 percent of the projected sales throughout the coming year andfixed costs will be $2 million per year. McDonald’s uses an 11 percent cost of capital for similar projects and is subject to a 35 percentmarginal tax rate. What will be this project’s expected cash flows? (See the solution at the end of the book.)

McTurkey Dinner Projections

Year Estimated Unit Sales Estimated Selling Price per Unit Estimated Variable Cost per Unit

1  400,000 $7.00 $3.352 1,000,000  7.21  3.523 1,000,000  7.43  3.704 1,000,000  7.65  3.895  500,000  7.88  4.08

LG12-1

The exact process that we’re going to use is more formally referred to as pro forma analysis, whichestimates expected future cash flows of a project using only the necessary parts of the balance sheet andincome statements; if a part of either financial statement doesn’t change because of the new project, we’llignore it. This approach will allow us to focus on the question, “What will be this project’s impact on thefirm’s total cash flows if we go forward?” ■

pro forma analysis Process of estimating expected future cash flows of a project using only the relevant parts of the balance sheet andincome statements.

12.1 • SAMPLE PROJECT DESCRIPTION LG12-1Let’s suppose that we are working for a game development company, First Strike Software (FSS). FSS isconsidering leasing a new plant in Gatlinburg, Tennessee, which it will use to produce copies of its new consolegame “FinProf,” a role-playing game where the player battles aliens invading a local college’s finance department.

FSS will price this game at $39.99, and the firm estimates sales for each of the next three years as shown in Table12.1. Given buyers’ rapidly changing tastes in console games, FSS does not expect to be able to sell any more copiesafter year 3.

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▼ TABLE 12.1 Sample Project Projected Unit Sales

Year Unit Sales

1 15,0002 27,0003  5,000

Variable costs per game are low ($4.25), and FSS expects fixed costs to total $150,000 per year, including rent.Start-up costs include $75,000 for the purchase of a software-duplicating machine, plus an additional $2,000 inshipping and installation costs. For our first stab at analyzing this project, we will assume that theduplicating machine will be straight-line depreciated to an estimated ending salvage value of $5,000 overthe life of the project. However, due to the rapidly declining market for such machines (many of FSS’s competitorsare switching to download-only games), we are also estimating that we’ll only be able to sell the machine for $2,000after we’re done using it.

salvage value The estimated amount for tax purposes that a company will receive when it disposes of an asset at the end of the asset’susable life.

personal APPLICATIONAchmed contemplates going back to school part time to get an MBA. He anticipates that it would take him four years to get his MBA,and the program would cost $15,000 per year in books and tuition (payable at the beginning of each year). He also thinks that hewould need to get a new laptop (which he was going to buy anyway as a portable gaming system) for $2,500 when he starts theprogram, and he just paid $250 to take the GMAT. After graduation, Achmed anticipates that he will be able to earn approximately$10,000 more per year with the MBA, and he thinks he’ll work for about another 20 years after getting the MBA. What total cash flowsshould Achmed consider in his decision? (See the solution at the end of the book.)

Thinking about an MBA? What returns can you expect from the investment?

FinProf is an updated version of an older game sold by FSS, MktProf. FSS intends to keep selling MktProf butanticipates that FinProf will decrease sales of MktProf by 2,000 units per year throughout the life of the new game.MktProf sells for $19.99 and has variable costs of $3.50 per unit. The decrease in MktProf sales will not affect eitherNWC or fixed assets.

Development costs totaled $150,000 throughout the creation of the game, and First Strike estimates its NWCrequirements at the beginning of each year will be approximately 10 percent of the projected sales during thecoming year. First Strike is in the 34 percent tax bracket and uses a discount rate of 15 percent on projects with riskprofiles such as this. The relevant question: Should FSS put FinProf into production or not?

