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Eugene F. Brigham UNIVERSITY OF FLORIDA

Joel F. Houston UNIVERSITY OF FLORIDA

F UN D AME N TAL S O F F I NANC I AL M ANAGE M E N T

Concise Sixth Edition

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Fundamentals of Financial Management: Concise Edition, 6th edition Eugene F. Brigham, Joel F. Houston

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iii

PREFAC E

The fi rst edition of Fundamentals was published 30 years ago. Since then, the body of fi nancial knowledge has expanded mightily, and this led us to continually add to the book. As Fundamentals got larger and larger, we heard more and more often that it was diffi cult to cover the entire book in a single term. Therefore, we asked our students and other professors for advice. Some said that we shouldn’t worry about the book’s size, because a larger, more complete book gives professors fl exi- bility in designing their courses, is a better reference for students after they have completed the course, and allows interested students to read chapters not covered in class on their own. Others disagreed, arguing that, as textbooks get larger, it becomes increasingly diffi cult for professors to develop a manageable syllabus, and it also forces students to buy a larger, more expensive text than they want or need. In the end, we concluded that both arguments have merit, so we decided to write a concise version for those who think a smaller, more concise textbook would better suit their needs.

When we fi rst created Concise, we debated between streamlining the book by covering all the topics but in less depth versus covering fewer topics but maintain- ing the depth and rigor of Fundamentals. We chose to retain the depth and level while eliminating some less essential topics. While the omitted topics are interest- ing and important, they are not critically important, and fi nance majors will study these topics later in their advanced courses.

STRUCTURE OF THE BOOK Our target audience is undergraduate students taking their fi rst, and often only, fi nance course. Some will decide to major in fi nance and go on to take courses in investments, money and capital markets, and advanced corporate fi nance. Others will choose marketing, management, or some other nonfi nance major. Still others will major in areas other than business and are taking fi nance and a few other business courses to gain information that will help them in law, real estate, or other fi elds.

Our challenge was to provide a book that serves all of these audiences well. Our conclusion was that we should focus on the core principles of fi nance, i.e., on basic topics such as the time value of money, risk analysis, and valuation. More- over, we concluded that we should address these topics from two points of view: (1) as an investor seeking to make intelligent investment choices and (2) as a busi- ness manager trying to maximize the value of his or her fi rm’s stock. Note that both investors and managers need to know the same set of principles, so the core topics are important to students regardless of what they choose to do after they fi nish the course.

In setting up the structure of the book, we fi rst listed the core topics in fi nance with which virtually everyone should be familiar. Included here are an overview of fi nancial markets, methods used to estimate the cash fl ows that determine assets’ values, the time value of money, the determinants of interest rates, the basics of risk analysis, and the basics of bond and stock valuation procedures. We cover these core topics in the fi rst nine chapters. Next, since most students in the course will probably work for a business fi rm, we wanted to show them how the core ideas are implemented in practice. Therefore, in the remainder of the book we discuss cost of capital, capital budgeting, capital structure, dividend policy, working capital management, fi nancial forecasting, and international operations.

iv Preface

Nonfi nance majors sometimes wonder why they need to learn about fi nance. As we structured the book, it should be obvious to everyone why they need to understand time value, risk, markets, and valuation. Virtually all students enrolled in the basic course expect at some point to have some money to invest, and they quickly realize that the knowledge gained from Chapters 1 through 9 will help them make better investment decisions. Moreover, students who plan to go into business soon realize that their own success requires that their fi rms be successful, and the topics covered in Chapters 10 through 17 will be helpful here. For exam- ple, good capital budgeting decisions require accurate forecasts from people in sales, marketing, production, and human resources, and those people need to understand how their actions affect the fi rm’s profi ts and future.

ORGANIZATION OF THE CHAPTERS: A VALUATION FOCUS As we discuss in Chapter 1, in an enterprise system such as that of the United States, the primary goal of fi nancial management is to help managers maximize their fi rms’ values, subject to constraints such as not polluting the environment, not engaging in unfair labor practices, not engaging in antitrust activities, and the like. Therefore, valuation underlies everything in Concise. In Chapter 1 we discuss the concept of valuation, explain how it depends on future cash fl ows and risk, and show why value maximization is good for society in general. The valuation theme runs throughout the text.

Values are not established in a vacuum—stock and bond values are deter- mined in the fi nancial markets, so an understanding of those markets is essential to anyone involved with fi nance. Therefore, Chapter 2 covers the major types of fi nancial markets, the returns that investors have historically earned, and the risks inherent in different types of securities. This information is important for anyone working in fi nance, and it is also important for anyone who has or hopes to own any fi nancial assets.

Asset values depend in a fundamental way on earnings and cash fl ows as reported in the accounting statements. Therefore, we review those statements in Chapter 3 and then, in Chapter 4, show how accounting data can be analyzed and used to measure how well a company has operated in the past and how it is likely to perform in the future.

Chapter 5 covers the Time Value of Money (TVM), perhaps the most funda- mental concept in fi nance. The basic valuation model, which ties together cash fl ows, risk, and interest rates, is based on TVM concepts, and these concepts are used throughout the remainder of the book. Therefore, students should be sure to allocate plenty of time to Chapter 5.

Chapter 6 deals with interest rates, a key determinant of asset values. We dis- cuss how interest rates are affected by risk, infl ation, liquidity, the supply of and demand for capital in the economy, and the actions of the Federal Reserve.

The discussion of interest rates leads directly to bonds in Chapter 7 and stocks in Chapters 8 and 9. We show how both stocks and bonds (and all other fi nancial assets) are valued using the basic TVM model.

Chapters 1 through 9 provide background information that is essential to both investors and corporate managers. These are “Finance” topics, not “Business” or “Corporate Finance” topics as those terms are commonly used. Thus, Chapters 1 through 9 discuss the concepts and models used to establish values, whereas Chapters 10 through 17 focus on specifi c actions managers can take to maximize their fi rms’ values.

As we noted above, most business students don’t plan to specialize in fi nance, so they might not think the “business fi nance” chapters are particularly relevant to

vPreface

them. This is not true, and in the later chapters we show that all really important business decisions involve all of the fi rm’s departments—marketing, accounting, production, and so on. Thus, while capital budgeting can be thought of as a fi nan- cial decision, marketing people provide inputs on likely unit sales and sales prices, manufacturing people provide inputs on costs, and so on. Moreover, capital bud- geting decisions infl uence the size of the fi rm, its products, and its profi ts, and those factors affect all the fi rm’s employees, from the CEO to the mail room staff.

STRUCTURAL CHANGES We made two important structural changes in this new edition: 1. We moved the material on fi nancial markets and institutions from Chapter 5 to

Chapter 2. Markets and institutions follow naturally from Chapter 1, and this material provides useful background information for the remainder of the book.

2. We moved the time value of money (TVM) chapter from Chapter 2 to Chapter 5. Under the previous structure, we covered TVM concepts, then covered the accounting and fi nancial markets chapters before applying TVM concepts to bond and stock valuation. We liked the idea of covering TVM early, but we con- cluded that it was pedagogically better to cover TVM concepts and then imme- diately focus on applications, as we do now.

These changes improve the fl ow of the text signifi cantly—there is a much smoother transition from chapter to chapter in the fi rst part of the book.

OTHER CHANGES We made many other changes, but the following are the most signifi cant: 1. Editing. We always edit each new edition to improve clarity, but we did more

in this edition than ever before. We put the entire text on digital fi les, which facilitated shifting things around to improve transitions and fl ow. Students will fi nd it easier to read the book than in the past.

2. Beginning-of-Chapter Vignettes and Within-Chapter Boxes. Many events have transpired in the fi nancial markets during the past three years. Credit markets have tightened almost to the point of collapse; the housing and auto markets are in terrible shape; a major investment bank (Bear Stearns) failed; the heads of a number of major corporations were fi red; and so on. We use these events as the subjects of many vignettes and boxes, and they illus- trate the points made in the chapters very well.

3. Learning Objectives. To help students see what we expect them to take away from the chapters, we added a set of learning objectives at the beginning of each chapter.

4. Excel. Spreadsheets, especially Excel, are becoming increasingly important in business, and students who are familiar with Excel have a signifi cant advan- tage in the job market and later on the job. We used Excel in two ways. First, we worked all the in-text examples, end-of-chapter problems, and test bank problems with both Excel and a calculator, using the calculator to make sure the problem is workable with a calculator and Excel to check for accuracy. Sec- ond, we used Excel to create many of the tables and graphs used in the text, we displayed them as Excel pictures, and we have made available the models we used. Students do not need to know how to use Excel to go through the book, but if they are somewhat familiar with it, they can see how many common

vi Preface

fi nancial problems can be set up and solved very effi ciently with Excel. Stu- dents who are not familiar with Excel should also be motivated to learn some- thing about it.

5. Tie-In between Self-Test Questions, End-of-Chapter Questions, and the Test Bank. Testing is obviously important, so we spent a lot of time improving the Test Bank. Every question and problem was reviewed for clar- ity, accuracy, and consistency with the text. Also, we set up self-test questions at the end of each major section within the text to enable students to take real- time tests on their own before moving on. Then, the end-of-chapter (EOC) questions and problems are similar to, but often go beyond, the self-test ques- tions, and the test bank questions and problems are similar to the EOC materi- als. If students read the text, do the self-test questions as they go along, and then work a sampling of the EOC questions and problems, they should do well on exams drawn from the test bank.

6. Accounting Statements and Free Cash Flow. Most students in the basic fi nance course are familiar with balance sheets and income statements, but many don’t really understand the statement of cash fl ows and its relationship to free cash fl ows. Reviewers told us that in the last edition we tried to do too many things—like present alternative ways to calculate free cash fl ow—and that we should delete some of these items and better explain what remained. We agreed, and this edition does a much better job in this regard.

7. Cash Flows and Risk in Capital Budgeting. In the last edition, the two chapters on capital budgeting (Chapters 11 and 12) were not tied together very well. In that edition, we used relatively simple and straightforward illustrative projects in Chapter 11 but switched to entirely different and much more com- plex projects in Chapter 12. For this edition, we rewrote Chapter 12, continu- ing with the Chapter 11 examples. We also re-ordered materials to present them in a more logical sequence. One reviewer stated that this chapter was the single biggest improvement in the 6th edition.

8. Financial Forecasting. As we were rewriting Chapter 16, GE’s chairman announced that he expected to report higher earnings shortly, but two weeks later he announced a signifi cant earnings decline, and that led to a sharp drop in GE’s stock price. We used this example to illustrate the importance of accu- rate forecasts and to liven up our discussion of strategic fi nancial planning. In addition, we used an improved Excel model to streamline our illustrative fore- cast and to make the forecasting process simpler and clearer to students.

We could continue to list changes in this edition, but the items we have just discussed provide instructors (particularly those familiar with the last edition) with a good idea of what revisions were made to this text, and it will also let students know how authors try to continually improve their texts.

ACKNOWLEDGMENTS The book refl ects the efforts of a great many people, both those who have worked on Concise and our related books in the past and those who worked specifi cally on this Sixth Edition. First, we would like to thank Dana Aberwald Clark, who worked closely with us at every stage of the revision—her assistance was absolutely invalu- able. Second, Susan Whitman provided great typing and logistical support.

Our colleagues Roy Crum, Jim Keys, Andy Naranjo, M. Nimalendran, Jay Ritter, Mike Ryngaert, Craig Tapley, and Carolyn Takeda Brown gave us many useful suggestions regarding the ancillaries and many parts of the book, including the integrated cases. We also benefi ted from the work of Mike Ehrhardt and Phillip

viiPreface

Daves of the University of Tennessee, and Roy Crum of the University of Florida, who worked with us on companion books. Also, Christopher Buzzard did an out- standing job helping us develop the Excel models, the web site, and the PowerPoint presentations.

Next, we would like to thank the following professors, who reviewed this edi- tion in detail and provided many useful comments and suggestions:

Rebecca Abraham—Nova Southeastern University Kavous Ardalan—Marist College Tom Arnold—University of Richmond Deborah Bauer—University of Oregon Gary Benesh—Florida State University Mark S. Bettner—Bucknell University Brian Boscaljon—Penn State University: Erie Elizabeth Booth—Michigan State University Rajesh Chakrabarti—Georgia Institute of Technology Brent Dalrymple—University of Central Florida Jim DeMello—Western Michigan University Anne M. Drougas—Dominican University Scott Ehrhorn—Liberty University David Feller—Brevard Community College Jennifer Foo—Stetson University Partha Gangopadhyay—St. Cloud State University Sharon H. Garrison—University of Arizona Robert P. Hoffman—College of St. Scholastica Benjamas Jirasakuldech—University of the Pacifi c Ashok Kapoor—Augsburg College Howard Keen—Temple University Christopher J. Lambert, J.D.—Fairmont State University Alice Lee—San Francisco State University Denise Letterman—Robert Morris University Yulong Ma—California State University—Long Beach Barry Marchman—Florida A&M Brian Maris—Northern Arizona University Matthew Morey—Pace University Tom C. Nelson—Leeds School of Business, Colorado University—Boulder Darshana Palkar—Minnesota State University, Mankato Narendar V. Rao—Northeastern Illinois University Charles R. Rayhorn—Northern Michigan University Oliver Schnusenberg—University of North Florida Dean S. Sommers—University of Delaware Michael Spivey—Clemson University Glenn L. Stevens—Franklin & Marshall College Lowell E. Stockstill—Wittenberg University Samantha Thapa—Western Kentucky University David O. Vang—University of St. Thomas Sheng Yang—Black Hills State University David Zalewski—Providence College Sijing Zong—California State University—Stanislaus

viii Preface

We would also like to thank the following professors, whose reviews and com- ments on our earlier books contributed to this edition:

Robert Adams Mike Adler Sharif Ahkam Syed Ahmad Ed Altman Bruce Anderson Ron Anderson Tom Anderson John Andrews Bob Angell Vince Apilado Harvey Arbalaez Henry Arnold Bob Aubey Gil Babcock Peter Bacon Kent Baker Robert Balik Tom Bankston Babu Baradwaj Les Barenbaum Charles Barngrover Sam Basu Greg Bauer Bill Beedles Brian Belt Moshe Ben-Horim Bill Beranek Tom Berry Will Bertin Scott Besley Dan Best Roger Bey Gilbert W. Bickum Dalton Bigbee John Bildersee Laurence E. Blose Russ Boisjoly Bob Boldin Keith Boles Michael Bond Geof Booth Waldo Born Steven Bouchard Rick Boulware

Kenneth Boudreaux

Helen Bowers Oswald Bowlin Don Boyd G. Michael Boyd Pat Boyer Joe Brandt Elizabeth

Brannigan Mary Broske David T. Brown Christopher Brown Kate Brown Larry Brown Bill Brueggeman Paul Bursik Alva Butcher Bill Campsey Bob Carlson Severin Carlson David Cary Steve Celec Mary Chaffi n Charles Chan Don Chance Antony Chang Susan Chaplinsky K. C. Chen Jay Choi S. K. Choudhary Lal Chugh Maclyn Clouse Bruce Collins Mitch Conover Margaret

Considine Phil Cooley Joe Copeland David Cordell Marsha Cornett M. P. Corrigan John Cotner Charles Cox David Crary

John Crockett, Jr. Bill Damon Morris Danielson Joel Dauten Steve Dawson Sankar De Fred Dellva Chad Denson James Desreumaux Bodie Dickerson Bernard Dill Gregg Dimkoff Les Dlabay Mark Dorfman Tom Downs Frank Draper Gene Drzycimski Dean Dudley David Durst Ed Dyl Fred J. Ebeid Daniel Ebels Richard Edelman Charles Edwards U. Elike John Ellis George Engler Suzanne Erickson Dave Ewert John Ezzell L. Franklin Fant Richard J. Fendler Michael Ferri Jim Filkins John Finnerty Robert Fiore Susan Fischer Peggy Fletcher Steven Flint Russ Fogler Jennifer Frazier Dan French Michael Garlington David Garraty Jim Garven

Adam Gehr, Jr. Jim Gentry Wafi ca Ghoul Erasmo Giambona Armand

Gilinsky, Jr. Philip Glasgo Rudyard Goode Raymond Gorman Walt Goulet Bernie Grablowsky Theoharry

Grammatikos Owen Gregory Ed Grossnickle John Groth Alan Grunewald Manak Gupta Darryl Gurley Sam Hadaway Don Hakala Gerald Hamsmith William Hardin John Harris Paul Hastings Bob Haugen Steve Hawke Stevenson Hawkey Del Hawley Eric M. Haye Robert Hehre Kath Henebry David Heskel George

Hettenhouse Hans Heymann Kendall Hill Roger Hill Tom Hindelang Linda Hittle Ralph Hocking J. Ronald

Hoffmeister Robert Hollinger Jim Horrigan

ixPreface

John Houston John Howe Keith Howe Steve Isberg Jim Jackson Keith Jakob Vahan Janjigian Narayanan

Jayaraman Zhenhn Jin Kose John Craig Johnson Keith Johnson Ramon Johnson Steve Johnson Ray Jones Frank Jordan Manuel Jose Sally Joyner Alfred Kahl Gus Kalogeras Rajiv Kalra Ravi Kamath John Kaminarides Michael Keenan Bill Kennedy Peppi M. Kenny Carol Kiefer Joe Kiernan Richard Kish Robert Kleiman Erich Knehans Don Knight Ladd Kochman Dorothy Koehl Jaroslaw

Komarynsky Duncan Kretovich Harold Krogh Charles Kroncke Don Kummer Robert A. Kunkel Reinhold Lamb Joan Lamm Larry Lang David Lange P. Lange Howard Lanser

Edward Lawrence Martin Lawrence Wayne Lee Jim LePage David E.

LeTourneau Jules Levine John Lewis Jason Lin Chuck Linke Bill Lloyd Susan Long Judy Maese Bob Magee Ileen Malitz Bob Malko Phil Malone Abbas

Mamoozadeh Terry Maness Chris Manning Surendra

Mansinghka Timothy Manuel Terry Martell David Martin D. J. Masson John Mathys Ralph May John McAlhany Andy McCollough Ambrose McCoy Thomas McCue Bill McDaniel John McDowell Charles McKinney Robyn McLaughlin James McNulty Jeanette Medewitz-

Diamond Jamshid Mehran Larry Merville Rick Meyer Jim Millar Ed Miller John Miller John Mitchell Carol Moerdyk

Bob Moore Scott Moore Barry Morris Gene Morris Dianne R.

Morrison Chris Muscarella David Nachman Tim Nantell Don Nast Edward Nelling Bill Nelson Bob Nelson William Nelson Bob Niendorf Bruce Niendorf Ben Nonnally, Jr. Tom O’Brien William O’Connell Dennis O’Connor John O’Donnell Jim Olsen Robert Olsen Dean Olson Jim Pappas Stephen Parrish Helen Pawlowski Barron Peake Michael Pescow Glenn Petry Jim Pettijohn Rich Pettit Dick Pettway Aaron Phillips Hugo Phillips H. R. Pickett John Pinkerton Gerald Pogue Eugene Poindexter R. Potter Franklin Potts R. Powell Dianna Preece Chris Prestopino John Primus Jerry Prock Howard Puckett Herbert Quigley

George Racette Bob Radcliffe David Rakowski Allen Rappaport Bill Rentz Ken Riener Charles Rini John Ritchie Bill Rives Pietra Rivoli Antonio

Rodriguez James Rosenfeld Stuart Rosenstein E. N. Roussakis Dexter Rowell Arlyn R. Rubash Marjorie Rubash Bob Ryan Jim Sachlis Abdul Sadik Travis Sapp Thomas Scampini Kevin Scanlon Frederick

Schadeler Patricia L. Schaeff David Schalow Mary Jane Scheuer David Schirm Robert Schwebach Carol Schweser John Settle Alan Severn James Sfi ridis Sol Shalit Frederic Shipley Dilip Shome Ron Shrieves Neil Sicherman J. B. Silvers Clay Singleton Joe Sinkey Stacy Sirmans Jaye Smith Patricia Smith Patricia Matisz

Smith

x Preface

Special thanks are due to Chris Barry, Texas Christian University, and Shirley Love, Idaho State University, who wrote many of the boxes relating to small- business issues that are on the Web; to Emery Trahan and Paul Bolster, North- eastern University, who developed and wrote the summaries and questions for NewsWire; to Dilip Shome, Virginia Polytechnic Institute, who helped greatly with the capital structure chapter; to Dave Brown and Mike Ryngaert, University of Florida, who helped us with the bankruptcy and merger material; to Roy Crum, Andy Naranjo, and Subu Venkataraman, who worked with us on the international materials; to Scott Below, East Carolina University, who developed the Web site information and references; to Laurie and Stan Eakins of East Caro- lina, who developed the materials on Excel for the Technology Supplement; and to Larry Wolken, Texas A&M University, who offered his hard work and advice for the development of the Lecture Presentation Software. Finally, the South-Western and LEAP Publishing staffs, especially Mike Guendelsberger, Malvine Litten, Jennifer Ziegler, Scott Fidler, Mike Reynolds, Mike Roche, Adele Scholtz, Suellen Ruttkay, and Alex Von Rosenberg, helped greatly with all phases of the text- book’s development and production.

ERRORS IN THE TEXTBOOK At this point, most authors make a statement like this: “We appreciate all the help we received from the people listed above, but any remaining errors are, of course, our own responsibility.” And generally there are more than enough remaining errors! Having experienced diffi culties with errors ourselves, both as students and instructors, we resolved to avoid this problem in Concise. As a result of our detec- tion procedures, we are convinced that few such errors remain, but primarily because we want to detect any errors that may have slipped by so that we can cor- rect them in subsequent printings, we decided to offer a reward of $10 per error to the fi rst person who reports it to us. For purpose of this reward, errors are defi ned as misspelled words, nonrounding numerical errors, incorrect statements, and any other error that inhibits comprehension. Typesetting problems such as irregular

Don Sorensen David Speairs Ken Stanley Kenneth Stanton Ed Stendardi Alan Stephens Don Stevens Jerry Stevens Glen Strasburg David Suk Katherine Sullivan Timothy Sullivan Philip Swensen Bruce Swenson Ernest Swift Paul Swink Eugene Swinnerton Gary Tallman

Dular Talukdar Dennis Tanner Russ Taussig John Teall Richard Teweles Ted Teweles Madeline Thimmes Francis D. Thomas Andrew Thompson John Thompson Arlene Thurman Dogan Tirtirogu Janet Todd Holland J. Toles William Tozer Emery Trahan George Trivoli George Tsetsekos

David Upton Howard Van

Auken Pretorious Van

den Dool Pieter Vandenberg Paul Vanderheiden JoAnn Vaughan Jim Verbrugge Patrick Vincent Steve Vinson Susan Visscher John Wachowicz Joe Walker Mike Walker Sam Weaver Marsha Weber Al Webster

Shelton Weeks Kuo-Chiang Wei Bill Welch Fred Weston Richard Whiston Norm Williams Tony Wingler Ed Wolfe Criss Woodruff Don Woods Yangru Wu Robert Wyatt Steve Wyatt Michael Yonan John Zietlow Dennis Zocco Kent Zumwalt

xiPreface

spacing and differences of opinion regarding grammatical or punctuation conven- tions do not qualify for this reward. Given the ever-changing nature of the World Wide Web, changes in web addresses also do not qualify as errors, although we would like to learn about them. Finally, any qualifying error that has follow- through effects is counted as two errors only. Please report any errors to Joel Hous- ton either through e-mail at [email protected] or by regular mail at the address below.

CONCLUSION Finance is, in a real sense, the cornerstone of the enterprise system—good fi nancial management is vitally important to the economic health of all fi rms, hence to the nation and the world. Because of its importance, fi nance should be widely and thoroughly understood, but this is easier said than done. The fi eld is complex, and it undergoes constant change due to shifts in economic conditions. All of this makes fi nance stimulating and exciting, but challenging and sometimes perplex- ing. We sincerely hope that this Sixth Edition of Concise will meet its own challenge by contributing to a better understanding of our fi nancial system.

EUGENE F. BRIGHAM JOEL F. HOUSTON 4723 N.W. 53rd Ave., Suite A Gainesville, Florida 32653

July 2008

xii

BRIEF C O N TEN T S

Preface iii

PART 1 Introduction to Financial Management 1 CHAPTER 1 An Overview of Financial Management 2

PART 2 Fundamental Concepts in Financial Management 25 CHAPTER 2 Financial Markets and Institutions 26 CHAPTER 3 Financial Statements, Cash Flow, and Taxes 54 CHAPTER 4 Analysis of Financial Statements 85 CHAPTER 5 Time Value of Money 123

PART 3 Financial Assets 161 CHAPTER 6 Interest Rates 162 CHAPTER 7 Bonds and Their Valuation 194 CHAPTER 8 Risk and Rates of Return 229 CHAPTER 9 Stocks and Their Valuation 269

PART 4 Investing in Long-Term Assets: Capital Budgeting 305 CHAPTER 10 The Cost of Capital 306 CHAPTER 11 The Basics of Capital Budgeting 335 CHAPTER 12 Cash Flow Estimation and Risk Analysis 364

PART 5 Capital Structure and Dividend Policy 399 CHAPTER 13 Capital Structure and Leverage 400 CHAPTER 14 Distributions to Shareholders: Dividends and Share Repurchases 440

PART 6 Working Capital Management, Forecasting, and Multinational Financial Management 471

CHAPTER 15 Working Capital Management 472 CHAPTER 16 Financial Planning and Forecasting 509 CHAPTER 17 Multinational Financial Management 534

Appendixes APPENDIX A Solutions to Self-Test Questions and Problems A-1 APPENDIX B Answers to Selected End-of-Chapter Problems A-24 APPENDIX C Selected Equations and Tables A-27

Index I-1

xiii

PREFACE iii

PART 1 Introduction to Financial Management 1

CHAPTER 1 An Overview of Financial Management 2 Striking the Right Balance 2

PUTTING THINGS IN PERSPECTIVE 3

1-1 What Is Finance 4 Finance Versus Economics and Accounting 4 Finance within an Organization 4 Corporate Finance, Capital Markets, and Investments 5

1-2 Jobs in Finance 6

1-3 Forms of Business Organization 6

1-4 Stock Prices and Shareholder Value 8

1-5 Intrinsic Values, Stock Prices, and Executive Compensation 10

1-6 Important Business Trends 14 Global Perspectives: Is Shareholder Wealth Maximization a Worldwide Goal? 14

1-7 Business Ethics 15 What Companies Are Doing 15 Consequences of Unethical Behavior 16 How Should Employees Deal with Unethical Behavior? 17 Protection for Whistle-Blowers 17

1-8 Conflicts Between Managers, Stockholders, and Bondholders 18 Managers versus Stockholders 18 Stockholders versus Bondholders 20

TYING IT ALL TOGETHER 21

PART 2 Fundamental Concepts in Financial Management 25

CHAPTER 2 Financial Markets and Institutions 26 Efficient Financial Markets Are Necessary for a Growing Economy 26

PUTTING THINGS IN PERSPECTIVE 27

2-1 The Capital Allocation Process 28

2-2 Financial Markets 30 Types of Markets 30 Recent Trends 31

2-3 Financial Institutions 34 Citigroup Built to Compete in a Changing Environment 37

2-4 The Stock Market 38 Global Perspectives: The NYSE and Nasdaq Go Global 38 Physical Location Stock Exchanges 39 Over-the-Counter (OTC) and the Nasdaq Stock Markets 39

2-5 The Market for Common Stock 40 Types of Stock Market Transactions 41

2-6 Stock Markets and Returns 43 Stock Market Reporting 43 Measuring the Market 45 Stock Market Returns 46

2-7 Stock Market Efficiency 46 A Closer Look at Behavioral Finance Theory 49 Conclusions about Market Efficiency 50

TYING IT ALL TOGETHER 51

INTEGRATED CASE Smyth Barry & Company 52

CHAPTER 3 Financial Statements, Cash Flow, and Taxes 54 The “Quality” of Financial Statements 54

PUTTING THINGS IN PERSPECTIVE 55

3-1 Financial Statements and Reports 55

3-2 The Balance Sheet 57 Allied’s Balance Sheet 58

3-3 The Income Statement 61

3-4 Statement of Cash Flows 63 Massaging the Cash Flow Statement 66

3-5 Statement of Stockholders’ Equity 67 Financial Analysis on the Internet 68

C O N TEN T S

xiv

3-6 Free Cash Flow 68 Free Cash Flow Is Important for Small Businesses 69

3-7 Income Taxes 70 Individual Taxes 70 Corporate Taxes 72

TYING IT ALL TOGETHER 76

INTEGRATED CASE D’Leon Inc., Part I 81 THOMSON ONE: BUSINESS SCHOOL EDITION Exploring Starbucks’ Financial Statements 84

CHAPTER 4 Analysis of Financial Statements 85 Can You Make Money Analyzing Stocks? 85

PUTTING THINGS IN PERSPECTIVE 86

4-1 Ratio Analysis 87

4-2 Liquidity Ratios 88 Current Ratio 88 Quick, or Acid Test, Ratio 89

4-3 Asset Management Ratios 89 Inventory Turnover Ratio 90 Days Sales Outstanding 90 Fixed Assets Turnover Ratio 91 Total Assets Turnover Ratio 92

4-4 Debt Management Ratios 92 Total Debt to Total Assets 94 Times-Interest-Earned Ratio 95

4-5 Profitability Ratios 96 Operating Margin 96 Profit Margin 96 Global Perspectives: Global Accounting Standards: Can One Size Fit All? 97 Return on Total Assets 97 Basic Earning Power (BEP) Ratio 98 Return on Common Equity 98

4-6 Market Value Ratios 99 Price/Earnings Ratio 99 Market/Book Ratio 99

4-7 Trend Analysis 100

4-8 The DuPont Equation 101

4-9 Ratios in Different Industries 103

4-10 Summary of Allied’s Ratios 104

4-11 Benchmarking 105 Looking for Warning Signs within the Financial Statements 106

4-12 Uses and Limitations of Ratios 106 Economic Value Added (EVA) versus Net Income 108

4-13 Potential Misuses of ROE 108

4-14 Looking Beyond the Numbers 109

TYING IT ALL TOGETHER 110

INTEGRATED CASE D’Leon Inc., Part II 118 THOMSON ONE: BUSINESS SCHOOL EDITION Conducting a Financial Ratio Analysis on Ford Motor Company 122

CHAPTER 5 Time Value of Money 123 Will You Be Able to Retire? 123

PUTTING THINGS IN PERSPECTIVE 124

5-1 Time Lines 124

5-2 Future Values 125 Step-by-Step Approach 126 Simple versus Compound Interest 126 Formula Approach 127 Financial Calculators 127 Spreadsheets 128 Graphic View of the Compounding Process 130

5-3 Present Values 131 Graphic View of the Discounting Process 132

5-4 Finding the Interest Rate, I 133

5-5 Finding the Number of Years, N 134

5-6 Annuities 134

5-7 Future Value of an Ordinary Annuity 135

5-8 Future Value of an Annuity Due 137

5-9 Present Value of an Ordinary Annuity 138

5-10 Finding Annuity Payments, Periods, and Interest Rates 139 Finding Annuity Payments, PMT 139 Finding the Number of Periods, N 139 Finding the Interest Rate, I 140

5-11 Perpetuities 141

5-12 Uneven Cash Flows 143

5-13 Future Value of an Uneven Cash Flow Stream 144

5-14 Solving for I with Uneven Cash Flows 145

5-15 Semiannual and Other Compounding Periods 146

5-16 Comparing Interest Rates 148

5-17 Fractional Time Periods 150

5-18 Amortized Loans 151

TYING IT ALL TOGETHER 152

Contents

INTEGRATED CASE First National Bank 159 WEB APPENDIX 5A Continuous Compounding and Discounting

WEB APPENDIX 5B Growing Annuities

PART 3 Financial Assets 161

CHAPTER 6 Interest Rates 162 Low Interest Rates Encourage Investment and Stimulate Consumer Spending 162

PUTTING THINGS IN PERSPECTIVE 163

6-1 The Cost of Money 163

6-2 Interest Rate Levels 165

6-3 The Determinants of Market Interest Rates 168 The Real Risk-Free Rate of Interest, r* 169 The Nominal, or Quoted, Risk-Free Rate of Interest, rRF ! r* " IP 170 Inflation Premium (IP) 170 An Almost Riskless Treasury Bond 171 Default Risk Premium (DRP) 172 Liquidity Premium (LP) 172 A 20% Liquidity Premium on a High-Grade Bond 173 Interest Rate Risk and the Maturity Risk Premium (MRP) 173

6-4 The Term Structure of Interest Rates 175

6-5 What Determines the Shape of the Yield Curve? 176 The Links between Expected Inflation and Interest Rates: A Closer Look 178

6-6 Using the Yield Curve to Estimate Future Interest Rates 180

6-7 Macroeconomic Factors That Influence Interest Rate Levels 183 Federal Reserve Policy 183 Federal Budget Deficits or Surpluses 184 International Factors 184 Business Activity 185

6-8 Interest Rates and Business Decisions 185

TYING IT ALL TOGETHER 187

INTEGRATED CASE Morton Handley & Company 192

CHAPTER 7 Bonds and Their Valuation 194 Sizing Up Risk in the Bond Market 194

PUTTING THINGS IN PERSPECTIVE 195

7-1 Who Issues Bonds? 195

7-2 Key Characteristics of Bonds 196 Par Value 197 Coupon Interest Rate 197 Maturity Date 197 Call Provisions 198 Sinking Funds 199 Other Features 199

7-3 Bond Valuation 200

7-4 Bond Yields 203 Yield to Maturity 203 Yield to Call 204

7-5 Changes in Bond Values Over Time 206

7-6 Bonds with Semiannual Coupons 209

7-7 Assessing a Bond’s Riskiness 210 Interest Rate Risk 210 Reinvestment Rate Risk 213 Comparing Interest Rate and Reinvestment Rate Risk 213

7-8 Default Risk 214 Various Types of Corporate Bonds 215 Bond Ratings 215 Bankruptcy and Reorganization 219

7-9 Bond Markets 220

TYING IT ALL TOGETHER 222

INTEGRATED CASE Western Money Management Inc. 228 WEB APPENDIX 7A Zero Coupon Bonds

WEB APPENDIX 7B Bankruptcy and Reorganization

CHAPTER 8 Risk and Rates of Return 229 A Tale of Three Markets—or Is It Four? 229

PUTTING THINGS IN PERSPECTIVE 230

8-1 Stock Prices Over the Last 20 Years 231

8-2 Stand-Alone Risk 232 Statistical Measures of Stand-Alone Risk 233 Measuring Stand-Alone Risk: The Standard Deviation 236 Using Historical Data to Measure Risk 237

Contents

xvi

Measuring Stand-Alone Risk: The Coefficient of Variation 238 Risk Aversion and Required Returns 238 The Trade-Off between Risk and Return 239

8-3 Risk in a Portfolio Context: The CAPM 240 Expected Portfolio Returns, r̂p 241 Portfolio Risk 242 Risk in a Portfolio Context: The Beta Coefficient 245 Global Perspectives: The Benefits of Diversifying Overseas 250

8-4 The Relationship between Risk and Rates of Return 251 Estimating the Market Risk Premium 252 The Impact of Expected Inflation 253 Changes in Risk Aversion 255 Changes in a Stock’s Beta Coefficient 256

8-5 Some Concerns about Beta and the CAPM 257

8-6 Some Concluding Thoughts: Implications for Corporate Managers and Investors 258

TYING IT ALL TOGETHER 259

INTEGRATED CASE Merrill Finch Inc. 266 THOMSON ONE: BUSINESS SCHOOL EDITION Using Past Information to Estimate Required Returns 268

WEB APPENDIX 8A Calculating Beta Coefficients

CHAPTER 9 Stocks and Their Valuation 269 Searching for the Right Stock 269

PUTTING THINGS IN PERSPECTIVE 270

9-1 Legal Rights and Privileges of Common Stockholders 270 Control of the Firm 271 The Preemptive Right 272

9-2 Types of Common Stock 272

9-3 Stock Price versus Intrinsic Value 273 Why Do Investors and Companies Care About Intrinsic Value? 274

9-4 The Discounted Dividend Model 275 Expected Dividends as the Basis for Stock Values 277

9-5 Constant Growth Stocks 278 Illustration of a Constant Growth Stock 279

Dividends versus Growth 280 Which Is Better: Current Dividends or Growth? 282 Required Conditions for the Constant Growth Model 282

9-6 Valuing Nonconstant Growth Stocks 283

9-7 Valuing the Entire Corporation 286 Evaluating Stocks That Don’t Pay Dividends 287 The Corporate Valuation Model 288 Other Approaches to Valuing Common Stocks 290 Comparing the Corporate Valuation and Discounted Dividend Models 290

9-8 Preferred Stock 291

TYING IT ALL TOGETHER 292

INTEGRATED CASE Mutual of Chicago Insurance Company 298 THOMSON ONE: BUSINESS SCHOOL EDITION Estimating ExxonMobil’s Intrinsic Stock Value 299

APPENDIX 9A Stock Market Equilibrium 301

PART 4 Investing in Long-Term Assets: Capital Budgeting 305

CHAPTER 10 The Cost of Capital 306 Creating Value at GE 306

PUTTING THINGS IN PERSPECTIVE 307

10-1 An Overview of the Weighted Average Cost of Capital (WACC) 307

10-2 Basic Definitions 309

10-3 Cost of Debt, rd(1 – T) 310

10-4 Cost of Preferred Stock, rp 312

10-5 The Cost of Retained Earnings, rs 312 The CAPM Approach 314 Bond-Yield-plus-Risk-Premium Approach 315 Dividend-Yield-plus-Growth-Rate, or Discounted Cash Flow (DCF), Approach 315 Averaging the Alternative Estimates 317

10-6 Cost of New Common Stock, re 318 Add Flotation Costs to a Project’s Cost 318 Increase the Cost of Capital 318

Contents

xvii

How Much Does It Cost to Raise External Capital? 319 When Must External Equity Be Used? 320

10-7 Composite, or Weighted Average, Cost of Capital, WACC 321

10-8 Factors That Affect the WACC 321 Factors the Firm Cannot Control 321 Factors the Firm Can Control 322 Global Perspectives: Global Variations in the Cost of Capital 322

10-9 Adjusting the Cost of Capital for Risk 323

10-10 Some Other Problems with Cost of Capital Estimates 325

TYING IT ALL TOGETHER 326

INTEGRATED CASE Coleman Technologies Inc. 333 THOMSON ONE: BUSINESS SCHOOL EDITION Calculating 3M’s Cost of Capital 334

WEB APPENDIX 10A The Cost of New Common Stock and WACC

CHAPTER 11 The Basics of Capital Budgeting 335 Competition in the Aircraft Industry: Airbus vs. Boeing 335

PUTTING THINGS IN PERSPECTIVE 336

11-1 An Overview of Capital Budgeting 336

11-2 Net Present Value (NPV) 338

11-3 Internal Rate of Return (IRR) 341 Why NPV Is Better Than IRR 343

11-4 Multiple Internal Rates of Return 344

11-5 Reinvestment Rate Assumptions 346

11-6 Modified Internal Rate of Return (MIRR) 347

11-7 NPV Profiles 349

11-8 Payback Period 353

11-9 Conclusions on Capital Budgeting Methods 355

11-10 Decision Criteria Used in Practice 356

TYING IT ALL TOGETHER 357

INTEGRATED CASE Allied Components Company 362

CHAPTER 12 Cash Flow Estimation and Risk Analysis 364 Home Depot Keeps Growing 364

PUTTING THINGS IN PERSPECTIVE 365

12-1 Conceptual Issues in Cash Flow Estimation 365 Cash Flow versus Accounting Income 365 Timing of Cash Flows 366 Incremental Cash Flows 366 Replacement Projects 366 Sunk Costs 366 Opportunity Costs Associated with Assets the Firm Owns 367 Externalities 367

12-2 Analysis of an Expansion Project 369 Effect of Different Depreciation Rates 371 Cannibalization 371 Opportunity Costs 371 Sunk Costs 371 Other Changes to the Inputs 372

12-3 Replacement Analysis 372

12-4 Risk Analysis in Capital Budgeting 374

12-5 Measuring Stand-Alone Risk 376 Sensitivity Analysis 376 Scenario Analysis 378 Monte Carlo Simulation 379 Global Perspectives: Capital Budgeting Practices in the Asian/Pacific Region 380

12-6 Within-Firm and Beta Risk 381

12-7 Real Options 382 Types of Real Options 382 Abandonment Options 383

12-8 The Optimal Capital Budget 385

12-9 The Post-Audit 386

TYING IT ALL TOGETHER 387

INTEGRATED CASE Allied Food Products 394 APPENDIX 12A Tax Depreciation 397

WEB APPENDIX 12B Refunding Operations

WEB APPENDIX 12C Using the CAPM to Estimate the Risk-Adjusted Cost of Capital

WEB APPENDIX 12D Techniques for Measuring Beta Risk

WEB APPENDIX 12E Comparing Mutually Exclusive Projects with Unequal Lives

WEB APPENDIX 12F Real Options: Investment Timing, Growth, and Flexibility

Contents

xviii

PART 5 Capital Structure and Dividend Policy 399

CHAPTER 13 Capital Structure and Leverage 400 Debt: Rocket Booster or Anchor? 400

PUTTING THINGS IN PERSPECTIVE 401

13-1 The Target Capital Structure 401

13-2 Business and Financial Risk 403 Business Risk 403 Operating Leverage 405 Financial Risk 408

13-3 Determining the Optimal Capital Structure 413 WACC and Capital Structure Changes 414 The Hamada Equation 415 The Optimal Capital Structure 416

13-4 Capital Structure Theory 419 Yogi Berra on the M&M Proposition 420 The Effect of Taxes 420 The Effect of Potential Bankruptcy 421 Trade-Off Theory 422 Signaling Theory 423 Using Debt Financing to Constrain Managers 424

13-5 Checklist for Capital Structure Decisions 425

13-6 Variations in Capital Structures 427 Global Perspectives: Taking a Look at Global Capital Structures 428

TYING IT ALL TOGETHER 429

INTEGRATED CASE Campus Deli Inc. 435 THOMSON ONE: BUSINESS SCHOOL EDITION Exploring the Capital Structures for Four of the World’s Leading Auto Companies 438

WEB APPENDIX 13A Degree of Leverage

CHAPTER 14 Distributions to Shareholders: Dividends and Share Repurchases 440 Microsoft Shifts Gears and Begins to Unload Part of Its Vast Cash Hoard 440

PUTTING THINGS IN PERSPECTIVE 441

14-1 Dividends versus Capital Gains: What Do Investors Prefer? 441

Dividend Irrelevance Theory 442 Reasons Some Investors Prefer Dividends 442 Reasons Some Investors Prefer Capital Gains 443

14-2 Other Dividend Policy Issues 444 Information Content, or Signaling, Hypothesis 444 Clientele Effect 445

14-3 Establishing the Dividend Policy in Practice 446 Setting the Target Payout Ratio: The Residual Dividend Model 446 Global Perspectives: Dividend Yields Around the World 449 Earnings, Cash Flows, and Dividends 451 Payment Procedures 453

14-4 Dividend Reinvestment Plans 454

14-5 Summary of Factors Influencing Dividend Policy 455 Constraints 456 Investment Opportunities 456 Alternative Sources of Capital 456 Effects of Dividend Policy on rs 457

14-6 Stock Dividends and Stock Splits 457 Stock Splits 457 Stock Dividends 458 Effect on Stock Prices 458

14-7 Stock Repurchases 459 The Effects of Stock Repurchases 460 Advantages of Repurchases 461 Disadvantages of Repurchases 462 Conclusions on Stock Repurchases 462

TYING IT ALL TOGETHER 463

INTEGRATED CASE Southeastern Steel Company 468 THOMSON ONE: BUSINESS SCHOOL EDITION Microsoft’s Dividend Policy 469

WEB APPENDIX 14A An Example: The Residual Dividend Model

PART 6 Working Capital Management, Forecasting, and Multinational Financial Management 471

Contents

xix

CHAPTER 15 Working Capital Management 472 Best Buy Manages Its Working Capital Well 472

PUTTING THINGS IN PERSPECTIVE 473

15-1 Background on Working Capital 473

15-2 Current Asset Investment Policies 474

15-3 Current Asset Financing Policies 475 Maturity Matching, or “Self-Liquidating,” Approach 476 Aggressive Approach 476 Conservative Approach 478 Choosing between the Approaches 478

15-4 The Cash Conversion Cycle 479 Calculating the Targeted CCC 479 Calculating the CCC from Financial Statements 480 Some Firms Operate with Negative Working Capital! 481

15-5 The Cash Budget 482

15-6 Cash and Marketable Securities 485 Currency 486 Demand Deposits 486 Marketable Securities 487

15-7 Inventories 488 Supply Chain Management 489

15-8 Accounts Receivable 490 Credit Policy 490 Setting and Implementing the Credit Policy 491 Monitoring Accounts Receivable 492

15-9 Accounts Payable (Trade Credit) 493

15-10 Bank Loans 495 Promissory Note 495 Line of Credit 496 Revolving Credit Agreement 497 Costs of Bank Loans 497

15-11 Commercial Paper 499

15-12 Accruals (Accrued Liabilities) 500

15-13 Use of Security in Short-Term Financing 500

TYING IT ALL TOGETHER 501

INTEGRATED CASE Ski Equipment Inc. 506 WEB APPENDIX 15A Inventory Management

WEB APPENDIX 15B Short-Term Loans and Bank Financing

CHAPTER 16 Financial Planning and Forecasting 509 The Miss That Hit Like a Bombshell 509

PUTTING THINGS IN PERSPECTIVE 510

16-1 Strategic Planning 511

16-2 The Sales Forecast 512

16-3 The AFN Equation 514 Excess Capacity Adjustments 517

16-4 Forecasted Financial Statements 518 Part I. Inputs 518 Part II. Forecasted Income Statement 521 Part III. Forecasted Balance Sheet 521 Part IV. Ratios and EPS 521 Using the Forecast to Improve Operations 522

16-5 Using Regression to Improve Forecasts 523

16-6 Analyzing the Effects of Changing Ratios 524 Modifying Accounts Receivable 524 Modifying Inventories 524 Other “Special Studies” 525

TYING IT ALL TOGETHER 525

INTEGRATED CASE New World Chemicals Inc. 531 THOMSON ONE: BUSINESS SCHOOL EDITION Forecasting the Future Performance of Abercrombie & Fitch 533

WEB APPENDIX 16A Forecasting Financial Requirements When Financial Ratios Change

CHAPTER 17 Multinational Financial Management 534 U.S. Firms Look Overseas to Enhance Shareholder Value 534

PUTTING THINGS IN PERSPECTIVE 535

17-1 Multinational or Global Corporations 535

17-2 Multinational versus Domestic Financial Management 538

17-3 The International Monetary System 540 International Monetary Terminology 540 Current Monetary Arrangements 541

17-4 Foreign Exchange Rate Quotations 542 Cross Rates 542

Contents

Interbank Foreign Currency Quotations 543

17-5 Trading in Foreign Exchange 544 Spot Rates and Forward Rates 545

17-6 Interest Rate Parity 546

17-7 Purchasing Power Parity 547 Hungry for a Big Mac? Go to China! 548

17-8 Inflation, Interest Rates, and Exchange Rates 550

17-9 International Money and Capital Markets 551 International Credit Markets 551 Stock Market Indices Around the World 552 International Stock Markets 553

17-10 Investing Overseas 554 Global Perspectives: Measuring Country Risk 555

Global Perspectives: Investing in International Stocks 555

17-11 International Capital Budgeting 556

17-12 International Capital Structures 558

TYING IT ALL TOGETHER 560

INTEGRATED CASE Citrus Products Inc. 563

APPENDIXES Appendix A Solutions to Self-Test Questions

and Problems A-1 Appendix B Answers to Selected End-of-

Chapter Problems A-24 Appendix C Selected Equations and

Tables A-27

INDEX I-1

Contents

INTRODUCTION TO FINANCIAL MANAGEMENT

1 An Overview of Financial Management

PART 1

C H

A P

T E

S t r i k i n g t h e R i g h t B a l a n ce

An Overview of Financial Management

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1 CHAPTER

In 1776, Adam Smith described how an “invisible hand” guides companies as they strive for profits; and that hand leads them to decisions that benefit society. Smith’s insights led him to conclude that profit maximization is the right goal for a business and that the free enterprise system is best for soci- ety. But the world has changed since 1776. Firms today are much larger, they operate globally, they have thousands of employees, and they are owned by millions of stockholders. This makes us wonder if the “invisible hand” still provides reliable guidance. Should companies still try to maximize profits; or should they take a broader view and take more bal- anced actions designed to benefit customers, employees, suppliers, and society as a whole?

Most academics today subscribe to the fol- lowing modified version of Adam Smith’s theory:

• A firm’s principal goal should be to maximize the wealth of its stockholders, which means maximizing the value of its stock.

• Free enterprise is still the best economic system for the country as a whole.

• However, some constraints are needed—firms should not be allowed to pollute the air and water, engage in unfair employment practices, or create monopolies that exploit consumers.

Profits depend on sales; and sales require that firms develop desirable products and services, produce them efficiently, and sell them at com- petitive prices, all of which benefit society. So the view today is that management should try to maximize stock prices, but their actions should be subject to government-imposed constraints.

Still, some argue that the constrained maxi- mization theory is inadequate. For example, GE Chief Executive Officer (CEO) Jeffrey Immelt believes that just obeying the law is not enough. GE is the world’s most valuable com- pany, and it has an excellent reputation.1

Immelt argues that value and reputation go

1 Marc Gunther, “Money and Morals at GE,” Fortune, November 15, 2004, pp. 176–182.

This chapter will give you an idea of what fi nancial management is all about. We begin the chapter by describing how fi nance is related to the overall business and by discussing the diff erent forms of business organization. For corporations, man- agement’s goal should be to maximize shareholder wealth, which means maximiz- ing the value of the stock. When we say “maximizing the value of the stock,” we mean the “true, long-run value,” which may be diff erent from the current stock price. Good managers understand the importance of ethics, and they recognize that maximizing long-run value is consistent with being socially responsible. We con- clude the chapter by discussing how fi rms must provide the right incentives if they are to get managers to focus on long-run value maximization. When you fi nish this chapter, you should be able to: • Explain the role of fi nance and the diff erent types of jobs in fi nance. • Identify the advantages and disadvantages of diff erent forms of business

organization. • Explain the links between stock price, intrinsic value, and executive compensation. • Discuss the importance of business ethics and the consequences of unethical

behavior. • Identify the potential confl icts that arise within the fi rm between stockholders

and managers and between stockholders and bondholders and discuss the tech- niques that fi rms can use to mitigate these potential confl icts.

hand in hand and that having a good reputation with customers, suppliers, employees, and regulators is essen- tial if value is to be maximized. According to Immelt, “The reason people come to work for GE is that they want to be part of something bigger than themselves. They want to work hard, win promotions, and be well compensated, but they also want to work for a company that makes a difference, a company that’s doing great things in the world. . . . It’s up to GE to be a good citizen. Not only is that a nice thing to do, it’s good for business and thus the price of our stock.”