12.2 • GUIDING PRINCIPLES FOR CASH FLOWESTIMATION LG12-2When we calculate a project’s expected cash flows, we must ensure that we cover all incremental cash flows; that is,the cash flow changes that we would expect throughout the entire firm, for both this project and for everything elsethe firm is already doing, because of the new project coming on board. Some incremental cash flow effects are fairlyobvious. For example, suppose a firm has to buy a new asset to support a new project but would not be buying theasset if the project were not adopted. Clearly, the cash associated with buying the asset is due to the project, and weshould therefore count it when we calculate the cash flows associated with that project. But we can hardly expect allincremental cash flows to be so obvious. Other incremental cash flows, as discussed in the following sections, aremore subtle, and we’ll have to watch for them very carefully.

incremental cash flows Cash flows directly attributable to the adoption of a new project.

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Opportunity CostsAs you likely remember from your microeconomics classes, an opportunity cost exists whenever a firm has to choosehow to allocate scarce resources. If those resources go into project A, the firm must forgo using them in any otherway. Those forgone choices represent lost opportunities, and we have to account for them when calculating cashflows attributable to project A.

For example, suppose that FSS already owned the piece of software-duplicating machinery discussed previously. Ifthe machinery was already being fully utilized by another project within the company, then obviously switching itover to the FinProf game would require that other project to find another source of software duplication. Therefore,to be fair, the FinProf project should be charged for the use of the machinery.

Even if the machinery was not currently being used in any other projects, it could still possibly have an opportunitycost associated with using it in the FinProf project. If FSS could potentially sell the machinery on the open marketfor $75,000, the company would have to give up receiving that $75,000 in order to use the piece of machinery forthe FinProf game. In the end, it would not really matter whether the firm had to buy the asset from outside sourcesor not; either way, the project will be tying up $75,000 worth of capital, and it should be charged for doing so.

The underlying concept behind charging the project for the opportunity cost of using an asset also applies toexpenses other than those associated with capital assets such as machinery: Overall, we should charge any newproject for any assets used by that project as well as any wages and benefits paid to employees working on it. Even ifthe firm was already employing those people prior to starting work on the new project, they are no longer availableto work on any existing projects; and if the firm did not have any new projects, it could have laid those employeesoff, saving their wages and benefits.

In the FSS project, wages and benefits to employees would constitute part of the variable costs we were quotedearlier. Just as with the software-duplicating machinery, whether these employees were previously working for FSSon another project would be irrelevant; if FSS is going to use these employees on this project, the project should becharged for them.

Sunk CostsIf a firm has already paid an expense in the past or is obligated to pay one in the future (i.e., there’s no way out ofpaying it), regardless of whether a particular project is undertaken, that expense is a sunk cost. A firm should nevercount sunk costs in project cash flows. Intuitively, if you have to pay the expense regardless of your decisionconcerning the project, it doesn’t meet the definition of being “incremental.”

opportunity cost The dollar cost or forgone opportunity of using an asset already owned by the firm, or a person already employed bythe firm, in a new project.

sunk cost A cost that has already been incurred and cannot be recovered.

For example, we are told that FSS incurred $150,000 in development costs as they developed the game.Development costs would presumably include items such as the salaries of the game’s programmers, marketresearch costs, and so forth. Since we are not told otherwise, we can sensibly assume that this money is gone, andthat FSS will never recoup the money, even if it decides not to go ahead with publishing the game. Thus those costsare sunk, and FSS should not even consider them as part of its decision about whether to move forward with puttingthe FinProf game into production.

Substitutionary and Complementary EffectsIf a new product or service will either reduce or increase sales, costs, or necessary assets for other, already existingproducts or services, then those changes to the cash flows of the other projects are incremental to the new projectand should rightfully be included in the new project’s cash flows.

For example, consider how FSS’s FinProf game may affect the existing MktProf game. The gross sales and variablecost figures for the new game might be as shown in Table 12.2.

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▼ TABLE 12.2 Gross Sales and Variable Costs for FinProf

Year Sales Variable Costs

1 15,000 × $39.99 = $599,850 15,000 × $4.25 = $63,7502 27,000 × $39.99 = $1,079,730 27,000 × $4.25 = $114,7503 5,000 × $39.99 = $199,950 5,000 × $ 4.25 = $21,250

However, FSS also expects the MktProf game to lose yearly sales of 2,000 × $19.99 = $39,980 when theFinProf game starts selling. Partially offsetting this, the decrease in sales of MktProf will also result in adecrease in yearly variable costs for MktProf of 2,000 × $3.50 = $7,000 in savings (i.e., forgone costs) per year. Sothe net incremental sales and variable cost figures for the project will be as shown in Table 12.3.

▼ TABLE 12.3 Net Incremental and Variable Costs for FinProf

Year Sales Variable Costs

1 $599,850 − $39,980 = $559,870 $63,750 − $7,000 = $56,7502 $1,079,730 − $39,980 = $1,039,750 $114,750 − $7,000 = $107,7503 $199,950 − $39,980 = $159,970 $21,250 − $7,000 = $14,250

As we see, we have to reduce FinProf’s sales each year by the $39,980 reduction in MktProf sales attributable to theFinprof game existing, but we also get to reduce FinProf’s costs by $7,000 each year due to the cost savings of nothaving to make so many copies of MktProf. Technically speaking, we are seeing a reduction in both sales andvariable costs because FinProf is a partial substitute for MktProf. If the new game had been a complement (i.e., if wehad sold more of the MktProf game due to the rollout of FinProf), then both sales and variable costs of the existingproduct would have increased instead.

Stock Dividends and Bond InterestOne final, important note concerning incremental project cash flows: We will never count any financing costs,including dividends paid on stock or interest paid on debt, as expenses of the project. The costs of capital are alreadyincluded as component costs in the weighted-average cost of capital (WACC) that we will be using to discount thesecash flows in the next chapter. If we were to include them in the cash flow figures as well, we would be double-counting them.

substitute and complement Effects that arise from a new product or service either decreasing or increasing sales, respectively, of thefirm’s existing products and services.

financing costs Interest paid to debt holders or dividends paid to stockholders.

time out!12-1 Suppose that your manager will be devoting half of her time to a new project, with the other half devoted to currently

existing projects. How would you reflect this in your calculation of the incremental cash flows of the project?

12-2 Could a new product have both substitutionary and complementary effects on existing products?

12.3 • TOTAL PROJECT CASH FLOW LG12-3In Chapter 2, we discussed the concept of free cash flow (FCF), which we defined as

(12-1)

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In this chapter, we are going to use this variable again as a measure of the total amount of available cash flow from aproject. However, we will observe two important differences from how we used it in Chapter 2. First, since we willbe considering potential projects rather than a particular firm’s actual, historic activities, the FCF numbers wecalculate will be, frankly, guesses—informed guesses, surely, but still guesses. Since we will be “calculating”guesses, we will introduce possible estimation error into our capital budgeting decision statistics, but we will holdoff on discussing that until the next chapter.

Second, we will now calculate FCF on potential projects individually, rather than across the firm as a whole as wedid in Chapter 2. In some ways, calculating FCF on individual projects will make our job much easier, since wedon’t have to worry about estimating an entire set of balance sheets for the firm. Instead, we will only have to beconcerned with the limited subset of pro forma statements necessary to keep track of the assets, expense categories,and so on, that a new project will affect. Unfortunately, the elements of that limited set will vary from situation tosituation, and the hard part will be identifying which parts of the balance sheets are necessary and which are not.

Calculating DepreciationExpected depreciation on equipment used during the life of the project will affect both the operating cash flows andthe change in gross fixed assets that will occur at the end of the project when we sell or abandon them, so let’s startour organizing there.

For First Strike’s proposed FinProf project, the firm will depreciate capital assets such as the software-duplicating machine using the straight-line method to an ending book value of $5,000. To calculate theannual depreciation amount, First Strike will first need to compute the machinery’s depreciable basis. According tothe Internal Revenue Service’s (IRS) Publication 946, the depreciable basis for real property is the sum of:

Its cost.Amounts paid for items such as sales tax.

Freight charges.Installation and testing fees.

depreciable basis An asset’s cost plus the amounts you paid for items such as sales tax, freight charges, and installation and testingfees.