GE is by no means alone. An increasing number of com- panies see their mission as more than just making money for their shareholders. Google Inc.’s well-known corporate motto is “Don’t Be Evil.” Taking things a step further, the company recently announced that it was setting aside another $30 million to be used for philanthropic ventures worldwide. The company’s in-house foundation now has

assets in excess of $2 billion. Days later Microsoft Corpora- tion’s chairperson, Bill Gates, gave a speech to the World Economic Forum in which he made the case for a “creative capitalism.” Gates stated that, “Such a system would have a twin mission: making profits and also improving lives for those who don’t fully benefit from market forces.”

Gates has certainly been true to his word. In 2000, he and his wife established the Bill & Melinda Gates Founda- tion. Today the fund has assets totaling $37.6 billion. It received a notable boost in 2006 when famed investor War- ren Buffett announced that he would donate a huge share of his fortune to the Foundation. To date, Buffett has con- tributed more than $3 billion; and over time, he is sched- uled to contribute additional shares of stock that are now worth in excess of $40 million. These efforts show that while there is more to life than money, it often takes money to do good things.

PU T TING THINGS IN PER SPECTIVE

Chapter 1 An Overview of Financial Management 3

Sources: Patricia Sellers, “Melinda Gates Goes Public,” CNNMoney.com, January 7, 2008; Kevin J. Delaney, “Google: From ‘Don’t Be Evil’ to How to Do Good,” The Wall Street Journal, January 18, 2008, p. B1; and Robert A. Guth, “Bill Gates Issues Call for Kinder Capitalism,” The Wall Street Journal, January 24, 2008, p. A1.

4 Part 1 Introduction to Financial Management

1-1 WHAT IS FINANCE? It’s hard to defi ne fi nance—the term has many facets, which makes it diffi cult to provide a clear and concise defi nition. The discussion in this section will give you an idea of what fi nance people do and what you might do if you enter the fi nance fi eld after you graduate.

1-1a Finance versus Economics and Accounting Finance as we know it today grew out of economics and accounting. Economists developed the notion that an asset’s value is based on the future cash fl ows the asset will provide, and accountants provided information regarding the likely size of those cash fl ows. Finance then grew out of and lies between economics and accounting, so people who work in fi nance need knowledge of those two fi elds. Also, as discussed next, in the modern corporation, the accounting department falls under the control of the chief fi nancial offi cer (CFO).

1-1b Finance within an Organization Most businesses and not-for-profi t organizations have an organization chart simi- lar to the one shown in Figure 1-1.

The board of directors is the top governing body, and the chairperson of the board is generally the highest-ranking individual. The CEO comes next, but note that the chairperson of the board often serves as the CEO as well. Below the CEO comes the chief operating offi cer (COO), who is often also designated as a fi rm’s president. The COO directs the fi rm’s operations, which include mar- keting, manufacturing, sales, and other operating departments. The CFO, who is generally a senior vice president and the third ranking offi cer, is in charge of

Chief Operating Officer (COO)

Marketing, Production, Human Resources, and Other Operating

Departments

Accounting, Treasury, Credit, Legal, Capital Budgeting,

and Investor Relations

Board of Directors

Chief Financial Officer (CFO)

Chief Executive Officer (CEO)

Finance within an OrganizationFIGURE 1-1

5Chapter 1 An Overview of Financial Management

accounting, fi nancing, credit policy, decisions regarding asset acquisitions, and investor relations, which involves communications with stockholders and the press.

If the firm is publicly owned, the CEO and the CFO must both certify to the Securities and Exchange Commission (SEC) that reports released to stock- holders, and especially the annual report, are accurate. If inaccuracies later emerge, the CEO and the CFO could be fined or even jailed. This requirement was instituted in 2002 as a part of the Sarbanes-Oxley Act. The Act was passed by Congress in the wake of a series of corporate scandals involving now- defunct companies such as Enron and WorldCom, where investors, workers, and suppliers lost billions of dollars due to false information released by those companies.

1-1c Corporate Finance, Capital Markets, and Investments

Finance as taught in universities is generally divided into three areas: (1) fi nancial management, (2) capital markets, and (3) investments.

Financial management, also called corporate fi nance, focuses on decisions re- lating to how much and what types of assets to acquire, how to raise the capital needed to buy assets, and how to run the fi rm so as to maximize its value. The same principles apply to both for-profi t and not-for-profi t organizations; and as the title suggests, much of this book is concerned with fi nancial management.

Capital markets relate to the markets where interest rates, along with stock and bond prices, are determined. Also studied here are the fi nancial institutions that supply capital to businesses. Banks, investment banks, stockbrokers, mutual funds, insurance companies, and the like bring together “savers” who have money to invest and businesses, individuals, and other entities that need capital for various purposes. Governmental organizations such as the Federal Reserve System, which regulates banks and controls the supply of money, and the SEC, which regulates the trading of stocks and bonds in public markets, are also stud- ied as part of capital markets.

Investments relate to decisions concerning stocks and bonds and include a number of activities: (1) Security analysis deals with finding the proper values of individual securities (i.e., stocks and bonds). (2) Portfolio theory deals with the best way to structure portfolios, or “baskets,” of stocks and bonds. Ratio- nal investors want to hold diversified portfolios in order to limit risks, so choosing a properly balanced portfolio is an important issue for any investor. (3) Market analysis deals with the issue of whether stock and bond markets at any given time are “too high,” “too low,” or “about right.” Behavioral finance, where investor psychology is examined in an effort to determine if stock prices have been bid up to unreasonable heights in a speculative bubble or driven down to unreasonable lows in a fit of irrational pessimism, is a part of market analysis.

Although we separate these three areas, they are closely interconnected. Banking is studied under capital markets, but a bank lending offi cer evaluating a business’ loan request must understand corporate fi nance to make a sound de- cision. Similarly, a corporate treasurer negotiating with a banker must under- stand banking if the treasurer is to borrow on “reasonable” terms. Moreover, a security analyst trying to determine a stock’s true value must understand corpo- rate fi nance and capital markets to do his or her job. In addition, fi nancial deci- sions of all types depend on the level of interest rates; so all people in corporate fi nance, investments, and banking must know something about interest rates and the way they are determined. Because of these interdependencies, we cover all three areas in this book.

Sarbanes-Oxley Act A law passed by Congress that requires the CEO and CFO to certify that their firm’s financial statements are accurate.

6 Part 1 Introduction to Financial Management

1-2 JOBS IN FINANCE Next to health care, jobs in fi nance have been growing faster than any other area. Finance prepares students for jobs in banking, investments, insurance, corporations, and the government. Accounting students need to know fi nance, marketing, man- agement, and human resources; they also need to understand fi nance, for it affects decisions in all those areas. For example, marketing people propose advertising pro- grams, but those programs are examined by fi nance people to judge the effects of the advertising on the fi rm’s profi tability. So to be effective in marketing, one needs to have a basic knowledge of fi nance. The same holds for management—indeed, most important management decisions are evaluated in terms of their effects on the fi rm’s value. This is called value-based management, and it is the “in” thing today.

It is also worth noting that fi nance is important to individuals regardless of their jobs. Some years ago most businesses provided pensions to their employees, so managing one’s personal investments was not critically important. That’s no longer true. Most fi rms today provide what’s called “defi ned contribution” pen- sion plans, where each year the company puts a specifi ed amount of money into an account that belongs to the employee. The employee must decide how those funds are to be invested—how much should be divided among stocks, bonds, or money funds and how risky the stocks and bonds should be. These decisions have a major effect on people’s lives, and the concepts covered in this book can improve decision-making skills.

1-3 FORMS OF BUSINESS ORGANIZATION The basics of fi nancial management are the same for all businesses, large or small, regardless of how they are organized. Still, a fi rm’s legal structure affects its opera- tions and thus should be recognized. There are four main forms of business organizations: (1) sole proprietorships, (2) partnerships, (3) corporations, and (4) limited liability companies (LLCs) and limited liability partnerships (LLPs). In terms of numbers, most businesses are sole proprietorships. However, based on the dollar value of sales, about 80% of all business is done by corporations. Because corporations conduct the most business and because most successful businesses eventually convert to corporations, we concentrate on them in this book. Still, it is important to understand the legal differences between fi rms.

A proprietorship is an unincorporated business owned by one individual. Going into business as a sole proprietor is easy—a person begins business operations. Pro- prietorships have three important advantages: (1) They are easily and inexpensively formed, (2) they are subject to few government regulations, and (3) they are subject to lower income taxes than are corporations. However, proprietorships also have three important limitations: (1) Proprietors have unlimited personal liability for the busi- ness’s debts, so they can lose more than the amount of money they invested in the

To find information about different finance careers, go to www.careers-in- finance.com. This web site provides information about different finance areas and recommends different books about jobs in finance.

Proprietorship An unincorporated business owned by one individual.

What is the relationship between economics, fi nance, and accounting?

Who is the CFO, where does this individual fi t into the corporate hierarchy, and what are some of his or her responsibilities?

Does it make sense for not-for-profi t organizations such as hospitals and universities to have CFOs?

What three areas of fi nance does this book cover? Are these areas indepen- dent of one another, or are they interrelated in the sense that someone work- ing in one area should know something about each of the other areas?

SEL F TEST

www.careers-in-finance.com

7Chapter 1 An Overview of Financial Management

company. You might invest $10,000 to start a business but be sued for $1 million if, during company time, one of your employees runs over someone with a car. (2) The life of the business is limited to the life of the individual who created it; and to bring in new equity, investors require a change in the structure of the business. (3) Because of the fi rst two points, proprietorships have diffi culty obtaining large sums of capital; hence, proprietorships are used primarily for small businesses. However, businesses are frequently started as proprietorships and then converted to corporations when their growth results in the disadvantages outweighing their advantages.

A partnership is a legal arrangement between two or more people who decide to do business together. Partnerships are similar to proprietorships in that they can be established relatively easily and inexpensively. Moreover, the fi rm’s income is allocated on a pro rata basis to the partners and is taxed on an individual basis. This allows the fi rm to avoid the corporate income tax. However, all of the part- ners are generally subject to unlimited personal liability, which means that if a partnership goes bankrupt and any partner is unable to meet his or her pro rata share of the fi rm’s liabilities, the remaining partners will be responsible for making good on the unsatisfi ed claims. Thus, the actions of a Texas partner can bring ruin to a millionaire New York partner who had nothing to do with the actions that led to the downfall of the company. Unlimited liability makes it diffi cult for partner- ships to raise large amounts of capital.2

A corporation is a legal entity created by a state, and it is separate and distinct from its owners and managers. It is this separation that limits stockholders’ losses to the amount they invested in the fi rm—the corporation can lose all of its money, but its owners can lose only the funds that they invested in the company. Corporations also have unlimited lives, and it is easier to transfer shares of stock in a corporation than one’s interest in an unincorporated business. These factors make it much easier for corporations to raise the capital necessary to operate large businesses. Thus, com- panies such as Hewlett-Packard and Microsoft generally begin as proprietorships or partnerships, but at some point they fi nd it advantageous to become a corporation.

A major drawback to corporations is taxes. Most corporations’ earnings are subject to double taxation—the corporation’s earnings are taxed; and then when its after-tax earnings are paid out as dividends, those earnings are taxed again as personal income to the stockholders. However, as an aid to small businesses, Con- gress created S corporations, which are taxed as if they were partnerships; thus, they are exempt from the corporate income tax. To qualify for S corporation status, a fi rm can have no more than 75 stockholders, which limits their use to relatively small, privately owned fi rms. Larger corporations are known as C corporations. The vast majority of small corporations elect S status and retain that status until they decide to sell stock to the public, at which time they become C corporations.

A limited liability company (LLC) is a relatively new type of organization that is a hybrid between a partnership and a corporation. A limited liability partnership (LLP) is similar to an LLC; but LLPs are used for professional fi rms in the fi elds of accounting, law, and architecture, while LLCs are used by other businesses. Both LLCs and LLPs have limited liability like corporations but are taxed like partner- ships. Further, unlike limited partnerships, where the general partner has full con- trol of the business, the investors in an LLC or LLP have votes in proportion to their ownership interest. LLCs and LLPs have been gaining in popularity in recent years,

Partnership An unincorporated business owned by two or more persons.

Corporation A legal entity created by a state, separate and distinct from its owners and managers, having unlimited life, easy transferability of ownership, and limited liability.

S Corporation A special designation that allows small businesses that meet qualifications to be taxed as if they were a proprietorship or a partnership rather than a corporation.

Limited Liability Company (LLC) A relatively new type of organization that is a hybrid between a partnership and a corporation.

Limited Liability Partnership (LLP) Similar to an LLC but used for professional firms in the fields of accounting, law, and architecture. It has limited liability like corporations but is taxed like partnerships.

Corporation A legal entity created by a state, separate and distinct from its owners and managers, having unlimited life, easy transferability of ownership, and limited liability.

S Corporation A special designation that allows small businesses that meet qualifications to be taxed as if they were a proprietorship or a partnership rather than a corporation.

Limited Liability Company (LLC) A relatively new type of organization that is a hybrid between a partnership and a corporation.

2 Originally, there were just “plain vanilla” partnerships; but over the years, lawyers have created a number of variations. We leave the variations to courses on business law, but we note that the variations are generally designed to limit the liabilities of some of the partners. For example, a “limited partnership” has a general partner, who has unlimited liabil- ity, and one or more limited partners, whose liability is limited to the amount of their investment. This sounds great from the standpoint of limited liability; but the limited partners must cede sole control to the general partner, which means that they have almost no say in the way the fi rm is managed. With a corporation, the owners (stockholders) have limited liability, but they also have the right to vote and thus change management if they think that a change is in order. Note too that LLCs and LLPs, discussed later in this section, are increasingly used in lieu of partnerships.

8 Part 1 Introduction to Financial Management

1-4 STOCK PRICES AND SHAREHOLDER VALUE The primary goal of a corporation should be to maximize its owners’ value, but a proprietor’s goal might be quite different. Consider Larry Jackson, the proprietor of a local sporting goods store. Jackson is in business to make money, but he likes to take time off to play golf on Fridays. He also has a few employees who are no longer very productive, but he keeps them on the payroll out of friendship and loyalty. Jackson is running the business in a way that is consistent with his own personal goals. He knows that he could make more money if he didn’t play golf or if he replaced some of his employees. But he is comfortable with his choices; and since it is his business, he is free to make those choices.

By contrast, Linda Smith is CEO of a large corporation. Smith manages the company; but most of the stock is owned by shareholders who purchased it be- cause they were looking for an investment that would help them retire, send their children to college, pay for a long-anticipated trip, and so forth. The shareholders

SEL F TEST What are the key diff erences between proprietorships, partnerships, and

corporations?

How are LLCs and LLPs related to the other forms of organization?

What is an S corporation, and what is its advantage over a C corporation? Why don’t fi rms such as IBM, GE, and Microsoft choose S corporation status?

What are some reasons the value of a business other than a small one is gen- erally maximized when it is organized as a corporation?

Suppose you are relatively wealthy and are looking for a potential invest- ment. You do not plan to be active in the business. Would you be more inter- ested in investing in a partnership or in a corporation? Why or why not?

but large companies still fi nd it advantageous to be C corporations because of the advantages in raising capital to support growth. LLCs/LLPs were dreamed up by lawyers, and it is necessary to hire a good lawyer when establishing one.3

When deciding on its form of organization, a fi rm must trade off the advan- tages of incorporation against a possibly higher tax burden. However, for the fol- lowing reasons, the value of any business other than a relatively small one will probably be maximized if it is organized as a corporation:

1. Limited liability reduces the risks borne by investors; and other things held constant, the lower the fi rm’s risk, the higher its value.

2. A fi rm’s value is dependent on its growth opportunities, which are dependent on its ability to attract capital. Because corporations can attract capital more easily than other types of businesses, they are better able to take advantage of growth opportunities.

3. The value of an asset also depends on its liquidity, which means the time and effort it takes to sell the asset for cash at a fair market value. Because the stock of a corporation is easier to transfer to a potential buyer than is an interest in a pro- prietorship or partnership and because more investors are willing to invest in stocks than in partnerships (with their potential unlimited liability), a corporate investment is relatively liquid. This too enhances the value of a corporation.

3 LLCs and LLPs are relatively complicated structures, and what they can do and how they must be set up varies by state. Moreover, they are still evolving. If you are interested in learning more about them, we recommend that you go to Google (or another search engine), enter LLC or LLP, and see the many references that are available.

9Chapter 1 An Overview of Financial Management

elected a board of directors, which then selected Smith to run the company. Smith and the fi rm’s other managers are working on behalf of the shareholders, and they were hired to pursue policies that enhance shareholder value. At the same time, the managers know that this does not mean maximize shareholder value “at all costs.” Managers have an obligation to behave ethically, and they must follow the laws and other society-imposed constraints that we discussed in the opening vignette to this chapter. Throughout this book, we focus primarily on publicly owned companies; hence, we operate on the assumption that management’s pri- mary goal is shareholder wealth maximization. That translates into this rule:

A manager should try to maximize the price of the fi rm’s stock, subject to the con- straints discussed in the opening vignette.

If a manager is to maximize shareholder wealth, he or she must know how that wealth is determined. Essentially, shareholder wealth is the number of shares out- standing times the market price per share. For example, if you own 100 shares of GE’s stock and the price is $40 per share, your wealth in GE is $4,000. The wealth of all of GE’s stockholders can be summed; and that is the value of the fi rm’s stock, the item that management should maximize. The number of shares outstanding is a given, so what really determines shareholder wealth is the price of the stock.

Throughout this book, we will see that the value of any asset is the present value of the stream of cash fl ows the asset provides to its owners. We discuss stock valuation in depth in Chapter 9, where we will see that a stock’s price at any given time depends on the cash fl ows a “marginal” investor expects to receive after buy- ing the stock. To illustrate, suppose investors are aware that GE earned $2.20 per share in 2007 and paid out 52% of that amount, or $1.15 per share, in dividends. Suppose further that most investors expect earnings, dividends, and the stock price to increase by about 6% per year. It might turn out that these expectations are met exactly. However, management might make a prudent decision that causes profi ts to rise at a 12% rate, causing the stock price to jump from $40 to $60 per share. Of course, management might make a big mistake, profi ts might suffer, and the stock price might decline to $20. Thus, investors are exposed to risk when they buy GE stock or any other company’s stock. If, instead, the investor bought a U.S. Treasury bond, he or she would receive a guaranteed interest payment every six months plus the bond’s par value when it matures; so his or her risk would be minimal.

We see then that if GE’s management makes good decisions, its stock price will increase; however, if its managers make bad decisions, the stock price will de- crease. Management’s goal should be to make decisions designed to maximize the stock’s price. Note, though, that factors beyond management’s control also affect stock prices. Thus, after the 9/11 terrorist attacks on the World Trade Center, the price of most stocks fell no matter how effective their management may have been.

Firms have a number of different departments, including marketing, account- ing, production, human resources, and fi nance. The fi nance department’s princi- pal task is to evaluate proposed decisions and judge how they will affect the stock price and thus shareholder wealth. For example, suppose the production manager wants to replace some old equipment with new automated machinery that will re- duce labor costs. The fi nance staff will evaluate that proposal and determine whether the savings seem to be worth the cost. Similarly, if marketing wants to sign a contract with Tiger Woods that will cost $10 million per year for 5 years, the fi nancial staff will evaluate the proposal, look at the probable increase in sales, and reach a conclusion as to whether signing Tiger will lead to a higher stock price. Most signifi cant decisions are evaluated in terms of their fi nancial consequences.

Note too that stock prices change over time as conditions change and as inves- tors obtain new information about a company’s prospects. For example, Apple Computer’s stock ranged from $77 to $193 per share during a recent 12-month period, rising and falling as good and bad news was released. Wal-Mart, which is in

Shareholder Wealth Maximization The primary goal for managers of publicly owned companies implies that decisions should be made to maximize the long-run value of the firm’s common stock.

10 Part 1 Introduction to Financial Management

1-5 INTRINSIC VALUES, STOCK PRICES, AND EXECUTIVE COMPENSATION

As noted in the preceding section, stock prices are based on cash fl ows expected in future years, not just in the current year. Thus, stock price maximization requires us to take a long-run view of operations. Academics have generally assumed that managers adhere to this long-run focus, but it is now clear that the focus for many companies shifted to the short run in recent years. To give managers an incentive to focus on stock prices, stockholders (acting through boards of directors) awarded executives stock options that could be exercised on a specifi ed future date. An executive could exercise the option on that date, receive stock, immediately sell it, and earn a profi t. The profi t was based on the stock price on the option exercise date, which led some managers to try to maximize the stock price on that specifi c date, not over the long run. That, in turn, led to some horrible abuses. Projects that looked good from a long-run perspective were turned down because they would penalize profi ts in the short run and thus lower the stock price on the option exer- cise day. Even worse, some managers deliberately overstated profi ts, temporarily boosted the stock price, exercised their options, sold the infl ated stock, and left outside stockholders “holding the bag” when the true situation was revealed. Enron and WorldCom are examples of companies whose managers did this, but there were many others.

Other companies have also used aggressive but legal accounting practices that boosted current profi ts but lowered profi ts in future years. For example, knowing that an asset would be usable for only 5 years, management might depreciate it over a 10-year life. This reduces reported costs—and raises reported income—for the next 5 years but raises costs and lowers income during the following 5 years.

SEL F TEST What is management’s primary goal?

What do investors expect to receive when they buy a share of stock? Do in- vestors know for sure how much they will receive? Explain.

Based just on the name, which company would you expect to be riskier— General Foods or South Seas Oil Exploration? Explain.

When Boeing decides to invest $5 billion in a new jet airliner, are its manag- ers certain of the project’s eff ects on Boeing’s future profi ts and stock price? Explain.

Who would be better able to judge the eff ect of a new airliner on Boeing’s profi ts—its managers or its stockholders? Explain.

Would all Boeing stockholders expect the same outcome from a given new project, and how would those expectations aff ect the stock’s price? Explain.

a more stable industry, had a narrower price range—from $42 to $52. Investors can predict future results for Wal-Mart more accurately than for Apple; thus, Wal-Mart is thought to be less risky. Also, some projects are relatively straightforward and easy to evaluate and, hence, not very risky. For example, if Wal-Mart were considering a proposed new store, the revenues, costs, and profi ts for this project would be eas- ier to estimate than for an Apple project related to a new voice-activated computer. The success or lack thereof of projects such as these determine the stock prices of Wal-Mart, Apple, and other companies.

11Chapter 1 An Overview of Financial Management

Many other legal but questionable accounting procedures have been used, all in an effort to boost reported profi ts and the stock price on the option exercise day. Obviously, all this can make it diffi cult for investors to decide how much a stock is really worth, and it helps explain why a fi rm’s reputation is an important determi- nant of its stock price.

Fortunately, most executives are honest. But even for honest companies, it is hard for investors to determine the proper price of a stock. Figure 1-2 illustrates the situation. The top box indicates that managerial actions, combined with the econ- omy, taxes, and political conditions, determine stock prices and thus investors’ re- turns. Remember that no one knows for sure what those future returns will be—we can estimate them, but expected and realized returns are often quite different. In- vestors like high returns, but they dislike risk; so the larger the expected profi ts and the lower the perceived risk, the higher the stock’s price.

The second row of boxes differentiates what we call “true expected returns” and “true risk” from “perceived” returns and “perceived” risk. By “true,” we mean the returns and risk that investors would expect if they had all of the infor- mation that existed about a company. “Perceived” means what investors expect, given the limited information they actually have. To illustrate, in early 2001, in- vestors had information that caused them to think that Enron was highly profi t- able and would enjoy high and rising future profi ts. They also thought that actual results would be close to the expected levels and hence, that Enron’s risk was low. However, true estimates of Enron’s profi ts, which were known by its executives but not the investing public, were much lower; and Enron’s true situation was ex- tremely risky.

The third row of boxes shows that each stock has an intrinsic value, which is an estimate of the stock’s “true” value as calculated by a competent analyst who has the best available risk and return data, and a market price, which is the actual market price based on perceived but possibly incorrect information as seen by the

Intrinsic Value An estimate of a stock’s “true” value based on accurate risk and return data. The intrinsic value can be estimated but not measured precisely.

Market Price The stock value based on perceived but possibly incorrect information as seen by the marginal investor.

Determinants of Intrinsic Values and Stock PricesFIGURE 1-2

Managerial Actions, the Economic Environment, Taxes, and the Political Climate

“True” Investor Returns

“True” Risk

“Perceived” Investor Returns

“Perceived” Risk

Stock’s Intrinsic Value

Stock’s Market Price

Market Equilibrium: Intrinsic Value = Stock Price

12 Part 1 Introduction to Financial Management

marginal investor.4 Not all investors agree, so it is the “marginal” investor who determines the actual price. For example, investors at the margin might expect a fi rm to pay a $1.00 dividend with a 5% growth rate thereafter; and on that basis, they might set the fi rm’s stock price at $45 per share. However, if they had all of the available facts, they might conclude that the dividend would be $1.30 with a 7% growth rate, which would lead to a price of $50 per share. In this case, the ac- tual market price would be $45 versus an intrinsic value of $50.

When a stock’s actual market price is equal to its intrinsic value, the stock is in equilibrium, which is shown in the bottom box in Figure 1-2; and when equilib- rium exists, there is no pressure for a change in the stock’s price. Market prices can and do differ from intrinsic values; but eventually, as the future unfolds, the two values tend to converge.

Actual stock prices are easy to determine—they can be found on the Internet and are published in newspapers every day. However, intrinsic values are esti- mates; and different analysts with different data and different views about the fu- ture form different estimates of a stock’s intrinsic value. Indeed, estimating intrinsic values is what security analysis is all about and is what distinguishes successful from un- successful investors. Investing would be easy, profi table, and essentially riskless if we knew all stocks’ intrinsic values; but, of course, we don’t. We can estimate in- trinsic values, but we can’t be sure that we are right. A fi rm’s managers have the best information about the fi rm’s future prospects, so managers’ estimates of in- trinsic values are generally better than those of outside investors. However, even managers can be wrong.

Figure 1-3 graphs a hypothetical company’s actual price and intrinsic value as estimated by its management over time.5 The intrinsic value rises because the fi rm retains and reinvests earnings each year, which tends to increase profi ts. The value jumped dramatically in 2003, when a research and development (R&D) break- through raised management’s estimate of future profi ts before investors had this information. The actual stock price tended to move up and down with the esti- mated intrinsic value; but investor optimism and pessimism, along with imperfect knowledge about the true intrinsic value, led to deviations between the actual prices and intrinsic values.

Intrinsic value is a long-run concept. It refl ects both improper actions (like Enron’s overstating earnings) and proper actions (like GE’s efforts to improve the environment). Management’s goal should be to take actions designed to maximize the fi rm’s intrinsic value, not its current market price. Note, though, that maximizing the intrinsic value will maximize the average price over the long run, but not necessar- ily the current price at each point in time. For example, management might make an investment that lowers profi ts for the current year but raises expected future profi ts. If investors are not aware of the true situation, the stock price will be held down by the low current profi t even though the intrinsic value was actually

Marginal Investor An investor whose views determine the actual stock price.

Equilibrium The situation in which the actual market price equals the intrinsic value, so investors are indifferent between buying or selling a stock.

4 Investors at the margin are the ones who actually set stock prices. Some stockholders think that a stock at its current price is a good deal, and they would buy more if they had more money. Others think that the stock is priced too high, so they would not buy it unless the price dropped sharply. Still others think that the current stock price is about where it should be; so they would buy more if the price fell slightly, sell it if the price rose slightly, and maintain their current holdings unless something were to change. These are the marginal investors, and it is their view that determines the current stock price. We discuss this point in more depth in Chapter 9, where we discuss the stock market in detail. 5 We emphasize that the intrinsic value is an estimate and that diff erent analysts have diff erent estimates for a company at any given time. Managers should also estimate their fi rm’s intrinsic value and then take actions to maximize that value. They should try to help outside security analysts improve their intrinsic value estimates by providing accurate information about the company’s fi nancial position and operations, but without releasing information that would help its competitors. Enron, WorldCom, and a number of other companies tried to deceive analysts; and they succeeded all too well.

13Chapter 1 An Overview of Financial Management

raised. Management should provide information that helps investors make better estimates of the fi rm’s intrinsic value, which will keep the stock price closer to its equilibrium level. However, there are times when management cannot divulge the true situation because doing so would provide information that helps its competitors.6

6 As we discuss in Chapter 2, many academics believe that stock prices embody all publicly available information—hence, that stock prices are typically reasonably close to their intrinsic values and thus at or close to an equilibrium. However, almost no one doubts that managers have better information than the public at large, that at times stock prices and equilibrium values diverge, and thus that stocks can be temporarily undervalued or overvalued (as we suggest in Figure 1-3).

SEL F TEST What’s the diff erence between a stock’s current market price and its intrin-

sic value?

Do stocks have known and “provable” intrinsic values, or might diff erent people reach diff erent conclusions about intrinsic values? Explain.

Should managers estimate intrinsic values or leave that to outside security analysts? Explain.

If a fi rm could maximize either its current market price or its intrinsic value, what would stockholders (as a group) want managers to do? Explain.

Should a fi rm’s managers help investors improve their estimates of the fi rm’s intrinsic value? Explain.

R&D breakthrough

Actual stock price

Intrinsic value

Stock undervalued

Stock overvalued

1983 1988 1993 1998 2003 2008

Stock Price and Intrinsic Value ($)

Graph of Actual Prices versus Intrinsic ValuesFIGURE 1-3

14 Part 1 Introduction to Financial Management

1-6 IMPORTANT BUSINESS TRENDS Four important business trends should be noted. First, the points discussed in the pre- ceding section have led to profound changes in business practices. Executives at Enron, WorldCom, and other companies lied when they reported fi nancial results, leading to huge stockholder losses. These companies’ CEOs later claimed not to have been aware of what was happening, and their knowledge (or lack thereof) was a central issue in their trials. As a result, Congress passed the Sarbanes-Oxley bill, which requires the CEO and CFO of a fi rm to certify that the fi rm’s fi nancial statements are accurate. These executives can be sent to jail if it later turns out that the statements did not meet the required standards. Consequently, businesses beefed up their internal and external auditing procedures, and the accuracy of published statements has improved.

A second trend is the increased globalization of business. Developments in com- munications technology have made it possible for Wal-Mart, for example, to obtain real-time data on the sales of hundreds of thousands of items in stores from China to Chicago and to manage all of its stores from Bentonville, Arkansas. IBM, Microsoft, and other high-tech companies now have research labs and help desks in China, India, and Romania; and customers of Home Depot and other retailers have their tele- phone and e-mail questions answered by call center operators in countries around the globe. Coca-Cola, Exxon Mobil, GE, and IBM, among others, generate more than half of their sales and income overseas. The trend toward globalization is likely to con- tinue, and companies that resist will have diffi culty competing in the 21st century.7

A third trend that’s having a profound effect on fi nancial management is ever- improving information technology (IT). Improvements in IT are spurring global- ization, and they are changing fi nancial management as it is practiced in the United States and elsewhere. Firms are collecting massive amounts of data and using it to take much of the guesswork out of fi nancial decisions. For example, when Wal-

7 To give you an idea of the prevalence of globalization, the computer programming that causes the test bank problems for this book to vary randomly was outsourced to programmers in Moscow, Russia. Our books have been translated into 11 languages, and they are sold throughout the world. Globalization is alive and well!

Most academics agree that shareholder wealth maximization should be a fi rm’s primary goal, but it’s not clear that people elsewhere really know how to implement it. Pricewater- houseCoopers (PWC), a global consulting fi rm, conducted a survey of 82 Singapore companies to test their understanding and implementation of shareholder value concepts. Ninety percent of the respondents said their fi rm’s primary goal was to enhance shareholder value, but only 44% had taken steps to achieve this goal. Moreover, almost half of the respondents who had shareholder value programs in place said they were dissatisfi ed with the results achieved thus far. Even so, respon- dents who focused on shareholder value were more likely to believe that their stock was fairly valued than those with other focuses, and 50% of those without a specifi c program said

they wanted to learn more and would probably adopt the goal of shareholder wealth maximization eventually. The study found that fi rms measure performance pri- marily with accounting-based measures such as the return on assets, equity, or invested capital. These measures are easy to understand and thus to implement, even though they are not the best conceptually. When compensation was tied to shareholder value, this was only for mid-level manag- ers and above. It is unclear how closely these results correspond to U.S. fi rms, but fi rms in the United States and Singapore would certainly agree on one thing: It is easier to set the goal of shareholder wealth maximization than it is to fi gure out how to achieve it.

Source: Kalpana Rashiwala, “Low Adoption of Shareholder Value Concepts Here,” The Business Times (Singapore), February 14, 2002.

IS SHAREHOLDER WEALTH MAXIMIZATION A WORLDWIDE GOAL?

15Chapter 1 An Overview of Financial Management

1-7 BUSINESS ETHICS As a result of the Enron scandal and other recent scandals, there has been a strong push to improve business ethics. This is occurring on several fronts—actions begun by former New York attorney general and former governor Elliot Spitzer and oth- ers who sued companies for improper acts; Congress’ passing of the Sarbanes Oxley bill to impose sanctions on executives who sign fi nancial statements later found to be false; and business schools trying to inform students about proper versus improper business actions.

As noted earlier, companies benefi t from having good reputations and are penalized by having bad ones; the same is true for individuals. Reputations re- fl ect the extent to which fi rms and people are ethical. Ethics is defi ned in Webster’s Dictionary as “standards of conduct or moral behavior.” Business ethics can be thought of as a company’s attitude and conduct toward its employees, customers, community, and stockholders. A fi rm’s commitment to business ethics can be measured by the tendency of its employees, from the top down, to adhere to laws, regulations, and moral standards relating to product safety and quality, fair em- ployment practices, fair marketing and selling practices, the use of confi dential information for personal gain, community involvement, and illegal payments to obtain business.

1-7a What Companies Are Doing Most fi rms today have strong written codes of ethical behavior; companies also conduct training programs to ensure that employees understand proper behavior in different situations. When confl icts arise involving profi ts and ethics, ethical considerations sometimes are so obviously important that they dominate. In other cases, however, the right choice is not clear. For example, suppose that Norfolk Southern’s managers know that its coal trains are polluting the air; but the amount

Business Ethics A company’s attitude and conduct toward its employees, customers, community, and stockholders.

SEL F TEST What four trends aff ect business management in general and fi nancial man-

agement in particular?

Mart is considering a potential site for a new store, it can draw on historical results from thousands of other stores to predict results at the proposed site. This lowers the risk of investing in new stores.

A fourth trend relates to corporate governance, or the way the top managers op- erate and interface with stockholders. Some years ago the chairperson of the board of directors was almost always also the CEO, and this individual decided who would be elected to the board. That made it almost impossible for stockholders to replace a poor management team. Today, though, active investors who control huge pools of capital (hedge funds and private equity groups) are constantly look- ing for underperforming fi rms; and they will quickly pounce on laggards, take control, and replace managers. At the same time, the SEC, which has jurisdiction over the way stockholders vote and the information they must be given, has been making it easier for activist stockholders to change the way things are done within fi rms. For example, the SEC is forcing companies to provide more transparent in- formation on CEO compensation, which is affecting managers’ actions.

16 Part 1 Introduction to Financial Management

of pollution is within legal limits, and further reduction would be costly. Are the managers ethically bound to reduce pollution? Similarly, several years ago Merck’s research indicated that its Vioxx pain medicine might be causing heart attacks. However, the evidence was not overly strong, and the product was clearly helping some patients. Over time, additional tests produced stronger evidence that Vioxx did pose a health risk. What should Merck have done, and when should Merck have done it? If the company released negative but perhaps incorrect information, this announcement would have hurt sales and possibly prevented some patients who could have benefi t from using the product. If the company delayed the release of this additional information, more patients might have suffered irreversible harm. At what point should Merck have made the potential problem known to the public? There are no obvious answers to questions such as these; but companies must deal with them, and a failure to handle them properly can lead to severe consequences.

1-7b Consequences of Unethical Behavior Over the past few years, ethical lapses have led to a number of bankruptcies. The recent collapses of Enron and WorldCom as well as the accounting fi rm Arthur Andersen dramatically illustrate how unethical behavior can lead to a fi rm’s rapid decline. In all three cases, top executives came under fi re because of misleading accounting practices that led to overstated profi ts. Enron and WorldCom execu- tives were busily selling their stock at the same time they were recommending the stock to employees and outside investors. These executives reaped millions before the stock declined, while lower-level employees and outside investors were left “holding the bag.” Some of these executives are now in jail, and Enron’s CEO had a fatal heart attack while awaiting sentencing after being found guilty of conspir- acy and fraud. Moreover, Merrill Lynch and Citigroup, which were accused of facilitating these frauds, were fi ned hundreds of millions of dollars.

These frauds also severely damaged other companies and even whole indus- tries. For example, WorldCom understated its costs by billions of dollars. It then used those artifi cially low costs when it set prices for its customers. Not knowing that WorldCom’s results were built on lies, AT&T’s CEO put pressure on his own managers to match WorldCom’s costs and prices. AT&T cut back on important projects, put far too much stress on its employees, acquired other companies at high prices, and ended up ruining a successful 100-year-old company.8 A similar situation occurred in the energy industry as a result of Enron’s cheating.

These and other improper actions caused many investors to lose faith in American business and to turn away from the stock market, which made it diffi - cult for fi rms to raise the capital they needed to grow, create jobs, and stimulate the economy. So unethical actions can have adverse consequences far beyond the com- panies that perpetrate them.

All this raises a question: Are companies unethical, or is it just a few of their em- ployees? That was a central issue that came up in the case of Arthur Andersen, the accounting fi rm that audited Enron, WorldCom, and several other companies that committed accounting fraud. Evidence showed that relatively few of Andersen’s accountants helped perpetrate the frauds. Its top managers argued that while a few rogue employees did bad things, most of the fi rm’s 85,000 employees,

8 The original AT&T was reorganized into a manufacturing company (Lucent), 8 regional telephone companies, and a long-distance company that retained the AT&T name. WorldCom was in the long-distance business and thus competed with the surviving AT&T. Partly as the result of its eff orts to match WorldCom’s phony costs and prices, AT&T lost billions. In the end, AT&T was acquired by the smallest of the 8 regional companies, which then took the AT&T name.

17Chapter 1 An Overview of Financial Management

and the fi rm itself, were innocent. The U.S. Justice Department disagreed, conclud- ing that the fi rm was guilty because it fostered a climate where unethical behavior was permitted and that Andersen used an incentive system that made such behav- ior profi table to both the perpetrators and the fi rm. As a result, Andersen was put out of business, its partners lost millions of dollars, and its 85,000 employees lost their jobs. In most other cases, individuals rather than fi rms were tried; and while the fi rms survived, they suffered damage to their reputations, which greatly low- ered their future profi t potential and value.

1-7c How Should Employees Deal with Unethical Behavior?

Far too often the desire for stock options, bonuses, and promotions drives manag- ers to take unethical actions such as fudging the books to make profi ts in the man- ager’s division look good, holding back information about bad products that would depress sales, and failing to take costly but needed measures to protect the environment. Generally, these acts don’t rise to the level of an Enron or a World- Com, but they are still bad. If questionable things are going on, who should take action and what should that action be? Obviously, in situations such as Enron and WorldCom, where fraud was being perpetrated at or close to the top, senior man- agers knew about the illegal activities. In other cases, the problem is caused by a mid-level manager trying to boost his or her unit’s profi ts and thus his or her bonus. In all cases, though, at least some lower-level employees are aware of what’s happening; they may even be ordered to take fraudulent actions. Should the lower- level employees obey their boss’s orders; refuse to obey those orders; or report the situation to a higher authority, such as the company’s board of directors, the com- pany’s auditors, or a federal prosecutor?

In the WorldCom and Enron cases, it was clear to a number of employees that unethical and illegal acts were being committed; but in cases such as Merck’s Vioxx product, the situation was less clear. Because early evidence that Vioxx led to heart attacks was weak and evidence of its pain reduction was strong, it was probably not appropriate to sound an alarm early on. However, as evidence accu- mulated, at some point the public needed to be given a strong warning or the product should have been taken off the market. But judgment comes into play

As a result of the recent accounting and other frauds, in 2002, Congress passed the Sarbanes-Oxley Act, which codi- fi ed certain rules pertaining to corporate behavior. One pro- vision in the bill was designed to protect whistle-blowers, or lower-level employees who sound an alarm over actions by their superiors. Employees who report improper actions are often fi red or otherwise penalized, which keeps many peo- ple from reporting activities that should be investigated. The Sarbanes-Oxley provision was designed to alleviate this problem. If someone reports a corporate wrongdoing and is

later penalized, he or she can ask the Occupational Safety & Health Administration (OSHA) to investigate the situation; if the employee was improperly penalized, the company can be required to reinstate the person, along with back pay and a sizable penalty award. According to The Wall Street Journal, some big awards have been handed out and a National Whistle-Blower Center has been established to help people sue companies. It’s still dangerous to blow the whistle, but less so than before the Sarbanes-Oxley Act was passed.

Source: Deborah Solomon and Kara Scannell, “SEC Is Urged to Enforce ‘Whistle-Blower’ Provision,” The Wall Street Journal, November 15, 2004, p. A6.

PROTECTION FOR WHISTLE-BLOWERS

18 Part 1 Introduction to Financial Management

1-8 CONFLICTS BETWEEN MANAGERS, STOCKHOLDERS, AND BONDHOLDERS9

1-8a Managers versus Stockholders It has long been recognized that managers’ personal goals may compete with share- holder wealth maximization. In particular, managers might be more interested in maximizing their own wealth than their stockholders’ wealth; therefore, managers might pay themselves excessive salaries. For example, Disney paid its former presi- dent Michael Ovitz $140 million as a severance package after just 14 months on the job—$140 million to go away—because he and Disney CEO Michael Eisner were having disagreements. Eisner was also handsomely compensated the year Ovitz was fi red—a $750,000 base salary plus a $9.9 million bonus plus $565 million in profi ts from stock options, for a total of just over $575 million. As another example of corporate excesses, Tyco CEO Dennis Kozlowski (who is now in jail) spent more than $1 million of the company’s money on a birthday party for his wife.

SEL F TEST How would you defi ne “business ethics”?

Can a fi rm’s executive compensation plan lead to unethical behavior? Explain.

Unethical acts are generally committed by unethical people. What are some things companies can do to help ensure that their employees act ethically?

9 These confl icts are studied under the heading of agency theory in fi nance literature. The classic work on agency theory is Michael C. Jensen and William H. Meckling, “Theory of the Firm, Managerial Behavior, Agency Costs, and Ownership Structure,” Journal of Financial Economics, October 1976, pp. 305–360.

when deciding on what action to take and when to take it. If a lower-level em- ployee thinks that a product should be pulled but the boss disagrees, what should the employee do? If an employee decides to report the problem, trouble may ensue regardless of the merits of the case. If the alarm is false, the company will have been harmed and nothing will have been gained. In that case, the employee will probably be fi red. Even if the employee is right, his or her career may still be ruined because many companies (or at least bosses) don’t like “disloyal, trouble- making” employees.

Such situations arise fairly often in contexts ranging from accounting fraud to product liability and environmental cases. Employees jeopardize their jobs if they come forward over their bosses’ objections. However, if they don’t speak up, they may suffer emotional problems and contribute to the downfall of their companies and the accompanying loss of jobs and savings. Moreover, if employees obey orders regarding actions they know are illegal, they may end up going to jail. Indeed, in most of the scandals that have gone to trial, the lower-level people who physically entered the bad data received longer jail sentences than the bosses who presumably gave the directives. So employees can be “stuck between a rock and a hard place,” that is, doing what they should do and possibly losing their jobs ver- sus going along with the boss and possibly ending up in jail.

This discussion shows why ethics is such an important consideration in busi- ness and in business schools—and why we are concerned with it in this book.

19Chapter 1 An Overview of Financial Management

Neither the Disney executives’ pay nor Kozlowski’s birthday party seem con- sistent with shareholder wealth maximization. Still, good executive compensation plans can motivate managers to act in their stockholders’ best interests. Useful motivational tools include (1) reasonable compensation packages, (2) fi ring of managers who don’t perform well, and (3) the threat of hostile takeovers.

Compensation packages should be suffi cient to attract and retain able manag- ers, but they should not go beyond what is needed. Also, compensation should be structured so that managers are rewarded on the basis of the stock’s perfor- mance over the long run, not the stock’s price on an option exercise date. This means that options (or direct stock awards) should be phased in over a number of years so that managers have an incentive to keep the stock price high over time. When the intrinsic value can be measured in an objective and verifi able manner, performance pay can be based on changes in intrinsic value. However, because intrinsic value is not observable, compensation must be based on the stock’s market price—but the price used should be an average over time rather than on a specifi c date.

Stockholders can intervene directly with managers. Years ago most stock was owned by individuals. Today, however, the majority of stock is owned by insti- tutional investors such as insurance companies, pension funds, hedge funds, and mutual funds; and private equity groups are ready and able to step in and take over underperforming fi rms. These institutional money managers have the clout to exercise considerable infl uence over fi rms’ operations. First, they can talk with managers and make suggestions about how the business should be run. In effect, institutional investors such as CalPERS (California Public Employ- ees’ Retirement System, with $165 billion of assets) and TIAA-CREF (Teachers Insurance and Annuity Association–College Retirement Equity Fund, a retire- ment plan originally set up for professors at private colleges that now has more than $300 billion of assets) act as lobbyists for the body of stockholders. When such large stockholders speak, companies listen. Second, any shareholder who has owned $2,000 of a company’s stock for one year can sponsor a proposal that may be voted on at the annual stockholders’ meeting, even if management op- poses the proposal.10 Although shareholder-sponsored proposals are nonbind- ing, the results of such votes are heard by top management. There is an ongoing debate regarding how much infl uence shareholders should have through the proxy process. For example, shareholder activists sharply criticized a recent SEC vote that continued to allow companies to exclude shareholder proposals related to director elections.11

Until recently, the probability of a large fi rm’s management being ousted by its stockholders was so remote that it posed little threat. Most fi rms’ shares were so widely distributed and the CEO had so much control over the voting mechanism that it was virtually impossible for dissident stockholders to get the votes needed to overthrow a management team. However, that situation has changed. In recent years, the top executives of AT&T, Coca-Cola, Fannie Mae, General Motors, IBM, and Xerox, to name a few, have been forced out. All of these departures were due to the fi rm’s poor performance.

If a fi rm’s stock is undervalued, corporate raiders will see it as a bargain and will attempt to capture the fi rm in a hostile takeover. If the raid is successful, the target’s executives will almost certainly be fi red. This situation gives managers a

Corporate Raider An individual who targets a corporation for takeover because it is undervalued.

Hostile Takeover The acquisition of a company over the opposition of its management.

10 Under current guidelines, shareholder proposals are restricted to governance issues and shareholders are not allowed to vote directly on items that are considered to be “operating issues.” 11 Kara Scannell, “Cox, in Denying Proxy Access, Puts His Legacy on the Line,” The Wall Street Journal Online, November 29, 2007, p. C1.

20 Part 1 Introduction to Financial Management

strong incentive to take actions to maximize their stock’s price. In the words of one executive, “If you want to keep your job, never let your stock become a bargain.”

Again, note that the price managers should be trying to maximize is not the price on a specifi c day. Rather, it is the average price over the long run, which will be maximized if management focuses on the stock’s intrinsic value. However, managers must communicate effectively with stockholders (without divulging in- formation that would aid their competitors) to keep the actual price close to the in- trinsic value. It’s bad for stockholders and managers when the intrinsic value is high but the actual price is low. In that situation, a raider may swoop in, buy the company at a bargain price, and fi re the managers. To repeat our earlier message: Managers should try to maximize their stock’s intrinsic value and then communicate ef- fectively with stockholders. That will cause the intrinsic value to be high and the actual stock price to remain close to the intrinsic value over time.

Because the intrinsic value cannot be observed, it is impossible to know whether it is really being maximized. Still, as we will discuss in Chapter 9, there are proce- dures for estimating a stock’s intrinsic value. Managers can use these valuation models to analyze alternative courses of action and thus see how these actions are likely to impact the fi rm’s value. This type of value-based management is not as precise as we would like, but it is the best way to run a business.

1-8b Stockholders versus Bondholders Confl icts can also arise between stockholders and bondholders. Bondholders gen- erally receive fi xed payment regardless of how well the company does, while stockholders do better when the company does better. This situation leads to con- fl icts between these two groups.12 To illustrate the problem, suppose a company has the chance to make an investment that will result in a profi t of $10 billion if it is successful but the company will be worthless and go bankrupt if the investment is unsuccessful. The fi rm has bonds that pay an 8% annual interest rate and have a value of $1,000 per bond and stock that sells for $10 per share. If the new project— say, a cure for the common cold—is successful, the price of the stock will jump to $2,000 per share, but the value of the bonds will remain just $1,000 per bond. The probability of success is 50% and the probability of failure is 50%, so the expected stock price is

Expected stock price ! 0.5($2,000) " 0.5($0) ! $1,000

versus a current price of $10. The expected percentage gain on the stock is

Expected percentage gain on stock ! ($1,000 # $10)/$10 $ 100% ! 9,900%

The project looks wonderful from the stockholders’ standpoint but lousy for the bondholders. They just break even if the project is successful, but they lose their entire investment if it is a failure.

Another type of bondholder/stockholder confl ict arises over the use of addi- tional debt. As we will see later in this book, the more debt a fi rm uses to fi nance a given amount of assets, the riskier the fi rm is. For example, if a fi rm has $100 mil- lion of assets and fi nances them with $5 million of bonds and $95 million of com- mon stock, things will have to go terribly bad before the bondholders will suffer a loss. On the other hand, if the fi rm uses $95 million of bonds and $5 million of stock, the bondholders will suffer a loss even if the value of the assets declines only slightly.

12 Managers represent stockholders; so saying “stockholders versus bondholders” is the same as saying “managers versus bondholders.”

21Chapter 1 An Overview of Financial Management

This chapter provides a broad overview of fi nancial management. Management’s pri- mary goal should be to maximize the long-run value of the stock, which means the in- trinsic value as measured by the stock’s price over time. To maximize value, fi rms must develop products that consumers want, produce the products effi ciently, sell them at competitive prices, and observe laws relating to corporate behavior. If fi rms are successful at maximizing the stock’s value, they will also be contributing to social welfare and citizens’ well-being.

Businesses can be organized as proprietorships, partnerships, corporations, lim- ited liability companies (LLCs), or limited liability partnerships (LLPs). The vast major- ity of all business is done by corporations, and the most successful fi rms end up as corporations, which explains the focus on corporations in this book. We also dis- cussed four important business trends: (1) the focus on business ethics that resulted from a series of scandals in the late 1990s, (2) the trend toward globalization, (3) the ever-improving information technology, and (4) the changes in corporate gover- nance. These four trends are changing the way business is done.

The primary tasks of the CFO are (1) to make sure the accounting system provides “good” numbers for internal decision making and for investors, (2) to ensure that the fi rm is fi nanced in the proper manner, (3) to evaluate the operating units to make sure they are performing in an optimal manner, and (4) to evaluate all proposed capi- tal expenditures to make sure they will increase the fi rm’s value. In the remainder of this book, we discuss exactly how fi nancial managers carry out these tasks.

Bondholders attempt to protect themselves by including covenants in the bond agreements that limit fi rms’ use of additional debt and constrain managers’ actions in other ways. We will address these issues later in this book, but they are quite important and everyone should be aware of them.

T YING I T ALL TO GETHER

KEY TERMS Define each of the following terms: a. Sarbanes-Oxley Act b. Proprietorship; partnership; corporation c. S corporations; limited liability companies (LLCs); limited liability partnerships (LLPs)

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

What are three techniques stockholders can use to motivate managers to maximize their stock’s long-run price?

Should managers focus directly on the stock’s actual market price or its in- trinsic value, or are both important? Explain.

Why might confl icts arise between stockholders and bondholders?

SEL F TEST

22 Part 1 Introduction to Financial Management

d. Stockholder wealth maximization e. Intrinsic value; market price f. Equilibrium; marginal investor g. Business ethics h. Corporate raider; hostile takeover

If you bought a share of stock, what would you expect to receive, when would you expect to receive it, and would you be certain that your expectations would be met?

If most investors expect the same cash flows from Companies A and B but are more confi- dent that A’s cash flows will be closer to their expected value, which company should have the higher stock price? Explain.

What is a firm’s intrinsic value? its current stock price? Is the stock’s “true long-run value” more closely related to its intrinsic value or to its current price?

When is a stock said to be in equilibrium? At any given time, would you guess that most stocks are in equilibrium as you defined it? Explain.

Suppose three honest individuals gave you their estimates of Stock X’s intrinsic value. One person is your current roommate, the second person is a professional security analyst with an excellent reputation on Wall Street, and the third person is Company X’s CFO. If the three estimates differed, in which one would you have the most confidence? Why?

Is it better for a firm’s actual stock price in the market to be under, over, or equal to its in- trinsic value? Would your answer be the same from the standpoints of stockholders in gen- eral and a CEO who is about to exercise a million dollars in options and then retire? Explain.

If a company’s board of directors wants management to maximize shareholder wealth, should the CEO’s compensation be set as a fixed dollar amount, or should the compensa- tion depend on how well the firm performs? If it is to be based on performance, how should performance be measured? Would it be easier to measure performance by the growth rate in reported profits or the growth rate in the stock’s intrinsic value? Which would be the better performance measure? Why?

What are the four forms of business organization? What are the advantages and disadvan- tages of each?

Should stockholder wealth maximization be thought of as a long-term or a short-term goal? For example, if one action increases a firm’s stock price from a current level of $20 to $25 in 6 months and then to $30 in 5 years but another action keeps the stock at $20 for several years but then increases it to $40 in 5 years, which action would be better? Think of some specific corporate actions that have these general tendencies.

What are some actions that stockholders can take to ensure that management’s and stock- holders’ interests are aligned?

The president of Southern Semiconductor Corporation (SSC) made this statement in the company’s annual report: “SSC’s primary goal is to increase the value of our common stockholders’ equity.” Later in the report, the following announcements were made:

a. The company contributed $1.5 million to the symphony orchestra in Birmingham, Alabama, its headquarters city.

b. The company is spending $500 million to open a new plant and expand operations in China. No profits will be produced by the Chinese operation for 4 years, so earnings will be depressed during this period versus what they would have been had the deci- sion been made not to expand in China.

c. The company holds about half of its assets in the form of U.S. Treasury bonds, and it keeps these funds available for use in emergencies. In the future, though, SSC plans to shift its emergency funds from Treasury bonds to common stocks.

Discuss how SSC’s stockholders might view each of these actions and how the actions might affect the stock price.

QUESTIONSQUESTIONS

1-11-1

1-21-2

1-31-3

1-41-4

1-51-5

1-61-6

1-71-7

1-81-8

1-91-9

1-101-10

1-111-11

23Chapter 1 An Overview of Financial Management

Investors generally can make one vote for each share of stock they hold. TIAA-CREF is the largest institutional shareholder in the United States; therefore, it holds many shares and has more votes than any other organization. Traditionally, this fund has acted as a passive investor, just going along with management. However, in 1993, it mailed a notice to all 1,500 companies whose stocks it held that henceforth, it planned to actively intervene if, in its opinion, management was not performing well. Its goal was to improve corporate per- formance to boost the prices of the stocks it held. It also wanted to encourage corporate boards to appoint a majority of independent (outside) directors; and it stated that it would vote against any directors of firms that “don’t have an effective, independent board that can challenge the CEO.” In the past, TIAA-CREF responded to poor performance by “voting with its feet,” which means selling stocks that were not doing well. However, by 1993, that position had become difficult to maintain for two reasons. First, the fund invested a large part of its as- sets in “index funds,” which hold stocks in accordance with their percentage value in the broad stock market. Furthermore, TIAA-CREF owns such large blocks of stocks in many companies that if it tried to sell out, doing so would severely depress the prices of those stocks. Thus, TIAA-CREF is locked in to a large extent, which led to its decision to become a more active investor.

a. Is TIAA-CREF an ordinary shareholder? Explain. b. Due to its asset size, TIAA-CREF owns many shares in a number of companies. The

fund’s management plans to vote those shares. However, TIAA-CREF is owned by many thousands of investors. Should the fund’s managers vote its shares; or should it pass those votes, on a pro rata basis, back to its own shareholders? Explain.

Edmund Enterprises recently made a large investment to upgrade its technology. While these improvements won’t have much effect on performance in the short run, they are ex- pected to reduce future costs significantly. What effect will this investment have on Ed- mund Enterprises’ earnings per share this year? What effect might this investment have on the company’s intrinsic value and stock price?

Suppose you were a member of Company X’s board of directors and chairperson of the company’s compensation committee. What factors should your committee consider when setting the CEO’s compensation? Should the compensation consist of a dollar salary, stock options that depend on the firm’s performance, or a mix of the two? If “performance” is to be considered, how should it be measured? Think of both theoretical and practical (that is, measurement) considerations. If you were also a vice president of Company X, might your actions be different than if you were the CEO of some other company?

Suppose you are a director of an energy company that has three divisions—natural gas, oil, and retail (gas stations). These divisions operate independently from one another, but all division managers report to the firm’s CEO. If you were on the compensation commit- tee as discussed in Question 1–14 and your committee was asked to set the compensation for the three division managers, would you use the same criteria as that used for the firm’s CEO? Explain your reasoning.

1-121-12

1-131-13

1-141-14

1-151-15

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FUNDAMENTAL CONCEPTS IN

FINANCIAL MANAGEMENT

2 Financial Markets and Institutions

3 Financial Statements, Cash Flow, and Taxes

4 Analysis of Financial Statements

5 Time Value of Money

PART 2

C H

A P

T E

E f f i c i e n t Fi n a n c i a l M a r ke t s A r e N e ce s s a r y f o r a G r ow i n g E co n o my

Financial Markets and Institutions

IR O

KO M

AS U

IK E/

G ET

TY IM

AG ES

2 CHAPTER

Over the past few decades, changing technology and improving communications have increased cross-border transactions and expanded the scope and efficiency of the global financial sys- tem. Companies routinely raise funds throughout the world; and with the click of a mouse, an inves- tor can buy GE stock on the New York Stock Exchange, deposit funds in a European bank, or purchase a mutual fund that invests in Chinese securities.

This globalization was dramatically illustrated in the fall of 2007. The U.S. housing market had been exceedingly strong, which bolstered the entire economy. Rising home values enabled people to borrow on home equity loans to buy everything from autos to Caribbean vacations. However, lenders had been making loans that required no down payment, that had “teaser” rates programmed to rise sharply after a year or two, and that were made to borrowers whose credit had not been carefully checked. These relaxed lending standards enabled people who

could not have bought homes in the past to buy a home now; but the loans were getting riskier, and about 30% were classified as “subprime.”

The risk buildup was obscured by fancy “finan- cial engineering.” A few years ago people obtained mortgage loans primarily from local banks. The banks kept the mortgages, collected the interest, and likely knew how risky the loans were. In recent years, the situation has changed. Now mortgage brokers originate, for example, 500 loans for $200,000 each, or $100 million in total, and then sell them to an investment bank. The bank uses the loans as collateral for $100 million of bonds, which are divided into classes such as A, B, and C. The A bonds have first claim on cash from the mortgages and are rated AAA; the Bs are next, which are also highly rated; and even the Cs are rated “investment grade.” Initially, times were good; the interest and repayment of principal from the mortgages were sufficient to cover required payments to all of the bonds. However, recently, some of the mortgages began going

In Chapter 1, we saw that a fi rm’s primary goal is to maximize the price of its stock. Stock prices are determined in the fi nancial markets; so if fi nancial managers are to make good decisions, they must understand how these markets operate. In addi- tion, individuals make personal investment decisions; so they too need to know something about fi nancial markets and the institutions that operate in those mar- kets. Therefore, in this chapter, we describe the markets where capital is raised, securities are traded, and stock prices are established and the institutions that operate in these markets. When you fi nish this chapter, you should be able to: • Identify the diff erent types of fi nancial markets and fi nancial institutions and

explain how these markets and institutions enhance capital allocation. • Explain how the stock market operates and list the distinctions between the dif-

ferent types of stock markets. • Explain how the stock market has performed in recent years. • Discuss the importance of market effi ciency and explain why some markets are

more effi cient than others.

into default, and inflows were no longer sufficient to cover required payments to all of the bonds.

When home prices are rising, borrowers’ equity also rises. That enables borrowers who cannot keep up with their payments to refinance—or sell the house for enough to pay off the mortgage. But when home prices start falling, refinancings and profitable sales are impossible. That trig- gers mortgage defaults, which, in turn, triggers defaults on the riskiest bonds. People become worried about the B and even the A bonds, so their values also fall. The banks and other institutions that own the bonds are forced to write them down on their balance sheets.

Institutions that hold mortgage-backed bonds— many of which are subsidiaries of banks—raised the money to buy the bonds by borrowing on a 3-month basis from money market funds of similar lenders. As risks became more apparent, the short-term lenders refused to roll over these loans; thus, the bondholders were forced to sell bonds to repay their short-term loans. Those sales depressed the bond market even further, causing further bond sales, lower bond prices, and more write-downs. A downward spiral and a severe credit crunch began.

Banks across the globe had invested in these bonds; and huge losses were reported by Citigroup, Deutsche Bank (Germany’s largest), and UBS (Switzerland’s largest). These losses reduced banks’ willingness and ability to make new loans, which threatened economies in many nations. The Federal Reserve and other central banks lowered interest rates and eased the terms under which they extended credit to banks, and the banks themselves joined forces to head off a downward spiral. The headline in The Wall Street Journal on October 13, 2007, read as follows: “Big Banks Push $100 Billion Plan to Avert Credit Crunch.” The article described how government officials are working with bankers to head off an impending crisis. However, working things out will be difficult. Many think that the banks whose actions contributed to the problems—especially Citigroup—should not be bailed out. Others think that the crisis must be averted because the U.S. economy and other economies will be badly damaged if the downward spiral continues.

All of this demonstrates the extent to which markets are interconnected, the impact markets can have on countries and on individual companies, and the complexity of capital markets.

PU T TING THINGS IN PER SPECTIVE

Chapter 2 Financial Markets and Institutions 27

Source: Carrick Mollenkamp, Ian McDonald, and Deborah Solomon, “Big Banks Push $100 Billion Plan To Avert Crunch: Fund Seeks to Prevent Mortgage-Debt Selloff; Advice From Treasury,” The Wall Street Journal, October 13, 2007, p. A1.

28 Part 2 Fundamental Concepts in Financial Management

2-1 THE CAPITAL ALLOCATION PROCESS Businesses, individuals, and governments often need to raise capital. For example, Carolina Power & Light (CP&L) forecasts an increase in the demand for electricity in North and South Carolina, so it will build a new power plant to meet those needs. Because CP&L’s bank account does not contain the $1 billion necessary to pay for the plant, the company must raise this capital in the fi nancial markets. Simi- larly, Mr. Fong, the proprietor of a San Francisco hardware store, wants to expand into appliances. Where will he get the money to buy the initial inventory of TV sets, washers, and freezers? Or suppose the Johnson family wants to buy a home that costs $200,000, but they have only $50,000 in savings. Where will they get the addi- tional $150,000? The city of New York needs $200 million to build a new sewer plant. Where can it obtain this money? Finally, the federal government needs more money than it receives from taxes. Where will the extra money come from?

On the other hand, some individuals and fi rms have incomes that exceed their current expenditures, in which case they have funds available to invest. For example, Carol Hawk has an income of $36,000, but her expenses are only $30,000. That leaves her with $6,000 to invest. Similarly, Microsoft has accumulated roughly $23.5 billion of cash. What can Microsoft do with this money until it is needed in the business?

People and organizations with surplus funds are saving today in order to ac- cumulate funds for some future use. Members of a household might save to pay for their children’s education and the parents’ retirement, while a business might save to fund future investments. Those with surplus funds expect to earn a return on their investments, while people and organizations that need capital understand that they must pay interest to those who provide that capital.

In a well-functioning economy, capital fl ows effi ciently from those with sur- plus capital to those who need it. This transfer can take place in the three ways de- scribed in Figure 2-1.

1. Direct transfers of money and securities, as shown in the top section, occur when a business sells its stocks or bonds directly to savers, without going through

Business

1. Direct Transfers

2. Indirect Transfers through Investment Bankers

3. Indirect Transfers through a Financial Intermediary

Savers

SaversFinancialIntermediary

Investment Banks

Securities (Stocks or Bonds)

Dollars

Securities

Dollars

Securities

Dollars

Intermediary’s Securities

Dollars

Business’ Securities

Dollars

Diagram of the Capital Formation ProcessFIGURE 2-1

29Chapter 2 Financial Markets and Institutions

any type of fi nancial institution. The business delivers its securities to savers, who, in turn, give the fi rm the money it needs. This procedure is used mainly by small fi rms, and relatively little capital is raised by direct transfers.

2. As shown in the middle section, transfers may also go through an investment bank (iBank) such as Merrill Lynch or Citigroup, which underwrites the issue. An underwriter serves as a middleman and facilitates the issuance of securi- ties. The company sells its stocks or bonds to the investment bank, which then sells these same securities to savers. The businesses’ securities and the savers’ money merely “pass through” the investment bank. However, because the investment bank buys and holds the securities for a period of time, it is taking a risk—it may not be able to resell the securities to savers for as much as it paid. Because new securities are involved and the corporation receives the proceeds of the sale, this transaction is called a primary market transaction.

3. Transfers can also be made through a fi nancial intermediary such as a bank, an insurance company, or a mutual fund. Here the intermediary obtains funds from savers in exchange for its securities. The intermediary uses this money to buy and hold businesses’ securities, while the savers hold the intermediary’s securities. For example, a saver deposits dollars in a bank, receiving a certifi - cate of deposit; then the bank lends the money to a business in the form of a mortgage loan. Thus, intermediaries literally create new forms of capital—in this case, certifi cates of deposit, which are safer and more liquid than mort- gages and thus are better for most savers to hold. The existence of intermediar- ies greatly increases the effi ciency of money and capital markets.

Often the entity needing capital is a business (and specifi cally a corporation); but it is easy to visualize the demander of capital being a home purchaser, a small business, or a government unit. For example, if your uncle lends you money to help you fund a new business, a direct transfer of funds will occur. Alternatively, if you borrow money to purchase a home, you will probably raise the funds through a fi nancial intermediary such as your local commercial bank or mortgage banker. That banker could sell your mortgage to an investment bank, which then might use it as collateral for a bond that is bought by a pension fund.

In a global context, economic development is highly correlated with the level and effi ciency of fi nancial markets and institutions.1 It is diffi cult, if not impossible, for an economy to reach its full potential if it doesn’t have access to a well- functioning fi nancial system. In a well-developed economy like that of the United States, an extensive set of markets and institutions has evolved over time to facilitate the effi - cient allocation of capital. To raise capital effi ciently, managers must understand how these markets and institutions work; and individuals need to know how the markets and institutions work to get high rates of returns on their savings.

SEL F TEST Name three ways capital is transferred between savers and borrowers.

Why are effi cient capital markets necessary for economic growth?

1 For a detailed review of the evidence linking fi nancial development to economic growth, see Ross Levine, “Finance and Growth: Theory and Evidence,” NBER Working Paper No. 10766, September 2004.

30 Part 2 Fundamental Concepts in Financial Management

2-2 FINANCIAL MARKETS People and organizations wanting to borrow money are brought together with those who have surplus funds in the fi nancial markets. Note that markets is plural; there are many different fi nancial markets in a developed economy such as that of the United States. We describe some of these markets and some trends in their development.

2-2a Types of Markets Different fi nancial markets serve different types of customers or different parts of the country. Financial markets also vary depending on the maturity of the securi- ties being traded and the types of assets used to back the securities. For these rea- sons, it is useful to classify markets along the following dimensions: 1. Physical asset markets versus fi nancial asset markets. Physical asset markets (also

called “tangible” or “real” asset markets) are for products such as wheat, autos, real estate, computers, and machinery. Financial asset markets, on the other hand, deal with stocks, bonds, notes, and mortgages. Financial markets also deal with derivative securities whose values are derived from changes in the prices of other assets. A share of Ford stock is a “pure fi nancial asset,” while an option to buy Ford shares is a derivative security whose value depends on the price of Ford stock. The bonds backed by subprime mortgages discussed at the beginning of this chapter are another type of derivative, as the values of these bonds are derived from the values of the underlying mortgages.

2. Spot markets versus futures markets. Spot markets are markets in which assets are bought or sold for “on-the-spot” delivery (literally, within a few days). Futures markets are markets in which participants agree today to buy or sell an asset at some future date. For example, a farmer may enter into a futures contract in which he agrees today to sell 5,000 bushels of soybeans 6 months from now at a price of $5 a bushel. To continue that example, a food processor that needs soybeans in the future may enter into a futures contract in which it agrees to buy soybeans 6 months from now. Such a transaction can reduce, or hedge, the risks faced by both the farmer and the food processor.

3. Money markets versus capital markets. Money markets are the markets for short-term, highly liquid debt securities. The New York, London, and Tokyo money markets are among the world’s largest. Capital markets are the mar- kets for intermediate- or long-term debt and corporate stocks. The New York Stock Exchange, where the stocks of the largest U.S. corporations are traded, is a prime example of a capital market. There is no hard-and-fast rule, but in a description of debt markets, short-term generally means less than 1 year, intermediate-term means 1 to 10 years, and long-term means more than 10 years.

4. Primary markets versus secondary markets. Primary markets are the markets in which corporations raise new capital. If GE were to sell a new issue of com- mon stock to raise capital, a primary market transaction would take place. The corporation selling the newly created stock, GE, receives the proceeds from the sale in a primary market transaction. Secondary markets are markets in which existing, already outstanding securities are traded among investors. Thus, if Jane Doe decided to buy 1,000 shares of GE stock, the purchase would occur in the secondary market. The New York Stock Exchange is a secondary market because it deals in outstanding, as opposed to newly issued, stocks and bonds. Secondary markets also exist for mortgages, other types of loans, and other fi nancial assets. The corporation whose securities are being traded is not involved in a secondary market transaction and thus does not receive funds from such a sale.

Spot Markets The markets in which assets are bought or sold for “on-the-spot” delivery.

Futures Markets The markets in which participants agree today to buy or sell an asset at some future date.

Money Markets The financial markets in which funds are borrowed or loaned for short periods (less than one year).

Capital Markets The financial markets for stocks and for intermediate- or long-term debt (one year or longer).

Primary Markets Markets in which corporations raise capital by issuing new securities.

Secondary Markets Markets in which securities and other financial assets are traded among investors after they have been issued by corporations.

31Chapter 2 Financial Markets and Institutions

5. Private markets versus public markets. Private markets, where transactions are negotiated directly between two parties, are differentiated from public markets, where standardized contracts are traded on organized exchanges. Bank loans and private debt placements with insurance companies are exam- ples of private market transactions. Because these transactions are private, they may be structured in any manner to which the two parties agree. By contrast, securities that are traded in public markets (for example, common stock and corporate bonds) are held by a large number of individuals. These securities must have fairly standardized contractual features because public investors do not generally have the time and expertise to negotiate unique, nonstandard- ized contracts. Broad ownership and standardization result in publicly traded securities being more liquid than tailor-made, uniquely negotiated securities.

Other classifi cations could be made, but this breakdown shows that there are many types of fi nancial markets. Also note that the distinctions among markets are often blurred and unimportant except as a general point of reference. For example, it makes little difference if a fi rm borrows for 11, 12, or 13 months, that is, whether the transaction is a “money” or “capital” market transaction. You should be aware of the important differences among types of markets, but don’t be overly con- cerned about trying to distinguish them at the boundaries.

A healthy economy is dependent on effi cient funds transfers from people who are net savers to fi rms and individuals who need capital. Without effi cient trans- fers, the economy could not function: Carolina Power & Light could not raise capi- tal, so Raleigh’s citizens would have no electricity; the Johnson family would not have adequate housing; Carol Hawk would have no place to invest her savings; and so forth. Obviously, the level of employment and productivity (i.e., the stan- dard of living) would be much lower. Therefore, it is essential that fi nancial mar- kets function effi ciently—not only quickly, but also inexpensively.2

Table 2-1 is a listing of the most important instruments traded in the various fi nancial markets. The instruments are arranged in ascending order of typical length of maturity. As we go through this book, we will look in more detail at many of the instruments listed in Table 2-1. For example, we will see that there are many varieties of corporate bonds, ranging from “plain vanilla” bonds to bonds that can be converted to common stocks to bonds whose interest payments vary depending on the infl ation rate. Still, the table provides an overview of the charac- teristics and costs of the instruments traded in the major fi nancial markets.

2-2b Recent Trends Financial markets have experienced many changes in recent years. Technological advances in computers and telecommunications, along with the globalization of banking and commerce, have led to deregulation, which has increased competi- tion throughout the world. As a result, there are more effi cient, internationally linked markets, which are far more complex than what existed a few years ago. While these developments have been largely positive, they have also created prob- lems for policy makers. At one conference, former Federal Reserve Board Chair- person Alan Greenspan stated that modern fi nancial markets “expose national economies to shocks from new and unexpected sources and with little if any lag.” He went on to say that central banks must develop new ways to evaluate and limit risks to the fi nancial system. Large amounts of capital move quickly around the

Private Markets Markets in which transactions are worked out directly between two parties.

Public Markets Markets in which standardized contracts are traded on organized exchanges.

2 As the countries of the former Soviet Union and other Eastern European nations move toward capitalism, as much attention must be paid to the establishment of cost-effi cient fi nancial markets as to electrical power, trans- portation, communications, and other infrastructure systems. Economic effi ciency is impossible without a good system for allocating capital within the economy.

Summary of Major Market Instruments, Market Participants, and Security CharacteristicsT a b l e 2 - 1

SECURITY CHARACTERISTICS

Instrument (1)

Market (2)

Major Participants (3)

Riskiness (4)

Original Maturity

(5)

Interest Rate on 2/5/08a

(6) U.S. Treasury bills Money Sold by U.S. Treasury to finance federal

expenditures Default-free, close to riskless 91 days to 1 year 2.23%

Bankers’ acceptances Money A firm’s note, but one guaranteed by a bank Low degree of risk if guaranteed by a strong bank Up to 180 days 3.11%

Dealer commercial paper Money Issued by financially secure firms to large investors

Low default risk Up to 270 days 3.05%

Negotiable certificates of deposit (CDs)

Money Issued by major money-center commercial banks to large investors

Default risk depends on the strength of the issuing bank

Up to 1 year 3.10%

Money market mutual funds

Money Invest in Treasury bills, CDs, and commercial paper; held by individuals and businesses

Low degree of risk No specific maturity (instant liquidity)

2.84%

Eurodollar market time deposits

Money Issued by banks outside the United States Default risk depends on the strength of the issuing bank

Up to 1 year 3.10%

Consumer credit, including credit card debt

Money Issued by banks, credit unions, and finance companies to individuals

Risk is variable Variable Variable, but goes up to 20% or more

U.S. Treasury notes and bonds

Capital Issued by U.S. government No default risk, but price will decline if interest rates rise; hence, there is some risk

2 to 30 years 1.919% on 2-year to 4.327% on 30-year bonds

Mortgages Capital Loans to individuals and businesses secured by real estate; bought by banks and other institutions

Risk is variable; risk is high in the case of subprime loans

Up to 30 years 5.14% adjustable 5-year rate, 5.62% 30-year fixed rate

State and local government bonds

Capital Issued by state and local governments; held by individuals and institutional investors

Riskier than U.S. government securities but exempt from most taxes

Up to 30 years 4.63% to 5.03% for A-rated, 20- to 40-year bonds

Corporate bonds Capital Issued by corporations; held by individuals and institutional investors

Riskier than U.S. government securities but less risky than preferred and common stocks; varying degree of risk within bonds depends on strength of issuer

Up to 40 yearsb 5.38% on AAA bonds, 6.63% on BBB bonds

Leases Capital Similar to debt in that firms can lease assets rather than borrow and then buy the assets

Risk similar to corporate bonds Generally 3 to 20 years

Similar to bond yields

Preferred stocks Capital Issued by corporations to individuals and institutional investors

Generally riskier than corporate bonds but less risky than common stock

Unlimited 5.5% to 9%

Common stocksc Capital Issued by corporations to individuals and institutional investors

Riskier than bonds and preferred stock; risk varies from company to company

Unlimited NA

a The yields reported are from the web site of The Wall Street Journal on February 5, 2008, http://online.wsj.com. Money market rates assume a 3-month maturity. b A few corporations have issued 100-year bonds; however, the majority have issued bonds with maturities that are less than 40 years. c While common stocks do not pay interest, they are expected to provide a “return” in the form of dividends and capital gains. As you will see in Chapter 8, historically, stock returns have averaged between 9% and 12% a year, but they can be much higher or lower in a given year. Of course, if you purchase a stock, your actual return may be considerably higher or lower than these historical averages.

http://online.wsj.com

33Chapter 2 Financial Markets and Institutions

world in response to changes in interest and exchange rates, and these movements can disrupt local institutions and economies. The subprime mortgage crisis dis- cussed in the opening chapter vignette illustrates how problems in one country quickly affect the economies of other nations.

Globalization has exposed the need for greater cooperation among regulators at the international level, but the task is not easy. Factors that complicate coordina- tion include (1) the different structures in nations’ banking and securities indus- tries; (2) the trend toward fi nancial services conglomerates, which obscures devel- opments in various market segments; and (3) the reluctance of individual countries to give up control over their national monetary policies. Still, regulators are unani- mous about the need to close the gaps in the supervision of worldwide markets.

Another important trend in recent years has been the increased use of deriva- tives. A derivative is any security whose value is derived from the price of some other “underlying” asset. An option to buy IBM stock is a derivative, as is a con- tract to buy Japanese yen 6 months from now or a bond backed by subprime mortgages. The value of the IBM option depends on the price of IBM’s stock, the value of the Japanese yen “future” depends on the exchange rate between yen and dollars, and the value of the bond depends on the value of the underlying mortgages. The market for derivatives has grown faster than any other market in recent years, providing investors with new opportunities, but also exposing them to new risks.

Derivatives can be used to reduce risks or to speculate. Suppose a wheat pro- cessor’s costs rise and its net income falls when the price of wheat rises. The pro- cessor could reduce its risk by purchasing derivatives—wheat futures—whose value increases when the price of wheat rises. This is a hedging operation, and its purpose is to reduce risk exposure. Speculation, on the other hand, is done in the hope of high returns; but it raises risk exposure. For example, several years ago Procter & Gamble disclosed that it lost $150 million on derivative investments, and Orange County (California) literally went bankrupt as a result of its treasurer’s speculation in derivatives.

The values of most derivatives are subject to more volatility than the values of the underlying assets. For example, someone might pay $500 for an option to buy 100 shares of IBM stock at $120 per share when the stock is selling for $120. If the stock rose by $5 per share, a gain of 4.17% would result. However, the options would be worth somewhere between $25 and $30; so the percentage gain would be between 400% and 500%.3 Of course, if IBM stayed at $120 or fell, the options would be worthless and the option purchaser would have a 100% loss. Many other derivatives have similar characteristics and are equally as risky or even more risky.

If a bank or any other company reports that it invests in derivatives, how can one tell if the derivatives are held as a hedge against something like an increase in the price of wheat or as a speculative bet that wheat prices will rise? The answer is that it is very diffi cult to tell how derivatives are affecting the risk profi le of the fi rm. In the case of fi nancial institutions, things are even more complicated—the derivatives are generally based on changes in interest rates, foreign exchange rates, or stock prices; and a large international bank might have tens of thousands of separate derivative contracts. The size and complexity of these transactions con- cern regulators, academics, and members of Congress. Former Fed Chairperson Greenspan noted that in theory, derivatives should allow companies to better manage risk but that it is not clear whether recent innovations have “increased or decreased the inherent stability of the fi nancial system.”

Derivative Any financial asset whose value is derived from the value of some other “underlying” asset.

3 For a discussion on options and option pricing, see Brigham and Houston, Fundamentals of Financial Manage- ment, 12th edition, (Mason, OH: Cengage Learning, 2009), Chapter 18.

34 Part 2 Fundamental Concepts in Financial Management

2-3 FINANCIAL INSTITUTIONS Direct funds transfers are common among individuals and small businesses and in economies where fi nancial markets and institutions are less developed. But large businesses in developed economies generally fi nd it more effi cient to enlist the services of a fi nancial institution when it comes time to raise capital.

In the United States and other developed nations, a set of highly effi cient fi nancial intermediaries has evolved. Their original roles were generally quite spe- cifi c, and regulation prevented them from diversifying. However, in recent years, regulations against diversifi cation have been largely removed; and today the dif- ferences between institutions have become blurred. Still, there remains a degree of institutional identity. Therefore, it is useful to describe the major categories of fi nancial institutions here. Keep in mind, though, that one company can own a number of subsidiaries that engage in the different functions described next. 1. Investment banks traditionally help companies raise capital. They (a) help

corporations design securities with features that are currently attractive to investors, (b) buy these securities from the corporation, and (c) resell them to savers. Although the securities are sold twice, this process is really one pri- mary market transaction, with the investment banker acting as a facilitator to help transfer capital from savers to businesses. Since the investment bank gen- erally guarantees that the fi rm will raise the needed capital, the investment bankers are also called underwriters.

2. Commercial banks, such as Bank of America, Citibank, Wells Fargo, Wacho- via, and JPMorgan Chase, are the traditional “department stores of fi nance” because they serve a variety of savers and borrowers. Historically, commercial banks were the major institutions that handled checking accounts and through which the Federal Reserve System expanded or contracted the money supply. Today, however, several other institutions also provide checking services and signifi cantly infl uence the money supply. Note too that the larger banks are generally part of fi nancial services corporations as described next.4

3. Financial services corporations are large conglomerates that combine many different fi nancial institutions within a single corporation. Most fi nancial ser- vices corporations started in one area but have now diversifi ed to cover most of the fi nancial spectrum. For example, Citigroup owns Citibank (a commer- cial bank), Smith Barney (an investment bank and securities brokerage organi- zation), insurance companies, and leasing companies.

Investment Bank An organization that underwrites and distributes new investment securities and helps businesses obtain financing.

Commercial Bank The traditional department store of finance serving a variety of savers and borrowers.

Financial Services Corporation A firm that offers a wide range of financial services, including investment banking, brokerage operations, insurance, and commercial banking.

SEL F TEST Distinguish between physical asset markets and fi nancial asset markets.

What’s the diff erence between spot markets and futures markets?

Distinguish between money markets and capital markets.

What’s the diff erence between primary markets and secondary markets?

Diff erentiate between private and public markets.

Why are fi nancial markets essential for a healthy economy and economic growth?

Give an example of a derivative and explain how its value is related to that of an “underlying asset.”

4 Two other institutions that were important a few years ago were savings and loan associations and mutual savings banks. Most of these organizations have now been merged into commercial banks.

35Chapter 2 Financial Markets and Institutions

4. Credit unions are cooperative associations whose members are supposed to have a common bond, such as being employees of the same fi rm. Members’ savings are loaned only to other members, generally for auto purchases, home improvement loans, and home mortgages. Credit unions are often the cheap- est source of funds available to individual borrowers.

5. Pension funds are retirement plans funded by corporations or government agencies for their workers and administered primarily by the trust depart- ments of commercial banks or by life insurance companies. Pension funds invest primarily in bonds, stocks, mortgages, and real estate.

6. Life insurance companies take savings in the form of annual premiums; invest these funds in stocks, bonds, real estate, and mortgages; and make payments to the benefi ciaries of the insured parties. In recent years, life insurance com- panies have also offered a variety of tax-deferred savings plans designed to provide benefi ts to participants when they retire.

7. Mutual funds are corporations that accept money from savers and then use these funds to buy stocks, long-term bonds, or short-term debt instruments issued by businesses or government units. These organizations pool funds and thus reduce risks by diversifi cation. They also achieve economies of scale in analyzing securities, managing portfolios, and buying and selling securi- ties. Different funds are designed to meet the objectives of different types of savers. Hence, there are bond funds for those who prefer safety, stock funds for savers who are willing to accept signifi cant risks in the hope of higher returns, and still other funds that are used as interest-bearing checking accounts (money market funds). There are literally thousands of different mutual funds with dozens of different goals and purposes.

Mutual funds have grown more rapidly than most other institutions in recent years, in large part because of a change in the way corporations provide for employees’ retirement. Before the 1980s, most corporations said, in effect, “Come work for us; and when you retire, we will give you a retirement income based on the salary you were earning during the last fi ve years before you retired.” The company was then responsible for setting aside funds each year to make sure it had the money available to pay the agreed-upon retirement benefi ts. That situ- ation is changing rapidly. Today new employees are likely to be told, “Come work for us, and we will give you some money each payday that you can invest for your future retirement. You can’t get the money until you retire (without paying a huge tax penalty); but if you invest wisely, you can retire in comfort.” Most workers recognize that they don’t know how to invest wisely, so they turn their retirement funds over to a mutual fund. Hence, mutual funds are growing rap- idly. Excellent information on the objectives and past performances of the various funds are provided in publications such as Value Line Investment Survey and Morn- ingstar Mutual Funds, which are available in most libraries and on the Internet.

8. Exchange Traded Funds (ETFs) are similar to regular mutual funds and are often operated by mutual fund companies. ETFs buy a portfolio of stocks of a cer- tain type—for example, the S&P 500 or media companies or Chinese companies—and then sell their own shares to the public. ETF shares are gener- ally traded in the public markets, so an investor who wants to invest in the Chinese market, for example, can buy shares in an ETF that holds stocks in that particular market.

9. Hedge funds are also similar to mutual funds because they accept money from savers and use the funds to buy various securities, but there are some impor- tant differences. While mutual funds (and ETFs) are registered and regulated by the Securities and Exchange Commission (SEC), hedge funds are largely unregulated. This difference in regulation stems from the fact that mutual funds typically target small investors, whereas hedge funds typically have

Mutual Funds Organizations that pool investor funds to purchase financial instruments and thus reduce risks through diversification.

Money Market Funds Mutual funds that invest in short-term, low-risk securities and allow investors to write checks against their accounts.

36 Part 2 Fundamental Concepts in Financial Management

large minimum investments (often exceeding $1 million) and are marketed primarily to institutions and individuals with high net worths. Hedge funds received their name because they traditionally were used when an individual was trying to hedge risks. For example, a hedge fund manager who believes that interest rate differentials between corporate and Treasury bonds are too large might simultaneously buy a portfolio of corporate bonds and sell a port- folio of Treasury bonds. In this case, the portfolio would be “hedged” against overall movements in interest rates, but it would perform especially well if the spread between these securities were to narrow.

However, some hedge funds take on risks that are considerably higher than that of an average individual stock or mutual fund. For example, in 1998, Long-Term Capital Management (LTCM), a high-profi le hedge fund whose managers included several well-respected practitioners as well as two Nobel Prize–winning professors who were experts in investment theory, made some incorrect assumptions and “blew up.”5 LTCM had many billions of dollars under management, and it owed large amounts of money to a number of banks. To avert a worldwide crisis, the Federal Reserve orchestrated a buyout of the fi rm by a group of New York banks.

As hedge funds have become more popular, many of them have begun to lower their minimum investment requirements. Perhaps not surprisingly, their rapid growth and shift toward smaller investors have also led to a call for more regulation.

10. Private equity companies are organizations that operate much like hedge funds; but rather than buying some of the stock of a fi rm, private equity players buy and then manage entire fi rms. Most of the money used to buy the target com- panies is borrowed. Recent examples include Cerberus Capital’s buyout of Chrysler and private equity company JC Flowers’ proposed $25 billion pur- chase of Sallie Mae, the largest student loan company. The Sallie Mae deal is in jeopardy—Flowers planned to borrow most of the money for the purchase, but the subprime situation has made borrowing more diffi cult and expensive. Flowers tried to back out of the deal, but Sallie Mae executives insisted that it complete the transaction or pay a $900 million “breakup fee.”

With the exception of hedge funds and private equity companies, fi nancial institu- tions are regulated to ensure the safety of these institutions and to protect investors. Historically, many of these regulations—which have included a prohibition on nation- wide branch banking, restrictions on the types of assets the institutions could buy, ceilings on the interest rates they could pay, and limitations on the types of services they could provide—tended to impede the free fl ow of capital and thus hurt the effi - ciency of the capital markets. Recognizing this fact, policy makers took several steps during the 1980s and 1990s to deregulate fi nancial services companies. For example, the restriction barring nationwide branching by banks was eliminated in 1999.

Panel A of Table 2-2 lists the 10 largest U.S. bank holding companies, while Panel B shows the leading world banking companies. Among the world’s 10 larg- est, only two (Citigroup and Bank of America) are based in the United States. While U.S. banks have grown dramatically as a result of recent mergers, they are still small by global standards. Panel C of the table lists the 10 leading underwrit- ers in terms of dollar volume of new debt and equity issues. Six of the top under- writers are also major commercial banks or are part of bank holding companies, which confi rms the continued blurring of distinctions between different types of fi nancial institutions.

5 See Franklin Edwards, “Hedge Funds and the Collapse of Long-Term Capital Management,” Journal of Economic Perspectives, Vol. 13, no. 2 (Spring 1999), pp. 189–210, for a thoughtful review of the implications of Long-Term Capital Management’s collapse.

37Chapter 2 Financial Markets and Institutions

Largest Banks and UnderwritersT a b l e 2 - 2

Panel A U.S. Bank Holding Companiesa

Panel B World Banking Companiesb

Panel C Leading Global Underwritersc

Citigroup Inc. UBS AG (Zurich) Citigroup Inc.

Bank of America Corp. Barclays PLC (London) JPMorgan

JPMorgan Chase & Co. BNP Paribas (Paris) Deutsche Bank AG

Wachovia Corp. Citigroup Inc. (New York) Merrill Lynch

Taunus Corp. HSBC Holdings PLC (London) Morgan Stanley

Wells Fargo & Co. Royal Bank of Scotland Group PLC (Edinburgh)

Lehman Brothers

HSBC North America Holdings Inc.

Credit Agricole (Paris) Goldman Sachs

U.S. Bancorp Mitsubishi UFJ Financial Group (Tokyo)

Barclays Capital

Bank of New York, The Mellon Corp.

Deutsche Bank AG (Frankfurt) UBS AG

SunTrust Banks, Inc. Bank of America Corp. (Charlotte) Credit Suisse

Notes: a Ranked by total assets as of December 31, 2007. Source: National Information Center, www.ffiec.gov/ nicpubweb/nicweb/Top50Form.aspx.

b Ranked by total assets as of December 31, 2007. Source: Thomson One Banker. c Ranked by dollar amount raised through new issues (stocks and bonds) in 2007. For this ranking, the lead underwriter (manager) is given credit for the entire issue. Source: Adapted from The Wall Street Journal, January 2, 2008, p. R18.

The fi nancial environment has been undergoing tremen- dous changes, including breakthroughs in technology, increased globalization, and shifts in the regulatory environ- ment. All of these factors have presented fi nancial managers and investors with opportunities, but those opportunities are accompanied by substantial risks. Consider the case of Citigroup Inc., which was created in 1998 when Citicorp and Travelers Group (which included the investment fi rm Salomon Smith Barney) merged. Citigroup today operates in more than 100 countries, has roughly 200 million customers and 275,000 employees, and holds more than $2.2 trillion (that’s over two thousand billion!) worth of assets. Citigroup resulted from three important trends: 1. Regulatory changes made it possible for U.S. corpora-

tions to engage in commercial banking, investment banking, insurance, and other activities.

2. Increased globalization made it essential for fi nancial in- stitutions to follow their clients and thus operate in many countries.

3. Changing technology led to increased economies of scale and scope, both of which increased the relative effi ciency of huge diversifi ed companies such as Citigroup.

Citigroup has grown, and it is now the largest fi nancial insti- tution in the world. But as the chapter opening vignette indi- cated, Citigroup has been hit hard by the mortgage debacle; and its chairperson, Charles Prince, recently lost his job. When you read this, you might access the Internet to fi nd the extent to which Citigroup has been able to rebound from its recent diffi culties.

CITIGROUP BUILT TO COMPETE IN A CHANGING ENVIRONMENT

www.ffiec.gov/nicpubweb/nicweb/Top50Form.aspx

38 Part 2 Fundamental Concepts in Financial Management

2-4 THE STOCK MARKET As noted earlier, outstanding, previously issued securities are traded in the sec- ondary markets. By far, the most active secondary market—and the most impor- tant one to fi nancial managers—is the stock market, where the prices of fi rms’ stocks are established. Because the primary goal of fi nancial managers is to maximize their fi rms’ stock prices, knowledge of the stock market is important to anyone involved in managing a business.

There are a number of different stock markets. The two leaders are the New York Stock Exchange (NYSE) and the Nasdaq stock market. Stocks are traded using a variety of market procedures, but there are just two basic types: (1) physical location exchanges, which include the NYSE, the American Stock Exchange (AMEX), and several regional stock exchanges, and (2) electronic dealer-based markets, which include the Nasdaq, the less formal over-the-counter market, and the recently de- veloped electronic communications networks (ECNs). (See the box entitled, “The NYSE and Nasdaq Go Global.”) Because the physical location exchanges are easier to describe and understand, we discuss them fi rst.

SEL F TEST What’s the diff erence between a commercial bank and an investment bank?

List the major types of fi nancial institutions and briefl y describe the primary function of each.

What are some important diff erences between mutual funds, Exchange Traded Funds, and hedge funds? How are they similar?

Advances in computers and telecommunications that spurred consolidation in the fi nancial services industry have also promoted online trading systems that bypass the tradi- tional exchanges. These systems, which are known as elec- tronic communications networks (ECNs), use electronic tech- nology to bring buyers and sellers together. The rise of ECNs accelerated the move toward 24-hour trading. U.S. investors who wanted to trade after the U.S. markets closed could uti- lize an ECN, thus bypassing the NYSE and Nasdaq. Recognizing the new threat, the NYSE and Nasdaq took action. First, both exchanges went public, which enabled them to use their stock as “currency” that could be used to buy ECNs and other exchanges across the globe. For exam- ple, Nasdaq acquired the American Stock Exchange (AMEX), several ECNs, and 25% of the London Stock Exchange; and it

is actively seeking to merge with other exchanges around the world. The NYSE has taken similar actions, including a merger with the largest European exchange, Euronext, to form NYSE Euronext. These actions illustrate the growing importance of global trading, especially electronic trading. Indeed, many pundits have concluded that the fl oor traders who buy and sell stocks on the NYSE and other physical exchanges will soon become a thing of the past. That may or may not be true, but it is clear that stock trading will continue to undergo dramatic changes in the upcoming years. To fi nd a wealth of up-to-date information on the NYSE and Nasdaq, go to Google (or another search engine) and do NYSE history and Nasdaq history searches.

THE NYSE AND NASDAQ GO GLOBAL

39Chapter 2 Financial Markets and Institutions

2-4a Physical Location Stock Exchanges Physical location exchanges are tangible entities. Each of the larger ones occupies its own building, allows a limited number of people to trade on its fl oor, and has an elected governing body—its board of governors. Members of the NYSE for- merly had “seats” on the exchange, although everybody stood up. Today the seats have been exchanged for trading licenses, which are auctioned to member organi- zations and cost about $50,000 per year. Most of the larger investment banks operate brokerage departments. They purchase seats on the exchanges and designate one or more of their offi cers as members. The exchanges are open on all normal working days, with the members meeting in a large room equipped with tele- phones and other electronic equipment that enable each member to communicate with his or her fi rm’s offi ces throughout the country.

Like other markets, security exchanges facilitate communication between buyers and sellers. For example, Merrill Lynch (the fourth largest brokerage fi rm) might re- ceive an order in its Atlanta offi ce from a customer who wants to buy shares of GE stock. Simultaneously, the Denver offi ce of Morgan Stanley (the fi fth largest brokerage fi rm) might receive an order from a customer wanting to sell shares of GE. Each broker communicates electronically with the fi rm’s representative on the NYSE. Other bro- kers throughout the country are also communicating with their own exchange mem- bers. The exchange members with sell orders offer the shares for sale, and they are bid for by the members with buy orders. Thus, the exchanges operate as auction markets.6

2-4b Over-the-Counter (OTC) and the Nasdaq Stock Markets

While the stocks of most large companies trade on the NYSE, a larger number of stocks trade off the exchange in what was traditionally referred to as the over-the- counter (OTC) market. An explanation of the term over-the-counter will help clarify how this term arose. As noted earlier, the exchanges operate as auction markets— buy and sell orders come in more or less simultaneously, and exchange members match these orders. When a stock is traded infrequently, perhaps because the fi rm is new or small, few buy and sell orders come in and matching them within a rea- sonable amount of time is diffi cult. To avoid this problem, some brokerage fi rms maintain an inventory of such stocks and stand prepared to make a market for them. These “dealers” buy when individual investors want to sell, and they sell part of their inventory when investors want to buy. At one time, the inventory of securities was kept in a safe; and the stocks, when bought and sold, were literally passed over the counter.

Physical Location Exchanges Formal organizations having tangible physical locations that conduct auction markets in designated (“listed”) securities.

Over-the-Counter (OTC) Market A large collection of brokers and dealers, connected electronically by telephones and computers, that provides for trading in unlisted securities.

6 The NYSE is actually a modifi ed auction market wherein people (through their brokers) bid for stocks. Originally—in 1792—brokers would literally shout, “I have 100 shares of Erie for sale; how much am I off ered?” and then sell to the highest bidder. If a broker had a buy order, he or she would shout, “I want to buy 100 shares of Erie; who’ll sell at the best price?” The same general situation still exists, although the exchanges now have members known as specialists who facilitate the trading process by keeping an inventory of shares of the stocks in which they specialize. If a buy order comes in at a time when no sell order arrives, the specialist will sell off some inventory. Similarly, if a sell order comes in, the specialist will buy and add to inventory. The specialist sets a bid price (the price the specialist will pay for the stock) and an asked price (the price at which shares will be sold out of inventory). The bid and asked prices are set at levels designed to keep the inventory in balance. If many buy orders start coming in because of favorable developments or many sell orders come in because of unfavorable events, the specialist will raise or lower prices to keep supply and demand in balance. Bid prices are somewhat lower than asked prices, with the diff erence, or spread, representing the specialist’s profi t margin.

Special facilities are available to help institutional investors such as mutual or pension funds sell large blocks of stock without depressing their prices. In essence, brokerage houses that cater to institutional clients will purchase blocks (defi ned as 10,000 or more shares) and then resell the stock to other institutions or individuals. Also, when a fi rm has a major announcement that is likely to cause its stock price to change sharply, it will ask the exchange to halt trading in its stock until the announcement has been made and the resulting information has been digested by investors.

40 Part 2 Fundamental Concepts in Financial Management

Today these markets are often referred to as dealer markets. A dealer market includes all facilities that are needed to conduct security transactions, but the trans- actions are not made on the physical location exchanges. The dealer market system consists of (1) the relatively few dealers who hold inventories of these securities and who are said to “make a market” in these securities; (2) the thousands of brokers who act as agents in bringing the dealers together with investors; and (3) the com- puters, terminals, and electronic networks that provide a communication link be- tween dealers and brokers. The dealers who make a market in a particular stock quote the price at which they will pay for the stock (the bid price) and the price at which they will sell shares (the ask price). Each dealer’s prices, which are adjusted as supply and demand conditions change, can be seen on computer screens across the world. The bid-ask spread, which is the difference between bid and ask prices, represents the dealer’s markup, or profi t. The dealer’s risk increases when the stock is more volatile or when the stock trades infrequently. Generally, we would expect volatile, infrequently traded stocks to have wider spreads in order to compensate the dealers for assuming the risk of holding them in inventory.

Brokers and dealers who participate in the OTC market are members of a self- regulatory body known as the National Association of Securities Dealers (NASD), which licenses brokers and oversees trading practices. The computerized network used by the NASD is known as the NASD Automated Quotation System (Nasdaq).