We aren’t told anything about sales tax on the machinery, so the depreciable basis for the new project’s software-duplicating machine will be the $75,000 purchase price plus the $2,000 shipping and installation cost, for a totaldepreciable basis of $77,000.

Under straight-line depreciation, the annual depreciation for each year will be equal to the depreciable basis minusthe projected ending book value, all over the number of years in the life of the asset:

(12-2)

We’ll discuss later in the chapter why this depreciation assumption is far too simple, and why other, morecomplicated depreciation methods can be much more advantageous to the company. For now, though, this straight-line depreciation approach will suffice for our initial go at calculating the project’s cash flows.

Calculating Operating Cash FlowWe defined operating cash flow (OCF) in Chapter 2 as EBIT (1 − Tax rate) + Depreciation. We will still calculateOCF as being mathematically equal to EBIT (1 − Tax rate) + Depreciation. But remember that we will beconstructing the FCF components ourselves instead of taking them off an income statement that someone else hasalready produced. So we will usually find it most helpful to conduct this calculation by using what we will call a“quasi-income statement” that leaves out some components that don’t matter for project cash flows, such as interestdeductions. (Note that the process of leaving out any interest deduction is exactly in line with our discussion of notcounting interest on debt as an expense of the project, but the resulting financial statement would not make an

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accountant happy).

The depreciable basis for real property includes freight charges.©Steve Boyko/Shutterstock

Such a statement is shown in Table 12.4 for First Strike’s proposed project. The primary benefit of calculating OCFthis way instead of as an algebraic formula is that with this format, we have space to expand subcalculations, such asthe impact of FinProf being a partial substitute for the MktProf product.

▼ TABLE 12.4 Calculation of OCF

Before we move on, notice that not only is EBIT negative in year 3 of OCF calculations, but we also assume thatthis negative EBIT, in turn, generates a “negative tax bill” (i.e., a tax credit, when we subtract the negative taxamount of −$9,615 from the negative EBIT). How, and when, can we get away with making this assumption?

Well, the rule for handling negative EBIT is that when calculating the cash flows for a single project for a firm, weassume that any loss by this project in a particular period can be applied against assumed before-tax profitsmade by the rest of the firm in that period. So, while our project is expected to have a loss of $28,280before taxes during year 3, the assumed ability of the firm to use that loss to shelter $28,280 in before-tax profitselsewhere in the firm means that the incremental after-tax net income for this project during year 3 is expected to be−$28,280 − (−$9,615) = −$18,665. This is still negative, but less negative than the EBIT because of this tax-sheltering effect.

What would we do if we expected a negative EBIT during a particular year and this was the only project the firmwas undertaking, or if this project was so big that a negative EBIT would overshadow any potential profitselsewhere in the firm? Long story short, we would not get to take the tax credit during that year . . . but we will leavethe discussion of just exactly when we would get to take it to a more advanced text.

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Calculating Changes in Gross Fixed AssetsGross fixed assets will change in almost every project at both the beginning (when assets are usually purchased) andat the end (when assets are usually sold). First Strike’s proposed project is no exception.

Calculating the change in gross fixed assets at the beginning of the project is fairly straightforward—it will simplyequal the asset’s depreciable basis. So, for FSS’s project, we will increase gross fixed assets by $77,000 at time zero.

At the end of a project, the change in gross fixed assets is a little more complicated, because whenever a firm sellsany asset, it has to consider the tax consequences of that sale. The IRS treats any sale of assets for more thandepreciated book value as a taxable gain and any sale for less than book value as a taxable loss. In either event, wecan calculate the after-tax cash flow (ATCF) from the sale of an asset using the following formula, where TC is thesame appropriate corporate tax rate discussed in the previous chapter.

(12-3)

Since the machinery for FSS’s project will be depreciated down to $5,000 but is expected to sell for only $2,000, theATCF for that asset’s sale will equal

EXAMPLE 12-1

ATCF for an Asset Sold at aGain LG12-3

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Suppose that a firm facing a marginal tax rate of 25 percent sells anasset for $4,000 when its depreciated book value is $2,000. What willbe the ATCF from the sale of this asset?