Nasdaq started as just a quotation system, but it has grown to become an orga- nized securities market with its own listing requirements. Over the past decade, the competition between the NYSE and Nasdaq has become increasingly fi erce. As noted earlier, the Nasdaq has invested in the London Stock Exchange and other market makers, while the NYSE merged with Euronext. Since most of the larger companies trade on the NYSE, the market capitalization of NYSE-traded stocks is much higher than for stocks traded on Nasdaq. However, reported volume (number of shares traded) is often larger on Nasdaq, and more companies are listed on Nasdaq.7

Interestingly, many high-tech companies such as Microsoft, Google, and Intel have remained on Nasdaq even though they meet the listing requirements of the NYSE. At the same time, however, other high-tech companies have left Nasdaq for the NYSE. Despite these defections, Nasdaq’s growth over the past decade has been impressive. In the years ahead, competition between Nasdaq and NYSE Eu- ronext will no doubt remain fi erce.

Dealer Market Includes all facilities that are needed to conduct security transactions not conducted on the physical location exchanges.

7 One transaction on Nasdaq generally shows up as two separate trades (the buy and the sell). This “double counting” makes it diffi cult to compare the volume between stock markets.

SEL F TEST What are the diff erences between the physical location exchanges and the

Nasdaq stock market?

What is the bid-ask spread?

2-5 THE MARKET FOR COMMON STOCK Some companies are so small that their common stocks are not actively traded; they are owned by relatively few people, usually the companies’ managers. These fi rms are said to be privately owned, or closely held, corporations; and their stock is called closely held stock. In contrast, the stocks of most large companies are owned by thousands of investors, most of whom are not active in management. These

Closely Held Corporation A corporation that is owned by a few individuals who are typically associated with the firm’s management.

41Chapter 2 Financial Markets and Institutions

companies are called publicly owned corporations, and their stock is called pub- licly held stock.

A recent study found that institutional investors owned about 46% of all pub- licly held common stocks. Included are pension plans (26%), mutual funds (10%), foreign investors (6%), insurance companies (3%), and brokerage fi rms (1%). How- ever, because these institutions buy and sell relatively actively, they account for about 75% of all transactions. Thus, institutional investors have a signifi cant infl u- ence on the prices of individual stocks.

2-5a Types of Stock Market Transactions We can classify stock market transactions into three distinct categories: 1. Outstanding shares of established publicly owned companies that are traded: the sec-

ondary market. Allied Food Products, the company we will study in Chapters 3 and 4, has 50 million shares of stock outstanding. If the owner of 100 shares sells his or her stock, the trade is said to have occurred in the secondary market. Thus, the market for outstanding shares, or used shares, is the secondary mar- ket. The company receives no new money when sales occur in this market.

2. Additional shares sold by established publicly owned companies: the primary market. If Allied Food decides to sell (or issue) an additional 1 million shares to raise new equity capital, this transaction is said to occur in the primary market.8

3. Initial public offerings made by privately held fi rms: the IPO market. In the summer of 2004, Google sold shares to the public for the fi rst time at $85 per share. By February 2008, the stock was selling for $495, so it had increased by over 480%. In 2006, McDonald’s owned Chipotle Mexican Grill. McDonald’s then sold its shares to the public for about $47.50 to raise capital to support its core busi- ness; and by February 2008, Chipotle’s stock price was $117. Making these types of offerings is called going public. Whenever stock in a closely held corporation is offered to the public for the fi rst time, the company is said to be going public. The market for stock that is just being offered to the public is called the initial public offering (IPO) market.9

The number of new IPOs rises and falls with the stock market. When the market is strong, many companies go public to bring in new capital and to give their found- ers an opportunity to cash out some of their shares. Table 2-3 lists the largest, the best performing, and the worst performing IPOs of 2007 and shows how they per- formed from their offering dates through year-end 2007. As the table shows, not all IPOs are as well received as Google and Chipotle. Moreover, even if you are able to identify a “hot” issue, it is often diffi cult to purchase shares in the initial offering. These deals are often oversubscribed, which means that the demand for shares at the offering price exceeds the number of shares issued. In such instances, investment bankers favor large institutional investors (who are their best customers); and small investors fi nd it hard, if not impossible, to get in on the ground fl oor. They can buy the stock in the aftermarket; but evidence suggests that when an investor does not get in on the ground fl oor, IPOs often underperform the overall market over the long run.10

Publicly Owned Corporation A corporation that is owned by a relatively large number of individuals who are not actively involved in the firm’s management.

Going Public The act of selling stock to the public at large by a closely held corporation or its principal stockholders.

Initial Public Offering (IPO) Market The market for stocks of companies that are in the process of going public.

8 Allied has 60 million shares authorized but only 50 million outstanding; thus, it has 10 million authorized but unissued shares. If it had no authorized but unissued shares, management could increase the authorized shares by obtaining stockholders’ approval, which would generally be granted without any arguments. 9 A number of years ago Coors, the beer company, off ered some of its shares to the public. These shares were designated Class B, and they were nonvoting. The Coors family retained the founders’ shares, called Class A stock, which carried full voting privileges. This illustrates how the managers of a company can use diff erent classes of shares to maintain control. However, the nonvoting shares always sell for less than the voting shares, so using nonvoting shares does not maximize the value of the fi rm. 10 See Jay R. Ritter, “The Long-Run Performance of Initial Public Off erings,” Journal of Finance, Vol. 46, no. 1 (March 1991), pp. 3–27.

42 Part 2 Fundamental Concepts in Financial Management

Initial Public Offerings in 2007T a b l e 2 - 3

THE BIGGEST IPOs

Percent Change From Offer

Issuer Issue Date

U.S. Proceeds (Millions) First-Day Trading

Through 12/31/07

Blackstone 06/21/07 $4,753.3 !13.1% "28.6% MF Global 07/18/07 2,921.4 "8.2 !4.9 MetroPCS Communications 04/18/07 1,322.5 !19.1 "15.4 Cosan 08/16/07 1,172.7 unch. !20.0 Och-Ziff Capital Management Group 11/13/07 1,152.0 "4.2 "17.9 VMware 08/13/07 1,100.6 !75.9 !193.1 Giant Interactive Group 10/31/07 1,019.5 !17.6 "16.3 National CineMedia 02/07/07 882.0 !22.2 !20.0 AECOM Technology 05/09/07 808.5 !5.5 !42.9 EnergySolutions 11/14/07 765.9 !0.04 !17.3

THE BEST PERFORMERS

Percent Change From Offer

Issuer Issue Date Offer Price

U.S. Proceeds (Millions) First-Day Trading

Through 12/31/07

JA Solar Holdings 02/06/07 $15.00 $ 258.8 !18.7% !365.4% MercadoLibre 08/09/07 18.00 332.8 !58.3 !310.4 Yingli Green Energy Holding 06/07/07 11.00 324.5 "4.6 !251.8 VMware 08/13/07 29.00 1,100.6 !75.9 !193.1 Lululemon Athletica 07/26/07 18.00 376.7 !55.6 !163.2 Masimo 08/07/07 17.00 233.0 !22.9 !132.1 MSCI 11/14/07 18.00 289.8 !38.7 !113.3 American Public Education 11/08/07 20.00 107.8 !79.6 !108.9 WuXi PharmaTech (Cayman) 08/08/07 14.00 212.3 !40.0 !108.9 Dolan Media 08/01/07 14.50 224.4 !22.2 !101.2

THE WORST PERFORMERS

Percent Change From Offer

Issuer Issue Date Offer Price

U.S. Proceeds (Millions) First-Day Trading

Through 12/31/07

Superior Offshore International 04/19/07 $15.00 $175.4 !16.9% "66.5% VeriChip 02/09/07 6.50 20.2 unch. "65.4 ImaRx Therapeutics 07/25/07 5.00 15.0 "4.2 "61.4 BigBand Networks 03/14/07 13.00 160.0 !30.8 "60.5 Meruelo Maddux Properties 01/24/07 10.00 455.5 !6.0 "60.0 HFF 01/30/07 18.00 296.0 !3.9 "57.0 Glu Mobile 03/21/07 11.50 86.2 !6.9 "54.6 Limelight Networks 06/07/07 15.00 276.0 !47.9 "54.1 Xinhua Finance Media 03/08/07 13.00 300.0 "12.7 "53.8 GSI Technology 03/29/07 5.50 35.4 "3.8 "53.6

Source: Lynn Cowan, “IPOs Tally Record Amount of Cash,” The Wall Street Journal, January 2, 2008, p. R10.

43Chapter 2 Financial Markets and Institutions

Google Inc.’s highly publicized IPO attracted attention because of its size (Google raised $1.67 billion in stock) and because of the way the sale was con- ducted. Rather than having the offer price set by its investment bankers, Google conducted a Dutch auction, where individual investors placed bids for shares directly. In a Dutch auction, the actual transaction price is set at the highest price (the clearing price) that causes all of the offered shares to be sold. All in- vestors who set their bids at or above the clearing price received all of the shares they subscribed to at the offer price, which turned out to be $85. While Google’s IPO was in many ways precedent-setting, few companies going pub- lic since then have been willing or able to use the Dutch auction method to al- locate their IPO shares.

It is important to recognize that fi rms can go public without raising any addi- tional capital. For example, the Ford Motor Company was once owned exclusively by the Ford family. When Henry Ford died, he left a substantial part of his stock to the Ford Foundation. When the Foundation later sold some of the stock to the gen- eral public, the Ford Motor Company went public, even though the company itself raised no capital in the transaction.

SEL F TEST Diff erentiate between closely held and publicly owned corporations.

Diff erentiate between primary and secondary markets.

What is an IPO?

What is a Dutch auction, and what company used this procedure for its IPO?

11 Most free sources provide quotes that are delayed 15 minutes. Real-time quotes can be obtained for a fee.

2-6 STOCK MARKETS AND RETURNS Anyone who has invested in the stock market knows that there can be (and gener- ally are) large differences between expected and realized prices and returns. Fig- ure 2-2 shows how total realized portfolio returns have varied from year to year. As logic would suggest (and as is demonstrated in Chapter 8), a stock’s expected return as estimated by investors at the margin is always positive; otherwise, inves- tors would not buy the stock. However, as Figure 2-2 shows, in some years, actual returns are negative.

2–6a Stock Market Reporting Up until a few years ago, the best source of stock quotations was the business section of daily newspapers such as The Wall Street Journal. One problem with newspapers, however, is that they report yesterday’s prices. Now it is possible to obtain real-time quotes throughout the day from a wide variety of Internet sources.11 One of the best is Yahoo!, and Figure 2-3 shows a detailed quote for GlaxoSmithKline PLC (GSK). As the heading shows, GlaxoSmithKline is traded on the NYSE under the symbol GSK. (The NYSE is just one of many world markets on which the stock trades.) The fi rst two rows of information show that GSK had last traded at $45.89 and that the stock had traded thus far on this day from as low as $45.42 to as high as $46.23. (Note that the price is reported in decimals rather than fractions, refl ecting a recent change in trading conventions.) The last trade shown was at 2:20 p.m. ET on February 5, 2008; and its price range during the past 52 weeks was between $45.89 and $59.98.

44 Part 2 Fundamental Concepts in Financial Management

The next three lines show that GSK opened trading on February 5 at $46.07, that it closed on February 4 at $46.87, and that its price fell by $0.98 (or a 2.09 % de- crease) from the previous close to the current price. So far during the day, 1,835,434 shares had traded hands. GSK’s average daily trading volume (based on the past three months) was 1,968,960 shares, so trading so far that day was close to the aver- age. The total value of all of GSK’s stock, called its market cap, was $125.39 billion.

The last three lines report other market information for GSK. If it were trading on Nasdaq rather than a listed exchange, the most recent bid and ask quotes from dealers would have been shown. However, because it trades on the NYSE, these data are not available. GSK’s P/E ratio (price per share divided by the most recent 12 months’ earnings) was 12.30, and its earnings per share for the most recent 12 months was $3.73 (ttm stands for “trailing 12 months”—in other words, the most

Stock Quote for GlaxoSmithKline, February 5, 2008FIGURE 2-3

Source: http://fi nance.yahoo.com.

Last Trade: Trade Time: Change: Prev Close: Open: Bid: Ask: 1y Target Est:

45.89 2.20PM ET 0.98 (2.09%) 46.87 46.07 N/A N/A 56.10

47.0 46.5 46.0 45.5 45.0 10am 12pm 2pm 4pm

New! Try our new Charts in Beta GSK 5-Feb 2:04pm (C) Yahoo!

1d 5d 3m 6m 1y 2y 5y max

Annual Report for GSK

Add Quotes to Your Web Site Add GSK to Portfolio Set Alert Download Data

Day’s Range: 52wk Range: Volume: Avg Vol (3m): Market Cap: P/E (ttm): EPS (ttm): Div & Yield:

45.42 - 46.23 45.89 - 59.98 1,835,434 1,968,960 125.39B 12.30 3.73 2.13 (4.50%)

GLAXOSMITHKLINE PLC (NYSE:GSK) Edit

Returns (%)

1992 1995 199819891983 198619801974 197719711968

–10

–20

–30

Years 2001 2004 2007

S&P 500 Index, Total Returns: Dividend Yield + Capital Gain or Loss, 1968–2007FIGURE 2-2

Source: Data taken from various issues of The Wall Street Journal “Investment Scoreboard” section.

http://finance.yahoo.com

45Chapter 2 Financial Markets and Institutions

Stock market indexes are designed to show the performance of the stock market. However, there are many stock indexes, and it is diffi cult to determine which index best refl ects mar- ket actions. Some are designed to represent the entire stock market, some track the returns of certain industry sectors, and others track the returns of small-cap, mid-cap, or large-cap stocks. In addition, there are indexes for diff erent countries. We discuss here the three leading U.S. indexes. These indexes are used as a benchmark for comparing individual stocks with the overall market, for measuring the trend in stock prices over time, and for determining how various economic factors aff ect the market.

Dow Jones Industrial Average Unveiled in 1896 by Charles H. Dow, the Dow Jones Indus- trial Average (DJIA) began with just 10 stocks, was expanded in 1916 to 20 stocks, and then was increased to 30 stocks in 1928, when the editors of The Wall Street Jour- nal began adjusting the index for stock splits and making periodic substitutions. Today the DJIA still includes 30 com- panies. They represent almost a fi fth of the market value of all U.S. stocks, and all are leading companies in their indus- tries and widely held by individual and institutional inves- tors. Visit www.dowjones.com to get more information about the DJIA. You can fi nd out how it is calculated, the companies that make up the DJIA, and more history about the DJIA. In addition, a DJIA time line shows various histori- cal events.

S&P 500 Index Created in 1926, the S&P 500 Index is widely regarded as the standard for measuring large-cap U.S. stock market per- formance. The stocks in the S&P 500 are selected by the Standard & Poor’s Index Committee, and they are the lead- ing companies in the leading industries. It is weighted by

each stock’s market value, so the largest companies have the greatest infl uence. The S&P 500 is used for benchmark- ing by 97% of all U.S. money managers and pension plan sponsors, and approximately $700 billion is held in index funds designed to mirror the same performance of the index.

Nasdaq Composite Index The Nasdaq Composite Index measures the performance of all stocks listed on the Nasdaq. Currently, it includes more than 5,000 companies; and because many companies in the technology sector are traded on the computer-based Nas- daq exchange, this index is generally regarded as an eco- nomic indicator of the high-tech industry. Microsoft, Intel, Google, and Cisco Systems are the four largest Nasdaq com- panies, and they make up a high percentage of the index’s value-weighted market capitalization. For this reason, sub- stantial movements in the same direction by these four com- panies can move the entire index.

Recent Performance The accompanying fi gure plots the value that an investor would now have if he or she had invested $1 in each of the three indexes on January 1, 1995. The returns on the three indexes are compared with an investment strategy that invests only in 1-year T-bills. Each of these indexes performed quite well through 1999. However, for a couple of years, each index stum- bled before beginning to rebound again in 2003. During the last 13 years, the average annualized returns of these indexes ranged from 8.8% for the S&P 500 to 9.6% for the Dow. Nasdaq experienced a huge bubble in 1999, refl ecting overly optimistic valuations of technology companies. However, in 2000, the bubble burst and technology stock valuations spiraled down- ward, causing the Nasdaq Index to revert back to a level compa- rable to the S&P 500 and Dow Jones Industrial Average Index.

MEASURING THE MARKET

1995 1996 1997 1998 1999 2000 2001 2002

Nasdaq

DJIA

S&P 500

T-bills

2003 2004 2005

Value of $1 Investment

2006 2007 2008 Years

Growth of a $1 Investment Made on January 1, 1995

www.dowjones.com

46 Part 2 Fundamental Concepts in Financial Management

12 If we constructed a graph like Figure 2-2 for individual stocks rather than for the index, far greater variability would be shown. Also, if we constructed a graph like Figure 2-2 for bonds, it would have similar ups and downs, but the bars would be far smaller, indicating that gains and losses on bonds are generally much smaller than those on stocks. Above-average bond returns occur in years when interest rates decline, losses occur when interest rates rise sharply, but interest payments tend to stabilize bonds’ total returns. We will discuss bonds in detail in Chapter 7.

recent 12 months). The mean of the analysts’ one-year target price for GSK was $56.10. GSK’s dividend was $2.13 per share, so the quarterly dividend was $0.5325 per share; and the dividend yield, which is the annual dividend divided by the pre- vious closing price, is 4.50%.

In Figure 2-3, the chart to the right plots the stock price during the day; however, the links below the chart allow you to pick different time intervals for plotting data. As you can see, Yahoo! provides a great deal of information in its de- tailed quote; and even more detail is available on the screen page below the basic quote information.

2-6b Stock Market Returns In Chapters 8 and 9, we will discuss in detail how a stock’s rate of return is calcu- lated, what the connection is between risk and returns, and what techniques ana- lysts use to value stocks. However, it is useful at this point to give you a rough idea of how stocks have performed in recent years. Figure 2-2 shows how the returns on large U.S. stocks have varied over the past years, and the box entitled “Measur- ing the Market” provides information on the major U.S. stock market indices and their performances since the mid-1990s.

The market trend has been strongly up since 1968, but by no means does it go up every year. Indeed, as we can see from Figure 2-2, the overall market was down in 9 of the 40 years, including the three consecutive years of 2000–2002. The stock prices of individual companies have likewise gone up and down.12 Of course, even in bad years, some individual companies do well; so “the name of the game” in se- curity analysis is to pick the winners. Financial managers attempt to do this, but they don’t always succeed. In subsequent chapters, we will examine the decisions managers make to increase the odds that their fi rms will perform well in the marketplace.

Would you expect a portfolio that consisted of the NYSE stocks to be more or less risky than a portfolio of Nasdaq stocks?

If we constructed a chart like Figure 2-2 for an average S&P 500 stock, do you think it would show more or less volatility? Explain.

SELF TEST

2-7 STOCK MARKET EFFICIENCY To begin this section, consider the following defi nitions: Market price: The current price of a stock. For example, the Internet showed

that on one day, GSK’s stock traded at $45.89. The market price had varied from $45.42 to $46.23 during that same day as buy and sell orders came in.

47Chapter 2 Financial Markets and Institutions

Intrinsic value: The price at which the stock would sell if all investors had all knowable information about a stock. This concept was discussed in Chapter 1, where we saw that a stock’s intrinsic value is based on its expected future cash fl ows and its risk. Moreover, the market price tends to fl uctuate around the intrinsic value; and the intrinsic value changes over time as the company suc- ceeds or fails with new projects, competitors enter or exit the market, and so forth. We can guess (or estimate) GSK’s intrinsic value, but different analysts will reach somewhat different conclusions.

Equilibrium price: The price that balances buy and sell orders at any given time. When a stock is in equilibrium, the price remains relatively stable until new information becomes available and causes the price to change. For example, GSK’s equilibrium price appears to be about $45.89, as it has been fl uctuating narrowly around this amount.

Effi cient market: A market in which prices are close to intrinsic values and stocks seem to be in equilibrium.

When markets are effi cient, investors can buy and sell stocks and be confi dent that they are getting good prices. When markets are ineffi cient, investors may be afraid to invest and may put their money “under the pillow,” which will lead to a poor allocation of capital and economic stagnation. So from an economic standpoint, market effi ciency is good.

Academics and fi nancial professionals have studied the issue of market effi - ciency extensively.13 As generally happens, some people think that markets are highly effi cient, others think that markets are highly ineffi cient, and others think that the issue is too complex for a simple answer.

Those who believe that markets are effi cient note that there are 100,000 or so full-time, highly trained professional analysts and traders operating in the market. Many have PhDs in physics, chemistry, and other technical fi elds in addition to advanced degrees in fi nance. Moreover, there are fewer than 3,000 major stocks; so if each analyst followed 30 stocks (which is about right, as analysts tend to focus on a specifi c industry), on average, 1,000 analysts would be following each stock. Further, these analysts work for organizations such as Goldman Sachs, Merrill Lynch, Citigroup, and Deutsche Bank or for Warren Buffett and other billionaire investors who have billions of dollars available to take advantage of bargains. Also, the SEC has disclosure rules which, combined with electronic information networks, means that new information about a stock is received by all analysts at about the same time, causing almost instantaneous revaluations. All of these fac- tors help markets be effi cient and cause stock prices to move toward their intrinsic values.

However, other people point to data that suggests that markets are not very effi cient. For example, on October 15, 1987, the S&P 500 lost 25% of its value. Many of the largest U.S. companies did worse, watching their prices get cut in half. In 2000, Internet stocks rose to phenomenally high prices, then fell to zero or close to it the following year. No truly important news was announced that could have

13 The general name for these studies is the effi cient markets hypothesis, or EMH. It was, and still is, a hypothesis that needs to be proved or disproved empirically. In the literature, researchers identifi ed three levels of effi ciency: weak form, which contends that information on past stock price movements cannot be used to predict future stock prices; semi-strong form, which contends that all publicly available information is immediately incorporated into stock prices (i.e., that one cannot analyze published reports and then beat the market); and strong form, which contends that even company insiders, with inside information, cannot earn abnormally high returns. Few people believe the strong form today, as a number of insiders have made large profi ts, been caught (it’s illegal to trade on inside information), and gone to jail. Martha Stewart is one, and she helped disprove the strong form of the EMH.

48 Part 2 Fundamental Concepts in Financial Management

caused either of these changes; and if the market was effi cient, it’s hard to see how such drastic changes could have occurred. Another situation that causes people to question market effi ciency is the apparent ability of some analysts to consistently outperform the market over long periods. Warren Buffett comes to mind, but there are others. If markets are truly effi cient, then each stock’s price should be close to its intrinsic value. That would make it hard for any analyst to consistently pick stocks that outperform the market.

The following diagram sums up where most observers seem to be today. There is an “effi ciency continuum,” with the market for some companies’ stocks being highly effi cient and the market for other stocks being highly ineffi cient. The key factor is the size of the company—the larger the fi rm, the more analysts tend to follow it and thus the faster new information is likely to be refl ected in the stock’s price. Also, different companies communicate better with analysts and investors; and the better the communications, the more effi cient the market for the stock.

Highly Ineffi cient Highly Effi cient

Small companies Large companies not followed by many followed by many analysts. Not much analysts. Good contact with investors. communications with investors.

As an investor, would you prefer to purchase a stock whose price was deter- mined in an effi cient or an ineffi cient market? If you thought you knew something that others didn’t know, you might prefer ineffi cient markets. But if you thought that those physics PhDs with unlimited buying power and access to company CEOs might know more than you, you would probably prefer effi cient markets, where the price you paid was likely to be the “right” price. From an economic standpoint, it is good to have effi cient markets in which everyone is willing to par- ticipate. So the SEC and other regulatory agencies should do everything they can to encourage market effi ciency.

Thus far we have been discussing the market for individual stocks. There is also a market for entire companies, where other companies, private equity groups, and large investors like Warren Buffett buy the entire company or a con- trolling stake in it. Suppose, for example, that Company X is in equilibrium, sell- ing at a price that is close to its intrinsic value but where the intrinsic value is based on it being operated by its current managers, who own 51% of the stock. However, suppose that astute analysts study the company and conclude that it could produce much higher earnings and cash fl ows under a different manage- ment team or if it were combined with some other company or if it were broken up into a number of separate pieces. In this case, the stock might be thought of as trading in an effi cient market while the company as a whole was not effi - ciently priced.

Some years ago, quite a few companies were ineffi ciently priced. But then along comes Warren Buffett, the private equity players, and hedge fund managers who are willing to contest entrenched managers. For example, Dow Jones, the owner of The Wall Street Journal, was controlled by its founding family, the Bancrofts. Dow Jones’s stock lagged the market for years. Then Rupert Murdoch, who

49Chapter 2 Financial Markets and Institutions

The effi cient markets hypothesis (EMH) remains one of the cor- nerstones of modern fi nance theory. It implies that, on aver- age, asset prices are about equal to their intrinsic values. The logic behind the EMH is straightforward. If a stock’s price is “too low,” rational traders will quickly take advantage of this opportunity and buy the stock, pushing prices up to the proper level. Likewise, if prices are “too high,” rational traders will sell the stock, pushing the price down to its equilibrium level. Proponents of the EMH argue that these forces keep prices from being systematically wrong. While the logic behind the EMH is compelling, many events in the real world seem inconsistent with the hypothesis, which has spurred a growing fi eld called behav- ioral fi nance. Rather than assuming that investors are ratio- nal, behavioral fi nance theorists borrow insights from psy- chology to better understand how irrational behavior can be sustained over time. Pioneers in this fi eld include psycholo- gists Daniel Kahneman, Amos Tversky, and Richard Thaler. Their work has encouraged a growing number of scholars to work in this promising area of research.14 Professor Thaler and his colleague Nicholas Barberis summarized much of this research in the article cited below. They argue that behavioral fi nance’s criticism of the EMH rests on two key points. First, it is often diffi cult or risky for traders to take advantage of mispriced assets. For example, even if you know that a stock’s price is too low because inves- tors have overreacted to recent bad news, a trader with lim- ited capital may be reluctant to buy the stock for fear that the same forces that pushed the price down may work to keep it artifi cially low for a long time. Similarly, during the recent stock market bubble, many traders who believed (correctly) that stock prices were too high lost a great deal of money selling stocks short in the early stages of the bubble, because prices went even higher before they eventually collapsed. Thus, mispricings may persist. The second point deals with why mispricings can occur in the fi rst place. Here insights from psychology come into play. For example, Kahneman and Tversky suggested that individuals view potential losses and gains diff erently. If you ask average individuals whether they would rather have $500 with certainty or fl ip a fair coin and receive $1,000 if a

head comes up and nothing if tails comes up, most would prefer the certain $500, which suggests an aversion to risk. However, if you ask people whether they would rather pay $500 with certainty or fl ip a coin and pay $1,000 if it’s heads and nothing if it’s tails, most would indicate that they prefer to fl ip the coin. Other studies suggest that people’s willing- ness to take a gamble depends on recent performance. Gam- blers who are ahead tend to take on more risks, whereas those who are behind tend to become more conservative. These experiments suggest that investors and manag- ers behave diff erently in down markets than they do in up markets, which might explain why those who made money early in the stock market bubble continued to invest their money in the market even as prices went ever higher. Other evidence suggests that individuals tend to overestimate their true abilities. For example, a large majority (upward of 90% in some studies) of people believe that they have above- average driving ability and above-average ability to get along with others. Barberis and Thaler point out that:

Overconfi dence may in part stem from two other biases, self-attribution bias and hindsight bias. Self-attribution bias refers to people’s tendency to ascribe any success they have in some activity to their own talents, while blaming failure on bad luck rather than on their inepti- tude. Doing this repeatedly will lead people to the pleas- ing, but erroneous, conclusion that they are very talented. For example, investors might become overconfi dent after several quarters of investing success [Gervais and Odean (2001)]. Hindsight bias is the tendency of people to believe, after an event has occurred, that they predicted it before it happened. If people think they predicted the past better than they actually did, they may also believe that they can predict the future better than they actually can.

Behavioral fi nance has been studied in both the corpo- rate fi nance and investments areas. Ulrike Malmendier of Stanford and Geoff rey Tate of Wharton found that overconfi - dence leads managers to overestimate their ability and thus the profi tability of their projects. This result may explain why so many corporate projects fail to live up to their stated expectations.

Sources: Nicholas Barberis and Richard Thaler, “A Survey of Behavioral Finance,” Chapter 18, Handbook of the Economics of Finance, edited by George Constantinides, Milt Harris, and René Stulz, part of the Handbooks in Economics Series (New York: Elsevier/North-Holland, 2003); and Ulrike Malmendier and Geoff rey Tate, “CEO Overconfi dence and Corporate Investment,” Stanford Graduate School of Business Research Paper #1799, June 2004.

A CLOSER LOOK AT BEHAVIORAL FINANCE THEORY

14 Three noteworthy sources for students interested in behavioral fi nance are Richard H. Thaler, Editor, Advances in Behavioral Finance (New York: Russell Sage Foundation, 1993); Hersh Shefrin, “Behavioral Corporate Finance,” Journal of Applied Corporate Finance, Vol. 14.3, Fall 2001, pp. 113–125; and Nicholas Barberis and Richard Thaler, “A Survey of Behavioral Finance,” Chapter 18, Handbook of the Economics of Finance, edited by George Constantinides, Milt Harris, and René Stulz , part of the Handbooks in Economics Series (New York: Elsevier/North-Holland, 2003). Students interested in learning more about the effi cient markets hypothesis should consult Burton G. Malkiel, A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing, 9th edition, (New York: W.W. Norton & Company, 2007).

50 Part 2 Fundamental Concepts in Financial Management

controls News Corporation, arguably the largest media company in the world, of- fered $60 per share for Dow Jones, which was then selling for about $35 per share. Murdoch planned to change The Wall Street Journal and combine its content with his Fox News and new fi nancial channel. To Murdoch, Dow Jones’ intrinsic value was $60. Without him or someone else who would operate the company differ- ently, the intrinsic value was about $35. One could, of course, argue that Dow Jones’ intrinsic value was $60 all along; but it was hard to know that until Murdoch came along and made his offer. Alternatively, one could argue that Murdoch raised the intrinsic value from $35 to $60. Finally, you can bet that many analysts on Wall Street are looking for the next Dow Jones. If they succeed, they will surely beat the market!

2-7a Conclusions about Market Efficiency As noted previously, if the stock market is effi cient, it is a waste of time for most people to seek bargains by analyzing published data on stocks. That follows because if stock prices already refl ect all publicly available information, they will be fairly priced; and a person can beat the market only with luck or inside informa- tion. So rather than spending time and money trying to fi nd undervalued stocks, it would be better to buy an index fund designed to match the overall market as refl ected in an index such as the S&P 500. However, if we worked for an institution with billions of dollars, we would try to fi nd undervalued stocks or companies because even a small undervaluation would amount to a great deal of money when investing millions rather than thousands. Also, markets are more effi cient for individual stocks than for entire companies; so for investors with enough capi- tal, it does make sense to seek out badly managed companies that can be acquired and improved. Note, though, that a number of private equity players are doing exactly that; so the market for entire companies may soon be as effi cient as that for individual stocks.

However, even if markets are effi cient and all stocks and companies are fairly priced, an investor should still be careful when selecting stocks for his or her port- folio. Most importantly, the portfolio should be diversifi ed, with a mix of stocks from various industries along with some bonds and other fi xed income securities. We will discuss diversifi cation in greater detail in Chapter 8, but it is an important consideration for most individual investors.

SEL F TEST What does it mean for a market to be “effi cient”?

Is the market for all stocks equally effi cient? Explain.

Why is it good for the economy that markets be effi cient?

Is it possible that the market for individual stocks could be highly effi cient but the market for whole companies could be less effi cient?

What is behavioral fi nance? What are the implications of behavioral fi nance for market effi ciency?

51Chapter 2 Financial Markets and Institutions

In this chapter, we provided a brief overview of how capital is allocated and discussed the fi nancial markets, instruments, and institutions used in the allocation process. We discussed physical location exchanges and electronic markets for common stocks, stock market reporting, and stock indexes. We demonstrated that security prices are volatile—investors expect to make money, which they generally do over time; but losses can be large in any given year. Finally, we discussed the effi ciency of the stock market and developments in behavioral fi nance. After reading this chapter, you should have a general understanding of the fi nancial environment in which busi- nesses and individuals operate, realize that actual returns are often diff erent from expected returns, and be able to read stock market quotations from business news- papers or various Internet sites. You should also recognize that the theory of fi nan- cial markets is a “work in progress,” and much work remains to be done.

KEY TERMS Define each of the following terms: a. Spot markets; futures markets b. Money markets; capital markets c. Primary markets; secondary markets d. Private markets; public markets e. Derivatives f. Investment banks (iBanks); commercial banks; financial services corporations g. Mutual funds; money market funds h. Physical location exchanges; over-the-counter (OTC) market; dealer market i. Closely held corporation; publicly owned corporation j. Going public; initial public offering (IPO) market k. Efficient markets hypothesis (EMH) l. Behavioral finance

How does a cost-efficient capital market help reduce the prices of goods and services?

Describe the different ways in which capital can be transferred from suppliers of capital to those who are demanding capital.

Is an initial public offering an example of a primary or a secondary market transaction? Explain.

Indicate whether the following instruments are examples of money market or capital mar- ket securities. a. U.S. Treasury bills b. Long-term corporate bonds c. Common stocks

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

QUESTIONSQUESTIONS

2-12-1 2-22-2

2-32-3

2-42-4

T YING I T ALL TO GETHER

52 Part 2 Fundamental Concepts in Financial Management

d. Preferred stocks e. Dealer commercial paper

What would happen to the U.S. standard of living if people lost faith in the safety of the financial institutions? Explain.

What types of changes have financial markets experienced during the last two decades? Have they been perceived as positive or negative changes? Explain.

Differentiate between dealer markets and stock markets that have a physical location.

Identify and briefly compare the two leading stock exchanges in the United States today.

Describe the three different forms of market efficiency.

Investors expect a company to announce a 10% increase in earnings; instead, the company announces a 1% increase. If the market is semi-strong form efficient, which of the follow- ing would you expect to happen? (Hint: Refer to Footnote 13 in this chapter.) a. The stock’s price will increase slightly because the company had a slight increase in

earnings. b. The stock’s price will fall because the earnings increase was less than expected. c. The stock’s price will stay the same because earnings announcements have no effect if

the market is semi-strong form efficient.

Briefly explain what is meant by the term efficiency continuum.

Explain whether the following statements are true or false. a. Derivative transactions are designed to increase risk and are used almost exclusively

by speculators who are looking to capture high returns. b. Hedge funds typically have large minimum investments and are marketed to institu-

tions and individuals with high net worths. c. Hedge funds have traditionally been highly regulated. d. The New York Stock Exchange is an example of a stock exchange that has a physical

location. e. A larger bid-ask spread means that the dealer will realize a lower profit. f. The efficient markets hypothesis assumes that all investors are rational.

2-52-5

2-62-6

2-72-7 2-82-8 2-92-9

2-102-10

2-112-11 2-122-12

FINANCIAL MARKETS AND INSTITUTIONS Assume that you recently graduated with a degree in finance and have just reported to work as an investment adviser at the brokerage firm of Smyth Barry & Co. Your first assignment is to explain the nature of the U.S. financial markets to Michelle Varga, a professional tennis player who recently came to the United States from Mexico. Varga is a highly ranked tennis player who expects to invest substantial amounts of money through Smyth Barry. She is very bright; therefore, she would like to understand in general terms what will happen to her money. Your boss has developed the following questions that you must use to explain the U.S. financial system to Varga.

a. What are the three primary ways in which capital is transferred between savers and borrowers? Describe each one.

b. What is a market? Differentiate between the following types of markets: physical asset markets versus finan- cial asset markets, spot markets versus futures markets, money markets versus capital markets, primary markets versus secondary markets, and public markets versus private markets.

c. Why are financial markets essential for a healthy economy and economic growth? d. What are derivatives? How can derivatives be used to reduce risk? Can derivatives be used to increase risk?

Explain. e. Briefly describe each of the following financial institutions: commercial banks, investment banks, mutual

funds, hedge funds, and private equity companies.

2-12-1

IN TEGRATED C ASE SMYTH BARRY & COMPANY

53Chapter 2 Financial Markets and Institutions

f. What are the two leading stock markets? Describe the two basic types of stock markets. g. If Apple Computer decided to issue additional common stock and Varga purchased 100 shares of this stock

from Smyth Barry, the underwriter, would this transaction be a primary or a secondary market transaction? Would it make a difference if Varga purchased previously outstanding Apple stock in the dealer market? Explain.

h. What is an initial public offering (IPO)? i. What does it mean for a market to be efficient? Explain why some stock prices may be more efficient than

others. j. After your consultation with Michelle, she asks to discuss these two scenarios with you:

(1) While in the waiting room of your office, she overheard an analyst on a financial TV network say that a particular medical research company just received FDA approval for one of its products. On the basis of this “hot” information, Michelle wants to buy many shares of that company’s stock. Assuming the stock market is highly efficient, what advice would you give her?

(2) She has read a number of newspaper articles about a huge IPO being carried out by a leading technol- ogy company. She wants to get as many shares in the IPO as possible and would even be willing to buy the shares in the open market immediately after the issue. What advice do you have for her?

T h e “Q ua l i t y ” o f Fi n a n c i a l S t a t e m e n t s

Financial Statements, Cash Flow, and Taxes

1 O

N LI

N E/

PH O

TO LI

BR AR

3 CHAPTER

The financial statements presented in a typical company’s annual report look quite official. They are signed by the firm’s top executives and are certified by a Big Four accounting firm, so one would think that they must be accurate. That may not be true, though, for three reasons: legiti- mate misjudgments in valuing assets and mea- suring costs, “flexible” accounting rules that result in differently reported results for similar companies, and outright cheating.

One blatant example of cheating involved WorldCom, which reported asset values that exceeded their true value by about $11 billion. This led to an understatement of costs and a cor- responding overstatement of profits. Enron is another example. That company overstated the value of certain assets, reported those artificial value increases as profits, and transferred the assets to subsidiary companies to hide the true facts. Enron’s and WorldCom’s investors eventu- ally learned what was happening, the companies were forced into bankruptcy, their top execu- tives went to jail, the accounting firm that audited

their books was forced out of business, and mil- lions of investors lost billions of dollars.

After the Enron and WorldCom blowups, Congress passed the Sarbanes-Oxley Act (SOX), which required companies to improve their internal auditing standards and required the CEO and CFO to certify that the financial statements were properly prepared. The SOX bill also cre- ated a new watchdog organization to help make sure that the outside accounting firms were doing their job. From all indications, financial statements are generally more accurate and clearer than they were in the past.

But the world is dynamic, and a new account- ing problem surfaced in 2007. Big banks, most notably Citigroup, owned many risky but high- yielding subprime mortgages. The banks invented a complex legal procedure that they called a structured investment vehicle (SIV) to conceal the fact that they held all of these risky mortgages. They correctly feared that people wouldn’t want to do business with a risky bank. But when the subprime market fell apart in 2007,

A manager’s primary goal is to maximize the value of his or her fi rm’s stock, and value is based on the fi rm’s future cash fl ows. But how do managers decide which actions are most likely to increase those fl ows, and how do investors estimate future cash fl ows? The answers to both questions lie in a study of fi nancial statements that pub- licly traded fi rms must provide to investors. Here investors include both institutions (banks, insurance companies, pension funds, and the like) and individuals like you. Much of the material in this chapter deals with concepts you covered in a basic accounting course. However, the information is important enough to warrant a review. Also, in accounting, you probably focused on how accounting statements are made; the focus here is on how investors and managers interpret and use them. Accounting is the basic language of business, so everyone engaged in business needs a good work- ing knowledge of it. It is used to “keep score”; and if investors and managers do not know the score, they won’t know whether their actions are appropriate. If you took midterm exams but were not told your scores, you would have a diffi cult time knowing whether you needed to improve. The same idea holds in business. If a fi rm’s managers— whether they are in marketing, personnel, production, or fi nance—do not understand fi nancial statements, they will not be able to judge the eff ects of their actions, which will make it hard for the fi rm to survive, much less to have a maximum value. When you fi nish this chapter you should be able to: • List each of the key fi nancial statements and identify the kinds of information

they provide to corporate managers and investors. • Estimate a fi rm’s free cash fl ow and explain why free cash fl ow has such an impor-

tant eff ect on fi rm value. • Discuss the major features of the federal income tax system.

3-1 FINANCIAL STATEMENTS AND REPORTS The annual report is the most important report that corporations issue to stockhold- ers, and it contains two types of information.2 First, there is a verbal section, often presented as a letter from the chairperson, which describes the fi rm’s operating

Annual Report A report issued annually by a corporation to its stockholders. It contains basic financial statements as well as management’s analysis of the firm’s past operations and future prospects.

the banks had to acknowledge their losses, which ran into many billions of dollars.

It turns out that the banks had tried to avoid writing down their mortgages; but a newly formed organization set up by the Big Four accounting firms, called the Center for

Audit Quality, took a hard line and forced the write-downs. That led Lynn Turner, former chief accountant for the SEC and a frequent critic of the accounting profession, to state, “The accounting firms are doing a much better job than they did in the past.”1

PU T TING THINGS IN PER SPECTIVE

Chapter 3 Financial Statements, Cash Flow, and Taxes 55

1 David Reilly, “Behind Bank’s Credit Rescue Fund: “With New, United Voice, Auditors Stand Ground On How to Treat Crunch,” The Wall Street Journal, October 17, 2007, p. C1. 2 Firms also provide quarterly reports, but these are much less comprehensive than the annual report. In addition, larger fi rms fi le even more detailed statements with the Securities and Exchange Commission (SEC), giving break- downs for each major division or subsidiary. These reports, called 10-K reports, are made available to stockholders upon request to a company’s corporate secretary. In this chapter, we focus on annual data—balance sheets at the ends of years and income statements for entire years rather than for shorter periods.

56 Part 2 Fundamental Concepts in Financial Management

results during the past year and discusses new developments that will affect future operations. Second, the report provides these four basic fi nancial statements: 1. The balance sheet, which shows what assets the company owns and who has

claims on those assets as of a given date—for example, December 31, 2008. 2. The income statement, which shows the fi rm’s sales and costs (and thus profi ts)

during some past period —for example, 2008. 3. The statement of cash fl ows, which shows how much cash the fi rm began the

year with, how much cash it ended up with, and what it did to increase or decrease its cash.

4. The statement of stockholders’ equity, which shows the amount of equity the stockholders had at the start of the year, the items that increased or decreased equity, and the equity at the end of the year.

These statements are related to one another; and taken together, they provide an accounting picture of the fi rm’s operations and fi nancial position.

The quantitative and verbal materials are equally important. The fi rm’s fi nancial statements report what has actually happened to its assets, earnings, and dividends over the past few years, whereas management’s verbal statements attempt to explain why things turned out the way they did and what might happen in the future.

For discussion purposes, we use data for Allied Food Products, a processor and distributor of a wide variety of food products, to illustrate the basic fi nancial statements. Allied was formed in 1981, when several regional fi rms merged; and it has grown steadily while earning a reputation as one of the best fi rms in its indus- try. Allied’s earnings dropped from $121.8 million in 2007 to $117.5 million in 2008. Management reported that the drop resulted from losses associated with a drought as well as increased costs due to a three-month strike. However, management then went on to describe a more optimistic picture for the future, stating that full opera- tions had been resumed, that several unprofi table businesses had been eliminated, and that 2009 profi ts were expected to rise sharply. Of course, an increase in profi t- ability may not occur; and analysts should compare management’s past statements with subsequent results. In any event, the information contained in the annual report can be used to help forecast future earnings and dividends. Therefore, investors are very interested in this report.

We should note that Allied’s fi nancial statements are relatively simple and straightforward; we also omitted some details often shown in the statements. Allied fi nances with only debt and common stock—it has no preferred stock, con- vertibles, or complex derivative securities. Also, the fi rm has made no acquisitions that resulted in goodwill that must be carried on the balance sheet. Finally, all of its assets are used in its basic business operations; hence, no nonoperating assets must be pulled out when we evaluate its operating performance. We deliberately chose such a company because this is an introductory text; as such, we want to explain the basics of fi nancial analysis, not wander into arcane accounting matters that are best left to accounting and security analysis courses. We do point out some of the pitfalls that can be encountered when trying to interpret accounting state- ments, but we leave it to advanced courses to cover the intricacies of accounting.

SEL F TEST What is the annual report, and what two types of information does it

provide?

What four fi nancial statements are typically included in the annual report?

Why is the annual report of great interest to investors?

57Chapter 3 Financial Statements, Cash Flow, and Taxes

3-2 THE BALANCE SHEET The balance sheet is a “snapshot” of a fi rm’s position at a specifi c point in time. Figure 3-1 shows the layout of a typical balance sheet. The left side of the state- ment shows the assets that the company owns, while the right side shows the fi rm’s liabilities and stockholders’ equity, which are claims against the fi rm’s assets.

As Figure 3-1 indicates, assets are divided into two major categories: current assets and fi xed, or long-term, assets. Current assets consist of assets that should be converted to cash within one year; and they include cash and cash equivalents, accounts receivable, and inventory.3 Long-term assets are assets expected to be used for more than one year; they include plant and equipment in addition to intellectual property such as patents and copyrights. Plant and equipment is generally reported net of accumulated depreciation. Allied’s long-term assets consist entirely of net plant and equipment, and we often refer to them as “net fi xed assets.”

Balance Sheet A statement of a firm’s financial position at a specific point in time.

A Typical Balance SheetFIGURE 3-1

Note: This is the typical layout of a balance sheet for one year. When balance sheets for two or more years are shown, assets are listed in the top section; liabilities and equity, in the bottom section. See Table 3-1.

Total Assets Total Liabilities andEquity

Current Assets Current Liabilities

Long-Term (Fixed) Assets Long-Term

Debt

Cash and equivalents Accounts receivable Inventory

Net plant and equipment Other long-term assets

Stockholders’ Equity

Common stock + Retained earnings must equal

Total Assets – Total Liabilities

Accrued wages and taxes Accounts payable Notes payable

3 Allied and most other companies hold some currency in addition to a bank checking account. They may also hold short-term interest-bearing securities that can be sold and thus converted to cash immediately with a simple telephone call. These securities are called “cash equivalents,” and they are generally included with checking account balances for fi nancial reporting purposes. If a company owns stocks or other marketable securities that it regards as short-term investments, these items will be shown separately on the balance sheet. Allied does not hold any marketable securities other than cash equivalents.

58 Part 2 Fundamental Concepts in Financial Management

The claims against assets are of two basic types—liabilities (or money the company owes to others) and stockholders’ equity. Liabilities consist of claims that must be paid off within one year (current liabilities), including accounts pay- able, accruals (total of accrued wages and accrued taxes), and notes payable to banks that are due within one year. Long-term debt includes bonds that mature in more than a year.

Stockholders’ equity can be thought of in two ways. First, it is the amount that stockholders paid to the company when they bought shares the company sold to raise capital, in addition to all of the earnings the company has retained over the years:

Stockholders’ equity ! Paid-in capital " Retained earnings

The retained earnings are not just the earnings retained in the latest year—they are the cumulative total of all of the earnings the company has earned during its life.

Stockholders’ equity can also be thought of as a residual:

Stockholders’ equity ! Total assets # Total liabilities

If Allied had invested surplus funds in bonds backed by subprime mortgages and the bonds’ value fell below their purchase price, the true value of the fi rm’s assets would have declined. The amount of its liabilities would not have changed—the fi rm would still owe the amount it had promised to pay its creditors. Therefore, the reported value of the common equity must decline. The accountants would make a series of entries, and the result would be a reduction in retained earn- ings—and thus in common equity. In the end, assets would equal liabilities and equity and the balance sheet would balance. This example shows why common stock is more risky than bonds—any mistake that management makes has a big impact on the stockholders. Of course, gains from good decisions also go to the stockholders; so with risk comes possible rewards.

Assets on the balance sheet are listed by the length of time before they will be converted to cash (inventories and accounts receivable) or used by the fi rm (fi xed as- sets). Similarly, claims are listed in the order in which they must be paid: Accounts payable must generally be paid within a few days, accruals must also be paid promptly, notes payable to banks must be paid within one year, and so forth, down to the stock- holders’ equity accounts, which represent ownership and need never be “paid off.”

3-2a Allied’s Balance Sheet Table 3-1 shows Allied’s year-end balance sheets for 2008 and 2007. From the 2008 statement, we see that Allied had $2 billion of assets—half current and half long term. These assets were fi nanced with $310 million of current liabilities, $750 million of long-term debt, and $940 million of common equity. Comparing the balance sheets for 2008 and 2007, we see that Allied’s assets grew by $320 million and its liabilities and equity necessarily grew by that same amount. Assets must, of course, equal liabilities and equity; otherwise, the balance sheet does not balance.

Several additional points about the balance sheet should be noted: 1. Cash versus other assets. Although assets are reported in dollar terms, only the

cash and equivalents account represents actual spendable money. Accounts receivable represents credit sales that have not yet been collected. Inventories show the cost of raw materials, work in process, and fi nished goods. Net fi xed assets represent the cost of the buildings and equipment used in operations minus the depreciation that has been taken on these assets. At the end of 2008, Allied has $10 million of cash; hence, it could write checks totaling that amount. The noncash assets should generate cash over time, but they do not represent cash in hand. And the cash they would bring in if they were sold today could be higher or lower than the values reported on the balance sheet.

59Chapter 3 Financial Statements, Cash Flow, and Taxes

2. Working capital. Current assets are often called working capital because these assets “turn over”; that is, they are used and then replaced throughout the year.4

3. Net working capital. When Allied buys inventory items on credit, its suppliers, in effect, lend it the money used to fi nance the inventory items. Allied could have borrowed from its bank or sold stock to obtain the money, but it received the funds from its suppliers. These loans are shown as accounts payable, and they typically are “free” in the sense that they do not bear interest. Similarly, Allied pays its workers every two weeks and it pays taxes quarterly; so Allied’s labor force and tax authorities provide it with loans equal to its accrued wages and taxes. If we

Working Capital Current assets. Working Capital Current assets.