SOLUTION:

The ATCF will equal

Similar to Problems 12-1, 12-8

Although it may be a little difficult to wrap your brain around the idea of reducing the $5,000 we were “supposed toget” (at least, according to the IRS) from the sale of the machinery at the end of the project by only 66 percent of theshortfall from that amount we actually expect to happen (i.e., $5,000 − $2,000 = $3,000), that’s exactly what we’redoing. “Losing” $3,000 of the $5,000 expected book value when we sell the machinery will let us hide $3,000 inrevenues elsewhere from the tax man, so we get credit for shielding $3,000 from our 34 percent tax rate loss (i.e.,$3,000 × 34% = $1,020) in addition to estimating that we’ll be able to sell the machinery for $2,000 cash.

If this really is making your brain hurt, just realize that, as long as you faithfully and precisely apply the formula forATCF, it will give you the net cash flow from the sale of the asset. In particular, note that this formula would workequally well on an asset sold at a gain.

Calculating Changes in Net Working Capital

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We can make several different assumptions concerning the NWC level necessary to support a project. The moststraightforward of these would be to simply assume that we add NWC at the beginning of the project and subtract itat the end. This assumption would be valid if the project is expected to have steady sales throughout its life, or ifvariations in NWC do not affect the project much.

FSS’s proposed project, however, features a more typical product life cycle. Its unit sales will follow an approximatebell-shaped curve, starting out low at the beginning, peaking in the middle of the project, and then dropping offagain at the end. When sales are timed in this way, FSS needs to give a little more thought to exactly when the firmneeds to set aside net working capital to support high sales volumes and when it can reduce NWC as sales drop off.

The assumption that First Strike’s NWC at any particular time will be a function of the next year’s sales might seemodd at first glance. But a little thought about how we measure balance sheet numbers (such as NWC) and incomestatement items (such as sales) will show that, really, this assumption makes a lot of sense.

Since income statements (and our quasi-income statement discussed previously) measure what happens during aperiod, the sales show up on the statement at the end of the year, even though they actually start accumulating at thebeginning of the year. The balance sheet “snapshots,” on the other hand, capture how much capital sits in NWCaccounts at a particular point in time. So, for example, the sales figures from our quasi-income statement for year 1that are used in the OCF calculation for year 1 must be supported when they start occurring, which would be at thestart of year 1. But remember, timelines are funny things: The start of year 1 is actually year 0, so we haveto plan to have the NWC shown on the year 0 balance sheet reflect capital earmarked for NWC that will besupporting year 1 sales.

Of course, this same line of reasoning can be generalized for all other time periods, too: Any sales figure thatappears in a time N OCF calculation needs NWC support at the beginning of year N, which is actually time N − 1.So NWC at time N − 1 should vary with time N sales. Therefore, the assumption that First Strike’s NWC at anyparticular time will be a function of the next year’s sales isn’t as crazy as we first thought.

Also, note that it is just the changes in the level of NWC, not the levels themselves, that will affect our cash flows.To explain why, we need to throw a little more intuition into the pot here.

First, we have to admit that we do not really care about the changes in NWC, either, at least not for their own sake;instead, what we are actually measuring is the investment in capital necessary to make those changes happen. (Andthat’s why there is a negative sign in front of NWC in our formula for free cash flow: It costs us money to makeNWC bigger, and vice versa).

First Strike’s NWC at any time will be a function of next year’s sales.©Brand X Pictures/Getty Images

Second, we need to think a little about exactly what we are measuring when we talk about using NWC to supportsales. Since NWC equals current assets minus current liabilities, it’s probably easier to think of it as being composedof cash, accounts receivable, and inventory, net of current liabilities. Do these types of assets get used up? Sure,when cash is used to make change, or when someone pays off an account receivable, or when we sell finished goodsout of inventory, the respective asset account will go down. But those accounts go down because we are bringing inmoney, and some of that money can be used to “restock the shelves,” so to speak; that is, when someone buys one ofour products out of inventory, we assume that part of the purchase price goes toward replenishing the inventory wejust sold, and when someone pays off an account receivable, we assume that allows us to turn around and lend thatmoney to someone else and so forth.