Allied Food Products: December 31 Balance Sheets (Millions of Dollars)T a b l e 3 - 1

2008 2007 Assets Current assets: Cash and equivalents $ 10 $ 80 Accounts receivable 375 315 Inventories 615 415 Total current assets $1,000 $ 810 Net fixed assets: Net plant and equipment (cost minus depreciation) 1,000 870 Other assets expected to last more than a year 0 0 Total assets $2,000 $1,680

Liabilities and Equity Current liabilities: Accounts payable $ 60 $ 30 Accruals 140 130 Notes payable 110 60 Total current liabilities $ 310 $ 220 Long-term bonds 750 580 Total debt $1,060 $ 800 Common equity: Common stock (50,000,000 shares) $ 130 $ 130 Retained earnings 810 750 Total common equity $ 940 $ 880 Total liabilities and equity $2,000 $1,680

Notes: 1 Inventories can be valued by several different methods, and the method chosen can affect both the

balance sheet value and the cost of goods sold, and thus net income, as reported on the income statement. Similarly, companies can use different depreciation methods. The methods used must be reported in the notes to the financial statements, and security analysts can make adjustments when they compare companies if they think the differences are material.

2 Book value per share ! Total common equity/Shares outstanding ! $940/50 ! $18.80. 3 Also note that a relatively few firms use preferred stock, which we discuss in Chapter 9. Preferred stock

can take several different forms, but it is generally like debt because it pays a fixed amount each year. However, it is like common stock because a failure to pay the preferred dividend does not expose the firm to bankruptcy. If a firm does use preferred stock, it is shown on the balance sheet between Total debt and Common stock. There is no set rule on how preferred stock should be treated when financial ratios are calculated—it could be considered as debt or as equity. Bondholders often think of it as equity, while stockholders think of it as debt because it is a fixed charge. In truth, it is a hybrid, somewhere between debt and common equity.

4 Any current assets not used in normal operations, such as excess cash held to pay for a plant under construc- tion, are deducted and thus not included in working capital. Allied requires all of its current assets for operations.

60 Part 2 Fundamental Concepts in Financial Management

subtract the sum of payables plus accruals from current assets, the difference is called net working capital. That represents the amount of money that Allied must obtain from non-free sources to carry its current assets, $800 million in 2008:

Net working capital ! Current assets # (Payables " Accruals) ! $1,000 # ($60 " $140) ! $800

4. Other sources of funds. Most companies (including Allied) fi nance their assets with a combination of current liabilities, long-term debt, and common equity. Some companies also use “hybrid” securities such as preferred stock, convertible bonds, and long-term leases. Preferred stock is a hybrid between common stock and debt, while convertible bonds are debt securities that give the bondholder an option to exchange their bonds for shares of common stock. In the event of bankruptcy, debt is paid off fi rst, then preferred stock. Common stock is last, receiving a payment only when something remains after the debt and preferred stock are paid off.5

5. Depreciation. Most companies prepare two sets of fi nancial statements—one is based on Internal Revenue Service (IRS) rules and is used to calculate taxes; the other is based on generally accepted accounting principles (GAAP) and is used for reporting to investors. Firms often use accelerated depreciation for tax purposes but straight line depreciation for stockholder reporting. Allied uses accelerated depreciation for both.6

6. Market values versus book values. Companies generally use GAAP to determine the values reported on their balance sheets. In most cases, these accounting numbers (or “book values”) are different from what the assets would sell for if they were put up for sale (or “market values”). For example, Allied purchased its headquarters in Chicago in 1988. Under GAAP, the company must report the value of this asset at its historical cost (what it originally paid for the building in 1988) less accumulated depreciation. Given that Chicago real estate prices have increased over the last 20 years, the market value of the building is higher than its book value. Other assets’ market values also differ from their book values.

We can also see from Table 3-1 that the book value of Allied’s common equity at the end of 2008 was $940 million. Because 50 million shares were outstanding, the book value per share was $940/50 ! $18.80. However, the market value of the common stock was $23.06. As is true for most companies in 2008, sharehold- ers are willing to pay more than book value for Allied’s stock. This occurs in part because the values of assets have increased due to infl ation and in part because shareholders expect earnings to grow. Allied, like most other companies, has learned how to make investments that will increase future profi ts.

Apple provides an example of the effect of growth on the stock price. When Apple fi rst introduced the iPod and iPhone, its balance sheet didn’t budge; but investors recognized that these were great products that would lead to higher future profi ts. So Apple’s stock quickly rose above its book value—it now (Spring 2008) has a stock price of $185 versus a $20 book value.

Net Working Capital Current assets minus accounts payable and accruals.

5 Other forms of fi nancing are discussed in Brigham and Daves, Intermediate Financial Management, 9th edition, (Mason, OH: Thomson/South-Western, 2007), Chapter 20. In Fundamentals of Financial Management, 12th edition, readers should refer to Chapter 20. 6 Depreciation over an asset’s life is equal to the asset’s cost, but accelerated depreciation results in higher initial depreciation charges—and thus lower taxable income—than straight line. Due to the time value of money, it is better to delay taxes; so most companies use accelerated depreciation for tax purposes. Either accelerated or straight line can be used for stockholder reporting. Allied is a relatively conservative company; hence, it uses accelerated depreciation for stockholder reporting. Had Allied elected to use straight line for stockholder reporting, its 2008 depreciation expense would have been $25 million lower, the $1 billion shown for “net plant” on its balance sheet would have been $25 million higher, and its reported income would also have been higher.

Depreciation is also important in capital budgeting, where we make decisions regarding new investments in fi xed assets. We will have more to say about depreciation in Chapter 12, when we take up capital budgeting.

61Chapter 3 Financial Statements, Cash Flow, and Taxes

If a company has problems, its stock price can fall below its book value. For example, Countrywide Financial, the largest originator of subprime mort- gages, saw its stock price fall to $13 versus a book value of $25 when the sub- prime market blew up in 2007.

7. The time dimension. The balance sheet is a snapshot of the fi rm’s fi nancial position at a point in time—for example, on December 31, 2008. Thus, we see that on December 31, 2007, Allied had $80 million of cash; but that balance fell to $10 million by year-end 2008. The balance sheet changes every day as inven- tories rise and fall, as bank loans are increased or decreased, and so forth. A company such as Allied, whose business is seasonal, experiences especially large balance sheet changes during the year. Its inventories are low just before the harvest season but high just after the fall crops have been harvested and processed. Similarly, most retailers have large inventories just before Christ- mas but low inventories (and high accounts receivable) just after Christmas. We will examine the effects of these changes in Chapter 4, when we compare companies’ fi nancial statements and evaluate their performance.

What is the balance sheet, and what information does it provide?

How is the order in which items are shown on the balance sheet determined?

What was Allied’s net working capital on December 31, 2007? ($650 million)

What items on Allied’s December 31 balance sheet would probably be diff erent from its June 30 values? Would these diff erences be as large if Allied were a grocery chain rather than a food processor? Explain. (Invento- ries, accounts receivable, and accounts payable would experience seasonal fl uctuations; no—less seasonality)

SEL F TEST

3-3 THE INCOME STATEMENT Table 3-2 shows Allied’s 2007 and 2008 income statements. Net sales are shown at the top of the statement; then operating costs, interest, and taxes are subtracted to obtain the net income available to common shareholders. We also show earnings and dividends per share, in addition to some other data, at the bottom of Table 3-2. Earnings per share (EPS) is often called “the bottom line,” denoting that of all items on the income statement, EPS is the one that is most important to stockhold- ers. Allied earned $2.35 per share in 2008, down from $2.44 in 2007. In spite of the decline in earnings, the fi rm still increased the dividend from $1.06 to $1.15.

A typical stockholder focuses on the reported EPS, but professional security analysts and managers differentiate between operating and non-operating income. Operating income is derived from the fi rm’s regular core business—in Allied’s case, from producing and selling food products. Moreover, it is calculated before deducting interest expenses and taxes, which are considered to be non-operating costs. Operating income is also called EBIT, or earnings before interest and taxes. Here is its equation:

Operating income (or EBIT) ! Sales revenues # Operating costs 3-1 ! $3,000.0 # $2,716.2 ! $283.8

This fi gure must, of course, match the one reported on the income statement. Different fi rms have different amounts of debt, different tax carry-backs and

carry-forwards, and different amounts of non-operating assets such as marketable

Income Statement A report summarizing a firm’s revenues, expenses, and profits during a reporting period, generally a quarter or a year.

Operating Income Earnings from operations before interest and taxes (i.e., EBIT).

62 Part 2 Fundamental Concepts in Financial Management

securities. These differences can cause two companies with identical operations to report signifi cantly different net incomes. For example, suppose two companies have identical sales, operating costs, and assets. However, one company uses some debt and the other uses only common equity. Despite their identical operating performances, the company with no debt (and therefore no interest expense) would report a higher net income because no interest was deducted from its oper- ating income. Consequently, if you want to compare two companies’ operating performances, it is best to focus on their operating income.7

From Allied’s income statement, we see that its operating income increased from $263.0 million in 2007 to $283.8 million in 2008, or by $20.8 million. However, its 2008 net income declined. This decline occurred because it increased its debt in 2008, and the $28 million interest increase lowered its net income.

Taking a closer look at the income statement, we see that depreciation and amortization are important components of operating costs. Recall from accounting

7 Operating income is important for several reasons. First, as we noted in Chapter 1, managers are generally compensated based on the performance of the units they manage. A division manager can control his or her division’s performance but not the fi rm’s capital structure policy or other corporate decisions. Second, if one fi rm is considering acquiring another, it will be interested in the value of the target fi rm’s operations; and that value is determined by the target fi rm’s operating income. Third, operating income is normally more stable than total income, as total income can be heavily infl uenced by write-off s of bonds backed by subprime mortgages and the like. Therefore, analysts focus on operating income when they estimate fi rms’ long-run stock values.

Allied Food Products: Income Statements for Years Ending December 31 (Millions of Dollars, Except for Per-Share Data)

T a b l e 3 - 2

2008 2007 Net sales $3,000.0 $2,850.0 Operating costs except depreciation and amortization 2,616.2 2,497.0 Depreciation and amortization 100.0 90.0 Total operating costs $2,716.2 $2,587.0 Operating income, or earnings before interest and taxes (EBIT) $ 283.8 $ 263.0 Less interest 88.0 60.0 Earnings before taxes (EBT) $ 195.8 $ 203.0 Taxes (40%) 78.3 81.2 Net income $ 117.5 $ 121.8

Here are some related items: Total dividends $ 57.5 $ 53.0 Addition to retained earnings = Net income " Total dividends $ 60.0 $ 68.8

Per-share data: Common stock price $ 23.06 $ 26.00 Earnings per share (EPS)a $ 2.35 $ 2.44 Dividends per share (DPS)a $ 1.15 $ 1.06 Book value per share (BVPS) $ 18.80 $ 17.60 a Allied has 50 million shares of common stock outstanding. Note that EPS is based on net income available to common stockholders. Calculations of EPS and DPS for 2008 are as follows:

Earnings per share ! EPS ! Net income _________________________ Common shares outstanding ! $117,500,000 ____________ 50,000,000 ! $2.35

Dividends per share ! DPS ! Dividends paid to common stockholders ___________________________________ Common shares outstanding ! $57,500,000 ___________ 50,000,000 ! $1.15

When a firm has options or convertibles outstanding or it recently issued new common stock, a more comprehensive EPS, “diluted EPS,” must be calculated. Its calculation is a bit more complicated, but you may refer to any financial accounting text for a discussion.

63Chapter 3 Financial Statements, Cash Flow, and Taxes

that depreciation is an annual charge against income that refl ects the estimated dollar cost of the capital equipment and other tangible assets that were used up in the production process. Amortization amounts to the same thing except that it represents the decline in value of intangible assets such as patents, copyrights, trademarks, and goodwill. Because depreciation and amortization are so similar, they are generally lumped together for purposes of fi nancial analysis on the in- come statement and for other purposes. They both write off, or allocate, the costs of assets over their useful lives.

Even though depreciation and amortization are reported as costs on the income statements, they are not cash expenses—cash was spent in the past, when the as- sets being written off were acquired, but no cash is paid out to cover depreciation. Therefore, managers, security analysts, and bank loan offi cers who are concerned with the amount of cash a company is generating often calculate EBITDA, an ac- ronym for earnings before interest, taxes, depreciation, and amortization. Allied has no amortization charges, so Allied’s depreciation and amortization consist en- tirely of depreciation. In 2008, Allied’s EBITDA was $383.8 million.

While the balance sheet represents a snapshot in time, the income statement reports on operations over a period of time. For example, during 2008, Allied had sales of $3 billion and its net income was $117.5 million. Income statements are prepared monthly, quarterly, and annually. The quarterly and annual statements are reported to investors, while the monthly statements are used internally for planning and control purposes.

Finally, note that the income statement is tied to the balance sheet through the retained earnings account on the balance sheet. Net income as reported on the income statement, less dividends paid, is the retained earnings for the year (e.g., 2008). Those retained earnings are added to the cumulative retained earnings from prior years to obtain the year-end 2008 balance for retained earnings. The retained earnings for the year are also reported in the statement of stockholders’ equity. All four of the statements provided in the annual report are tied together.

Depreciation The charge to reflect the cost of assets used up in the production process. Depreciation is not a cash outlay.

Amortization A noncash charge similar to depreciation except that it is used to write off the costs of intangible assets.

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

Why is earnings per share called “the bottom line”?

What is EBIT, or operating income?

What is EBITDA?

Which is more like a snapshot of the fi rm’s operations—the balance sheet or the income statement? Explain your answer.

SEL F TEST

3-4 STATEMENT OF CASH FLOWS Net income as reported on the income statement is not cash; and in fi nance, “cash is king.” Management’s goal is to maximize the price of the fi rm’s stock; and the value of any asset, including a share of stock, is based on the cash fl ows the asset is expected to produce. Therefore, managers strive to maximize the cash fl ows available to investors. The statement of cash fl ows as shown in Table 3-3 is the accounting report that shows how much cash the fi rm is generating. The statement is divided into four sections, and we explain it on a line-by-line basis.8

Statement of Cash Flows A report that shows how things that affect the balance sheet and income statement affect the firm’s cash flows.

8 Our statement of cash fl ows is relatively simple because Allied is a relatively uncomplicated company. Many cash fl ow statements are more complicated; but if you understand Table 3-3, you should be able to follow more complicated statements.

64 Part 2 Fundamental Concepts in Financial Management

Here is a line-by-line explanation of the statement shown in Table 3-3: a. Operating Activities. This section deals with items that occur as part of normal

ongoing operations. b. Net income. The fi rst operating activity is net income, which is the fi rst source of

cash. If all sales were for cash, if all costs required immediate cash payments, and if the fi rm were in a static situation, net income would equal cash from operations. However, these conditions don’t hold; so net income is not equal to cash from operations. Adjustments shown in the remainder of the statement must be made.

c. Depreciation and amortization. The fi rst adjustment relates to depreciation and amortization. Allied’s accountants subtracted depreciation (it has no amorti- zation expense), which is a noncash charge, when they calculated net income. Therefore, depreciation must be added back to net income when net cash fl ow is determined.

d. Increase in inventories. To make or buy inventory items, the fi rm must use cash. It may get some of this cash as loans from its suppliers and workers (payables and accruals); but ultimately, any increase in inventories requires cash. Allied increased its inventories by $200 million in 2008. That amount is shown in parentheses on Line d because it is negative (i.e., a use of cash). If Allied had reduced its inventories, it would have generated positive cash.

e. Increase in accounts receivable. If Allied chooses to sell on credit, when it makes a sale, it will not immediately get the cash that it would have received had it not extended credit. To stay in business, it must replace the inventory that it sold on credit; but it won’t yet have received cash from the credit sale. So if the fi rm’s accounts receivable increase, this will amount to a use of cash. Allied’s

Allied Food Products: Statement of Cash Flows for 2008 (Millions of Dollars)

T a b l e 3 - 3

2008 a. I. Operating Activities b. Net income $117.5 c. Depreciation and amortization 100.0 d. Increase in inventories (200.0) e. Increase in accounts receivable (60.0) f. Increase in accounts payable 30.0 g. Increase in accrued wages and taxes 10.0 h. Net cash provided by (used in) operating activities ($ 2.5)

i. II. Long-Term Investing Activities j. Additions to property, plant, and equipment ($230.0) k. Net cash used in investing activities ($230.0)

l. III. Financing Activities m. Increase in notes payable $ 50.0 n. Increase in bonds outstanding 170.0 o. Payment of dividends to stockholders (57.5) p. Net cash provided by financing activities $162.5

q. IV. Summary r. Net decrease in cash (Net sum of I, II, and III) ($ 70.0) s. Cash and equivalents at the beginning of the year 80.0 t. Cash and equivalents at the end of the year $ 10.0

Note: Here and throughout the book, parentheses are sometimes used to denote negative numbers.

65Chapter 3 Financial Statements, Cash Flow, and Taxes

receivables rose by $60 million in 2008, and that use of cash is shown as a nega- tive on Line e. If Allied had reduced its receivables, this would have showed up as a positive cash fl ow. (Once cash is received for the sale, the accompany- ing accounts receivable will be eliminated.)

f. Increase in accounts payable. Accounts payable represent a loan from suppliers. Allied bought goods on credit, and its payables increased by $30 million this year. That is treated as a $30 million increase in cash on Line f. If Allied had reduced its payables, that would have required, or used, cash. Note that as Allied grows, it will purchase more inventories. That will give rise to addi- tional payables, which will reduce the amount of new outside funds required to fi nance inventory growth.

g. Increase in accrued wages and taxes. The same logic applies to accruals as to accounts payable. Allied’s accruals increased by $10 million this year, which means that in 2008, it borrowed an additional $10 million from its workers and tax authorities. So this represents a $10 million cash infl ow.

h. Net cash provided by operating activities. All of the previous items are part of nor- mal operations—they arise as a result of doing business. When we sum them, we obtain the net cash fl ow from operations. Allied had positive fl ows from net income, depreciation, and increases in payables and accruals; but it used cash to increase inventories and to carry receivables. The net result was that operations led to a $2.5 million net outfl ow of cash.

i. Long-Term Investing Activities. All activities involving long-term assets are cov- ered in this section. Allied had only one long-term investment activity—the acquisition of some fi xed assets, as shown on Line j. If Allied had sold some fi xed assets, its accountants would have reported it in this section as a positive amount (i.e., as a source of cash).

j. Additions to property, plant, and equipment. Allied spent $230 million on fi xed assets during the current year. This is an outfl ow; therefore, it is shown in parentheses. If Allied had sold some of its fi xed assets, this would have been a cash infl ow.9

k. Net cash used in investing activities. Since Allied had only one investment activ- ity, the total on this line is the same as that on the previous line.

l. Financing Activities. Allied’s fi nancing activities are shown in this section. m. Increase in notes payable. Allied borrowed an additional $50 million from its

bank this year, which was a cash infl ow. When Allied repays the loan, this will be an outfl ow.

n. Increase in bonds (long-term debt). Allied borrowed an additional $170 million from long-term investors this year, giving them newly issued bonds in exchange for cash. This is shown as an infl ow. When the bonds are repaid some years hence, this will be an outfl ow.

o. Payment of dividends to stockholders. Dividends are paid in cash, and the $57.5 million that Allied paid out is shown as a negative amount.

p. Net cash provided by fi nancing activities. The sum of the three fi nancing entries, which is a positive $162.5 million, is shown here. These funds were used to help pay for the $230 million of new plant and equipment and to help cover the defi cit resulting from operations.

q. Summary. This section summarizes the change in cash and cash equivalents over the year.

9 The number on Line j is “gross” investment, or total expenditures. It is also equal to the change in net plant and equipment (from the balance sheet) plus depreciation as shown on Line c: Gross investment ! Net investment # Depreciation ! $130 # $100 ! $230.

66 Part 2 Fundamental Concepts in Financial Management

r. Net decrease in cash. The net sum of the operating activities, investing activities, and fi nancing activities is shown here. These activities resulted in a $70 million net decrease in cash during 2008, mainly due to expenditures on new fi xed assets.

s. Cash and equivalents at the beginning of the year. Allied began the year with the $80 million of cash, which is shown here.

t. Cash and equivalents at the end of the year. Allied ended the year with $10 million of cash, the $80 million it started with minus the $70 million net decrease as shown previously. Clearly, Allied’s cash position is weaker than it was at the beginning of the year.

Allied’s statement of cash fl ows should be of concern to its managers and investors. The company was able to cover the small operating defi cit and the large investment in fi xed assets by borrowing and reducing its beginning balances of cash and equivalents. However, that can’t continue indefi nitely. In the long run, Section I needs to show positive operating cash fl ows. In addition, we would expect Section II to show expenditures on fi xed assets that are about equal to (1) its depreciation charges (to replace worn out fi xed assets) along with (2) some addi- tional spending to provide for growth. Section III would normally show some net borrowing in addition to a “reasonable” amount of dividends.10 Finally, Section IV should show a reasonably stable cash balance from year to year. These conditions don’t hold for Allied, so something should be done to correct the situation. We will consider corrective actions in Chapter 4, when we analyze the fi rm’s fi nancial statements.

10 The average company pays out about one third of its earnings as dividends, but there is a great deal of variation between companies depending on each company’s needs for retained earnings to support its growth. We cover dividends in detail later in the text in Distributions to Shareholders: Dividends and Share Repurchases.

Profi ts as reported on the income statement can be “mas- saged” by changes in depreciation methods, inventory valu- ation procedures, and so on, but “cash is cash,” so manage- ment can’t mess with the cash fl ow statement, right? Nope—wrong. A recent article in The Wall Street Journal described how Ford, General Motors, and several other com- panies overstated their operating cash fl ows, the most important section of the cash fl ow statement. Indeed, GM reported more than twice as much cash from operations as it really generated, $7.6 billion versus a true $3.5 billion. What happened is that when GM sold cars to a dealer on credit, it created an account receivable, which should be shown in the “Operating Activities” section as a use of cash. However, GM classifi ed these receivables as loans to dealers and reported them as a fi nancing activity. That decision more than dou- bled the reported cash fl ow from operations. It didn’t aff ect the end-of-year cash balance, but it made operations look stronger than they really were.

If Allied Foods, in Table 3-3, had done this, the $60 mil- lion increase in receivables, which is correctly shown as a use of cash, would have been shifted to the “Financing Activities” section, causing Allied’s cash provided by operations to rise from "$2.5 million to +$57.5 million. That would have made Allied look better to investors and credit analysts, but it would have been just smoke and mirrors. GM’s treatment was fi rst reported by Charles Mulford, a professor at Georgia Tech. The SEC then sent GM a letter that basically required it to change its procedures. The company issued a statement saying that it thought at the time that it was acting in accordance with GAAP but that it would reclassify its accounts in the future. GM’s action was not in the league of WorldCom’s or Enron’s fraudulent accounting, but it does show that companies sometimes do things to make their statements look better than they really are.

Source: Diya Gullapalli, “Little Campus Lab Shakes Big Firms,” The Wall Street Journal, March 1, 2005, p. C3.

MASSAGING THE CASH FLOW STATEMENT

67Chapter 3 Financial Statements, Cash Flow, and Taxes

3-5 STATEMENT OF STOCKHOLDERS’ EQUITY Changes in stockholders’ equity during the accounting period are reported in the statement of stockholders’ equity. Table 3-4 shows that Allied earned $117.5 mil- lion during 2008, paid out $57.5 million in common dividends, and plowed $60 million back into the business. Thus, the balance sheet item “Retained earnings” increased from $750 million at year-end 2007 to $810 million at year-end 2008.11

Note that “retained earnings” represents a claim against assets, not assets per se. Stockholders allowed management to retain earnings and reinvest them in the business, using the retained earnings to increase plant and equipment, add to inventories, and the like. Companies do not just pile up cash in a bank account. Thus, retained earnings as reported on the balance sheet do not represent cash and are not “available” for dividends or anything else.12

Statement of Stockholders’ Equity A statement that shows by how much a firm’s equity changed during the year and why this change occurred.

11 If they had been applicable, columns would have been used to show Additional Paid-in Capital and Treasury Stock. Also, additional rows would have contained information on such things as new issues of stock, treasury stock acquired or reissued, stock options exercised, and unrealized foreign exchange gains or losses. 12 Cash (as of the balance sheet date) is found in the cash account, an asset account. A positive number in the retained earnings account indicates only that the fi rm has in the past earned income and has not paid it all out as dividends. Even though a company reports record earnings and shows an increase in retained earnings, it still may be short of cash if it is using its available cash to purchase current and fi xed assets to support growth. The same situation holds for individuals. You might own a new BMW (no loan), many clothes, and an expensive stereo (hence, have a high net worth); but if you had only $0.23 in your pocket plus $5.00 in your checking account, you would still be short of cash.

What is the statement of cash fl ows, and what are some questions it answers?

Identify and briefl y explain the three types of activities shown in the statement of cash fl ows.

If a company has high cash fl ows from operations, does this mean that cash as shown on its balance sheet will also be high? Explain. (Not necessarily. The company may have invested heavily in working capital and/or fi xed assets, it may have borrowed a great deal, or it may not have had much initial cash.)

SEL F TEST

What is the statement of stockholders’ equity designed to tell us?

Why do changes in retained earnings occur?

Explain why the following statement is true: The retained earnings account reported on the balance sheet does not represent cash and is not “available” for dividend payments or anything else.

SEL F TEST

Statement of Stockholders’ Equity, December 31, 2008 (Millions of Dollars)T a b l e 3 - 4

COMMON STOCK Retained Earnings

Total Stockholders’

Equity Shares (000) Amount

Balances, December 31, 2007 50,000 $130.0 $750.0 $880.0 2008 Net Income $117.5 Cash Dividends ($ 57.5) Addition to Retained Earnings $ 60.0 Balances, December 31, 2008 50,000 $130.0 $810.0 $940.0

68 Part 2 Fundamental Concepts in Financial Management

3-6 FREE CASH FLOW Thus far, we have focused on fi nancial statements as they are prepared by accoun- tants. However, accounting statements are designed primarily for use by creditors and tax collectors, not for managers and stock analysts. Therefore, corporate deci- sion makers and security analysts often modify accounting data to meet their needs. The most important modifi cation is the concept of free cash fl ow (FCF), defi ned as “the amount of cash that could be withdrawn without harming a fi rm’s ability to operate and to produce future cash fl ows.” Here is the equation used to calculate free cash fl ow:

FCF ! EBIT(1 # T) " Depreciation # ! ( Capital expenditures " Increase in net working capital ) " ! $283.8 (1 # 0.4) " $100 # ! ( $230 " Change in current assets # Change in payables and accruals ) " ! $170.3 " $100 # ($230 " [($1,000 # $810) # ($200 # $160)]) ! $170.3 " $100 # $230 # $150 ! #$109.7 million

Free Cash Flow (FCF) The amount of cash that could be withdrawn from a firm without harming its ability to operate and to produce future cash flows.

A wide range of valuable fi nancial information is available on the Internet. With just a couple of clicks, an investor can fi nd the key fi nancial statements for most publicly traded companies. Suppose you are thinking of buying some Disney stock, and you want to analyze its recent performance. Here’s a par- tial (but by no means complete) list of sites you can access to get started: • One source is Yahoo!’s fi nance web site, http://fi nance.

yahoo.com. Here you will fi nd updated market information along with links to a variety of interesting research sites. Enter a stock’s ticker symbol, click “Go,” and you will see the stock’s current price along with recent news about the company. Click “Key Statistics” to fi nd a report on the com- pany’s key fi nancial ratios. Links to the company’s fi nancials (income statement, balance sheet, and statement of cash fl ows) can also be found. The Yahoo! site also has a list of insider transactions that will tell you whether a company’s CEO and other key insiders are buying or selling the com- pany’s stock. In addition, the site has a message board where investors share opinions about the company and a link is provided to the company’s fi lings with the Securities and Exchange Commission (SEC). Note also that, in most cases, a more complete listing of SEC fi lings can be found at www.sec.gov.

• Two other web sites with similar information are Google Finance (http://fi nance.google.com) and MSN Money (http://moneycentral.msn.com). After entering a stock’s

ticker symbol, you will see the current stock price and a list of recent news stories. At either of these sites, you will fi nd links to a company’s fi nancial statements and key ra- tios, as well as other information including analyst rat- ings, historical charts, earnings estimates, and a summary of insider transactions. Google Finance, MSN Money, and Yahoo! Finance allow you to export the fi nancial state- ments and historical prices to an Excel spreadsheet.

• Other sources for up-to-date market information are http://money.cnn.com and www.marketwatch.com. On these sites, you also can obtain stock quotes, fi nancial statements, links to Wall Street research and SEC fi lings, company profi les, and charts of a fi rm’s stock price over time.

• After accumulating all of this information, you may want to look at a site that provides opinions regarding the direction of the overall market and a particular stock. Two popular sites are The Motley Fool’s web site, www.fool. com, and the site for TheStreet.com, www.thestreet.com.

• A popular source is the online web site of The Wall Street Journal, http://online.wsj.com. It is a great resource, but you have to subscribe to access the full range of materials.

Keep in mind that this list is just a small subset of the information available online. Also, sites come and go and change their content over time. New and interesting sites are constantly being added to the Internet.

FINANCIAL ANALYSIS ON THE INTERNET

www.marketwatch.com

www.fool.com

www.thestreet.com

http://online.wsj.com

www.sec.gov

http://finance.google.com

http://moneycentral.msn.com

http://finance.yahoo.com

http://money.cnn.com

69Chapter 3 Financial Statements, Cash Flow, and Taxes

EBIT(1 " T) is the after-tax operating income that would exist if the fi rm had no debt and therefore no interest payments.13 For Allied, EBIT(1 " T) ! $283.8(1 " 0.4) ! $170.3. Depreciation is then added back because it is a noncash expense. Allied’s business plan called for $230 million of capital expenditures plus a $150 million increase in net working capital. Those investments are necessary to sustain ongoing operations.

Allied’s FCF is negative, which is not good. Note, though, that the negative FCF is largely attributable to the $230 million expenditure for a new processing plant. This plant is large enough to meet production for several years, so another new plant will not be needed until 2012. Therefore, Allied’s FCF for 2009 and the next few years should increase, which means that things are not as bad as the neg- ative FCF might suggest.

Note also that most rapidly growing companies have negative FCFs—the fi xed assets and working capital needed to support rapid growth generally exceed cash fl ows from existing operations. This is not bad, provided the new invest- ments are eventually profi table and contribute to FCF.

Many analysts regard FCF as being the single most important number that can be developed from accounting statements, even more important than net income. After all, FCF shows how much the fi rm can distribute to its investors. We will dis- cuss FCF again in Chapter 9, which deals with stock valuation, and in Chapters 11 and 12, which deal with capital budgeting.

13 After tax operating income = EBIT – Taxes = EBIT – EBIT(T) = EBIT(1 – T), where T is the fi rm’s marginal tax rate.

Free cash fl ow is important to large companies like Allied Foods. Security analysts use FCF to help estimate the value of the stock, and Allied’s managers use it to assess the value of proposed capital budgeting projects and potential merger candidates. Note, though, that the concept is also relevant for small businesses. Let’s assume that your aunt and uncle own a small pizza shop and that they have an accountant who prepares their fi nancial statements. The income statement shows their accounting profi t for each year. While they are certainly interested in this number, what they probably care more about is how much money they can take out of the business each year to maintain their standard of living. Let’s assume that the shop’s net income for 2008 was $75,000. However, your aunt and uncle had to spend $50,000 to refurbish the kitchen and restrooms. So while the business is generating a great deal of “profi t,” your aunt and uncle can’t take much money out because they have to put money back into the pizza shop. Stated another way, their free cash fl ow is much less than their net income. The required investments could be so large that they even exceed the money made from selling pizza. In this case, your aunt and uncle’s free cash fl ow would be neg- ative. If so, this means they must fi nd funds from other sources just to maintain the pizza business.

As astute businesspeople, your aunt and uncle recog- nize that investments in the restaurant, such as updating the kitchen and restrooms, are nonrecurring; and if noth- ing else comes up unexpectedly, your aunt and uncle should be able to take more out of the business in upcoming years, when their free cash fl ow increases. But some businesses never seem to produce cash for their owners—they consis- tently generate positive net income, but this net income is swamped by the amount of cash that has to be plowed back into the business. Thus, when it comes to valuing the pizza shop (or any business small or large), what really matters is the amount of free cash fl ow that the business generates over time. Looking ahead, your aunt and uncle face competition from national chains that are moving into the area. To meet the competition, your aunt and uncle will have to modernize the dining room. This will again drain cash from the business and reduce its free cash fl ow, although the hope is that it will enable them to increase sales and free cash fl ow in the years ahead. As we will see when we discuss capital budgeting, evaluating projects requires us to estimate whether the future increases in free cash fl ow are suffi cient to more than off set the initial project cost. And this comes down to free cash fl ows.

FREE CASH FLOW IS IMPORTANT FOR SMALL BUSINESSES

70 Part 2 Fundamental Concepts in Financial Management

What is free cash fl ow (FCF)?

Why is FCF an important determinant of a fi rm’s value?

A company has EBIT of $30 million, depreciation of $5 million, and a 40% tax rate. It needs to spend $10 million on new fi xed assets and $15 million to increase its current assets, and it expects its payables to increase by $2 million and its accruals to increase by $3 million. What is its free cash fl ow? ($3 million)

SEL F TEST

3-7 INCOME TAXES Individuals and corporations pay out a signifi cant portion of their income as taxes, so taxes are important in both personal and corporate decisions. We summarize the key aspects of the U.S. tax system for individuals in this section and for corpo- rations in the next section, using 2008 data. The details of our tax laws change fairly often—annually for things that are indexed for infl ation—but the basic nature of the tax system is likely to remain intact.

3-7a Individual Taxes Individuals pay taxes on wages and salaries, on investment income (dividends, interest, and profi ts from the sale of securities), and on the profi ts of proprietor- ships and partnerships. The tax rates are progressive—that is, the higher one’s income, the larger the percentage paid in taxes. Table 3-5 gives the tax rates that were in effect April 2008.

Taxable income is defi ned as “gross income less a set of exemptions and deductions.” When fi ling a tax return in 2008 for the tax year 2007, taxpayers received an exemption of $3,400 for each dependent, including the taxpayer, which reduces taxable income. However, this exemption is indexed to rise with infl ation, and the exemption is phased out (taken away) for high-income taxpayers. Also, certain expenses, including mortgage interest paid, state and local income taxes paid, and charitable contributions, can be deducted and thus be used to reduce taxable income; but again, high-income taxpayers lose most of these deductions.

The marginal tax rate is defi ned as “the tax rate on the last dollar of income.” Marginal rates begin at 10% and rise to 35%. Note, though, that when consider- ation is given to the phase-out of exemptions and deductions, to Social Security and Medicare taxes, and to state taxes, the marginal tax rate may actually exceed 50%. Average tax rates can be calculated from the data in Table 3-5. For example, if a single individual had taxable income of $35,000, his or her tax bill would be $4,386.25 # ($35,000 " $31,850)(0.25) ! $4,386.25 # $787.50 ! $5,173.75. Her average tax rate would be $5,173.75/$35,000 ! 14.78% versus a marginal rate of 25%. If she received a raise of $1,000, bringing her income to $36,000, she would have to pay $250 of it as taxes; so her after-tax raise would be $750.

Note too that interest income received by individuals from corporate securities is added to other income and thus is taxed at federal rates going up to 35%, plus state taxes.14 Capital gains and losses, on the other hand, are treated differently. Assets such as stocks, bonds, and real estate are defi ned as capital assets. When you buy a capital asset and later sell it for more than you paid, you earn a profi t that is called a capital gain; when you suffer a loss, it is called a capital loss. If you held

Progressive Tax A tax system where the tax rate is higher on higher incomes. The personal income tax in the United States, which ranges from 0% on the lowest incomes to 35% on the highest incomes, is progressive.

Marginal Tax Rate The tax rate applicable to the last unit of a person’s income.

Average Tax Rate Taxes paid divided by taxable income.

Capital Gain or Loss The profit (loss) from the sale of a capital asset for more (less) than its purchase price.

14 Under U.S. tax laws, interest on most state and local government bonds, called municipals or “munis,” is not subject to federal income taxes. This has a signifi cant eff ect on the values of munis and on their rates of return. We discuss rates and returns in Chapter 8.

71Chapter 3 Financial Statements, Cash Flow, and Taxes

the asset for less than one year, you will have a short-term gain or loss, while if you held it for more than a year, you will have a long-term gain or loss. Thus, if you buy 100 shares of Disney stock for $42 per share and sell it for $52 per share, you make a capital gain of 100 $ $10, or $1,000. However, if you sell the stock for $32 per share, you will have a $1,000 capital loss. Depending on how long you hold the stock, you will have a short-term or long-term gain or loss.15 If you sell the stock for exactly $42 per share, you make neither a gain nor a loss; so no tax is due.

A short-term capital gain is added to such ordinary income as wages and interest, then is taxed at the same rate as ordinary income. However, long-term capital gains are taxed differently. The top rate on long-term gains in 2008 is 15%. Thus, if in 2008, you were in the 35% tax bracket, any short-term gains you earned would be taxed just like ordinary income; but your long-term gains would be taxed at 15%. Thus, capital gains on assets held for more than 12 months are better than ordinary income for many people because the tax bite is smaller. However,

SINGLE INDIVIDUALS

If Your Taxable Income Is

You Pay This Amount on the

Base of the Bracket

Plus This Percentage on the Excess over the Base (Marginal Rate)

Average Tax Rate at Top of Bracket

Up to $7,825 $ 0 10.0% 10.0% $7,825–$31,850 782.50 15.0 13.8 $31,850–$77,100 4,386.25 25.0 20.4 $77,100–$160,850 15,698.75 28.0 24.3 $160,850–$349,700 39,148.75 33.0 29.0 Over $349,700 101,469.25 35.0 35.0

MARRIED COUPLES FILING JOINT RETURNS

If Your Taxable Income Is

You Pay This Amount on the

Base of the Bracket

Plus This Percentage on the Excess over the Base (Marginal Rate)

Average Tax Rate at Top of Bracket

Up to $15,650 $ 0 10.0% 10.0% $15,650–$63,700 1,565.00 15.0 13.8 $63,700–$128,500 8,772.50 25.0 19.4 $128,500–$195,850 24,972.50 28.0 22.4 $195,850–$349,700 43,830.50 33.0 27.0 Over $349,700 94,601.00 35.0 35.0

Notes: a. These are the tax rates as of April 2008. The income ranges at which each tax rate takes effect are indexed with inflation, so they change

each year. b. The average tax rates are always below the marginal rates, but the average at the top of the brackets approaches 35% as taxable income rises

without limit. c. In 2007, a personal exemption of $3,400 per person or dependent could be deducted from gross income to determine taxable income. Thus, a

husband and wife with two children would have a 2007 exemption of 4 $ $3,400 = $13,600. The exemption increases with inflation; but if gross income exceeds certain limits, the exemption is phased out, which has the effect of raising the effective tax rate on incomes over the specified limit. In addition, taxpayers can claim itemized deductions for charitable contributions and certain other items, but these deductions are also phased out for high-income taxpayers. In addition, there are Social Security and Medicare taxes. All of this pushes the effective tax rate to well above 35%.

Individual Tax Rates in April 2008T a b l e 3 - 5

15 If you have a net capital loss (your capital losses exceed your capital gains) for the year, you can deduct up to $3,000 of this loss against your other income (for example, salary, interest, and dividends).

72 Part 2 Fundamental Concepts in Financial Management

the 15% maximum rate is scheduled to increase to 20% after 2010. That’s still better than 35%, though; so from a tax standpoint, capital gains income is good.

Dividends received by individuals in 2008 are also taxed at the same 15% rate as long-term capital gains. However, the rate is scheduled to rise after 2010. Note that since corporations pay dividends out of earnings that have already been taxed, there is double taxation of corporate income—income is fi rst taxed at the corporate rate; and when what is left is paid out as dividends, it is taxed again. This double taxation motivated Congress to reduce the tax rate on dividends.

Tax rates on dividends and capital gains have varied over time, but they have generally been lower than rates on ordinary income. Congress wants the economy to grow. For growth, we need investment in productive assets; and low capital gains and dividend tax rates encourage investment. Individuals with money to invest understand the tax advantages associated with making equity investments in newly formed companies versus buying bonds, so new ventures have an easier time attracting capital under the tax system. All in all, lower capital gains and divi- dend tax rates stimulate capital formation and investment.

One other tax feature should be addressed—the Alternative Minimum Tax (AMT). The AMT was created in 1969 because Congress learned that 155 million- aires with high incomes paid no taxes because they had so many tax shelters from items such as depreciation on real estate and municipal bond interest. Under the AMT law, people must calculate their tax under the “regular” system and then under the AMT system, where many deductions are added back to income and then taxed at a special AMT rate. The law was not indexed for infl ation; and by 2007, literally millions of taxpayers’ found themselves subject to this very complex tax.16

3-7b Corporate Taxes The corporate tax structure, shown in Table 3-6, is relatively simple. To illustrate, if a fi rm had $65,000 of taxable income, its tax bill would be $11,250.

Taxes ! $7,500 " 0.25($15,000) ! $7,500 " $3,750 ! $11,250

Its average tax rate would be $11,250/$65,000 ! 17.3%. Note that corporate income above $18,333,333 has an average and marginal tax rate of 35%.

Interest and Dividends Received by a Corporation Corporations earn most of their income from operations, but they may also own securities—bonds and stocks—and receive interest and dividend income. Interest

Alternative Minimum Tax (AMT) Created by Congress to make it more difficult for wealthy individuals to avoid paying taxes through the use of various deductions.

16 On December 26, 2007, President Bush signed legislation that (1) increases the AMT exemption amounts for 2007 to $44,350 for single taxpayers and $66,250 for joint fi lers and (2) allows taxpayers to take several tax credits for AMT purposes through 2007.

If a Corporation’s Taxable Income Is

It Pays This Amount on the

Base of the Bracket

Plus This Percentage on the Excess over the Base (Marginal Rate)

Average Tax Rate at Top of

Bracket Up to $50,000 $ 0 15% 15.0% $50,000–$75,000 7,500 25 18.3 $75,000–$100,000 13,750 34 22.3 $100,000–$335,000 22,250 39 34.0 $335,000–$10,000,000 113,900 34 34.0 $10,000,000–$15,000,000 3,400,000 35 34.3 $15,000,000–$18,333,333 5,150,000 38 35.0 Over $18,333,333 6,416,667 35 35.0

Corporate Tax Rates as of January 2008T a b l e 3 - 6

73Chapter 3 Financial Statements, Cash Flow, and Taxes

17 The exclusion depends on the percentage of the paying company’s stock the receiving company owns. If it owns 100% (hence, the payer is a subsidiary), all of the dividend will be excluded. If it owns less than 20%, which is the case if the stock held is just an investment, 70% will be excluded. Also, state tax rules vary; but in our example, we assume that Allied also has a state tax exclusion.

income received by a corporation is taxed as ordinary income at regular corporate tax rates. However, dividends are taxed more favorably: 70% of dividends received is excluded from taxable income, while the remaining 30% is taxed at the ordinary tax rate.17 Thus, a corporation earning more than $18,333,333 and paying a 40% marginal federal plus state tax rate would normally pay only (0.30)(0.4) ! 0.12 ! 12% of its dividend income as taxes. If this fi rm had $10,000 in pretax dividend income, its after-tax dividend income would be $8,800.

A-T income ! B-T income(1 # T) ! $10,000(1 # 0.12) ! $8,800

The reason for this exclusion is that when a corporation receives dividends and then pays out its own after-tax income as dividends to its stockholders, the divi- dends received are subjected to triple taxation: (1) The original corporation is taxed, (2) the second corporation is taxed on the dividends it receives, and (3) the individuals who receive the fi nal dividends are taxed again. This explains the 70% intercorporate dividend exclusion.

Suppose a fi rm has excess cash that it does not need for operations, and it plans to invest this cash in marketable securities. The tax factor favors stocks, which pay dividends, rather than bonds, which pay interest. For example, sup- pose Allied had $100,000 to invest, and it could buy bonds that paid 8% interest, or $8,000 per year, or stock that paid 7% in dividends, or $7,000. Allied is in the 40% federal-plus-state tax bracket. Therefore, if Allied bought bonds and received interest, its tax on the $8,000 of interest would be 0.4($8,000) ! $3,200 and its after- tax income would be $4,800. If it bought stock, its tax would be $7,000(0.12) ! $840 and its after-tax income would be $6,160. Other factors might lead Allied to invest in bonds, but the tax factor favors stock investments when the investor is a corporation.

Interest and Dividends Paid by a Corporation A fi rm like Allied can fi nance its operations with either debt or stock. If a fi rm uses debt, it must pay interest, whereas if it uses stock, it is expected to pay dividends. Interest paid can be deducted from operating income to obtain taxable income, but divi- dends paid cannot be deducted. Therefore, Allied would need $1 of pretax income to pay $1 of interest; but since it is in the 40% federal-plus-state tax bracket, it must earn $1.67 of pretax income to pay $1 of dividends:

Pretax income needed to pay $1 of dividends ! $1 ___________ 1 # Tax rate !

$1 ____ 0.60 ! $1.67

Working backward, if Allied has $1.67 in pretax income, it must pay $0.67 in taxes [(0.4)($1.67) ! $0.67]. This leaves it with after-tax income of $1.00.

Table 3-7 shows the situation for a fi rm with $10 million of assets, sales of $5 mil- lion, and $1.5 million of earnings before interest and taxes (EBIT). As shown in Col- umn 1, if the fi rm were fi nanced entirely by bonds and if it made interest payments of $1.5 million, its taxable income would be zero, taxes would be zero, and its inves- tors would receive the entire $1.5 million. (The term investors includes both stock- holders and bondholders.) However, as shown in Column 2, if the fi rm had no debt and was therefore fi nanced entirely by stock, all of the $1.5 million of EBIT would be taxable income to the corporation, the tax would be $1,500,000(0.40) ! $600,000, and investors would receive only $0.9 million versus $1.5 million under debt fi nancing. Therefore, the rate of return to investors on their $10 million investment is much higher when debt is used.

74 Part 2 Fundamental Concepts in Financial Management

Of course, it is generally not possible to fi nance exclusively with debt; and the risk of doing so would offset the benefi ts of the higher expected income. Still, the fact that interest is a deductible expense has a profound effect on the way businesses are fi nanced—the corporate tax system favors debt fi nancing over equity fi nancing. This point is discussed in more detail in the chapters on cost of capital and capital structure.18

Corporate Capital Gains Before 1987, corporate long-term capital gains were taxed at lower rates than cor- porate ordinary income; so the situation was similar for corporations and individ- uals. Currently, though, corporations’ capital gains are taxed at the same rates as their operating income.

Corporate Loss Carry-Back and Carry-Forward Ordinary corporate operating losses can be carried back (carry-back) to each of the preceding 2 years and carried forward (carry-forward) for the next 20 years and used to offset taxable income in those years. For example, an operating loss in 2008 could be carried back and used to reduce taxable income in 2006 and 2007; it also could be carried forward, if necessary, and used in 2009, 2010, up until 2028. The loss is applied to the earliest year fi rst, then to the next earliest year, and so forth, until losses have been used up or the 20-year carry-forward limit has been reached.

To illustrate, suppose Company X had $2 million of pretax profi ts (taxable income) in 2006 and 2007 and then in 2008, it lost $12 million. Its federal-plus-state tax rate is 40%. As shown in Table 3-8, Company X would use the carry-back feature to recom- pute its taxes for 2006, using $2 million of the 2008 operating losses to reduce the 2006 pretax profi t to zero. This would permit it to recover the taxes paid in 2006. Therefore, in 2008, it would receive a refund of its 2006 taxes because of the loss experienced in 2008. Because $10 million of the unrecovered losses would still be available, X would repeat this procedure for 2007. Thus, in 2008, the company would pay zero taxes for 2008 and would receive a refund for taxes paid in 2006 and 2007. It would still have $8 million of unrecovered losses to carry forward, subject to the 20-year limit. This $8 million could be used until the entire $12 million loss had been used to offset taxable income. The purpose of permitting this loss treatment is to avoid penalizing corpora- tions whose incomes fl uctuate substantially from year to year.

Consolidated Corporate Tax Returns If a corporation owns 80% or more of another corporation’s stock, it can aggregate income and fi le one consolidated tax return. This allows the losses of one company

Tax Loss Carry-Back or Carry-Forward Ordinary corporate operating losses can be carried backward for 2 years and carried forward for 20 years to offset taxable income in a given year.

18 A company could, in theory, refrain from paying dividends to help prevent its stockholders from having to pay taxes on dividends received. The IRS has a rule against the improper accumulation of retained earnings that would permit this. However, in our experience, it is easy for fi rms to justify retaining earnings; and we have never seen a fi rm have a problem with the improper accumulation rule.

Use Bonds (1)

Use Stock (2)

Sales $5,000,000 $5,000,000 Operating costs 3,500,000 3,500,000 Earnings before interest and taxes (EBIT) $1,500,000 $1,500,000 Interest 1,500,000 0 Taxable income $ 0 $1,500,000 Federal-plus-state taxes (40%) 0 600,000 After-tax income $ 0 $ 900,000 Income to investors $1,500,000 $ 900,000 Rate of return on $10 million of assets 15.0% 9.0%

Returns to Investors under Bond and Stock FinancingT a b l e 3 - 7

75Chapter 3 Financial Statements, Cash Flow, and Taxes

to be used to offset the profi ts of another. (Similarly, one division’s losses can be used to offset another division’s profi ts.) No business wants to incur losses; but tax offsets make it more feasible for large, multidivisional corporations to undertake risky new ventures or ventures that will suffer losses during a developmental period.

Taxation of Small Businesses: S Corporations As we noted in Chapter 1, the Tax Code allows small businesses that meet certain conditions to be set up as corporations and thus receive the benefi ts of the corpo- rate form of organization—especially limited liability—yet still be taxed as propri- etorships or partnerships rather than as corporations. These corporations are called S corporations. (Regular corporations are called C corporations.) If a corporation elects S, all of its income is reported as personal income by its stockholders, on a pro rata basis, and thus is taxed at the stockholders’ individual rates. Because the income is taxed only once, this is an important benefi t to the owners of small cor- porations in which all or most of the income earned each year will be distributed as dividends. The situation is similar for LLCs.

Depreciation Depreciation plays an important role in income tax calculations—the larger the depreciation, the lower the taxable income, the lower the tax bill, and thus the higher the operating cash fl ow. Congress specifi es the life over which assets can be depreciated for tax purposes and the depreciation methods that can be used. We will discuss in detail how depreciation is calculated and how it affects income and cash fl ows when we study capital budgeting.