The basic point here is that cash, once invested in NWC, pretty much replenishes itself until we manually take itback out. So when we are looking at the levels of NWC throughout the life of a project, it is the changes in thoselevels that we have to finance, not the levels themselves. Once we put a million dollars into inventory, it sort of stays

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there because of this idea of replenishment, even when we sell some of the inventory. And if we are keeping track ofthe amount of money that we have to invest in inventory or some other type of NWC account, we will findinvestment necessary only when we need to grow NWC by adding to that million dollars (or when wedecide to take some of it back out).

So, we can use the given information for the First Strike project to compute the NWC necessary to support salesthroughout the project’s life, and then in turn use NWC levels to compute the necessary changes in NWC, as shownin Table 12.5. Notice that the NWC level at each time is simply 10 percent of the following year’s sales figures fromTable 12.4.

▼ TABLE 12.5 Change in NWC

This method for computing changes in NWC levels has several appealing features:The changes in NWC at the beginning of a project will always equal the level at time 0, as NWC will be going from a presumed zero levelbefore the project starts up to that new, non-zero level.

Allowing NWC to vary as a percentage of coming sales like this allows FSS to add NWC during periods when it expects sales to increase(e.g., years 0 and 1 in this example) and to decrease NWC when it expects sales to fall off (e.g., years 2 and 3 in this example). NWClevels fall off the last two years of this project precisely because FSS expects sales to fall off and is adjusting NWC to compensate.Finally, one especially nice feature of this approach is that it will always automatically bring NWC back down to a zero level when theproject ends. Since sales in the year after the project ends are always zero, 10 percent of zero will also be zero. This corresponds to whatwe would expect to see in the real world: when a project ends, the firm sells off inventory, collects from customers, pays off accountsreceivable, and so forth.

Bringing It All TogetherUsing the numbers that we calculated for OCF, change in gross fixed assets, and change in NWC, First Strike’sexpected total cash flows from the new project would be as shown in Table 12.6.

▼ TABLE 12.6 Total Cash Flows

Note, in particular, that correct use of the after-tax cash flow from selling the machinery at the end of the projectrequires that we change the cash flows’ sign to negative when we enter it for year 3. Why? Because the ATCFformula shown in equation 12-3 does a little too much work for us. It computes cash flow effects of selling the asset,while the formula we are using for FCF wants us to enter the change in fixed assets. Or, to put it another way, cashflow at the end of the project should go up because fixed assets decrease. We subtract that decrease in our FCF =OCF − (ΔFA + ΔNWC) calculation, which has the effect of “subtracting a minus.” Eventually, then, we increase thefinal year’s FCF above that which we would have generated by just combining OCF with the cash freed up fromdecreasing NWC.

time out!12-3 Explain why an increase in NWC is treated as a cash outflow rather than as an inflow.12-4 Will OCF typically be larger or smaller than net income? Why?

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12.4 • ACCELERATED DEPRECIATION AND THE HALF-YEAR CONVENTION LG12-4Our FCF calculation in the previous section was complete, but we used a rather simplistic assumption concerningdepreciation in the calculations. In reality, the IRS requires that depreciation must be calculated using the half-yearconvention, which basically says that all property placed in service during a given period is assumed to be placed inservice at the midpoint of that period.1 By implication, three years of asset life, such as the machinery in the FirstStrike example, will extend over four calendar years of the firm, starting a half-year before the project starts andending a half-year after it ends.

Just to make things a little more confusing, the IRS names an asset’s class life in its depreciation tables according tohow long the asset will live, not according to how many of the firm’s calendar years the depreciation will stretchacross. For example, Table 12.7 shows an excerpt from the IRS depreciation table for straight-line depreciationusing the half-year convention.

▼ TABLE 12.7 Excerpt of Straight-Line Depreciation Table with Half-Year Convention

class life The number of years of assumed usage for an asset to be used in the calculation of depreciation.

Note that assets falling in, for example, the three-year class life (denoted by the column headings along the top) getdepreciation taken during the first four calendar years after purchase, with the percentage figures in the relevantcolumn denoting how much of the asset’s depreciable basis may be deducted in each respective firm calendar year.For example, an asset with a depreciable basis of $100,000 falling into the three-year class life would be depreciated$100,000 × 0.1667 = $16,670 during the first calendar year the firm owned it, $33,330 during the second and thirdyears of ownership, and another $16,670 during the fourth year of ownership.

The IRS provides guidance on which categories various assets fall into, so it’s usually pretty easy to figure outwhich column to use. For this text, we will assume that we are always told which column to use.

Note that the IRS’s interpretation of the half-year convention is not as direct as simply taking one-half of the firstyear’s depreciation and moving it to the end of the asset’s life. For example, the column for 3.5-year depreciationshows that such an asset would have 14.29 percent of its value depreciated during the first year and 28.57 percentduring each of the second, third, and fourth years. So, rather than using a formula to compute the depreciationpercentage, it’s preferable to look the percentages up from the appropriate IRS table. A copy of the entire table forstraight-line depreciation using the half-year convention appears as Appendix 12A at the end of this chapter.

MACRS Depreciation CalculationThough the IRS allows firms to use the straight-line method with the half-year convention to depreciate assets, mostbusinesses probably benefit from using some form of accelerated depreciation. Accelerated depreciation allowsfirms to expense more of an asset’s cost earlier in the asset’s life. An example of this is the double-declining-balance(DDB or 200 percent declining balance) depreciation method, under which the depreciation rate is double that usedin the straight-line method.

To make all of this completely confusing, the IRS also uses the half-year convention with DDB depreciation andtends to switch back and forth between DDB and SL depreciation methods in the same table, depending upon whichmethod is more advantageous to the taxpayer.

For example, MACRS (modified accelerated cost recovery system) depreciation tables use DDB for 3- to 10-yearproperty, the 150 percent declining balance method for 15- to 20-year property, and straight-line

depreciation whenever it becomes more advantageous to the taxpayer. But for real estate, MACRS uses straight-linedepreciation and the mid-month convention for all asset classes.

This all can be more than enough to make you want to cry, but the good news is that the applicable depreciationpercentages are provided for you in the MACRS depreciation tables compiled by the IRS. We have provided this foryou in Appendix 12A. An excerpt of the DDB section of the MACRS table appears as Table 12.8. MACRS isgenerally the depreciation method of choice for firms since it provides the most advantageous method ofdepreciation.

▼ TABLE 12.8 DDB Depreciation with Half-Year Convention

Normal Recovery Period

Year 3 5 7 10

1 33.33% 20.00% 14.29% 10.00%2 44.45  32.00  24.49  18.00  3 14.81  19.20  17.49  14.40  4 7.41  11.52  12.49  11.52  5 0.00  11.52  8.93  9.22  6 0.00  5.76  8.92  7.37  7 0.00  0.00  8.93  6.55  8 0.00  0.00  4.46  6.55  9 0.00  0.00  0.00  6.56  10 0.00  0.00  0.00  6.55  11 0.00  0.00  0.00  3.28  12 0.00  0.00  0.00  0.00  13 0.00  0.00  0.00  0.00  14 0.00  0.00  0.00  0.00  15 0.00  0.00  0.00  0.00  16 0.00  0.00  0.00  0.00  17 0.00  0.00  0.00  0.00  18 0.00  0.00  0.00  0.00  19 0.00  0.00  0.00  0.00  20 0.00  0.00  0.00  0.00  21 0.00  0.00  0.00  0.00 

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Section 179 DeductionsIn certain circumstances, we can accelerate asset expensing even further by expensing assets immediately in the yearof purchase rather than having to depreciate them over time. The IRS allows most businesses to immediatelyexpense up to $500,000 of property placed in service each year under what is referred to as a Section 179 deduction.The Section179 deduction is obviously targeted at helping small businesses, so it places an annual limit on theamount of deductible property. If the cost of qualifying Section 179 property you put into service in a single tax yearexceeds the current statutory base of $2 million (as of the 2015 tax year), then you cannot take the full deduction.The maximum deduction is also limited to the annual taxable income from the active conduct of the business.