S Corporation A small corporation that, under Subchapter S of the Internal Revenue Code, elects to be taxed as a proprietorship or a partnership yet retains limited liability and other benefits of the corporate form of organization.

2006 2007 Original taxable income $ 2,000,000 $ 2,000,000 Carry-back credit "2,000,000 "2,000,000 Adjusted profit $ 0 $ 0 Taxes previously paid (40%) 800,000 800,000 Difference = Tax refund $ 800,000 $ 800,000

Total refund check received in 2009: $800,000 + $800,000 = $1,600,000 Amount of loss carry-forward available for use in 2009–2028: 2008 loss $12,000,000 Carry-back losses used 4,000,000 Carry-forward losses still available $ 8,000,000

Calculation of Loss Carry-Back and Carry-Forward for 2006–2007 Using a $12 Million 2008 Loss

T a b l e 3 - 8

Explain this statement: Our tax rates are progressive.

What’s the diff erence between marginal and average tax rates?

What’s the AMT, and why was it instituted?

What’s a muni bond, and how are these bonds taxed?

What are long-term capital gains? Are they taxed like other income? Explain.

How does our tax system infl uence the use of debt fi nancing by corporations?

What is the logic behind allowing tax loss carry-backs/carry-forwards?

Diff erentiate between S and C corporations.

SEL F TEST

76 Part 2 Fundamental Concepts in Financial Management

The primary purposes of this chapter were to describe the basic fi nancial statements, to present background information on cash fl ows, to diff erentiate between cash fl ow and accounting income, and to provide an overview of the federal income tax sys- tem. In the next chapter, we build on this information to analyze a fi rm’s fi nancial statements and to determine its fi nancial health.

KEY TERMS Define each of the following terms: a. Annual report; balance sheet; income statement; statement of cash flows; statement of

stockholders’ equity b. Stockholders’ equity; retained earnings; working capital; net working capital c. Depreciation; amortization; operating income; EBITDA; free cash flow d. Progressive tax; marginal tax rate; average tax rate e. Tax loss carry-back; carry-forward; AMT f. Capital gain (loss) g. S corporation

NET INCOME AND CASH FLOW Last year Rattner Robotics had $5 million in operating income (EBIT). Its depreciation expense was $1 million, its interest expense was $1 million, and its corporate tax rate was 40%. At year-end, it had $14 million in current assets, $3 million in accounts payable, $1 million in accruals, and $15 million in net plant and equipment. Assume that Rattner’s only noncash item was depreciation. a. What was the company’s net income? b. What was its net working capital (NWC)? c. Rattner had $12 million in net plant and equipment the prior year. Its net working

capital has remained constant over time. What is the company’s free cash flow (FCF) for the year that just ended?

d. If the firm had $4.5 million in retained earnings at the beginning of the year and paid out total dividends of $1.2 million, what was its retained earnings at the end of the year? Assume that all dividends declared were actually paid.

What four financial statements are contained in most annual reports?

Who are some of the basic users of financial statements, and how do they use them?

If a “typical” firm reports $20 million of retained earnings on its balance sheet, could its directors declare a $20 million cash dividend without having any qualms about what they were doing? Explain your answer.

Explain the following statement: While the balance sheet can be thought of as a snapshot of a firm’s financial position at a point in time, the income statement reports on operations over a period of time.

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

QUESTIONSQUESTIONS

3-13-1 3-23-2 3-33-3

3-43-4

T YING I T ALL TO GETHER

77Chapter 3 Financial Statements, Cash Flow, and Taxes

Financial statements are based on generally accepted accounting principles (GAAP) and are audited by CPA firms. Therefore, do investors need to worry about the validity of those statements? Explain your answer.

What is free cash flow? If you were an investor, why might you be more interested in free cash flow than net income?

Would it be possible for a company to report negative free cash flow and still be highly val- ued by investors; that is, could a negative free cash flow ever be a good thing in the eyes of investors? Explain your answer.

What is meant by the following statement: Our tax rates are progressive.

What does double taxation of corporate income mean? Could income ever be subject to triple taxation? Explain your answer.

How does the deductibility of interest and dividends by the paying corporation affect the choice of financing (that is, the use of debt versus equity)?

INCOME STATEMENT Little Books Inc. recently reported $3 million of net income. Its EBIT was $6 million, and its tax rate was 40%. What was its interest expense? [Hint: Write out the headings for an income statement and fill in the known values. Then divide $3 million of net income by (1 " T) ! 0.6 to find the pretax income. The difference between EBIT and taxable income must be the interest expense. Use this same procedure to com- plete similar problems.]

INCOME STATEMENT Pearson Brothers recently reported an EBITDA of $7.5 million and net income of $1.8 million. It had $2.0 million of interest expense, and its corporate tax rate was 40%. What was its charge for depreciation and amortization?

STATEMENT OF STOCKHOLDERS’ EQUITY In its most recent financial statements, Newhouse Inc. reported $50 million of net income and $810 million of retained earnings. The previous retained earnings were $780 million. How much in dividends were paid to shareholders during the year? Assume that all dividends declared were actually paid.

BALANCE SHEET Which of the following actions are most likely to directly increase cash as shown on a firm’s balance sheet? Explain and state the assumptions that underlie your answer. a. It issues $2 million of new common stock. b. It buys new plant and equipment at a cost of $3 million. c. It reports a large loss for the year. d. It increases the dividends paid on its common stock.

STATEMENT OF STOCKHOLDERS’ EQUITY Computer World Inc. paid out $22.5 million in total common dividends and reported $278.9 million of retained earnings at year-end. The prior year’s retained earnings were $212.3 million. What was the net income? Assume that all dividends declared were actually paid.

STATEMENT OF CASH FLOWS W.C. Cycling had $55,000 in cash at year-end 2007 and $25,000 in cash at year-end 2008. Cash flow from long-term investing activities totaled –$250,000, and cash flow from financing activities totaled #$170,000. a. What was the cash flow from operating activities? b. If accruals increased by $25,000, receivables and inventories increased by $100,000,

and depreciation and amortization totaled $10,000, what was the firm’s net income?

FREE CASH FLOW Bailey Corporation’s financial statements (dollars and shares are in millions) are provided here.

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PROBLEMS PROBLEMS

3-13-1Easy Problems 1–3 Easy Problems 1–3

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3-43-4Intermediate Problems 4–7 Intermediate Problems 4–7

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78 Part 2 Fundamental Concepts in Financial Management

Balance Sheets as of December 31 2008 2007

Assets Cash and equivalents $ 14,000 $ 13,000 Accounts receivable 30,000 25,000 Inventories 28,125 21,000 Total current assets $ 72,125 $ 59,000 Net plant and equipment 50,000 47,000 Total assets $122,125 $106,000

Liabilities and Equity Accounts payable $ 10,800 $ 9,000 Notes payable 6,700 5,150 Accruals 7,600 6,000 Total current liabilities $ 25,100 $ 20,150 Long-term bonds 15,000 15,000 Total debt $ 40,100 $ 35,150 Common stock (5,000 shares) 50,000 50,000 Retained earnings 32,025 20,850 Common equity $ 82,025 $ 70,850 Total liabilities and equity $122,125 $106,000

Income Statement for Year Ending December 31, 2008 Sales $214,000 Operating costs excluding depreciation and amortization 170,000 EBITDA $ 44,000 Depreciation & amortization 5,000 EBIT $ 39,000 Interest 1,750 EBT $ 37,250 Taxes (40%) 14,900 Net income $ 22,350

Dividends paid $ 11,175

a. What was net working capital for 2007 and 2008? b. What was Bailey’s 2008 free cash flow? c. Construct Bailey’s 2008 statement of stockholders’ equity.

INCOME STATEMENT Hermann Industries is forecasting the following income statement:

Sales $8,000,000 Operating costs excluding depr. & amort. 4,400,000 EBITDA $3,600,000 Depreciation & amortization 800,000 EBIT $2,800,000 Interest 600,000 EBT $2,200,000 Taxes (40%) 880,000 Net income $1,320,000

The CEO would like to see higher sales and a forecasted net income of $2,500,000. Assume that operating costs (excluding depreciation and amortization) are 55% of sales and that depreciation and amortization and interest expenses will increase by 10%. The tax rate, which is 40%, will remain the same. What level of sales would generate $2,500,000 in net income?

3-83-8Challenging Problems 8–10 Challenging Problems 8–10

79Chapter 3 Financial Statements, Cash Flow, and Taxes

FINANCIAL STATEMENTS The Davidson Corporation’s balance sheet and income state- ment are provided here.

Davidson Corporation: Balance Sheet as of December 31, 2008 (Millions of Dollars)

Assets Liabilities and Equity Cash and equivalents $ 15 Accounts payable $ 120 Accounts receivable 515 Notes payable 220 Inventories 880 Accruals 280 Total current assets $1,410 Total current liabilities $ 620 Net plant and equipment 2,590 Long-term bonds 1,520

Total debt $ 2,140 Common stock (100 million shares) 260 Retained earnings 1,600 Common equity $ 1,860

Total assets $4,000 Total liabilities and equity $ 4,000

Davidson Corporation: Income Statement For Year Ending December 31, 2008 (Millions of Dollars)

Sales $6,250 Operating costs excluding depreciation and amortization 5,230 EBITDA $1,020 Depreciation & amortization 220 EBIT $ 800 Interest 180 EBT $ 620 Taxes (40%) 248 Net income $ 372

Common dividends paid $ 146 Earnings per share $ 3.72

a. Construct the statement of stockholders’ equity for December 31, 2008. b. How much money has been reinvested in the firm over the years? c. At the present time, how large a check could be written without it bouncing? d. How much money must be paid to current creditors within the next year?

FREE CASH FLOW Financial information for Powell Panther Corporation is shown here.

Powell Panther Corporation: Income Statements For Year Ending December 31 (Millions of Dollars)

2008 2007 Sales $1,200.0 $1,000.0 Operating costs excluding depreciation and amortization 1,020.0 850.0 EBITDA $ 180.0 $ 150.0 Depreciation & amortization 30.0 25.0 Earnings before interest and taxes $ 150.0 $ 125.0 Interest 21.7 20.2 Earnings before taxes $ 128.3 $ 104.8 Taxes (40%) 51.3 41.9 Net income $ 77.0 $ 62.9

Common dividends $ 60.5 $ 46.4

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80 Part 2 Fundamental Concepts in Financial Management

Powell Panther Corporation: Balance Sheets as of December 31 (Millions of Dollars)

2008 2007 Assets Cash and equivalents $ 12.0 $ 10.0 Accounts receivable 180.0 150.0 Inventories 180.0 200.0 Total current assets $372.0 $360.0 Net plant and equipment 300.0 250.0 Total assets $672.0 $610.0

Liabilities and Equity Accounts payable $108.0 $ 90.0 Notes payable 67.0 51.5 Accruals 72.0 60.0 Total current liabilities $247.0 $201.5 Long-term bonds 150.0 150.0 Total debt $397.0 $351.5 Common stock (50 million shares) 50.0 50.0 Retained earnings 225.0 208.5 Common equity $275.0 $258.5 Total liabilities and equity $672.0 $610.0

a. What was net working capital for 2007 and 2008? b. What was the 2008 free cash flow? c. How would you explain the large increase in 2008 dividends?

FINANCIAL STATEMENTS, CASH FLOW, AND TAXES Laiho Industries’ 2007 and 2008 bal- ance sheets (in thousands of dollars) are shown.

2008 2007 Cash $102,850 $ 89,725 Accounts receivable 103,365 85,527 Inventories 38,444 34,982 Total current assets $244,659 $210,234 Net fixed assets 67,165 42,436 Total assets $311,824 $252,670

Accounts payable $ 30,761 $ 23,109 Accruals 30,477 22,656 Notes payable 16,717 14,217 Total current liabilities $ 77,955 $ 59,982 Long-term debt 76,264 63,914 Total liabilities $154,219 $123,896 Common stock 100,000 90,000 Retained earnings 57,605 38,774 Total common equity $157,605 $128,774 Total liabilities and equity $311,824 $252,670

a. Sales for 2008 were $455,150,000, and EBITDA was 15% of sales. Furthermore, deprecia- tion and amortization were 11% of net fixed assets, interest was $8,575,000, the corporate tax rate was 40%, and Laiho pays 40% of its net income in dividends. Given this informa- tion, construct the firm’s 2008 income statement.

b. Construct the statement of stockholders’ equity for the year ending December 31, 2008, and the 2008 statement of cash flows.

c. Calculate 2007 and 2008 net working capital and 2008 free cash flow. d. If Laiho increased its dividend payout ratio, what effect would this have on corporate

taxes paid? What effect would this have on taxes paid by the company’s shareholders?

COMPREHENSIVE/SPREADSHEET PROBLEMCOMPREHENSIVE/SPREADSHEET PROBLEM

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81Chapter 3 Financial Statements, Cash Flow, and Taxes

FINANCIAL STATEMENTS AND TAXES Donna Jamison, a 2003 graduate of the University of Florida with 4 years of banking experience, was recently brought in as assistant to the chairperson of the board of D’Leon Inc., a small food producer that operates in north Florida and whose specialty is high-quality pecan and other nut products sold in the snack foods market. D’Leon’s president, Al Watkins, decided in 2007 to undertake a major expansion and to “go national” in competition with Frito-Lay, Eagle, and other major snack foods companies. Watkins believed that D’Leon’s products were of higher quality than the competition’s; that this quality differen- tial would enable it to charge a premium price; and that the end result would be greatly increased sales, profits, and stock price. The company doubled its plant capacity, opened new sales offices outside its home territory, and launched an expensive advertising campaign. D’Leon’s results were not satisfactory, to put it mildly. Its board of directors, which consisted of its president, vice president, and major stockholders (who were all local businesspeople), was most upset when directors learned how the expansion was going. Unhappy suppliers were being paid late; and the bank was complaining about the deteriorating situation, threatening to cut off credit. As a result, Watkins was informed that changes would have to be made—and quickly; otherwise, he would be fired. Also, at the board’s insistence, Donna Jamison was brought in and given the job of assistant to Fred Campo, a retired banker who was D’Leon’s chairperson and largest stockholder. Campo agreed to give up a few of his golfing days and help nurse the company back to health, with Jamison’s help. Jamison began by gathering the financial statements and other data given in Tables IC3-1, IC3-2, IC3-3, and IC3-4. Assume that you are Jamison’s assistant. You must help her answer the following questions for Campo. (Note: We will continue with this case in Chapter 4, and you will feel more comfortable with the analysis there. But answering these questions will help prepare you for Chapter 4. Provide clear explanations.)

a. What effect did the expansion have on sales, after-tax operating income, net working capital (NWC), and net income?

b. What effect did the company’s expansion have on its free cash flow? c. D’Leon purchases materials on 30-day terms, meaning that it is supposed to pay for purchases within 30 days

of receipt. Judging from its 2008 balance sheet, do you think that D’Leon pays suppliers on time? Explain, including what problems might occur if suppliers are not paid in a timely manner.

d. D’Leon spends money for labor, materials, and fixed assets (depreciation) to make products—and spends still more money to sell those products. Then the firm makes sales that result in receivables, which eventu- ally result in cash inflows. Does it appear that D’Leon’s sales price exceeds its costs per unit sold? How does this affect the cash balance?

e. Suppose D’Leon’s sales manager told the sales staff to start offering 60-day credit terms rather than the 30-day terms now being offered. D’Leon’s competitors react by offering similar terms, so sales remain con- stant. What effect would this have on the cash account? How would the cash account be affected if sales doubled as a result of the credit policy change?

f. Can you imagine a situation in which the sales price exceeds the cost of producing and selling a unit of out- put, yet a dramatic increase in sales volume causes the cash balance to decline? Explain.

g. Did D’Leon finance its expansion program with internally generated funds (additions to retained earnings plus depreciation) or with external capital? How does the choice of financing affect the company’s financial strength?

h. Refer to Tables IC3-2 and IC3-4. Suppose D’Leon broke even in 2008 in the sense that sales revenues equaled total operating costs plus interest charges. Would the asset expansion have caused the company to experi- ence a cash shortage that required it to raise external capital? Explain.

i. If D’Leon starts depreciating fixed assets over 7 years rather than 10 years, would that affect (1) the physical stock of assets, (2) the balance sheet account for fixed assets, (3) the company’s reported net income, and (4) the company’s cash position? Assume that the same depreciation method is used for stockholder reporting and for tax calculations and that the accounting change has no effect on assets’ physical lives.

j. Explain how earnings per share, dividends per share, and book value per share are calculated and what they mean. Why does the market price per share not equal the book value per share?

k. Explain briefly the tax treatment of (1) interest and dividends paid, (2) interest earned and dividends received, (3) capital gains, and (4) tax loss carry-back and carry-forward. How might each of these items affect D’Leon’s taxes?

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IN TEGRATED C ASE D’LEON INC., PART I

82 Part 2 Fundamental Concepts in Financial Management

2008 2007 Assets Cash $ 7,282 $ 57,600 Accounts receivable 632,160 351,200 Inventories 1,287,360 715,200 Total current assets $1,926,802 $1,124,000 Gross fixed assets 1,202,950 491,000 Less accumulated depreciation 263,160 146,200 Net fixed assets $ 939,790 $ 344,800 Total assets $2,866,592 $1,468,800

Liabilities and Equity Accounts payable $ 524,160 $ 145,600 Notes payable 636,808 200,000 Accruals 489,600 136,000 Total current liabilities $1,650,568 $ 481,600 Long-term debt 723,432 323,432 Common stock (100,000 shares) 460,000 460,000 Retained earnings 32,592 203,768 Total equity $ 492,592 $ 663,768 Total liabilities and equity $2,866,592 $1,468,800

Balance SheetsT a b l e I C 3 - 1

2008 2007 Sales $6,034,000 $3,432,000 Cost of goods sold 5,528,000 2,864,000 Other expenses 519,988 358,672 Total operating costs excluding depreciation and amortization $6,047,988 $3,222,672 Depreciation and amortization 116,960 18,900 EBIT ($ 130,948) $190,428 Interest expense 136,012 43,828 EBT ($ 266,960) $ 146,600 Taxes (40%) (106,784)a 58,640 Net income ($ 160,176) $ 87,960

EPS ($ 1.602) $ 0.880 DPS $ 0.110 $ 0.220 Book value per share $ 4.926 $ 6.638 Stock price $ 2.25 $ 8.50 Shares outstanding 100,000 100,000 Tax rate 40.00% 40.00% Lease payments 40,000 40,000 Sinking fund payments 0 0

Note: a The firm had sufficient taxable income in 2006 and 2007 to obtain its full tax refund in 2008.

Income StatementsT a b l e I C 3 - 2

83Chapter 3 Financial Statements, Cash Flow, and Taxes

Statement of Stockholders’ Equity, 2008T a b l e I C 3 - 3

COMMON STOCK Retained Earnings

Total Stockholders’

EquityShares Amount

Balances, 12/31/07 100,000 $460,000 $ 203,768 $663,768 2008 Net Income (160,176) Cash Dividends (11,000) Addition (Subtraction) to Retained Earnings (171,176) Balances, 12/31/08 100,000 $460,000 $ 32,592 $492,592

Operating Activities Net income ($160,176) Depreciation and amortization 116,960 Increase in accounts payable 378,560 Increase in accruals 353,600 Increase in accounts receivable (280,960) Increase in inventories (572,160) Net cash provided by operating activities ($164,176)

Long-Term Investing Activities Additions to property, plant, and equipment ($711,950) Net cash used in investing activities ($711,950)

Financing Activities Increase in notes payable $436,808 Increase in long-term debt 400,000 Payment of cash dividends (11,000) Net cash provided by financing activities $825,808

Summary Net decrease in cash ($ 50,318) Cash at beginning of year 57,600 Cash at end of year $ 7,282

Statement of Cash Flows, 2008T a b l e I C 3 - 4

84 Part 2 Fundamental Concepts in Financial Management

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to answer this chapter’s questions.

Exploring Starbucks’ Financial Statements Over the past decade, Starbucks coffee shops have become an increasingly familiar part of the urban landscape. Currently (2008), the company operates more than 8,000 coffee shops in all 50 states, in the District of Columbia, and in international markets; and in 2008, it had approximately 145,000 employees.

Thomson ONE can access a wealth of fi nancial information for companies such as Starbucks. To fi nd some background information, begin by entering the company’s ticker symbol, SBUX, and then select- ing “GO.” On the opening screen, you will see a great deal of useful information, including a summary of what Starbucks does, a chart of its recent stock price, EPS estimates, recent news stories, and a list of key fi nancial data and ratios.

In researching a company’s operating performance, a good place to start is the recent stock price performance. At the top of the Stock Price Chart, click on the section labeled “Interactive Chart.” From this point, you can obtain a chart of the company’s stock price performance relative to the overall market (as measured by the S&P 500) between 1998 and 2008. To obtain a 10-year chart, go to “Time Frame,” click on the down arrow, and select “10 years.” Then click on “Draw”; a 10-year price chart should appear.

As you can see, Starbucks has had its ups and downs. But the company’s overall performance has been quite strong, and it has beaten the overall market handily.

You can also fi nd Starbucks’ recent fi nancial statements. Click on Financials to fi nd the company’s annual balance sheets for the past 5 years. Selecting Thomson Financials provides balance sheets, income statements, and statements of cash fl ows for various time periods. Clicking on the Microsoft Excel icon downloads these statements directly to a spreadsheet.

Discussion Questions 1. Looking at the most recent year available, what is the amount of total assets on Starbucks’ balance sheet? What

percentage is fixed assets, such as plant and equipment? What percentage is current assets? How much has the company grown over the years that are shown?

2. Does Starbucks have very much long-term debt? What are the chief ways in which Starbucks has financed assets?

3. Looking at the statement of cash flows, what factors can explain the change in the company’s cash position over the last couple of years?

4. Looking at the income statement, what are the company’s most recent sales and net income? Over the past sev- eral years, what has been the sales growth rate? What has been the growth rate in net income?

5. Over the past few years, has there been a strong correlation between stock price performance and reported earnings? Explain.

Discussion Questions 1. Looking at the most recent year available, what is the amount of total assets on Starbucks’ balance sheet? What

percentage is fixed assets, such as plant and equipment? What percentage is current assets? How much has the company grown over the years that are shown?

2. Does Starbucks have very much long-term debt? What are the chief ways in which Starbucks has financed assets?

3. Looking at the statement of cash flows, what factors can explain the change in the company’s cash position over the last couple of years?

5. Over the past few years, has there been a strong correlation between stock price performance and reported earnings? Explain.

Ca n Yo u M a ke M o n ey A n a l y z i n g S t o c k s ?

Analysis of Financial Statements

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4 CHAPTER

For the past 40 years, a debate has raged over the question posed above. Some argue that the stock market is highly efficient and that all avail- able information regarding a stock is already reflected in its price. The “efficient market advo- cates” point out that there are thousands of smart, well-trained analysts working for institu- tions with billions of dollars. These analysts have access to the latest information, and they spring into action—buying or selling—as soon as a firm releases any information that has a bearing on its future profits. The “efficient markets advo- cates” also point out that few mutual funds, which hire good people and pay them well, actually beat the averages. If these experts earn only average returns, how can the rest of us expect to beat the market?

Others disagree, arguing that analysis can pay off. They point out that some fund manag- ers perform better than average year after year. Also, they note that some “activist” investors analyze firms carefully, identify those with weak- nesses that appear to be correctable, and then

persuade their managers to take actions to improve the firms’ performances. One such investor is Warren Buffett, perhaps the best known U.S. investor. Another is Carl Icahn—not a household name, but someone whose invest- ments have made him the 18th wealthiest American. Buffett and Icahn now have billions of dollars to work with, and those billions give them better access to corporate managers than most of us have. However, neither of them started as billionaires—they worked their way up, doing careful analysis of the type described in this chapter.

When investors learn that an activist investor such as Icahn has bought a stock, the price of that stock generally rises. Thus, in the fall of 2007, Icahn began buying shares in BEA Sys- tems, a billion dollar software company, that had been selling for about $10.50. Once inves- tors learned of Icahn’s interest, the price jumped to $18.94. You can bet that Icahn and his staff went through the type of analysis discussed in this chapter, identified BEA’s strengths and

86 Part 2 Fundamental Concepts in Financial Management

weaknesses, and concluded that managerial actions could boost the firm’s cash flows and value. Icahn’s views were shared by Larry Ellison, chairperson of Oracle Corporation, a $17 billion software company. As we write this, Oracle and Icahn have combined forces and are trying to force a

change in BEA’s operations. Thousands of analysts are doing similar analyses of thousands of other companies, trying to find the next BEA and becoming the next Buffett or Icahn. It’s fun; and unless the efficient markets folks are correct, it can be profitable.

PU T TING THINGS IN PER SPECTIVE The primary goal of fi nancial management is to maximize shareholders’ wealth, not accounting measures such as net income or EPS. However, accounting data infl uence stock prices, and this data can be used to see why a company is performing the way it is and where it is heading. Chapter 3 described the key fi nancial statements and showed how they change as a fi rm’s operations change. Now, in Chapter 4, we show how the statements are used by managers to improve the fi rm’s stock price; by lend- ers to evaluate the likelihood that borrowers will be able to pay off loans; and by security analysts to forecast earnings, dividends, and stock prices. If management is to maximize a fi rm’s value, it must take advantage of the fi rm’s strengths and correct its weaknesses. Financial analysis involves (1) comparing the fi rm’s performance to that of other fi rms in the same industry and (2) evaluating trends in the fi rm’s fi nancial position over time. These studies help managers identify defi ciencies and then take corrective actions. In this chapter, we focus on how man- agers and investors evaluate a fi rm’s fi nancial position. Then, in later chapters, we examine the types of actions managers can take to improve future performance and thus increase the fi rm’s stock price. The most important ratio is the ROE, or return on equity, which tells us how much stockholders are earning on the funds they provide to the fi rm. When ROE is high, the stock price also tends to be high; so actions that increase ROE generally in crease the stock price. Other ratios provide information about how well assets such as inventory, accounts receivable, and fi xed assets are managed and about the fi rm’s capital structure. Managers use ratios related to these factors to help develop plans to improve ROE. When you fi nish this chapter, you should be able to: • Explain what ratio analysis is. • List the 5 groups of ratios and identify, calculate, and interpret the key ratios in

each group. In addition, discuss each ratio’s relationship to the balance sheet and income statement.

• Discuss why ROE is the key ratio under management’s control, how the other ratios aff ect ROE, and explain how to use the DuPont equation to see how the ROE can be improved.

• Compare a fi rm’s ratios with those of other fi rms (benchmarking) and analyze a given fi rm’s ratios over time (trend analysis).

• Discuss the tendency of ratios to fl uctuate over time, which may or may not be problematic. Explain how they can be infl uenced by accounting practices and other factors and why they must be used with care.

87Chapter 4 Analysis of Financial Statements

4-1 RATIO ANALYSIS Ratios help us evaluate fi nancial statements. For example, at the end of 2008, Allied Food Products had $1,060 million of debt and interest charges of $88 million while Midwest Products had $52 million of debt and interest charges of $4 million. Which company is stronger? The burden of these debts and the companies’ ability to repay them can best be evaluated by comparing each fi rm’s debt to its assets and comparing interest expense to the income and cash available to pay that interest. Ratios are used to make such comparisons. We calculate Allied’s ratios for 2008 using data from the balance sheets and income statements given in Tables 3-1 and 3-2. We also evaluate the ratios relative to food industry averages, using data in millions of dollars.1 As you will see, we can calculate many different ratios, with different ones used to examine different aspects of the fi rm’s operations. You will get to know some ratios by name, but it’s better to understand what they are designed to do than to memorize names and equations.

We divide the ratios into fi ve categories: 1. Liquidity ratios, which give us an idea of the fi rm’s ability to pay off debts that

are maturing within a year. 2. Asset management ratios, which give us an idea of how effi ciently the fi rm is

using its assets. 3. Debt management ratios, which give us an idea of how the fi rm has fi nanced its

assets as well as the fi rm’s ability to repay its long-term debt. 4. Profi tability ratios, which give us an idea of how profi tably the fi rm is operating

and utilizing its assets. 5. Market value ratios, which bring in the stock price and give us an idea of what

investors think about the fi rm and its future prospects.

Satisfactory liquidity ratios are necessary if the fi rm is to continue operating. Good asset management ratios are necessary for the fi rm to keep its costs low and thus its net income high. Debt management ratios give us an idea of how risky the fi rm is and how much of its operating income must be paid to bondholders rather than stockholders. Profi tability ratios bring together the asset and debt manage- ment ratios and show their effects on ROE. Finally, market value ratios tell us what investors think about the company and its prospects.

All of the ratios are important, but different ones are more important for some companies than for others. For example, if a fi rm borrowed too much in the past and its debt now threatens to drive it into bankruptcy, the debt ratios are key. Simi- larly, if a fi rm expanded too rapidly and now fi nds itself with excess inventory and manufacturing capacity, the asset management ratios take center stage. The ROE

1 Financial statement data for most publicly traded fi rms can be obtained from the Internet. A couple of free sites that provide this information include Google Finance and Yahoo Finance. These sites provide the fi nancial statements, which can be copied to an Excel fi le and used to create your own ratios; but the web sites also provide calculated ratios.

In addition to the ratios discussed in this chapter, fi nancial analysts often employ a tool known as common size analysis. To form a common size balance sheet, simply divide each asset, liability, and equity item by total assets and then express the results as percentages. To develop a common size income statement, divide each income statement item by sales. The resultant percentage statements can be compared with statements of larger or smaller fi rms or with those of the same fi rm over time. One would normally obtain the basic statements from a source such as Google Finance and copy them to Excel, so constructing common size statements is quite easy. Note too that industry average data are generally given as percentages, which makes them easy to compare with a fi rm’s own common size statements.

88 Part 2 Fundamental Concepts in Financial Management

is always important; but a high ROE depends on maintaining liquidity, on effi cient asset management, and on the proper use of debt. Managers are, of course, vitally concerned with the stock price; but managers have little direct control over the stock market while they do have control over their fi rm’s ROE. So ROE tends to be the main focal point.

4-2 LIQUIDITY RATIOS The liquidity ratios help answer this question: Will the fi rm be able to pay off its debts as they come due and thus remain a viable organization? If the answer is no, liquidity must be the fi rst order of business.

A liquid asset is one that trades in an active market and thus can be quickly converted to cash at the going market price. As shown in Table 3-1 in Chapter 3, Allied has $310 million of debt that must be paid off within the coming year. Will it have trouble meeting that obligation? A full liquidity analysis requires the use of a cash budget, which we discuss in the working capital management chapter; however, by relating cash and other current assets to current liabilities, ratio analy- sis provides a quick and easy-to-use measure of liquidity. Two of the most com- monly used liquidity ratios are discussed below.

4-2a Current Ratio The primary liquidity ratio is the current ratio, which is calculated by dividing current assets by current liabilities:

Current ratio ! Current assets _______________ Current liabilities

! $1,000 ______ $310 ! 3.2"

Industry average ! 4.2"

Current assets include cash, marketable securities, accounts receivable, and invento- ries. Allied’s current liabilities consist of accounts payable, accrued wages and taxes, and short-term notes payable to its bank, all of which are due within one year.

If a company is having fi nancial diffi culty, it typically begins to pay its accounts payable more slowly and to borrow more from its bank, both of which increase current liabilities. If current liabilities are rising faster than current assets, the cur- rent ratio will fall; and this is a sign of possible trouble. Allied’s current ratio is 3.2, which is well below the industry average of 4.2. Therefore, its liquidity position is somewhat weak but by no means desperate.2

Although industry average fi gures are discussed later in some detail, note that an industry average is not a magic number that all fi rms should strive to maintain; in fact, some very well-managed fi rms may be above the average while other good fi rms are below it. However, if a fi rm’s ratios are far removed from the averages for its industry, an analyst should be concerned about why this variance occurs. Thus, a deviation from the industry average should signal the analyst (or management) to check further. Note too that a high current ratio generally indicates a very strong, safe liquidity position; it might also indicate that the fi rm has too much old inven- tory that will have to be written off and too many old accounts receivable that may

Liquid Asset An asset that can be converted to cash quickly without having to reduce the asset’s price very much.

Liquidity Ratios Ratios that show the relationship of a firm’s cash and other current assets to its current liabilities.

Current Ratio This ratio is calculated by dividing current assets by current liabilities. It indicates the extent to which current liabilities are covered by those assets expected to be converted to cash in the near future.

2 Since current assets should be convertible to cash within a year, it is likely that they could be liquidated at close to their stated value. With a current ratio of 3.2, Allied could liquidate current assets at only 31% of book value and still pay off current creditors in full: 1/3.2 ! 0.31, or 31%. Note also that 0.31($1,000) ! $310, the current liabilities balance.

89Chapter 4 Analysis of Financial Statements

turn into bad debts. Or the high current ratio might indicate that the fi rm has too much cash, receivables, and inventory relative to its sales, in which case these assets are not being managed effi ciently. So it is always necessary to look deeply into the full set of ratios before forming a judgment as to how well the fi rm is performing.

4-2b Quick, or Acid Test, Ratio The second liquidity ratio is the quick, or acid test, ratio, which is calculated by deducting inventories from current assets and then dividing the remainder by cur- rent liabilities:

Quick, or acid test, ratio ! Current assets # Inventories _________________________ Current liabilities

! $385 _____ $310 ! 1.2"

Industry average ! 2.2"

Inventories are typically the least liquid of a fi rm’s current assets; and if sales slow down, they might not be converted to cash as quickly as expected. Also, invento- ries are the assets on which losses are most likely to occur in the event of liquida- tion. Therefore, the quick ratio, which measures the fi rm’s ability to pay off short- term obligations without relying on the sale of inventories, is important.

The industry average quick ratio is 2.2, so Allied’s 1.2 ratio is relatively low. Still, if the accounts receivable can be collected, the company can pay off its current liabilities even if it has trouble disposing of its inventories.

Quick (Acid Test) Ratio This ratio is calculated by deducting inventories from current assets and then dividing the remainder by current liabilities.

4-3 ASSET MANAGEMENT RATIOS The second group of ratios, the asset management ratios, measure how effectively the fi rm is managing its assets. These ratios answer this question: Does the amount of each type of asset seem reasonable, too high, or too low in view of current and projected sales? These ratios are important because when Allied and other compa- nies acquire assets, they must obtain capital from banks or other sources and capital is expensive. Therefore, if Allied has too many assets, its cost of capital will be too

Asset Management Ratios A set of ratios that measure how effectively a firm is managing its assets.

SEL F TEST What are the characteristics of a liquid asset? Give examples of some liquid

assets.

What question are the two liquidity ratios designed to answer?

Which is the least liquid of the fi rm’s current assets?

A company has current liabilities of $500 million, and its current ratio is 2.0. What is the total of its current assets? ($1,000 million) If this fi rm’s quick ratio is 1.6, how much inventory does it have? ($200 million) (Hint: To an- swer this problem and some of the other problems in this chapter, write out the equation for the ratio in the question, insert the given data, and solve for the missing value.)

Examples:

Current ratio ! 2.0 ! CA/CL ! CA/$500, so CA ! 2($500) ! $1,000

Quick ratio ! 1.6 ! (CA " Inventories)/CL ! ($1,000 " Inventories)/$500, so $1,000 " Inventories ! 1.6($500) and Inventories ! $1,000 " $800 ! $200

90 Part 2 Fundamental Concepts in Financial Management

high, which will depress its profi ts. On the other hand, if its assets are too low, prof- itable sales will be lost. So Allied must strike a balance between too many and too few assets, and the asset management ratios will help it strike this proper balance.

4-3a Inventory Turnover Ratio “Turnover ratios” divide sales by some asset: Sales/Various assets. As the name implies, these ratios show how many times the particular asset is “turned over” during the year. Here is the inventory turnover ratio:

Inventory turnover ratio ! Sales __________ Inventories

! $3,000 ______ $615 ! 4.9"

Industry average ! 10.9"

As a rough approximation, each item of Allied’s inventory is sold and restocked, or “turned over,” 4.9 times per year. Turnover is a term that originated many years ago with the old Yankee peddler who would load up his wagon with pots and pans, then go off on his route to peddle his wares. The merchandise was called working capital because it was what he actually sold, or “turned over,” to produce his profi ts, whereas his “turnover” was the number of trips he took each year. Annual sales divided by inventory equaled turnover, or trips per year. If he made 10 trips per year, stocked 100 pots and pans, and made a gross profi t of $5 per item, his annual gross profi t was (100)($5)(10) ! $5,000. If he went faster and made 20 trips per year, his gross profi t doubled, other things held constant. So his turn- over directly affected his profi ts.

Allied’s inventory turnover of 4.9 is much lower than the industry average of 10.9. This suggests that it is holding too much inventory. Excess inventory is, of course, unproductive and represents an investment with a low or zero rate of return. Allied’s low inventory turnover ratio also makes us question the current ratio. With such a low turnover, the fi rm may be holding obsolete goods that are not worth their stated value.3

Note that sales occur over the entire year, whereas the inventory fi gure is for one point in time. For this reason, it might be better to use an average inventory mea- sure.4 If the business is highly seasonal or if there has been a strong upward or down- ward sales trend during the year, it is especially useful to make an adjustment. Al- lied’s sales are not growing especially rapidly though; and to maintain comparability with industry averages, we used year-end rather than average inventories.

4-3b Days Sales Outstanding Accounts receivable are evaluated by the days sales outstanding (DSO) ratio, also called the average collection period (ACP).5 It is calculated by dividing accounts

Inventory Turnover Ratio This ratio is calculated by dividing sales by inventories.

Days Sales Outstanding (DSO) This ratio is calculated by dividing accounts receivable by average sales per day; it indicates the average length of time the firm must wait after making a sale before it receives cash.

3 Our measure of inventory turnover is frequently used by established compilers of fi nancial ratio statistics such as Value Line and Dun & Bradstreet. However, you should recognize that other sources calculate inventory using cost of goods sold in place of sales in the formula’s numerator. The rationale for this alternative measure is that sales are stated at market prices; so if inventories are carried at cost, as they generally are, the calculated turnover overstates the true turnover ratio. Therefore, it might be more appropriate to use cost of goods sold in place of sales in the formula’s numerator. When evaluating and comparing fi nancial ratios from various sources, it is important to understand how those sources are specifi cally calculating fi nancial ratios. 4 Preferably, the average inventory value should be calculated by summing the monthly fi gures during the year and dividing by 12. If monthly data are not available, the beginning and ending fi gures can be added and then divided by 2. Both methods adjust for growth but not for seasonal eff ects. 5 We could use the receivables turnover to evaluate receivables. Allied’s receivables turnover is $3,000/$375 ! 8#. However, the DSO ratio is easier to interpret and judge.

91Chapter 4 Analysis of Financial Statements

receivable by the average daily sales to fi nd how many days’ sales are tied up in receivables. Thus, the DSO represents the average length of time the fi rm must wait after making a sale before receiving cash. Allied has 46 days sales outstand- ing, well above the 36-day industry average:

Days sales outstanding (DSO) ! Receivables ___________________ Average sales per day ! Receivables _______________ Annual sales/365

! $375 __________ $3,000/365 ! $375 _______ $8.2192 ! 45.625 days ≈ 46 days

Industry average ! 36 days

The DSO can be compared with the industry average, but it is also evaluated by comparing it with Allied’s credit terms. Allied’s credit policy calls for payment within 30 days. So the fact that 46 days’ sales are outstanding, not 30 days’, indi- cates that Allied’s customers, on average, are not paying their bills on time. This deprives the company of funds that could be used to reduce bank loans or some other type of costly capital. Moreover, the high average DSO indicates that if some customers are paying on time, quite a few must be paying very late. Late-paying customers often default, so their receivables may end up as bad debts that can never be collected.6 Note too that the trend in the DSO over the past few years has been rising, but the credit policy has not been changed. This reinforces our belief that Allied’s credit manager should take steps to collect receivables faster.

4-3c Fixed Assets Turnover Ratio The fi xed assets turnover ratio, which is the ratio of sales to net fi xed assets, mea- sures how effectively the fi rm uses its plant and equipment:

Fixed assets turnover ratio ! Sales ______________ Net fi xed assets

! $3,000 ______ $1,000 ! 3.0"

Industry average ! 2.8"

Allied’s ratio of 3.0 times is slightly above the 2.8 industry average, indicating that it is using its fi xed assets at least as intensively as other fi rms in the industry. There- fore, Allied seems to have about the right amount of fi xed assets relative to its sales.

Potential problems may arise when interpreting the fi xed assets turnover ratio. Recall that fi xed assets are shown on the balance sheet at their historical costs less depreciation. Infl ation has caused the value of many assets that were purchased in the past to be seriously understated. Therefore, if we compare an old fi rm whose fi xed assets have been depreciated with a new company with similar operations that acquired its fi xed assets only recently, the old fi rm will probably have the higher fi xed assets turnover ratio. However, this would be more refl ective of the age of the assets than of ineffi ciency on the part of the new fi rm. The accounting profession is trying to develop procedures for making fi nancial statements refl ect current values rather than historical values, which would help us make better comparisons. How- ever, at the moment, the problem still exists; so fi nancial analysts must recognize this problem and deal with it judgmentally. In Allied’s case, the issue is not serious

Fixed Assets Turnover Ratio The ratio of sales to net fixed assets.

6 For example, if further analysis along the lines suggested in Part 6 of this text indicates that 85% of the customers pay in 30 days, for the DSO to average 46 days, the remaining 15% must be paying, on average, in 136.67 days. Paying that late suggests fi nancial diffi culties. A DSO of 46 days would alert a good analyst of the need to dig deeper.

92 Part 2 Fundamental Concepts in Financial Management

because all fi rms in the industry have been expanding at about the same rate; hence, the balance sheets of the comparison fi rms are reasonably comparable.7

4-3d Total Assets Turnover Ratio The fi nal asset management ratio, the total assets turnover ratio, measures the turn- over of all of the fi rm’s assets; and it is calculated by dividing sales by total assets:

Total assets turnover ratio ! Sales __________ Total assets

! $3,000 ______ $2,000 ! 1.5"

Industry average ! 1.8"

Allied’s ratio is somewhat below the industry average, indicating that it is not generating enough sales given its total assets. We just saw that Allied’s fi xed assets turnover is in line with the industry average; so the problem is with its current assets, inventories and accounts receivable, whose ratios were below the industry standards. Inventories should be reduced and receivables collected faster, which would improve operations.

Total Assets Turnover Ratio This ratio is calculated by dividing sales by total assets.

4-4 DEBT MANAGEMENT RATIOS The use of debt will increase, or “leverage up,” a fi rm’s ROE if the fi rm earns more on its assets than the interest rate it pays on debt. However, debt exposes the fi rm to more risk than if it fi nanced only with equity. In this section we discuss debt management ratios.

Table 4-1 illustrates the potential benefi ts and risks associated with debt.8 Here we analyze two companies that are identical except for how they are fi nanced. Firm U (for Unleveraged) has no debt; thus, it uses 100% common equity. Firm L (for Leveraged) obtained 50% of its capital as debt at an interest rate of 10%. Both fi rms have $100 of assets, and their sales are expected to range from a high of $150 down to $75 depending on business conditions. Some of their operating costs (e.g.,

Debt Management Ratios A set of ratios that measure how effectively a firm manages its debt.

7 See FASB #89, Financial Reporting and Changing Prices (December 1986), for a discussion of the eff ects of infl a- tion on fi nancial statements. The report’s age indicates how diffi cult it has been to solve this problem. 8 We discuss ROE in more depth later in this chapter, and we examine the eff ects of leverage in detail in the capital structure and leverage chapter.

SEL F TEST Write the equations for four ratios that are used to measure how eff ectively a

fi rm manages its assets.

If one fi rm is growing rapidly and another is not, how might this distort a comparison of their inventory turnover ratios?

If you wanted to evaluate a fi rm’s DSO, with what could you compare it? (Other companies and the same company over time)

How might diff erent ages distort comparisons of diff erent fi rms’ fi xed assets turnover ratios?

A fi rm has annual sales of $100 million, $20 million of inventory, and $30 mil- lion of accounts receivable. What is its inventory turnover ratio? (5") What is its DSO? (109.5 days)

93Chapter 4 Analysis of Financial Statements

rent and the president’s salary) are fi xed and will be the same regardless of the level of sales, while other costs (e.g., manufacturing labor and materials costs) vary with sales.9

Notice that everything is the same in the table for the leveraged and unlever- aged fi rms down through operating income—thus, their EBITs are the same in each state of the economy. However, things differ below operating income. Firm U has no debt, it pays no interest, its taxable income is the same as its operating income, it pays a 40% state and federal tax rate, and its net income ranges from $27 under

T a b l e 4 . 1 Effects of Financial Leverage on Stockholder ReturnsT a b l e 4 - 1

STATE OF THE ECONOMY Good Expected Bad

Sales revenues $150.0 $100.0 $75.0 Operating costs Fixed 45.0 45.0 45.0 Variable 60.0 40.0 30.0 Total operating costs 105.0 85.0 75.0 Operating income (EBIT) $ 45.0 $ 15.0 $ 0.0 Interest (Rate = 10%) 0.0 0.0 0.0 Earnings before taxes (EBT) $ 45.0 $ 15.0 $ 0.0 Taxes (Rate = 40%) 18.0 6.0 0.0 Net income (NI) $ 27.0 $ 9.0 $ 0.0 ROEU 27.0% 9.0% 0.0%

FIRM L [LEVERAGED (SOME DEBT)] Current assets $ 50 Debt $ 50 Fixed assets 50 Common equity 50 Total assets $100 Total liabilities and equity $100

STATE OF THE ECONOMY Good Expected Bad

Sales revenues $150.0 $100.0 $75.0 Operating costs Fixed 45.0 45.0 45.0 Variable 60.0 40.0 30.0 Total operating costs 105.0 85.0 75.0 Operating income (EBIT) $ 45.0 $ 15.0 $ 0.0 Interest (Rate ! 10%) 5.0 5.0 5.0 Earnings before taxes (EBT) $ 40.0 $ 10.0 "$ 5.0 Taxes (Rate ! 40%) 16.0 4.0 0.0 Net income (NI) $ 24.0 $ 6.0 "$ 5.0 ROEL 48.0% 12.0% "10.0%

9 The fi nancial statements do not show the breakdown between fi xed and variable operating costs, but companies can and do make this breakdown for internal purposes. Of course, the distinction is not always clear because what’s a fi xed cost in the very short run can become a variable cost over a longer time horizon. It’s interesting to note that companies are moving toward making more of their costs variable, using such techniques as increasing bonuses rather than base salaries, switching to profi t-sharing plans rather than fi xed pension plans, and outsourcing various operations.

FIRM U [UNLEVERAGED (NO DEBT)] Current assets $ 50 Debt $ 0 Fixed assets 50 Common equity 100 Total assets $100 Total liabilities and equity $100

94 Part 2 Fundamental Concepts in Financial Management

good conditions down to $0 under bad conditions. When U’s net income is di- vided by its common equity, its ROEs range from 27% to 0% depending on the state of the economy.

Firm L has the same EBIT as U under each state of the economy, but L uses $50 of debt with a 10% interest rate; so it has $5 of interest charges regardless of the economy. This $5 is deducted from EBIT to arrive at taxable income; taxes are taken out; and the result is net income, which ranges from $24 to "$5 depending on conditions.10 At fi rst, it looks as though Firm U is better off under all condi- tions; but this is not correct—we need to consider how much the two fi rms’ stock- holders have invested. Firm L’s stockholders have put up only $50; so when that investment is divided into net income, we see that their ROE under good condi- tions is a whopping 48% (versus 27% for U) and is 12% (versus 9% for U) under expected conditions. However, L’s ROE falls to "10% under bad conditions, which means that Firm L would go bankrupt if those conditions persisted for several years.

There are two reasons for the leveraging effect: (1) Interest is deductible, so the use of debt lowers the tax bill and leaves more of the fi rm’s operating income avail- able to its investors. (2) If the rate of return on assets exceeds the interest rate on debt, as is generally expected, a company can use debt to acquire assets, pay the in- terest on the debt, and have something left over as a “bonus” for its stockholders. Under the expected conditions, our hypothetical fi rms expect to earn 15% on assets versus a 10% cost of debt. This, combined with the tax benefi t of debt, pushes L’s expected ROE far above that of U.

Thus, fi rms with relatively high debt ratios typically have higher expected returns when the economy is normal but lower returns and possibly bankruptcy if the economy goes into a recession. Therefore, decisions about the use of debt re- quire fi rms to balance higher expected returns against increased risk. Determining the optimal amount of debt is a complicated process, and we defer a discussion of that subject until the capital structure chapter. For now, we simply look at two pro- cedures that analysts use to examine the fi rm’s debt: (1) They check the balance sheet to determine the proportion of total funds represented by debt, and (2) they review the income statement to see the extent to which interest is covered by oper- ating profi ts.

4-4a Total Debt to Total Assets The ratio of total debt to total assets, generally called the debt ratio, measures the percentage of funds provided by creditors:

Debt ratio ! Total debt __________ Total assets

! $310 $ $750 ____________ $2,000 ! $1,060 ______ $2,000 ! 53.0%

Industry average ! 40.0%

Total debt includes all current liabilities and long-term debt. Creditors prefer low debt ratios because the lower the ratio, the greater the cushion against creditors’ losses in the event of liquidation. Stockholders, on the other hand, may want more leverage because it can magnify expected earnings, as we saw in Table 4-1.

Allied’s debt ratio is 53.0%, which means that its creditors have supplied more than half of its total funds. As we will discuss in the capital structure chapter, a

Debt Ratio The ratio of total debt to total assets.

10 As we discussed in the last chapter, fi rms can carry losses back or forward for several years. Therefore, if Firm L had profi ts and thus paid taxes in recent 2007, it could carry back the 2008 loss under bad conditions and receive a credit (a check from the government). In Table 4-1, we disregard the carry-back/carry-forward provision.