Section 179 deduction A deduction targeted at small businesses that allows them to immediately expense asset purchases up to acertain limit rather than depreciating them over the assets’ useful lives.

For example, consider a manufacturer who completely re-equips his facility in 2015, at a cost of $2.1 million. This is$100,000 more than allowed, so he must reduce his eligible deductible limit to $400,000, which is the current$500,000 expensing limit minus the $100,000 excess over the current statutory base limit. To take this deduction,the firm must have at least $400,000 of taxable income for the year. A company that spent $2.5 million (= $2 million+ $500,000) or more on qualifying Section 179 property would not be able to take the deduction at all, regardless ofits taxable income. Property that does not qualify for a Section 179 deduction can be depreciated using MACRS.

Property eligible for a Section 179 deduction includesMachinery and equipment.

Furniture and fixtures.Most storage facilities.

Single-purpose agricultural or horticultural structures.Off-the-shelf computer software.

Certain qualified real property (limited to $250,000 of the $500,000 expensing limit).

Ineligible property includesBuildings and their structural components (unless specifically qualified).Income-producing property (investment or rental property).

Property held by an estate or trust.Property acquired by gift or inheritance.

Property used in a passive activity.Property purchased from related parties.

Property used outside of the United States.

Like many IRS deductions, there are several terms and conditions that apply, so be sure to get all the facts if youintend to use this method of depreciation.

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Machinery is eligible for a Section 179 deduction.©Brand X Pictures/Getty Images

Impact of Accelerated DepreciationSo, let’s return to our FSS example and FinProf. Remember that our initial, simplistic view of depreciation had ustaking $24,000 per year in depreciation for each of the three years of the project’s life. If the software reproductionmachinery fell into the three-year life class, we could instead have taken the following depreciation amounts byusing either the straight-line or DDB approaches, as shown in Table 12.9.

▼ TABLE 12.9 FSS’s Yearly Depreciation and Ending Book Values under Alternative Depreciation

Year 1 Year 2 Year 3 Ending BV

Straight-line

$77,000 − 16.67% =$12,835.90

$77,000 − 33.33% =$25,664.10

$77,000 − 33.33% =$25,664.10

$12,835.90

DDB $77,000 − 33.33% =$25,664.10

$77,000 − 44.45% =$34,226.50

$77,000 − 14.81% =$11,403.70

$5,705.70

If First Strike could take advantage of the Section 179 deduction that would probably be the mostadvantageous way to deduct the cost of the new machinery—it could deduct the entire $77,000 in year 1. IfFSS could not use a Section 179 deduction, the DDB depreciation available under MACRS would result in the nextquickest recovery of the tax breaks associated with the machinery purchase.

And why is it better to depreciate the cost of an asset as quickly as possible? Well, taking the depreciation over alonger time span doesn’t get you more dollars of depreciation tax shield; it just stretches the same total amount ofdollars over that longer time span. So, think about it in the context of time value of money: The present value of $X

of total income tax shield will be highest when we get the $X as soon as possible.

time out!12-5 Explain why, under MACRS, “five-year” depreciation is actually spread over six years, six-year depreciation spreads into

seven years, and so forth.12-6 If the IRS wanted to encourage businesses to invest in certain types of assets, would it put them into shorter or longer

MACRS life-class categories?

12.5 • “SPECIAL” CASES AREN’T REALLY THATSPECIAL LG12-5As long as we are consistent in using incremental FCF to calculate total project cash flows, we can handle manyproject types that are habitually viewed as “special” cases requiring extraordinary treatment with some relativelysimple revisions to the methods we used for valuing First Strike’s proposed new project.

EXAMPLE 12-2 Replacement Problem LG12-5

For interactive versionsof this example, log in

to Connect or go tomhhe.com/CornettM4e.

Suppose that Just-in-Time Don