95Chapter 4 Analysis of Financial Statements

number of factors affect a company’s optimal debt ratio. Nevertheless, the fact that Allied’s debt ratio exceeds the industry average by a fairly large amount raises a red fl ag, and this will make it relatively costly for Allied to borrow additional funds without fi rst raising more equity. Creditors will be reluctant to lend the fi rm more money, and management would probably be subjecting the fi rm to too high a risk of bankruptcy if it sought to borrow a substantial amount of additional funds.11

4-4b Times-Interest-Earned Ratio The times-interest-earned (TIE) ratio is determined by dividing earnings before interest and taxes (EBIT in Table 3-2) by the interest charges:

Times-interest-earned (TIE) ratio ! EBIT ______________ Interest charges

! $283.8 ______ $88 ! 3.2"

Industry average ! 6.0"

The TIE ratio measures the extent to which operating income can decline before the fi rm is unable to meet its annual interest costs. Failure to pay interest will bring legal action by the fi rm’s creditors and probably result in bankruptcy. Note that earnings before interest and taxes, rather than net income, is used in the numera- tor. Because interest is paid with pretax dollars, the fi rm’s ability to pay current interest is not affected by taxes.

Allied’s interest is covered 3.2 times. The industry average is 6 times, so Allied is covering its interest charges by a relatively low margin of safety. Thus, the TIE ratio reinforces our conclusion from the debt ratio, namely, that Allied would face diffi culties if it attempted to borrow much additional money.12

Times-Interest-Earned (TIE) Ratio The ratio of earnings before interest and taxes (EBIT) to interest charges; a measure of the firm’s ability to meet its annual interest payments.

11 The ratio of debt to equity is also used in fi nancial analysis. The debt-to-assets (D/A) and debt-to-equity (D/E) ratios are simply transformations of each other:

D/E ! D/A _______ 1 " D/A and D/A ! D/E _______ 1 $ D/E

With a D/A ratio of 53%, or 0.53, Allied’s Debt/Equity ratio is 0.53/(1 – 0.53) = 1.13. 12 Another commonly used debt management ratio is the following:

EBITDA coverage ! EBITDA $ Lease payments

________________________________________ Interest $ Principal payments $ Lease payments

This ratio is more complete than the TIE ratio in that it recognizes that depreciation and amortization expenses are not cash charges and thus are available to service debt and that lease payments and principal repayments on debt are fi xed charges. For more on this ratio, see E. F. Brigham and P. R. Daves, Intermediate Financial Manage- ment, 9th Edition, (Mason, OH: Thomson/South-Western, 2007), p. 258.

SEL F TEST How does the use of fi nancial leverage aff ect stockholders’ control position?

How does the U.S. tax structure infl uence a fi rm’s willingness to fi nance with debt?

How does the decision to use debt involve a risk-versus-return trade-off ?

Explain the following statement: Analysts look at both balance sheet and in- come statement ratios when appraising a fi rm’s fi nancial condition.

Name two ratios that are used to measure fi nancial leverage and write their equations.

96 Part 2 Fundamental Concepts in Financial Management

4-5 PROFITABILITY RATIOS Accounting statements refl ect events that happened in the past, but they also pro- vide clues about what’s really important—what’s likely to happen in the future. The liquidity, asset management, and debt ratios covered thus far tell us some- thing about the fi rm’s policies and operations. Now we turn to the profi tability ratios,which refl ect the net result of all of the fi nancing policies and operating decisions.

4-5a Operating Margin The operating margin, calculated by dividing operating income (EBIT) by sales, gives the operating profi t per dollar of sales:

Operating margin ! Operating income (EBIT)

______________________ Sales

! $283.8 ______ $3,000 ! 9.5%

Industry average ! 10.0%

Allied’s 9.5% operating margin is below the industry average of 10.0%. This sub- par result indicates that Allied’s operating costs are too high. This is consistent with the low inventory turnover and high days’ sales outstanding ratios that we calculated earlier.

4-5b Profit Margin The profi t margin, also sometimes called the net profi t margin, is calculated by dividing net income by sales:

Profi t margin = Net income __________ Sales

= $117.5 ______ $3,000 = 3.9%

Industry average = 5.0%

Allied’s 3.9% profi t margin is below the industry average of 5.0%, and this sub- par result occurred for two reasons. First, Allied’s operating margin was below the industry average because of the fi rm’s high operating costs. Second, the profi t margin is negatively impacted by Allied’s heavy use of debt. To see this second point, recognize that net income is after interest. Suppose two fi rms have identical operations in the sense that their sales, operating costs, and operating income are identical. However, one fi rm uses more debt; hence, it has higher interest charges. Those interest charges pull down its net income; and since sales are constant, the result is a relatively low net profi t margin for the fi rm with more debt. We see then that Allied’s operating ineffi ciency and its high debt ratio combine to lower its net profi t margin below the food processing industry average. It also follows that when two companies have the same operating margin but different debt ratios, we can expect the company with a higher debt ratio to have a lower profi t margin.

Note too that while a high return on sales is good, other things held constant, other things may not be held constant—we must also be concerned with turnover. If a fi rm sets a very high price on its products, it may get a high return on each sale but fail to make many sales. That strategy might result in a high profi t margin, low sales, and hence a low net income. We will see shortly how, through the use of the DuPont equation, profi t margins, the use of debt, and turnover ratios interact to affect overall stockholder returns.

Profitability Ratios A group of ratios that show the combined effects of liquidity, asset management, and debt on operating results.

Operating Margin This ratio measures operating income, or EBIT, per dollar of sales; it is calculated by dividing operating income by sales.

Profitability Ratios A group of ratios that show the combined effects of liquidity, asset management, and debt on operating results.

Operating Margin This ratio measures operating income, or EBIT, per dollar of sales; it is calculated by dividing operating income by sales.

Profit Margin This ratio measures net income per dollar of sales and is calculated by dividing net income by sales.

97Chapter 4 Analysis of Financial Statements

4-5c Return on Total Assets Net income divided by total assets gives us the return on total assets (ROA):

Return on total assets (ROA) ! Net income __________ Total assets

! $117.5 ______ $2,000 ! 5.9%

Industry average ! 9.0%

Allied’s 5.9% return is well below the 9.0% industry average. This is not good—it is obviously better to have a higher than a lower return on assets. Note, though, that a low ROA can result from a conscious decision to use a great deal of debt, in which case high interest expenses will cause net income to be relatively low. That is part of the reason for Allied’s low ROA. Never forget—you must look at a number of ratios, see what each suggests, and then look at the overall situation when you judge the performance of a company and consider what actions it should undertake to improve.

Return on Total Assets (ROA) The ratio of the net income to total assets.

These days you must be a good fi nancial detective to analyze fi nancial statements, especially when the company operates overseas. Despite attempts to standardize accounting practices, there are still many diff erences in fi nancial reporting in diff erent countries; and those diff erences create headaches for investors making cross-border company comparisons. However, as busi- nesses become more global and as more foreign companies list on U.S. stock exchanges, accountants and regulators are realiz- ing the need for a global convergence of accounting standards. As a result, the “writing is on the wall” regarding accounting standards and diff erences are disappearing. The eff ort to internationalize accounting standards began in 1973 with the formation of the International Accounting Standards Committee. However, in 1998, it became apparent that a full-time rule-making body with global representation was necessary; so the International Accounting Standards Board (IASB), with members repre- senting 9 major countries, was established. The IASB was charged with the responsibility for creating a set of Interna- tional Financial Reporting Standards (IFRS). A survey of senior executives from 85 fi nancial institutions worldwide found that 92% of those responding favored a sin- gle set of international standards. The U.S. SEC has proposed allowing non-U.S. companies that operate in the United States

to base their reports on IFRS rather than GAAP, and it is consid- ering requiring U.S. companies to shift to IFRS. Obviously, the globalization of accounting standards is a huge endeavor— one that will involve compromises between the IASB and FASB. The main problem is that U.S. GAAP takes a rules-based approach, while the IASB insists on using a principles-based approach. With a rules-based system, companies can tell whether they are in compliance, but they can also devise ways to get around a rule and thus subvert its intent. With a princi- ples-based system, there is more uncertainty about whether certain borderline procedures will be allowed; but such a sys- tem makes it easier to prosecute on the basis of intent. A global accounting structure would enable investors and practitioners around the world to read and understand fi nancial reports produced anywhere in the world. According to SEC Chairman Christopher Cox, “Having a set of globally accepted accounting standards is critical to the rapidly accel- erating global integration of the world’s capital markets.” Even the chairman of the U.S. Financial Accounting Stan- dards Board, Robert Herz, has recommended that a target date be set for U.S. companies to transition from GAAP to IFRS. So it seems that the issue is when, not if, all companies will be playing by the same set of accounting rules.

GLOBAL ACCOUNTING STANDARDS: CAN ONE SIZE FIT ALL?

Sources: “All Accountants Soon May Speak the Same Language,” The Wall Street Journal, August 29, 1995, p. A15; “For and Against; Standards Need Time to Work,” Accountancy Age, June 5, 2003, p. 16; and James Turley (CEO, Ernst & Young), “Mind the GAAP,” The Wall Street Journal, November 9, 2007, p. A18.

98 Part 2 Fundamental Concepts in Financial Management

4-5d Basic Earning Power (BEP) Ratio The basic earning power (BEP) ratio is calculated by dividing operating income (EBIT) by total assets:

Basic earning power (BEP) ! EBIT __________ Total assets

! $283.8 ______ $2,000 ! 14.2%

Industry average ! 18.0%

This ratio shows the raw earning power of the fi rm’s assets before the infl uence of taxes and debt, and it is useful when comparing fi rms with different debt and tax situations. Because of its low turnover ratios and poor profi t margin on sales, Allied has a lower BEP ratio than the average food processing company.13

4-5e Return on Common Equity The most important, or bottom-line, accounting ratio is the return on common equity (ROE), found as follows:

Return on common equity (ROE) ! Net income ______________ Common equity

! $117.5 ______ $940 ! 12.5%

Industry average ! 15.0%

Stockholders expect to earn a return on their money, and this ratio tells how well they are doing in an accounting sense. Allied’s 12.5% return is below the 15.0% industry average, but not as far below as the return on total assets. This somewhat better ROE results from the company’s greater use of debt, a point discussed ear- lier in the chapter.

Basic Earning Power (BEP) Ratio This ratio indicates the ability of the firm’s assets to generate operating income; it is calculated by dividing EBIT by total assets.

Return on Common Equity (ROE) The ratio of net income to common equity; measures the rate of return on common stockholders’ investment.

SEL F TEST Identify fi ve profi tability ratios and write their equations.

Why does the use of debt lower the net profi t margin and the ROA?

Using more debt lowers profi ts and thus the ROA. Why doesn’t debt have the same negative eff ect on the ROE? (Debt lowers net income, but it also lowers the fi rm’s equity; and the equity reduction can off set the lower net income.)

A company has $20 billion of sales and $1 billion of net income. Its total assets are $10 billion, fi nanced half by debt and half by common equity. What is its profi t margin? (5%) What is its ROA? (10%) What is its ROE? (20%) Would this fi rm’s ROA increase if it used less leverage? (yes) Would its ROE increase? (no)

13 A related ratio is the return on investors’ capital, defi ned as follows:

Return on investors’ capital (ROIC) ! Net income $ Interest __________________ Debt $ Equity

The numerator shows the dollar returns to all investors, the denominator shows the money investors have put up, and the resulting ratio shows the rate of return on total investor capital. This ratio is especially important in r egulated industries such as electric utilities, where regulators are concerned about companies using their monopoly power to earn excessive returns on investors’ capital. In fact, regulators often try to set electricity prices at a level that will force the return on investors’ capital to equal a company’s cost of capital, as defi ned in Chapter 10.

99Chapter 4 Analysis of Financial Statements

4-6 MARKET VALUE RATIOS ROE refl ects the effects of all of the other ratios, and it is the single best accounting measure of performance. Investors like a high ROE, and high ROEs are correlated with high stock prices. However, other things come into play. For example, fi nan- cial leverage generally increases the ROE but also increases the fi rm’s risk; so if a high ROE is achieved by using a great deal of debt, the stock price might end up lower than if the fi rm had been using less debt and had a lower ROE. We use the fi nal set of ratios—the market value ratios, which relate the stock price to earnings and book value price—to help address this situation. If the liquidity, asset manage- ment, debt management, and profi tability ratios all look good and if investors think these ratios will continue to look good in the future, the market value ratios will be high, the stock price will be as high as can be expected, and management will be judged to have been doing a good job.

The market value ratios are used in three primary ways: (1) by investors when they are deciding to buy or sell a stock, (2) by investment bankers when they are setting the share price for a new stock issue (an IPO), and (3) by fi rms when they are deciding how much to offer for another fi rm in a potential merger.

4-6a Price/Earnings Ratio The price/earnings (P/E) ratio shows how much investors are willing to pay per dollar of reported profi ts. Allied’s stock sells for $23.06; so with an EPS of $2.35, its P/E ratio is 9.8#:

Price/Earnings (P/E) ratio ! Price per share ________________ Earnings per share

! $23.06 ______ $2.35 ! 9.8"

Industry average ! 11.3"

As we will see in Chapter 9, P/E ratios are relatively high for fi rms with strong growth prospects and little risk but low for slowly growing and risky fi rms. Allied’s P/E ratio is below its industry average; so this suggests that the company is regarded as being relatively risky, as having poor growth prospects, or both.

There is no “correct” P/E ratio; but the S&P 500’s historical average is 15.9#, and it has ranged from 48.1# to 7.1# over the last 30 years. In the winter of 2008, the S&P’s ratio was 21.7# versus 37.8# for Google. Countrywide Financial, which was badly hurt by the subprime mortgage debacle, had negative earnings and thus a negative P/E. The Google and Countrywide data demonstrate that strong companies with good growth prospects have high P/Es while weaker companies with poor prospects have low ratios.14

4-6b Market/Book Ratio The ratio of a stock’s market price to its book value gives another indication of how investors regard the company. Companies that are well regarded by investors—which

Market Value Ratios Ratios that relate the firm’s stock price to its earnings and book value per share.

Price/Earnings (P/E) Ratio The ratio of the price per share to earnings per share; shows the dollar amount investors will pay for $1 of current earnings.

14 Security analysts also look at the Price-to-Free-Cash-Flow ratio. In addition, analysts consider the PEG, or P/E to growth, ratio where the P/E is divided by the fi rm’s forecasted growth rate. Allied’s growth rate as forecasted by a number of security analysts for the next 5 years is 7.0%, so its PEG ! 9.8/7.0 ! 1.4#. The lower the ratio, the better; and most fi rms have ratios in the range of 1.0# to 2.0#. We note, though, that P/E ratios jump around from year to year because earnings and forecasted growth rates fl uctuate. Like other ratios, PEG ratios are interesting, but must be interpreted with care and judgment.

100 Part 2 Fundamental Concepts in Financial Management

4-7 TREND ANALYSIS It is important to analyze trends in ratios as well as their absolute levels, for trends give clues as to whether a fi rm’s fi nancial condition is likely to improve or to deteriorate. To do a trend analysis, simply plot a ratio over time, as shown in Figure 4-1. This graph shows that Allied’s ROE has been declining since 2005 even though the industry average has been relatively stable. All of the other ratios could be analyzed similarly, and such an analysis can be quite useful in gaining insights as to why the ROE behaved as it did.

Trend Analysis An analysis of a firm’s financial ratios over time; used to estimate the likelihood of improvement or deterioration in its financial condition.

SEL F TEST Describe two ratios that relate a fi rm’s stock price to its earnings and book

value per share and write their equations.

In what sense do these market value ratios refl ect investors’ opinions about a stock’s risk and expected future growth?

What does the price/earnings (P/E) ratio show? If one fi rm’s P/E ratio is lower than that of another fi rm, what factors might explain the diff erence?

How is book value per share calculated? Explain how infl ation and R&D pro- grams might cause book values to deviate from market values.

means low risk and high growth—have high M/B ratios. For Allied, we fi rst fi nd its book value per share:

Book value per share ! Common equity

_________________ Shares outstanding

! $940 _____ 50 ! $18.80

We then divide the market price per share by the book value per share to get the market/book (M/B) ratio, which for Allied is 1.2#:

Market/book (M/B) ratio ! Market price per share ____________________ Book value per share

! $23.06 ______ $18.80 ! 1.2"

Industry average ! 1.7"

Investors are willing to pay less for a dollar of Allied’s book value than for one of an average food processing company. This is consistent with our other fi ndings.

M/B ratios typically exceed 1.0, which means that investors are willing to pay more for stocks than the accounting book values of the stocks. This situation occurs primarily because asset values, as reported by accountants on corporate balance sheets, do not refl ect either infl ation or goodwill. Assets purchased years ago at pre-infl ation prices are carried at their original costs even though infl ation might have caused their actual values to rise substantially; and successful com- panies’ values rise above their historical costs, whereas unsuccessful ones have low M/B ratios.15 This point is demonstrated by Google and Countrywide: In the winter of 2008, Google’s M/B ratio was 6.9#, while Countrywide’s was only 0.26#. Google’s stockholders now have $6.90 in market value per $1.00 of equity, whereas Countrywide’s stockholders have only $0.26 for each dollar they invested.

Market/Book (M/B) ratio The ratio of a stock’s market price to its book value.

15 The second point is known as “survivor bias.” Successful companies survive and are refl ected in the averages, whereas unsuccessful companies vanish and their low numbers are not refl ected in the averages.

101Chapter 4 Analysis of Financial Statements

4-8 THE DUPONT EQUATION We have discussed many ratios, so it would be useful to see how they work together to determine the ROE. For this, we use the DuPont equation, a formula developed by the chemical giant’s fi nancial staff in the 1920s. It is shown here for Allied and the food processing industry.

ROE ! Profi t margin " Total assets turnover " Equity multiplier

! Net income ___________ Sales " Sales ___________ Total assets "

Total assets ___________________ Total common equity 4-1

! $117.5 ______ $3,000 " $3,000 ______ $2,000 "

$2,000 ______ $940

! 3.92% " 1.5 times " 2.13 times ! 12.5%

Industry ! 5.0% " 1.8 times " 1.67 times ! 15.0%

• The fi rst term, the profi t margin, tells us how much the fi rm earns on its sales. This ratio depends primarily on costs and sales prices—if a fi rm can command a premium price and hold down its costs, its profi t margin will be high, which will help its ROE.

• The second term is the total assets turnover. It is a “multiplier” that tells us how many times the profi t margin is earned each year—Allied earned 3.92% on each dollar of sales, and its assets were turned over 1.5 times each year; so its return on assets was 3.92% # 1.5 ! 5.9%. Note, though, that this entire 5.9% belongs to the common stockholders—the bondholders earned a return in the form of interest, and that interest was deducted before we calculated net income to stockholders. Therefore, the whole 5.9% return on assets belongs to the

DuPont Equation A formula that shows that the rate of return on equity can be found as the product of net profit margin, total assets turnover, and the equity multiplier. It shows the relationships among asset management, debt management, and profitability ratios.

ROE (%)

2004 2005 2006 2007 2008

Industry

Allied

Rate of Return on Common Equity, 2004–2008FIGURE 4-1 SEL

F TEST How is a trend analysis done?

What important information does a trend analysis provide?

102 Part 2 Fundamental Concepts in Financial Management

stockholders. Therefore, the return on assets must be adjusted upward to obtain the return on equity.

• That brings us to the third term, the equity multiplier, which is the adjust- ment factor. Allied’s assets are 2.13 times its equity, so we must multiply the 5.9% return on assets by the 2.13# equity multiplier to arrive at its ROE of 12.5%.

Note that ROE as calculated using the DuPont equation is identical to Allied’s ROE, 12.5%, which we calculated earlier. What’s the point of going through all of the steps required to implement the DuPont equation to fi nd ROE? The answer is that the DuPont equation helps us see why Allied’s ROE is only 12.5% versus 15.0% for the industry. First, its profi t margin is below average, which indicates that its costs are not being controlled as well as they should be and that it cannot charge premium prices. In addition, because it uses more debt than most companies, its high interest charges also reduce the net profi t margin. Second, its total assets turnover is below the industry average, which indicates that it has more assets than it needs. Finally, because its equity multiplier is relatively high, its heavy use of debt offsets to some extent its low profi t margin and turnover. However, the high debt ratio exposes Allied to above-average bankruptcy risk; so it might want to cut back on its fi nancial leverage. But if it reduced its debt to the same level as the average fi rm in its industry, its ROE would decline signifi cantly, to 3.92% # 1.5 # 1.67 ! 9.8%.16

Allied’s management can use the DuPont equation to help identify ways to improve its performance. Focusing on the profi t margin, its marketing people can study the effects of raising sales prices or of introducing new products with higher margins. Its cost accountants can study various expense items and, working with engineers, purchasing agents, and other operating personnel, seek ways to cut costs. The credit manager can investigate ways to speed up collections, which would reduce accounts receivable and therefore improve the quality of the total assets turnover ratio. And the fi nancial staff can analyze the effects of alternative debt policies, showing how changes in leverage would affect both the expected ROE and the risk of bankruptcy.

As a result of this analysis, Ellen Jackson, Allied’s chief executive offi cer (CEO), undertook a series of moves that are expected to cut operating costs by more than 20%. Jackson and Allied’s other executives have a strong incentive to improve the fi rm’s fi nancial performance—their compensation depends on how well the com- pany operates. If Allied meets or exceeds its growth and profi t targets, Jackson and the other executives—and the stockholders—will do well. Otherwise, someone like Warren Buffett or Carl Icahn, whom we discussed at the beginning of the chapter, may come calling.

SEL F TEST Write the equation for the basic DuPont equation.

What is the equity multiplier, and why is it used?

How can management use the DuPont equation to analyze ways of improving the fi rm’s performance?

16 The ROE reduction would actually be somewhat less because if debt were lowered, interest payments would also decline, which would raise the profi t margin. Allied’s analysts determined that the net eff ect of a reduction in debt would still be a signifi cant reduction in ROE.

103Chapter 4 Analysis of Financial Statements

4-9 RATIOS IN DIFFERENT INDUSTRIES Table 4-2 provides a list of the ratios for a number of different industries in early 2008. ROEs vary across industries, ranging from 45.7% for education and training services to 0.9% for newspapers. The education and training services industry has been positively impacted by enrollment growth of online operations in schools. The newspaper industry has been in decline because the proportion of the popula- tion that reads newspapers has been in a long-term decline, which has a negative impact on the demand for newspaper advertising. Industry rankings change from year to year because fi rms and industries go through cycles of good and bad times. When times are good, companies often overexpand, which leads to hard times. Note too that there are huge differences between individual companies in a given industry. That point isn’t illustrated in Table 4-2, but it shows up dramatically in Table 4-4 in Section 4-11.

SEL F TEST Why might railroads have such low total assets turnovers and food wholesal-

ers and grocery stores such high turnovers? (Railroads require many long- term assets; while grocery companies have more perishable products and thus high turnovers.)

If competition causes all companies to have similar ROEs in the long run, would companies with high turnovers tend to have high or low profi t mar- gins? Explain your answer. (Low)

DuPont Financial Ratios for Selected IndustriesaT a b l e 4 - 2

Industry Name ROE = Profit

Margin × Total Assets

Turnover × Equity

Multiplierb

Aerospace/defense—major diversified 41.4% 6.8% 1.0 6.1 Apparel stores 37.2 6.7 1.8 3.1 Auto mfg.—major 12.9 3.9 0.8 4.1 Beverage (soft drink) 21.6 14.1 0.8 1.9 Education and training services 45.7 13.0 1.4 2.5 Electronics—equipment 6.8 4.7 0.9 1.6 Food wholesaling 17.8 1.5 3.3 3.6 Grocery stores 19.1 3.7 2.5 2.1 Lodging 30.6 12.6 0.9 2.7 Medical instruments and supplies 9.6 4.5 0.7 3.0 Metals and minerals—industrial 34.8 10.9 0.7 4.6 Newspapers 0.9 8.5 0.3 0.4 Paper and paper products 15.1 13.5 0.8 1.4 Railroad 15.3 15.0 0.4 2.6 Restaurant 15.3 8.1 0.7 2.7 Retail—department stores 18.4 4.8 1.7 2.3 Scientific and technical instruments 12.9 9.0 0.8 1.8 Sporting goods 15.2 4.1 1.7 2.2 Steel and iron 36.3 23.5 0.8 1.9 Telecommunications services— domestic

11.9 10.1 0.4 2.9

Tobacco (cigarettes) 14.4 15.4 0.3 3.1

aThe ratios presented are averages for each industry. Ratios for the individual companies are also available. bCalculated as ROE/ROA. Source: Data obtained from the Key Ratios section, http://moneycentral.msn.com, February 7, 2008.

http://moneycentral.msn.com

104 Part 2 Fundamental Concepts in Financial Management

Allied Food Products: Summary of Financial Ratios (Millions of Dollars)T a b l e 4 - 3

Ratio Formula Calculation Ratio Industry Average Comment

Liquidity

Current Current assets _______________ Current liabilities $1,000 ______ $310 = 3.2# 4.2# Poor

Quick Current assets " Inventories ________________________ Current liabilities $385 _____ $310 = 1.2# 2.2# Poor

Asset Management

Inventory turnover Sales __________ Inventories $3,000 ______ $615 = 4.9# 10.9# Poor

Days sales outstanding (DSO)

Receivables _______________ Annual sales/365 $375 _______ $8.2192 = 46 days 36 days Poor

Fixed assets turnover Sales ______________ Net fixed assets $3,000 ______ $1,000 = 3.0# 2.8# OK

Total assets turnover Sales __________ Total assets $3,000 ______ $2,000 = 1.5# 1.8# Somewhat low

Debt Management

Total debt to total assets Total debt __________ Total assets $1,060 ______ $2,000 = 53.0% 40.0% High (risky)

Times interest earned (TIE) Earnings before interest and taxes (EBIT)

__________________________________ Interest charges $283.8 ______ $88 = 3.2# 6.0# Low (risky)

Profitability

Operating margin Operating income (EBIT)

_____________________ Sales $283.8 ______ $3,000 = 9.5% 10.0% Low

Profit margin Net income __________ Sales $117.5 ______ $3,000 = 3.9% 5.0% Poor

Return on total assets (ROA) Net income __________ Total assets $117.5 ______ $2,000 = 5.9% 9.0% Poor

Basic earning power (BEP) Earnings before interest and taxes (EBIT)

__________________________________ Total assets $283.8 ______ $2,000 = 14.2% 18.0% Poor

Return on common equity (ROE)

Net income ______________ Common equity $117.5 ______ $940 = 12.5% 15.0% Poor

Market Value

Price/earnings (P/E) Price per share

________________ Earnings per share $23.06 ______ $2.35 = 9.8# 11.3# Low

Market/book (M/B) Market price per share

___________________ Book value per share $23.06 ______ $18.80 = 1.2# 1.7# Low

4-10 SUMMARY OF ALLIED’S RATIOS Table 4-3 provides a summary of the ratios we have discussed in the chapter. This table is useful as a quick reference for the formulas, for calculations, and for the ratios of Allied and the average food processing company.

105Chapter 4 Analysis of Financial Statements

4-11 BENCHMARKING Ratio analysis involves comparisons with industry average fi gures, but Allied and many other fi rms also compare themselves with the top fi rms in their industry. This is called benchmarking, and the companies used for the comparison are called benchmark companies. Table 4-4 provides data for Allied and its seven benchmarks. The companies are ranked by ROE, and the other ratios used in a DuPont analysis are shown in the table as well. The ROE makes it easy for Allied’s managers to see where the fi rm stands relative to top food processors, and the other data give management an idea of why Allied’s ROE ranking compares unfa- vorably with most of the other benchmark companies.

Perhaps the most interesting feature of Table 4-4 is the wide range of ROEs. This range is caused primarily by variations in profi t margins and equity multipli- ers. These companies also have the most widely recognized brands—their excel- lent marketing programs enabled them to charge relatively high prices, which boosted their profi t margins and thus their ROEs. Their high and stable profi ts enable them to use a great deal of debt, which boosted their equity multipliers and provided another boost to their ROEs.

Note too that the averages for Allied and its benchmark companies differ sig- nifi cantly from the averages for its industry. The benchmarks are all very large companies, while there are many small food processing companies whose data are included in the industry averages. Since Allied is a relatively large company, its chief fi nancial offi cer (CFO) believes it makes more sense to compare Allied to other large companies than to industry averages.

Benchmarking The process of comparing a particular company with a set of benchmark companies.

SEL F TEST Why are comparative ratio analyses useful?

Benchmark Companies Ranked by ROET a b l e 4 - 4

ROE ! Profit

Margin " Turnover " Equity

Multiplier

Campbell Soup 59.4% 10.3% 1.1 5.24 H.J. Heinz 39.3 8.8 0.9 4.96 Hershey Foods 33.6 4.3 1.2 6.51 Sara Lee 21.9 4.8 1.1 4.15 Dean Foods 17.4 1.6 1.6 6.80 Flowers Foods 15.5 4.8 2.2 1.47 Allied Foods 12.5 3.9 1.5 2.13 Del Monte Foods 8.0 3.2 0.7 3.57 Averages 25.9% 5.2% 1.3 4.35 Averages for entire food industry 26.8% 10.5% 1.1 2.32

Note: Rounding causes some variations in the numbers. Source: Data on the benchmark companies were obtained from http://moneycentral.msn.com, February 11, 2008. Similar data can be obtained from Yahoo, Google, and a number of other online and print sources.

http://moneycentral.msn.com

106 Part 2 Fundamental Concepts in Financial Management

4-12 USES AND LIMITATIONS OF RATIOS As noted earlier, ratio analysis is used by three main groups: (1) managers, who use ratios to help analyze, control, and thus improve their fi rms’ operations; (2) credit analysts, including bank loan offi cers and bond rating analysts, who analyze ratios to help judge a company’s ability to repay its debts; and (3) stock analysts, who are interested in a company’s effi ciency, risk, and growth prospects. In later chapters, we will look more closely at the basic factors that underlie each ratio. Note, though, that while ratio analysis can provide useful information concerning a company’s operations and fi nancial condition, it does have limitations. Some potential prob- lems are listed here: 1. Many fi rms have divisions that operate in different industries; and for such

companies, it is diffi cult to develop a meaningful set of industry averages. Therefore, ratio analysis is more useful for narrowly focused fi rms than for multidivisional ones.

2. Most fi rms want to be better than average, so merely attaining average perfor- mance is not necessarily good. As a target for high-level performance, it is best to focus on the industry leaders’ ratios. Benchmarking helps in this regard.

3. Infl ation has distorted many fi rms’ balance sheets—book values are often dif- ferent from market values. Market values would be more appropriate for most purposes, but we cannot generally get market value fi gures because assets

Enron’s decline spurred a renewed interest in fi nancial accounting, and analysts now scour companies’ fi nancial statements to see if trouble is lurking. This renewed interest has led to a list of red fl ags to consider when reviewing a company’s fi nancial statements. For example, after confer- ring with New York University Accounting Professor Baruch Lev, Fortune magazine’s Shawn Tully identifi ed the following warning signs: • Year after year a company reports restructuring charges

and/or write-downs. This practice raises concerns be- cause companies can use write-downs to mask operat- ing expenses, which results in overstated earnings.

• A company’s earnings have been propped up through a series of acquisitions. Acquisitions can increase earnings if the acquiring company has a higher P/E than the ac- quired fi rm, but such “growth” cannot be sustained over the long run.

• A company depreciates its assets more slowly than the industry average. Lower depreciation boosts current earnings, but again this cannot be sustained because eventually depreciation must be recognized.

• A company routinely has high earnings but low cash fl ow. As Tully points out, this warning sign would have exposed Enron’s problems. In the second quarter of

2001 (a few months before its problems began to un- fold), Enron reported earnings of $423 million versus a cash fl ow of minus $527 million.

Along similar lines, after consulting with various profession- als, Ellen Simon of the Newark Star Ledger came up with her list of red fl ags: • You wouldn’t buy the stock at today’s price. • You don’t really understand the company’s fi nancial

statements. • The company is in a business that lends itself to “creative

accounting.” • The company keeps taking nonrecurring charges. • Accounts receivable and inventory are increasing faster

than sales revenues. • The company’s insiders are selling their stock. • The company is making aggressive acquisitions, espe-

cially in unrelated fi elds. There is some overlap between these two lists. Also, none of these items automatically means there is something wrong with the company—instead, the items should be viewed as warning signs that cause you to take a closer look at the company’s performance before making an investment.

LOOKING FOR WARNING SIGNS WITHIN THE FINANCIAL STATEMENTS

To find information about a company quickly, link to www.reuters.com. Here you can find company profiles and snapshots, stock price quotes and share information, key ratios, and comparative ratios.

www.reuters.com

107Chapter 4 Analysis of Financial Statements

such as used machinery are not traded in the marketplace. Further, infl ation affects asset values, depreciation charges, inventory costs, and thus profi ts. Therefore, a ratio analysis for one fi rm over time or a comparative analysis of fi rms of different ages must be interpreted with care and judgment.

4. Seasonal factors can also distort a ratio analysis. For example, the inventory turnover ratio for a food processor will be radically different if the balance sheet fi gure used for inventory is the one just before versus just after the close of the canning season. This problem can be mitigated by using monthly aver- ages for inventory (and receivables) when calculating turnover ratios.

5. Firms can employ “window dressing” techniques to improve their fi nancial statements. To illustrate, people tend to think that larger hedge funds got large because their high returns attracted many investors. However, we learned in 2007 that some funds simply borrowed and invested money to increase their apparent size. One fund, Wharton Asset Management, reported $2 billion “under manage- ment,” but it had actually attracted less than $100 million of investors’ capital.

6. Different accounting practices can distort comparisons. As noted earlier, inven- tory valuation and depreciation methods can affect fi nancial statements and thus distort comparisons among fi rms. Also, if one fi rm leases much of its productive equipment, its fi xed assets turnover may be artifi cially high because leased assets often do not appear on the balance sheet. At the same time, the liability associ- ated with the lease may not appear as debt, keeping the debt ratio low even though failure to make lease payments can bankrupt the fi rm. Therefore, leasing can artifi cially improve both turnover and the debt ratios. The accounting profes- sion has taken steps to reduce this problem, but it still can cause distortions.

7. It is diffi cult to generalize about whether a particular ratio is “good” or “bad.” For example, a high current ratio may indicate a strong liquidity position, which is good, but it can also indicate excessive cash, which is bad because excess cash in the bank is a nonearning asset. Similarly, a high fi xed assets turnover ratio may indicate that the fi rm uses its assets effi ciently, but it could also indicate that the fi rm is short of cash and cannot afford to make needed fi xed asset investments.

8. Firms often have some ratios that look “good” and others that look “bad,” making it diffi cult to tell whether the company is, on balance, strong or weak. To deal with this problem, banks and other lending organizations often use statistical procedures to analyze the net effects of a set of ratios and to classify fi rms according to their probability of getting into fi nancial trouble.17

We see then that ratio analysis is useful, but analysts should be aware of the problems just listed and make adjustments as necessary. Ratio analysis conducted in a mechanical, unthinking manner is dangerous; but used intelligently and with good judgment, it can provide useful insights into fi rms’ operations. Your judg- ment in interpreting ratios is bound to be weak at this point, but it will improve as you go through the remainder of the book.

“Window Dressing” Techniques Techniques employed by firms to make their financial statements look better than they really are.

17 The technique used is discriminant analysis. The seminal work on this subject was undertaken by Edward I. Altman, “Financial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy,” Journal of Finance, September 1968, pp. 589–609.

SEL F TEST List three types of users of ratio analysis. Would the diff erent users empha-

size the same or diff erent types of ratios? Explain.

List several potential diffi culties with ratio analysis.

108 Part 2 Fundamental Concepts in Financial Management

4-13 POTENTIAL MISUSES OF ROE We know that managers should strive to maximize shareholder wealth. If a fi rm takes steps that improve its ROE, does that mean that shareholder wealth will also be increased? The answer is, “not necessarily.” Indeed, three problems are likely to arise if a fi rm relies too heavily on ROE to measure performance.

First, ROE does not consider risk. Shareholders care about ROE, but they also care about risk. To illustrate, consider two divisions within the same fi rm. Division

Economic Value Added (EVA) is a measure of how much management has added to shareholders’ wealth during the year. To better understand the idea behind EVA, let’s look at Allied’s 2008 numbers (in millions). All of the fi rm’s capital was supplied by investors except for $60 of accounts pay- able and $140 of accruals, or $200 in total; so its investor- supplied capital consists of $110 of notes payable, $750 of long-term debt, and $940 of common equity, totaling $1,800. Debt represents 47.78% of this total, and equity is 52.22%. Later in the text we will discuss how to calculate the cost of Allied’s capital; but for now, to simplify things, we will esti- mate its capital cost at 10%. Thus, the fi rm’s total dollar cost of capital (which includes both debt and equity) per year is 0.10($1,800) ! $180. Now let’s look at Allied’s income statement. Its operat- ing income, EBIT, is $283.8; and its interest expense is $88.0. Therefore, its taxable income is $283.8 " $88.0 ! $195.8. Taxes equal 40% of taxable income, or 0.4($195.8) ! $78.3; so the fi rm’s net income is $117.5. Its return on equity, ROE, is $117.5/$940 ! 12.5%. Given this data, we can now calculate Allied’s EVA. The basic formula for EVA is as follows:

EVA ! EBIT (1 # Corporate tax rate) # [(Total investors’ capital) " (After-tax cost of

capital)] ! $283.8(1 # 0.40) # ($1,800)(0.10) ! $170.3 # $180 ! #$9.7

This negative EVA indicates that Allied’s shareholders actually earned $9.7 million less than they could have earned elsewhere by investing in other stocks with the same risk as Allied. To see where this "$9.7 comes from, let’s trace what happened to the money. • The fi rm generated $283.8 of operating income. • $78.3 went to the government to pay taxes, leaving $205.5

available for investors—stockholders and bondholders. • $88.0 went to the bondholders in the form of interest

payments, thus leaving $117.5 for the stockholders.

• However, Allied’s shareholders must also earn a return on the equity capital they have invested in the fi rm because they could have invested in other companies of comparable risk. We call this the cost of Allied’s equity.

• Once Allied’s shareholders are “paid” their return, the fi rm comes up $9.7 million short—that’s the economic value management added, and it is negative. In a sense, Allied’s management created negative wealth because it provided shareholders with a lower return than they could have earned on alternative investments with the same risk as Allied’s stock.

• In practice, it is often necessary to make several adjust- ments to arrive at a “better” measure of EVA. The adjust- ments deal with nonoperating assets, leased assets, depreciation, and other accounting details that we leave to advanced fi nance courses.

The Connection between ROE and EVA EVA is diff erent from traditional accounting profi t because EVA refl ects the cost of equity as well as the cost of debt. Indeed, using the previous example, we could also express EVA as net income minus the dollar cost of equity:

EVA ! Net Income #

! Equity capital " Cost of equity capital " That expression could be rewritten as follows:

EVA ! Equity capital "

! Net income ____________ Equity capital # Cost of equity capital " which can be rewritten as

EVA ! (Equity capital)(ROE # Cost of equity capital)

This last expression implies that EVA depends on three factors: rate of return, as refl ected in ROE; risk, which aff ects the cost of equity; and size, which is measured by the equity employed. Recall that earlier in this chapter, we said that shareholder value depends on risk, return, and capital invested. This fi nal equation illustrates that point.

ECONOMIC VALUE ADDED (EVA) VERSUS NET INCOME

109Chapter 4 Analysis of Financial Statements

S has stable cash fl ows and a predictable 15% ROE. Division R has a 16% expected ROE, but its cash fl ows are quite risky; so the expected ROE may not materialize. If managers were compensated solely on the basis of ROE and if the expected ROEs were actually achieved during the coming year, Division R’s manager would receive a higher bonus than S’s even though S might actually be creating more value for shareholders as a result of its lower risk. Similarly, fi nancial leverage can increase expected ROE, but more leverage means higher risk; so raising ROE through the use of leverage may not be good.

Second, ROE does not consider the amount of invested capital. To illustrate, consider a company that is choosing between two mutually exclusive projects. Proj- ect A calls for investing $50,000 at an expected ROE of 50%, while Project B calls for investing $1,000,000 at a 45% ROE. The projects are equally risky, and the compa- ny’s cost of capital is 10%. Project A has the higher ROE, but it is much smaller. Project B should be chosen because it would add more to shareholder wealth.

Third, a focus on ROE can cause managers to turn down profi table projects. For example, suppose you manage a division of a large fi rm and the fi rm deter- mines bonuses solely on the basis of ROE. You project that your division’s ROE for the year will be an impressive 45%. Now you have an opportunity to invest in a large, low-risk project with an estimated ROE of 35%, which is well above the fi rm’s 10% cost of capital. Even though this project is extremely profi table, you might still be reluctant to undertake it because it would reduce your division’s av- erage ROE and therefore your year-end bonus.

These three examples suggest that a project’s ROE must be combined with its size and risk to determine its effect on the fi rm’s stock price:

Contribution of a project to stock price ! f(ROE, Risk, Size)

We will discuss this in more depth when we consider capital budgeting, where we look in detail at how projects are selected so as to maximize stock prices.

4-14 LOOKING BEYOND THE NUMBERS Working through this chapter should increase your ability to understand and interpret fi nancial statements. This is critically important for anyone making busi- ness decisions or forecasting stock prices. However, sound fi nancial analysis involves more than just numbers—good analysis requires that certain qualitative factors also be considered. These factors, as summarized by the American Associa- tion of Individual Investors (AAII), include the following: 1. Are the company’s revenues tied to one key customer? If so, the company’s

performance may decline dramatically if that customer goes elsewhere. On the other hand, if the customer has no alternative to the company’s products, this might actually stabilize sales.

2. To what extent are the company’s revenues tied to one key product? Firms that focus on a single product are often effi cient, but a lack of diversifi cation also

Students might want to refer to AAII’s educational web site at www.aaii. com. The site provides information on investing basics, financial planning, portfolio management, and the like, so that individuals can manage their own assets more effectively.

SEL F TEST If a fi rm takes steps that increase its expected future ROE, does this necessar-

ily mean that the stock price will also increase? Explain.

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110 Part 2 Fundamental Concepts in Financial Management

increases risk because having revenues from several products stabilizes profi ts and cash fl ows in a volatile world.

3. To what extent does the company rely on a single supplier? Depending on a single supplier may lead to an unanticipated shortage and a hit to sales and profi ts.

4. What percentage of the company’s business is generated overseas? Compa- nies with a large percentage of overseas business are often able to realize higher growth and larger profi t margins. However, overseas operations may expose the fi rm to political risks and exchange rate problems.

5. How much competition does the fi rm face? Increases in competition tend to lower prices and profi t margins; so when forecasting future performance, it is important to assess the likely actions of current competitors and the entry of new ones.

6. Is it necessary for the company to continually invest in research and develop- ment? If so, its future prospects will depend critically on the success of new products in the pipeline. For example, investors in a pharmaceutical com- pany want to know whether the company has a strong pipeline of potential blockbuster drugs and whether those products are doing well in the required tests.

7. Are changes in laws and regulations likely to have important implications for the fi rm? For example, when the future of electric utilities are forecasted, it is crucial to factor in the effects of proposed regulations affecting the use of coal, nuclear, and gas-fi red plants.

SEL F TEST What are some qualitative factors that analysts should consider when evalu-

ating a company’s likely future fi nancial performance?

In the last chapter, we discussed the key fi nancial statements; and in this one, we de- scribed how ratios are used to analyze the statements to identify weaknesses that need to be strengthened to maximize the stock price. Ratios are grouped into fi ve categories: • Liquidity • Asset management • Debt management • Profi tability • Market value

The fi rm’s ratios are compared with averages for its industry and with the leading fi rms in the industry (benchmarking), and these comparisons are used to help for- mulate policies that will lead to improved future performance. Similarly, the fi rm’s own ratios can be analyzed over time to see if its fi nancial situation is getting better or worse (trend analysis).

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111Chapter 4 Analysis of Financial Statements

The single most important ratio over which management has control is the ROE—the other ratios are also important, but mainly because they aff ect the ROE. One tool used to show how ROE is determined is the DuPont equation: ROE ! Profi t margin " Total assets turnover " Equity multiplier. If the fi rm’s ROE is below the in- dustry average and that of the benchmark companies, a DuPont analysis can help identify problem areas that should be strengthened. In later chapters, we consider specifi c actions that can be taken to improve ROE and thus a fi rm’s stock price. One closing note: Although ratio analysis is useful, it must be applied with care and good judgment. Actions taken to improve one ratio can have negative eff ects on some other ratio or ratios. For example, it might be possible to improve the ROE by using more debt, but the risk of the additional debt may lead to a decrease in the P/E ratio and thus in the fi rm’s stock price. Quantitative analysis such as ratio analysis can be useful, but thinking through the results is even more important.

KEY TERMS Define each of the following terms: a. Liquidity ratios: current ratio; acid test ratio b. Asset management ratios: inventory turnover ratio; days sales outstanding (DSO);

fixed assets turnover ratio; total assets turnover ratio c. Debt management ratios: debt ratio; times-interest-earned (TIE) ratio d. Profitability ratios: operating margin; profit margin; basic earning power (BEP) ratio;

return on total assets (ROA); return on common equity (ROE) e. Market value ratios: price/earnings (P/E) ratio; market/book (M/B) ratio f. Trend analysis g. DuPont equation h. Benchmarking i. “Window dressing” techniques

DEBT RATIO Last year K. Billingsworth & Co. had earnings per share of $4 and divi- dends per share of $2. Total retained earnings increased by $12 million during the year, while book value per share at year-end was $40. Billingsworth has no preferred stock, and no new common stock was issued during the year. If its year-end total debt was $120 mil- lion, what was the company’s year-end debt/assets ratio?

RATIO ANALYSIS The following data apply to A.L. Kaiser & Company (millions of dollars):

Cash and equivalents $100.00

Fixed assets 283.50

Sales 1,000.00

Net income 50.00

Current liabilities 105.50

Current ratio 3.0#

DSOa 40.55 days

ROE 12%

a This calculation is based on a 365-day year.

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

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112 Part 2 Fundamental Concepts in Financial Management

Total Current Assets

Current Ratio

Effect on Net Income

a. Cash is acquired through issuance of additional common stock. _____ _____ _____

b. Merchandise is sold for cash. _____ _____ _____ c. Federal income tax due for the previous year is paid. _____ _____ _____ d. A fixed asset is sold for less than book value. _____ _____ _____ e. A fixed asset is sold for more than book value. _____ _____ _____ f. Merchandise is sold on credit. _____ _____ _____ g. Payment is made to trade creditors for previous

purchases. _____ _____ _____

Kaiser has no preferred stock—only common equity, current liabilities, and long-term debt. a. Find Kaiser’s (1) accounts receivable, (2) current assets, (3) total assets, (4) ROA,

(5) common equity, (6) quick ratio, and (7) long-term debt. b. In Part a, you should have found that Kaiser’s accounts receivable (A/R) ! $111.1

million. If Kaiser could reduce its DSO from 40.55 days to 30.4 days while holding other things constant, how much cash would it generate? If this cash were used to buy back common stock (at book value), thus reducing common equity, how would this affect (1) the ROE, (2) the ROA, and (3) the total debt/total assets ratio?

Financial ratio analysis is conducted by three main groups of analysts: credit analysts, stock analysts, and managers. What is the primary emphasis of each group, and how would that emphasis affect the ratios they focus on?

Why would the inventory turnover ratio be more important for someone analyzing a gro- cery store chain than an insurance company?

Over the past year, M. D. Ryngaert & Co. had an increase in its current ratio and a decline in its total assets turnover ratio. However, the company’s sales, cash and equivalents, DSO, and fixed assets turnover ratio remained constant. What balance sheet accounts must have changed to produce the indicated changes?

Profit margins and turnover ratios vary from one industry to another. What differences would you expect to find between the turnover ratios, profit margins, and DuPont equa- tions for a grocery chain and a steel company?

How does inflation distort ratio analysis comparisons for one company over time (trend analysis) and for different companies that are being compared? Are only balance sheet items or both balance sheet and income statement items affected?

If a firm’s ROE is low and management wants to improve it, explain how using more debt might help.

Give some examples that illustrate how (a) seasonal factors and (b) different growth rates might distort a comparative ratio analysis. How might these problems be alleviated?

Why is it sometimes misleading to compare a company’s financial ratios with those of other firms that operate in the same industry?

Suppose you were comparing a discount merchandiser with a high-end merchandiser. Suppose further that both companies had identical ROEs. If you applied the DuPont equa- tion to both firms, would you expect the three components to be the same for each com- pany? If not, explain what balance sheet and income statement items might lead to the component differences.

Indicate the effects of the transactions listed in the following table on total current assets, current ratio, and net income. Use (+) to indicate an increase, (") to indicate a decrease, and (0) to indicate either no effect or an indeterminate effect. Be prepared to state any nec- essary assumptions and assume an initial current ratio of more than 1.0. (Note: A good ac- counting background is necessary to answer some of these questions; if yours is not strong, answer just the questions you can.)

QUESTIONSQUESTIONS

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113Chapter 4 Analysis of Financial Statements

Total Current Assets

Current Ratio

Effect on Net Income

h. A cash dividend is declared and paid. _____ _____ _____ i. Cash is obtained through short-term bank loans. _____ _____ _____ j. Short-term notes receivable are sold at a discount. _____ _____ _____ k. Marketable securities are sold below cost. _____ _____ _____ l. Advances are made to employees. _____ _____ _____ m. Current operating expenses are paid. _____ _____ _____ n. Short-term promissory notes are issued to trade

creditors in exchange for past due accounts payable. _____ _____ _____ o. 10-year notes are issued to pay off accounts payable. _____ _____ _____ p. A fully depreciated asset is retired. _____ _____ _____ q. Accounts receivable are collected. _____ _____ _____ r. Equipment is purchased with short-term notes. _____ _____ _____ s. Merchandise is purchased on credit. _____ _____ _____ t. The estimated taxes payable are increased. _____ _____ _____

DAYS SALES OUTSTANDING Baker Brothers has a DSO of 40 days, and its annual sales are $7,300,000. What is its accounts receivable balance? Assume that it uses a 365-day year.

DEBT RATIO Bartley Barstools has an equity multiplier of 2.4, and its assets are financed with some combination of long-term debt and common equity. What is its debt ratio?

DUPONT ANALYSIS Doublewide Dealers has an ROA of 10%, a 2% profit margin, and an ROE of 15%. What is its total assets turnover? What is its equity multiplier?

MARKET/BOOK RATIO Jaster Jets has $10 billion in total assets. Its balance sheet shows $1 billion in current liabilities, $3 billion in long-term debt, and $6 billion in common equity. It has 800 million shares of common stock outstanding, and its stock price is $32 per share. What is Jaster’s market/book ratio?

PRICE/EARNINGS RATIO A company has an EPS of $2.00, a cash flow per share of $3.00, and a price/cash flow ratio of 8.0#. What is its P/E ratio?

DUPONT AND ROE A firm has a profit margin of 2% and an equity multiplier of 2.0. Its sales are $100 million, and it has total assets of $50 million. What is its ROE?

DUPONT AND NET INCOME Ebersoll Mining has $6 million in sales, its ROE is 12%, and its total assets turnover is 3.2#. The company is 50% equity financed. What is its net income?

BASIC EARNING POWER Duval Manufacturing recently reported the following information:

Net income $600,000 ROA 8% Interest expense $225,000

Duval’s tax rate is 35%. What is its basic earning power (BEP)?

M/B AND SHARE PRICE You are given the following information: Stockholders’ equity ! $3.75 billion, price/earnings ratio ! 3.5, common shares outstanding ! 50 million, and market/book ratio ! 1.9. Calculate the price of a share of the company’s common stock.

RATIO CALCULATIONS Assume the following relationships for the Brauer Corp.:

Sales/total assets 1.5# Return on assets (ROA) 3% Return on equity (ROE) 5%

Calculate Brauer’s profit margin and debt ratio.

RATIO CALCULATIONS Graser Trucking has $12 billion in assets, and its tax rate is 40%. Its basic earning power (BEP) ratio is 15%, and its return on assets (ROA) is 5%. What is its times-interest-earned (TIE) ratio?

PROBLEMS PROBLEMS

Easy Problems 1–6 Easy Problems 1–6

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114 Part 2 Fundamental Concepts in Financial Management

TIE RATIO The H.R. Pickett Corp. has $500,000 of debt outstanding, and it pays an annual interest rate of 10%. Its annual sales are $2 million, its average tax rate is 30%, and its net profit margin is 5%. What is its TIE ratio?

RETURN ON EQUITY Midwest Packaging’s ROE last year was only 3%; but its management has developed a new operating plan that calls for a total debt ratio of 60%, which will result in annual interest charges of $300,000. Management projects an EBIT of $1,000,000 on sales of $10,000,000, and it expects to have a total assets turnover ratio of 2.0. Under these conditions, the tax rate will be 34%. If the changes are made, what will be the company’s return on equity?

RETURN ON EQUITY AND QUICK RATIO Lloyd Inc. has sales of $200,000, a net income of $15,000, and the following balance sheet:

Cash $ 10,000 Accounts payable $ 30,000 Receivables 50,000 Other current liabilities 20,000 Inventories 150,000 Long-term debt 50,000 Net fixed assets 90,000 Common equity 200,000 Total assets $300,000 Total liabilities and equity $300,000

The new owner thinks that inventories are excessive and can be lowered to the point where the current ratio is equal to the industry average, 2.5#, without affecting sales or net income. If inventories are sold off and not replaced (thus reducing the current ratio to 2.5#), if the funds generated are used to reduce common equity (stock can be repurchased at book value), and if no other changes occur, by how much will the ROE change? What will be the firm’s new quick ratio?

RETURN ON EQUITY Central City Construction (CCC) needs $1 million of assets to get started, and it expects to have a basic earning power ratio of 20%. CCC will own no secu- rities, so all of its income will be operating income. If it so chooses, CCC can finance up to 50% of its assets with debt, which will have an 8% interest rate. Assuming a 40% tax rate on all taxable income, what is the difference between CCC’s expected ROE if it finances with 50% debt versus its expected ROE if it finances entirely with common stock?

CONCEPTUAL: RETURN ON EQUITY Which of the following statements is most correct? (Hint: Work Problem 4-15 before answering 4-16 and consider the solution setup for 4-15 as you think about 4-16.) a. If a firm’s expected basic earning power (BEP) is constant for all of its assets and ex-

ceeds the interest rate on its debt, adding assets and financing them with debt will raise the firm’s expected return on common equity (ROE).

b. The higher a firm’s tax rate, the lower its BEP ratio, other things held constant. c. The higher the interest rate on a firm’s debt, the lower its BEP ratio, other things held

constant. d. The higher a firm’s debt ratio, the lower its BEP ratio, other things held constant. e. Statement a is false; but statements b, c, and d are true.

TIE RATIO AEI Incorporated has $5 billion in assets, and its tax rate is 40%. Its basic earn- ing power (BEP) ratio is 10%, and its return on assets (ROA) is 5%. What is AEI’s times- interest-earned (TIE) ratio?

CURRENT RATIO The Petry Company has $1,312,500 in current assets and $525,000 in current liabilities. Its initial inventory level is $375,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can its short-term debt (notes payable) increase without pushing its current ratio below 2.0?

DSO AND ACCOUNTS RECEIVABLE Harrelson Inc. currently has $750,000 in accounts receivable, and its days sales outstanding (DSO) is 55 days. It wants to reduce its DSO to 35 days by pressuring more of its customers to pay their bills on time. If this policy is adopted, the company’s average sales will fall by 15%. What will be the level of accounts receivable following the change? Assume a 365-day year.

P/E AND STOCK PRICE Fontaine Inc. recently reported net income of $2 million. It has 500,000 shares of common stock, which currently trades at $40 a share. Fontaine contin- ues to expand and anticipates that 1 year from now, its net income will be $3.25 million. Over the next year, it also anticipates issuing an additional 150,000 shares of stock so that 1 year from now it will have 650,000 shares of common stock. Assuming Fontaine’s price/earnings ratio remains at its current level, what will be its stock price 1 year from now?

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Challenging Problems 19–23 Challenging Problems 19–23

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115Chapter 4 Analysis of Financial Statements

BALANCE SHEET ANALYSIS Complete the balance sheet and sales information using the following financial data: Debt ratio: 50% Current ratio: 1.8# Total assets turnover: 1.5# Days sales outstanding: 36.5 daysa Gross profit margin on sales: (Sales " Cost of goods sold)/Sales ! 25% Inventory turnover ratio: 5#

aCalculation is based on a 365-day year.

Balance Sheet Cash Accounts payable Accounts receivable Long-term debt 60,000 Inventories Common stock Fixed assets Retained earnings 97,500 Total assets $300,000 Total liabilities and equity Sales Cost of goods sold

RATIO ANALYSIS Data for Barry Computer Co. and its industry averages follow. a. Calculate the indicated ratios for Barry. b. Construct the DuPont equation for both Barry and the industry. c. Outline Barry’s strengths and weaknesses as revealed by your analysis. d. Suppose Barry had doubled its sales as well as its inventories, accounts receivable,

and common equity during 2008. How would that information affect the validity of your ratio analysis? (Hint: Think about averages and the effects of rapid growth on ratios if averages are not used. No calculations are needed.)

Barry Computer Company: Balance Sheet as of December 31, 2008 (In Thousands)

Cash $ 77,500 Accounts payable $129,000 Receivables 336,000 Notes payable 84,000 Inventories 241,500 Other current liabilities 117,000 Total current assets $655,000 Total current liabilities $330,000

Long-term debt 256,500 Net fixed assets 292,500 Common equity 361,000 Total assets $947,500 Total liabilities and equity $947,500

Barry Computer Company: Income Statement for Year Ended December 31, 2008 (In Thousands)

Sales $1,607,500 Cost of goods sold Materials $ 717,000 Labor 453,000 Heat, light, and power 68,000 Indirect labor 113,000 Depreciation 41,500 1,392,500 Gross profit $ 215,000 Selling expenses 115,000 General and administrative expenses 30,000 Earnings before interest and taxes (EBIT) $ 70,000 Interest expense 24,500 Earnings before taxes (EBT) $ 45,500 Federal and state income taxes (40%) 18,200 Net income $ 27,300

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116 Part 2 Fundamental Concepts in Financial Management

Ratio Barry Industry Average

Current _____ 2.0#

Quick _____ 1.3#

Days sales outstandinga _____ 35 days

Inventory turnover _____ 6.7#

Total assets turnover _____ 3.0#

Net profit margin _____ 1.2%

ROA _____ 3.6%

ROE _____ 9.0%

Total debt/total assets _____ 60.0%

aCalculation is based on a 365-day year.

DUPONT ANALYSIS A firm has been experiencing low profitability in recent years. Per- form an analysis of the firm’s financial position using the DuPont equation. The firm has no lease payments but has a $2 million sinking fund payment on its debt. The most recent industry average ratios and the firm’s financial statements are as follows:

Industry Average Ratios Current ratio 2# Fixed assets turnover 6# Debt/total assets 30% Total assets turnover 3# Times interest earned 7# Profit margin 3% EBITDA coverage 9# Return on total assets 9% Inventory turnover 10# Return on common equity 12.86% Days sales outstandinga 24 days

aCalculation is based on a 365-day year.

Balance Sheet as of December 31, 2008 (Millions of Dollars) Cash and equivalents $ 78 Accounts payable $ 45 Net receivables 66 Notes payable 45 Inventories 159 Other current liabilities 21 Total current assets $303 Total current liabilities $111

Long-term debt 24 Total liabilities $135

Gross fixed assets 225 Less depreciation 78 Common stock 114 Net fixed assets $147 Retained earnings 201

Total stockholders’ equity $315 Total assets $450 Total liabilities and equity $450

Income Statement for Year Ended December 31, 2008 (Millions of Dollars) Net sales $795.0 Cost of goods sold 660.0 Gross profit $135.0 Selling expenses 73.5 EBITDA $ 61.5 Depreciation expense 12.0 Earnings before interest and taxes (EBIT) $ 49.5 Interest expense 4.5 Earnings before taxes (EBT) $ 45.0 Taxes (40%) 18.0 Net income $ 27.0

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117Chapter 4 Analysis of Financial Statements

a. Calculate those ratios that you think would be useful in this analysis. b. Construct a DuPont equation and compare the company’s ratios to the industry aver-

age ratios. c. Do the balance sheet accounts or the income statement figures seem to be primarily

responsible for the low profits? d. Which specific accounts seem to be most out of line relative to other firms in the

industry? e. If the firm had a pronounced seasonal sales pattern or if it grew rapidly during the

year, how might that affect the validity of your ratio analysis? How might you correct for such potential problems?

RATIO ANALYSIS The Corrigan Corporation’s 2007 and 2008 financial statements follow, along with some industry average ratios. a. Assess Corrigan’s liquidity position and determine how it compares with peers and

how the liquidity position has changed over time. b. Assess Corrigan’s asset management position and determine how it compares with

peers and how its asset management efficiency has changed over time. c. Assess Corrigan’s debt management position and determine how it compares with

peers and how its debt management has changed over time. d. Assess Corrigan’s profitability ratios and determine how they compare with peers

and how its profitability position has changed over time. e. Assess Corrigan’s market value ratios and determine how its valuation compares

with peers and how it has changed over time. f. Calculate Corrigan’s ROE as well as the industry average ROE using the DuPont

equation. From this analysis, how does Corrigan’s financial position compare with the industry average numbers?

g. What do you think would happen to its ratios if the company initiated cost-cutting measures that allowed it to hold lower levels of inventory and substantially decreased the cost of goods sold? No calculations are necessary. Think about which ratios would be affected by changes in these two accounts.

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Corrigan Corporation: Balance Sheets as of December 31

2008 2007 Cash $ 72,000 $ 65,000 Accounts receivable 439,000 328,000 Inventories 894,000 813,000 Total current assets $1,405,000 $1,206,000 Land and building 238,000 271,000 Machinery 132,000 133,000 Other fixed assets 61,000 57,000 Total assets $1,836,000 $1,667,000

Accounts and notes payable $ 432,000 $ 409,500 Accrued liabilities 170,000 162,000 Total current liabilities $ 602,000 $ 571,500 Long-term debt 404,290 258,898 Common stock 575,000 575,000 Retained earnings 254,710 261,602 Total liabilities and equity $1,836,000 $1,667,000

118 Part 2 Fundamental Concepts in Financial Management

Per-Share Data 2008 2007

EPS $0.80 $4.17 Cash dividends $1.10 $0.95 Market price (average) $12.34 $23.57 P/E ratio 15.4# 5.65# Number of shares outstanding 23,000 23,000

Industry Financial Ratiosa

2008 Current ratio 2.7# Inventory turnoverb 7.0# Days sales outstandingc 32 days Fixed assets turnoverb 13.0# Total assets turnoverb 2.6# Return on assets 9.1% Return on equity 18.2% Debt ratio 50.0% Profit margin 3.5% P/E ratio 6.0# Price/cash flow ratio 3.5# aIndustry average ratios have been constant for the past 4 years. bBased on year-end balance sheet figures. cCalculation is based on a 365-day year.

Corrigan Corporation: Income Statements for Years Ending December 31 2008 2007

Sales $4,240,000 $3,635,000 Cost of goods sold 3,680,000 2,980,000 Gross operating profit $ 560,000 $ 655,000 General administrative and selling expenses 236,320 213,550 Depreciation 159,000 154,500 Miscellaneous 134,000 127,000 Earnings before taxes (EBT) $ 30,680 $ 159,950 Taxes (40%) 12,272 63,980 Net income $ 18,408 $ 95,970

FINANCIAL STATEMENT ANALYSIS Part I of this case, presented in Chapter 3, discussed the situation of D’Leon Inc., a regional snack foods producer, after an expansion program. D’Leon had increased plant capac- ity and undertaken a major marketing campaign in an attempt to “go national.” Thus far, sales have not been up to the forecasted level, costs have been higher than were projected, and a large loss occurred in 2008 rather than the expected profit. As a result, its managers, directors, and investors are concerned about the firm’s survival. Donna Jamison was brought in as assistant to Fred Campo, D’Leon’s chairman, who had the task of getting the company back into a sound financial position. D’Leon’s 2007 and 2008 balance sheets and income statements, together with projections for 2009, are given in Tables IC4-1 and IC4-2. In addition, Table IC4-3 gives the

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119Chapter 4 Analysis of Financial Statements

company’s 2007 and 2008 financial ratios, together with industry average data. The 2009 projected financial state- ment data represent Jamison’s and Campo’s best guess for 2009 results, assuming that some new financing is ar- ranged to get the company “over the hump.” Jamison examined monthly data for 2008 (not given in the case), and she detected an improving pattern dur- ing the year. Monthly sales were rising, costs were falling, and large losses in the early months had turned to a small profit by December. Thus, the annual data look somewhat worse than final monthly data. Also, it appears to be taking longer for the advertising program to get the message out, for the new sales offices to generate sales, and for the new manufacturing facilities to operate efficiently. In other words, the lags between spending money and deriving benefits were longer than D’Leon’s managers had anticipated. For these reasons, Jamison and Campo see hope for the company—provided it can survive in the short run. Jamison must prepare an analysis of where the company is now, what it must do to regain its financial health, and what actions should be taken. Your assignment is to help her answer the following questions. Pro- vide clear explanations, not yes or no answers.

a. Why are ratios useful? What are the five major categories of ratios? b. Calculate D’Leon’s 2009 current and quick ratios based on the projected balance sheet and income statement

data. What can you say about the company’s liquidity positions in 2007, in 2008, and as projected for 2009? We often think of ratios as being useful (1) to managers to help run the business, (2) to bankers for credit analysis, and (3) to stockholders for stock valuation. Would these different types of analysts have an equal interest in the company’s liquidity ratios?

c. Calculate the 2009 inventory turnover, days sales outstanding (DSO), fixed assets turnover, and total assets turnover. How does D’Leon’s utilization of assets stack up against other firms in the industry?

d. Calculate the 2009 debt and times-interest-earned ratios. How does D’Leon compare with the industry with respect to financial leverage? What can you conclude from these ratios?

e. Calculate the 2009 operating margin, profit margin, basic earning power (BEP), return on assets (ROA), and return on equity (ROE). What can you say about these ratios?

f. Calculate the 2009 price/earnings ratio and market/book ratio. Do these ratios indicate that investors are expected to have a high or low opinion of the company?

g. Use the DuPont equation to provide a summary and overview of D’Leon’s financial condition as projected for 2009. What are the firm’s major strengths and weaknesses?

h. Use the following simplified 2009 balance sheet to show, in general terms, how an improvement in the DSO would tend to affect the stock price. For example, if the company could improve its collection procedures and thereby lower its DSO from 45.6 days to the 32-day industry average without affecting sales, how would that change “ripple through” the financial statements (shown in thousands below) and influence the stock price?

Accounts receivable $ 878 Debt $1,545 Other current assets 1,802 Net fixed assets 817 Equity 1,952 Total assets $3,497 Liabilities plus equity $3,497

i. Does it appear that inventories could be adjusted? If so, how should that adjustment affect D’Leon’s profit- ability and stock price?

j. In 2008, the company paid its suppliers much later than the due dates; also, it was not maintaining financial ratios at levels called for in its bank loan agreements. Therefore, suppliers could cut the company off, and its bank could refuse to renew the loan when it comes due in 90 days. On the basis of data provided, would you, as a credit manager, continue to sell to D’Leon on credit? (You could demand cash on delivery—that is, sell on terms of COD—but that might cause D’Leon to stop buying from your company.) Similarly, if you were the bank loan officer, would you recommend renewing the loan or demand its repayment? Would your ac- tions be influenced if in early 2009 D’Leon showed you its 2009 projections along with proof that it was going to raise more than $1.2 million of new equity?

k. In hindsight, what should D’Leon have done in 2007? l. What are some potential problems and limitations of financial ratio analysis? m. What are some qualitative factors that analysts should consider when evaluating a company’s likely future

financial performance?

120 Part 2 Fundamental Concepts in Financial Management

2009E 2008 2007 Assets Cash $ 85,632 $ 7,282 $ 57,600 Accounts receivable 878,000 632,160 351,200 Inventories 1,716,480 1,287,360 715,200 Total current assets $2,680,112 $1,926,802 $1,124,000 Gross fixed assets 1,197,160 1,202,950 491,000 Less accumulated depreciation 380,120 263,160 146,200 Net fixed assets $ 817,040 $ 939,790 $ 344,800 Total assets $3,497,152 $2,866,592 $1,468,800

Liabilities and Equity Accounts payable $ 436,800 $ 524,160 $ 145,600 Notes payable 300,000 636,808 200,000 Accruals 408,000 489,600 136,000 Total current liabilities $1,144,800 $1,650,568 $ 481,600 Long-term debt 400,000 723,432 323,432 Common stock 1,721,176 460,000 460,000 Retained earnings 231,176 32,592 203,768 Total equity $1,952,352 $ 492,592 $ 663,768 Total liabilities and equity $3,497,152 $2,866,592 $1,468,800

Note: E indicates estimated. The 2009 data are forecasts.

Balance SheetsT a b l e I C 4 - 1

Income StatementsT a b l e I C 4 - 2

2009E 2008 2007 Sales $7,035,600 $6,034,000 $3,432,000 Cost of goods sold 5,875,992 5,528,000 2,864,000 Other expenses 550,000 519,988 358,672 Total operating costs excluding depreciation & amortization $6,425,992 $6,047,988 $3,222,672 EBITDA $ 609,608 ($ 13,988) $ 209,328 Depreciation & amortization 116,960 116,960 18,900 EBIT $ 492,648 ($ 130,948) $ 190,428 Interest expense 70,008 136,012 43,828 EBT $ 422,640 ($ 266,960) $ 146,600 Taxes (40%) 169,056 (106,784)a 58,640 Net income $ 253,584 ($ 160,176) $ 87,960

EPS $1.014 ($1.602) $0.880 DPS $0.220 $0.110 $0.220 Book value per share $7.809 $4.926 $6.638 Stock price $12.17 $2.25 $8.50 Shares outstanding 250,000 100,000 100,000 Tax rate 40.00% 40.00% 40.00% Lease payments $40,000 $40,000 $40,000 Sinking fund payments 0 0 0

Note: E indicates estimated. The 2009 data are forecasts. aThe firm had sufficient taxable income in 2006 and 2007 to obtain its full tax refund in 2008.

121Chapter 4 Analysis of Financial Statements

Industry 2009E 2008 2007 Average

Current 1.2# 2.3# 2.7# Quick 0.4# 0.8# 1.0# Inventory turnover 4.7# 4.8# 6.1# Days sales outstanding (DSO)a 38.2 37.4 32.0 Fixed assets turnover 6.4# 10.0# 7.0# Total assets turnover 2.1# 2.3# 2.6# Debt ratio 82.8% 54.8% 50.0% TIE "1.0# 4.3# 6.2# Operating margin "2.2% 5.6% 7.3% Profit margin "2.7% 2.6% 3.5% Basic earning power "4.6% 13.0% 19.1% ROA "5.6% 6.0% 9.1% ROE "32.5% 13.3% 18.2% Price/earnings "1.4# 9.7# 14.2# Market/book 0.5# 1.3# 2.4# Book value per share $4.93 $6.64 n.a.

Note: E indicates estimated. The 2009 data are forecasts. aCalculation is based on a 365-day year.

Ratio AnalysisT a b l e I C 4 - 3

122 Part 2 Fundamental Concepts in Financial Management

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to answer this chapter’s questions.

Conducting a Financial Ratio Analysis on Ford Motor Company In Chapter 3, we looked at Starbucks’ fi nancial statements. Now we use Thomson ONE to analyze Ford Motor Company.

Enter Ford’s ticker symbol (F) and select “GO.” Select “Financial Statements” and “Thomson Finan- cials” to fi nd Ford’s key fi nancial statements for the past several years. Click on “Financial Ratios” and then “SEC Ratios.” From here you can select either annual or quarterly ratios.

Under annual ratios, there is an in-depth summary of Ford’s various ratios over the past 3 years. This information enables you to evaluate Ford’s performance over time for each of the ratio categories mentioned in the text (liquidity, asset management, debt management, profi tability, and market-based ratios).

The text mentions that fi nancial statement analysis has two major components: a trend analysis, where we evaluate changes in the key ratios over time, and a peer analysis, where we compare fi nancial ratios with fi rms that are in the same industry and/or line of business. We have already used Thomson ONE to conduct a trend analysis—next, we use this tool to conduct a peer analysis. Click on “Compara- bles” to fi nd some summary fi nancial information for Ford and a few of its peers. By clicking on the Peer Sets, you can modify the list of peer fi rms. The default setup is “Peers set by SIC Code.” To obtain a com- parison of many of the key ratios presented in the text, click on “Financials” and select “Key Financial Ratios.”

Discussion Questions 1. What has happened to Ford’s liquidity position over the past 3 years? How does Ford’s liquidity compare with

that of its peers? (Hint: You may use both the peer key financial ratios and liquidity comparison to answer this question.)

2. Take a look at Ford’s inventory turnover ratio. How does this ratio compare with that of its peers? Have there been any interesting changes over time in this measure? Do you consider Ford’s inventory management to be a strength or a weakness? Explain.

3. Construct a DuPont analysis for Ford and its peers. What are Ford’s strengths and weaknesses compared to those of its competitors?

1. What has happened to Ford’s liquidity position over the past 3 years? How does Ford’s liquidity compare with that of its peers? (Hint: You may use both the peer key financial ratios and liquidity comparison to answer this question.)

3. Construct a DuPont analysis for Ford and its peers. What are Ford’s strengths and weaknesses compared to those of its competitors?

CHAPTER

123

Your reaction to that question is probably, “First things first! I’m worried about getting a job, not about retiring!” However, understanding the retirement situation can help you land a job because (1) this is an important issue today, (2) employers like to hire people who know what’s happening in the real world, and (3) pro- fessors often test on the time value of money with problems related to saving for future pur- poses (including retirement).

A recent Fortune article began with some interesting facts: (1) The U.S. savings rate is the lowest of any industrial nation. (2) The ratio of U.S. workers to retirees, which was 17 to 1 in 1950, is now down to 3 to 1; and it will decline to less than 2 to 1 after 2020. (3) With so few people paying into the Social Security system and so

many drawing funds out, Social Security is going to be in serious trouble. The article concluded that even people making $85,000 per year will have trouble maintaining a reasonable standard of living after they retire, and many of today’s college students will have to support their parents.

This is an important issue for millions of Americans, but many don’t know how to deal with it. When Fortune studied the retirement issue, using the tools and techniques described in this chapter, they concluded that most Ameri- cans have been ignoring what is most certainly going to be a huge personal and social problem. However, if you study this chapter carefully, you can avoid the trap that is likely to catch so many people.

Wi l l Yo u B e A b l e t o Re t i r e ?

5 Time Value of Money

EI M

AR /A

LA M

124 Part 2 Fundamental Concepts in Financial Management

Excellent retirement calculators are available at www.ssa.gov and www. choosetosave .org/ calculators. These calculators allow you to input hypothetical retirement savings information; the program then shows if current retirement savings will be sufficient to meet retirement needs.

1 Calculator manuals tend to be long and complicated, partly because they cover a number of topics that aren’t required in the basic fi nance course. Therefore, on the textbook’s web site, we provide tutorials for the most commonly used calculators. The tutorials are keyed to this chapter, and they show exactly how to do the required calculations. If you don’t know how to use your calculator, go to the textbook’s web site, fi nd the relevant tutorial, and work through it as you study the chapter.

Time value analysis has many applications, including planning for retirement, valu- ing stocks and bonds, setting up loan payment schedules, and making corporate decisions regarding investing in new plant and equipment. In fact, of all fi nancial con- cepts, time value of money is the single most important concept. Indeed, time value analysis is used throughout the book; so it is vital that you understand this chapter before continuing. You need to understand basic time value concepts, but conceptual knowledge will do you little good if you can’t do the required calculations. Therefore, this chapter is heavy on calculations. Most students studying fi nance have a fi nancial or scientifi c calculator; some also own or have access to a computer. Moreover, one of these tools is necessary to work many fi nance problems in a reasonable length of time. However, when students start on this chapter, many of them don’t know how to use the time value functions on their calculator or computer. If you are in that situation, you will fi nd yourself simultaneously studying concepts and trying to learn to use your calcu- lator and you will need more time to cover this chapter than you might expect.1

When you fi nish this chapter, you should be able to: • Explain how the time value of money works and discuss why it is such an impor-

tant concept in fi nance. • Calculate the present value and future value of lump sums. • Identify the diff erent types of annuities and calculate the present value and future

value of both an ordinary annuity and an annuity due. You should also be able to calculate relevant annuity payments.

• Calculate the present value and future value of an uneven cash fl ow stream. You will use this knowledge in later chapters that show how to value common stocks and corporate projects.

• Explain the diff erence between nominal, periodic, and eff ective interest rates. • Discuss the basics of loan amortization.

PU T TING THINGS IN PER SPECTIVE

5-1 TIME LINES The fi rst step in time value analysis is to set up a time line, which will help you visualize what’s happening in a particular problem. As an illustration, consider the following diagram, where PV represents $100 that is on hand today and FV is the value that will be in the account on a future date:

0 21 3 5%

Periods

Cash PV = $100 FV = ?

The intervals from 0 to 1, 1 to 2, and 2 to 3 are time periods such as years or months. Time 0 is today, and it is the beginning of Period 1; Time 1 is one period from today, and it is both the end of Period 1 and the beginning of Period 2; and so forth.

Time Line An important tool used in time value analysis; it is a graphical representation used to show the timing of cash flows.

www.ssa.gov

www.choosetosave.org/calculators

125Chapter 5 Time Value of Money

Do time lines deal only with years, or can other periods be used?

Set up a time line to illustrate the following situation: You currently have $2,000 in a 3-year certifi cate of deposit (CD) that pays a guaranteed 4% annually.

SEL F TEST

5-2 FUTURE VALUES A dollar in hand today is worth more than a dollar to be received in the future because if you had it now, you could invest it, earn interest, and end up with more than a dollar in the future. The process of going to future values (FVs) from present values (PVs) is called compounding. For an illustration, refer back to our 3-year time line and assume that you plan to deposit $100 in a bank that pays a guaran- teed 5% interest each year. How much would you have at the end of Year 3? We fi rst defi ne some terms, after which we set up a time line and show how the future value is calculated.

Future Value (FV) The amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate.

Present Value (PV) The value today of a future cash flow or series of cash flows.

Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied.

Future Value (FV) The amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate.

Present Value (PV) The value today of a future cash flow or series of cash flows.

Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied.

PV ! Present value, or beginning amount. In our example, PV ! $100. FVN ! Future value, or ending amount, of your account after N periods.

Whereas PV is the value now, or the present value, FVN is the value N periods into the future, after the interest earned has been added to the account.

CFt ! Cash fl ow. Cash fl ows can be positive or negative. The cash fl ow for a par- ticular period is often given as a subscript, CFt , where t is the period. Thus, CF0 ! PV ! the cash fl ow at Time 0, whereas CF3 is the cash fl ow at the end of Period 3.

I ! Interest rate earned per year. Sometimes a lowercase i is used. Interest earned is based on the balance at the beginning of each year, and we assume that it is paid at the end of the year. Here I ! 5% or, expressed as a decimal,

Although the periods are often years, periods can also be quarters or months or even days. Note that each tick mark corresponds to both the end of one period and the beginning of the next one. Thus, if the periods are years, the tick mark at Time 2 represents the end of Year 2 and the beginning of Year 3.

Cash fl ows are shown directly below the tick marks, and the relevant interest rate is shown just above the time line. Unknown cash fl ows, which you are trying to fi nd, are indicated by question marks. Here the interest rate is 5%; a single cash outfl ow, $100, is invested at Time 0; and the Time 3 value is an unknown infl ow. In this example, cash fl ows occur only at Times 0 and 3, with no fl ows at Times 1 or 2. Note that in our example, the interest rate is constant for all 3 years. That condi- tion is generally true; but if it were not, we would show different interest rates for the different periods.

Time lines are essential when you are fi rst learning time value concepts, but even experts use them to analyze complex fi nance problems; and we use them throughout the book. We begin each problem by setting up a time line to show what’s happening, after which we provide an equation that must be solved to fi nd the answer. Then we explain how to use a regular calculator, a fi nancial calculator, and a spreadsheet to fi nd the answer.

126 Part 2 Fundamental Concepts in Financial Management

0.05. Throughout this chapter, we designate the interest rate as I because that symbol (or I/YR, for interest rate per year) is used on most fi nancial calculators. Note, though, that in later chapters, we use the symbol r to de- note rates because r (for rate of return) is used more often in the fi nance lit- erature. Note too that in this chapter, we generally assume that interest payments are guaranteed by the U.S. government; hence, they are certain. In later chapters, we will consider risky investments, where the interest rate earned might differ from its expected level.

INT ! Dollars of interest earned during the year ! Beginning amount " I. In our example, INT ! $100(0.05) ! $5.

N ! Number of periods involved in the analysis. In our example, N ! 3. Some- times the number of periods is designated with a lowercase n, so both N and n indicate a number of periods.

2 A fi fth procedure, using tables that show “interest factors,” was used before fi nancial calculators and computers became available. Now, though, calculators and spreadsheets such as Excel are programmed to calculate the specifi c factor needed for a given problem and then to use it to fi nd the FV. This is more effi cient than using the tables. Moreover, calculators and spreadsheets can handle fractional periods and fractional interest rates, such as the FV of $100 after 3.75 years when the interest rate is 5.375%, whereas tables provide numbers only for whole periods and rates. For these reasons, tables are not used in business today; hence, we do not discuss them in the text.

We can use four different procedures to solve time value problems.2 These methods are described in the following sections.

5-2a Step-by-Step Approach The time line used to fi nd the FV of $100 compounded for 3 years at 5%, along with some calculations, is shown.

Multiply the initial amount and each succeeding amount by (1 # I) ! (1.05):

Time

Amount at beginning of period $100.00

0 215% 3

$105.00 $110.25 $115.76

As noted in the text, interest earned on the interest earned in prior periods, as was true in our example and is always true when we apply Equation 5-1, is called compound interest. If interest is not earned on interest, we have sim- ple interest. The formula for FV with simple interest is FV ! PV # PV(I)(N); so in our example, FV would have been $100 # $100(0.05)(3) ! $100 # $15 ! $115 based on sim- ple interest. Most financial contracts are based on com- pound interest; but in legal proceedings, the law often specifies that simple interest must be used. For example, Maris Distributing, a company founded by home run king Roger Maris, won a lawsuit against Anheuser-Busch (A-B)

because A-B had breached a contract and taken away Maris’s franchise to sell Budweiser beer. The judge awarded Maris $50 million plus interest at 10% from 1997 (when A-B breached the contract) until the payment is actually made. The interest award was based on simple interest, which as of 2008 had raised the total from $50 million to $50 million # 0.10($50 million)(11 years) ! $105 million. If the law had allowed compound interest, the award would have totaled ($50 million)(1.10)11 ! $142.66 million, or $37.66 million more. This legal procedure dates back to the days before calculators and computers. The law moves slowly!

Compound Interest Occurs when interest is earned on prior periods’ interest.

Simple Interest Occurs when interest is not earned on interest.

Compound Interest Occurs when interest is earned on prior periods’ interest.

Simple Interest Occurs when interest is not earned on interest.

SIMPLE VERSUS COMPOUND INTEREST

127Chapter 5 Time Value of Money

You start with $100 in the account—this is shown at t ! 0: • You earn $100(0.05) ! $5 of interest during the fi rst year, so the amount at the

end of Year 1 (or t ! 1) is $100 # $5 ! $105. • You begin the second year with $105, earn 0.05($105) ! $5.25 on the now larger

beginning-of-period amount, and end the year with $110.25. Interest during Year 2 is $5.25; and it is higher than the fi rst year’s interest, $5.00, because you earned $5(0.05) ! $0.25 interest on the fi rst year’s interest. This is called com- pounding, and interest earned on interest is called compound interest.

• This process continues; and because the beginning balance is higher each suc- cessive year, the interest earned each year increases.

• The total interest earned, $15.76, is refl ected in the fi nal balance, $115.76.

The step-by-step approach is useful because it shows exactly what is happening. However, this approach is time-consuming, especially when a number of years are involved; so streamlined procedures have been developed.

5-2b Formula Approach In the step-by-step approach, we multiply the amount at the beginning of each period by (1 # I) ! (1.05). If N ! 3, we multiply by (1 # I) three different times, which is the same as multiplying the beginning amount by (1 # I)3. This concept can be extended, and the result is this key equation:

FVN ! PV(1 " I) N 5-1

We can apply Equation 5-1 to fi nd the FV in our example:

FV3 ! $100(1.05) 3 ! $115.76

Equation 5-1 can be used with any calculator that has an exponential function, making it easy to fi nd FVs no matter how many years are involved.

5-2c Financial Calculators Financial calculators are extremely helpful in working time value problems. Their manuals explain calculators in detail; and on the textbook’s web site, we provide summaries of the features needed to work the problems in this book for several popular calculators. Also see the box entitled “Hints on Using Financial Calcula- tors,” on page 129, for suggestions that will help you avoid common mistakes. If you are not yet familiar with your calculator, we recommend that you work through the tutorial as you study this chapter.

First, note that fi nancial calculators have fi ve keys that correspond to the fi ve variables in the basic time value equations. We show the inputs for our example above the keys and the output, the FV, below its key. Because there are no periodic payments, we enter 0 for PMT. We describe the keys in more detail below the diagram.

FVPVI/YRN PMT

0–1003 5

115.76

128 Part 2 Fundamental Concepts in Financial Management

As noted in our example, you fi rst enter the known values (N, I/YR, PMT, and PV) and then press the FV key to get the answer, 115.76. Again, note that if you enter the PV as 100 without a minus sign, the FV will be given as a negative. The calculator assumes that either the PV or the FV is negative. This should not be con- fusing if you think about what you are doing.

5-2d Spreadsheets3

Students generally use calculators for homework and exam problems; but in busi- ness, people generally use spreadsheets for problems that involve the time value of money (TVM). Spreadsheets show in detail what is happening, and they help reduce both conceptual and data-entry errors. The spreadsheet discussion can be skipped without loss of continuity; but if you understand the basics of Excel and have access to a computer, we recommend that you read through this section. Even if you aren’t familiar with spreadsheets, the discussion will still give you an idea of how they operate.

We used Excel to create Table 5-1, which summarizes the four methods of fi nding the FV and shows the spreadsheet formulas toward the bottom. Note that spreadsheets can be used to do calculations; but they can also be used like a word processor to create exhibits like Table 5-1, which includes text, drawings, and cal- culations. The letters across the top designate columns, the numbers to the left designate rows, and the rows and columns jointly designate cells. Thus, C14 is the cell in which we specify the $$100 investment, C15 shows the interest rate, and C16 shows the number of periods. We then created a time line on Rows 17 to 19; and on Row 21, we have Excel go through the step-by-step calculations, multiply- ing the beginning-of-year values by (1 # I) to fi nd the compounded value at the end of each period. Cell G21 shows the fi nal result. Then on Row 23, we illustrate the formula approach, using Excel to solve Equation 5-1, and fi nd the FV, $115.76. Next, on Rows 25 to 27, we show a picture of the calculator solution. Finally, on Rows 29 and 30, we use Excel’s built-in FV function to fi nd the answers given in Cells G29 and G30. The G29 answer is based on fi xed inputs, while the G30 an- swer is based on cell references, which makes it easy to change inputs and see the effects on the output.

Table 5-1 demonstrates that all four methods get the same result, but they use different calculating procedures. It also shows that with Excel, all inputs are shown

3 If you have never worked with spreadsheets, you may choose to skip this section. However, you might want to read through it and refer to this chapter’s Excel model to get an idea of how spreadsheets work.

N ! Number of periods. Some calculators use n rather than N. I/YR ! Interest rate per period. Some calculators use i or I rather than I/YR. PV ! Present value. In our example, we begin by making a deposit, which is an

outfl ow; so the PV should be entered with a negative sign. On most calcu- lators, you must enter the 100, then press the #/$ key to switch from #100 to $100. If you enter $100 directly, 100 will be subtracted from the last number in the calculator, giving you an incorrect answer.

PMT ! Payment. This key is used when we have a series of equal, or constant, payments. Because there are no such payments in our illustrative prob- lem, we enter PMT ! 0. We will use the PMT key when we discuss annui- ties later in this chapter.

FV ! Future value. In this example, the FV is positive because we entered the PV as a negative number. If we had entered the 100 as a positive number, the FV would have been negative.

129Chapter 5 Time Value of Money

in one place, which makes checking data entries relatively easy. Finally, it shows that Excel can be used to create exhibits, which are quite important in the real world. In business, it’s often as important to explain what you are doing as it is to “get the right answer” because if decision makers don’t understand your analysis, they may reject your recommendations.

$115.76

A B C D E F G 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Investment Interest rate No. of periods

= = =

= !$100.00 5.00%

CF0 I N

Periods:

Cash Flow Time Line:

!$100

$100 $105.00 $110.25Step-by-Step Approach:

FV = ?

1 2 3

$115.76Formula Approach: FVN = PV(1 " I)N

Calculator Approach:

In the Excel formula, the terms are entered in this sequence: interest, periods, 0 to indicate no intermediate cash flows, and then the PV. The data can be entered as fixed numbers or as cell references.

Excel Approach: Fixed inputs: Cell references:

N I/YR PV PMT 3 5 !$100.00 $0

FV $115.76

$115.76=FV(0.05,3,0,!100) = =FV(C15,C16,0,C14) = $115.76

FVN = $100(1.05)3

FVN = FVN =

Summary of Future Value CalculationsT a b l e 5 - 1

HINTS ON USING FINANCIAL CALCULATORS

When using a fi nancial calculator, make sure your machine is set up as indicated here. Refer to your calculator manual or to our calculator tutorial on the text’s web site for information on set- ting up your calculator.

• One payment per period. Many calculators “come out of the box” assuming that 12 payments are made per year; that is, they assume monthly payments. However, in this book, we generally deal with problems in which only one payment is made each year. Therefore, you should set your calculator at one payment per year and leave it there. See our tutorial or your calculator manual if you need assistance.

• End mode. With most contracts, payments are made at the end of each period. However, some contracts call for payments at the beginning of each period. You can switch between “End Mode” and “Begin Mode” depending on the problem you are solving. Because most of the prob- lems in this book call for end-of-period payments, you should return your calculator to End Mode after you work a problem where payments are made at the beginning of periods.

• Negative sign for outfl ows. Outfl ows must be entered as negative numbers. This generally means typing the outfl ow as a positive number and then pressing the #/$ key to convert from # to $ before hitting the enter key.

• Decimal places. With most calculators, you can specify from 0 to 11 decimal places. When work- ing with dollars, we generally specify two decimal places. When dealing with interest rates, we generally specify two places when the rate is expressed as a percentage (e.g., 5.25%), but we spec- ify four places when the rate is expressed as a decimal (e.g., 0.0525).

• Interest rates. For arithmetic operations with a nonfi nancial calculator, the 0.0525 must be used; but with a fi nancial calculator, you must enter 5.25, not .0525, because fi nancial calcu- lators assume that rates are stated as percentages.

130 Part 2 Fundamental Concepts in Financial Management

5-2e Graphic View of the Compounding Process Figure 5-1 shows how a $1 investment grows over time at different interest rates. We made the curves by solving Equation 5-1 with different values for N and I. The interest rate is a growth rate: If a sum is deposited and earns 5% interest per year, the funds on deposit will grow by 5% per year. Note also that time value concepts can be applied to anything that grows—sales, population, earnings per share, or future salary.

Future Value of $1

8 9 106 74 521 30

1.00

2.00

3.00

4.00

5.00

6.00

I = 0%

I = 5%

I = 10%

I = 20%

Periods

Growth of $1 at Various Interest Rates and Time PeriodsFIGURE 5-1

Explain why this statement is true: A dollar in hand today is worth more than a dollar to be received next year.

What is compounding? What’s the diff erence between simple interest and compound interest? What would the future value of $100 be after 5 years at 10% compound interest? at 10% simple interest? ($161.05; $150.00)

Suppose you currently have $2,000 and plan to purchase a 3-year certifi cate of deposit (CD) that pays 4% interest compounded annually. How much will you have when the CD matures? How would your answer change if the inter- est rate were 5% or 6% or 20%? ($2,249.73; $2,315.25; $2,382.03; $3,456.00) (Hint: With a calculator, enter N = 3, I/YR = 4, PV = #2000, and PMT = 0; then press FV to get 2,249.73. Enter I/YR = 5 to override the 4% and press FV again to get the second answer. In general, you can change one input at a time to see how the output changes.)

A company’s sales in 2008 were $100 million. If sales grow at 8%, what will they be 10 years later, in 2018? ($215.89 million)

How much would $1, growing at 5% per year, be worth after 100 years? What would FV be if the growth rate was 10%? ($131.50; $13,780.61)

SEL F TEST

131Chapter 5 Time Value of Money

5-3 PRESENT VALUES Finding a present value is the reverse of fi nding a future value. Indeed, we simply solve Equation 5-1, the formula for the future value, for the PV to produce the basic present value equation, 5-2:

Future value = FVN = PV(1 + I) N 5-1

Present value = PV = FV N ______ (1 + I) N 5-2

We illustrate PVs with the following example. A broker offers to sell you a Treasury bond that will pay $115.76 3 years from now. Banks are currently offer- ing a guaranteed 5% interest on 3-year certifi cates of deposit (CDs); and if you don’t buy the bond, you will buy a CD. The 5% rate paid on the CDs is defi ned as your opportunity cost, or the rate of return you could earn on an alternative invest- ment of similar risk. Given these conditions, what’s the most you should pay for the bond? We answer this question using the four methods discussed in the last section—step-by-step, formula, calculator, and spreadsheet. Table 5-2 summarizes the results.

First, recall from the future value example in the last section that if you in- vested $100 at 5%, it would grow to $115.76 in 3 years. You would also have $115.76 after 3 years if you bought the T-bond. Therefore, the most you should pay for the bond is $100—this is its “fair price.” If you could buy the bond for less than $100, you should buy it rather than invest in the CD. Conversely, if its price was more than $100, you should buy the CD. If the bond’s price was exactly $100, you should be indifferent between the T-bond and the CD.

The $100 is defi ned as the present value, or PV, of $115.76 due in 3 years when the appropriate interest rate is 5%. In general, the present value of a cash fl ow due N years in the future is the amount which, if it were on hand today, would grow to equal the given future amount. Because $100 would grow to $115.76 in 3 years at a 5% interest rate, $100 is the present value of $115.76 due in 3 years at a 5% rate. Finding pres- ent values is called discounting; and as noted above, it is the reverse of compound- ing—if you know the PV, you can compound to fi nd the FV, while if you know the FV, you can discount to fi nd the PV.

Opportunity Cost The rate of return you could earn on an alternative investment of similar risk.

Discounting The process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding.

$115.76

A B C D E F G 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

Future payment Interest rate No. of periods

= = =

= $115.76 5.00%

CFN I N

Periods:

Cash Flow Time Line:

PV = ?

$100.00 $105.00 $110.25Step-by-Step Approach:

$115.76

1 2 3

$100.00Formula Approach: PV = FVN/(1 " I)N

Calculator Approach:

In the Excel formula, 0 indicates that there are no intermediate cash flows.

Excel Approach: Fixed inputs: Cell references:

N I/YR PV PMT 3 5

!$100.00

$0 FV

$115.76

!$100.00=PV(0.05,3,0,115.76) = =PV(C65,C66,0,C64) = !$100.00

PV = $115.76/(1.05)3

PV = PV =

Summary of Present Value CalculationsT a b l e 5 - 2

132 Part 2 Fundamental Concepts in Financial Management

The top section of Table 5-2 calculates the PV using the step-by-step approach. When we found the future value in the previous section, we worked from left to right, multiplying the initial amount and each subsequent amount by (1 # I). To fi nd present values, we work backward, or from right to left, dividing the future value and each subsequent amount by (1 # I). This procedure shows exactly what’s happening, which can be quite useful when you are working complex problems. However, it’s ineffi cient, especially when you are dealing with a number of years.

With the formula approach, we use Equation 5-2, simply dividing the future value by (1 # I)N. This is more effi cient than the step-by-step approach, and it gives the same result. Equation 5-2 is built into fi nancial calculators; and as shown in Table 5-2, we can fi nd the PV by entering values for N, I/YR, PMT, and FV and then pressing the PV key. Finally, spreadsheets have a function that’s essentially the same as the calculator, which also solves Equation 5-2.

The fundamental goal of fi nancial management is to maximize the fi rm’s value, and the value of a business (or any asset, including stocks and bonds) is the present value of its expected future cash fl ows. Because present value lies at the heart of the valuation process, we will have much more to say about it in the re- mainder of this chapter and throughout the book.

5-3a Graphic View of the Discounting Process Figure 5-2 shows that the present value of a sum to be received in the future decreases and approaches zero as the payment date is extended further into the future and that the present value falls faster at higher interest rates. At relatively high rates, funds due in the future are worth very little today; and even at rela- tively low rates, present values of sums due in the very distant future are quite small. For example, at a 20% discount rate, $1 million due in 100 years would be worth only $0.0121 today. This is because $0.0121 would grow to $1 million in 100 years when compounded at 20%.

Present Value of $1

40 5020 3010

0.20

0.40

0.60

0.80

1.00

I = 20%

I = 10%

I = 5%

I = 0%

Periods

Present Value of $1 at Various Interest Rates and Time PeriodsFIGURE 5-2

133Chapter 5 Time Value of Money

5-4 FINDING THE INTEREST RATE, I Thus far we have used Equations 5-1 and 5-2 to fi nd future and present values. Those equations have four variables; and if we know three of the variables, we can solve for the fourth. Thus, if we know PV, I, and N, we can solve 5-1 for FV, while if we know FV, I, and N, we can solve 5-2 to fi nd PV. That’s what we did in the pre- ceding two sections.

Now suppose we know PV, FV, and N and we want to fi nd I. For example, suppose we know that a given bond has a cost of $100 and that it will return $150 after 10 years. Thus, we know PV, FV, and N; and we want to fi nd the rate of return we will earn if we buy the bond. Here’s the situation:

FV ! PV(1 " I)N $150 ! $100(1 " I)10 $150/$100 ! (1 " I)10 1.5 ! (1 " I)10

Unfortunately, we can’t factor I out to produce as simple a formula as we could for FV and PV—we can solve for I, but it requires a bit more algebra.4 However, fi nancial calculators and spreadsheets can fi nd interest rates almost instantly. Here’s the calculator setup:

FVPVI/YRN PMT

0 150–10010

4.14

Enter N ! 10, PV ! $100, PMT = 0 because there are no payments until the secu- rity matures, and FV ! 150. Then when you press the I/YR key, the calculator gives the answer, 4.14%. You would get this same answer with a spreadsheet.

SEL F TEST What is discounting, and how is it related to compounding? How is the

future value equation (5-1) related to the present value equation (5-2)?

How does the present value of a future payment change as the time to receipt is lengthened? as the interest rate increases?

Suppose a U.S. government bond promises to pay $2,249.73 three years from now. If the going interest rate on three-year government bonds is 4%, how much is the bond worth today? How would your answer change if the bond matured in 5 years rather than 3? What if the interest rate on the 5-year bond was 6% rather than 4%? ($2,000; $1,849.11; $1,681.13)

How much would $1,000,000 due in 100 years be worth today if the dis- count rate was 5%? if the discount rate was 20%? ($7,604.49; $0.0121)

4 Raise the left side of the equation, the 1.5, to the power 1/N ! 1/10 ! 0.1, getting 1.0414. That number is 1 plus the interest rate, so the interest rate is 0.0414 ! 4.14%.

134 Part 2 Fundamental Concepts in Financial Management

5-5 FINDING THE NUMBER OF YEARS, N We sometimes need to know how long it will take to accumulate a certain sum of money, given our beginning funds and the rate we will earn on those funds. For example, suppose we believe that we could retire comfortably if we had $1 mil- lion. We want to fi nd how long it will take us to acquire $1 million, assuming we now have $500,000 invested at 4.5%. We cannot use a simple formula—the situ- ation is like that with interest rates. We can set up a formula that uses logarithms, but calculators and spreadsheets fi nd N very quickly. Here’s the calculator setup:

FVPVI/YRN PMT

0 1000000–5000004.5

15.7473

Enter I/YR ! 4.5, PV ! $500000, PMT ! 0, and FV ! 1000000. Then when you press the N key, you get the answer, 15.7473 years. If you plug N ! 15.7473 into the FV formula, you can prove that this is indeed the correct number of years:

FV ! PV(1 " I)N ! $500,000(1.045)15.7473 ! $1,000,000

You would also get N ! 15.7473 with a spreadsheet.

SEL F TEST The U.S. Treasury off ers to sell you a bond for $585.43. No payments will be

made until the bond matures 10 years from now, at which time it will be re- deemed for $1,000. What interest rate would you earn if you bought this bond for $585.43? What rate would you earn if you could buy the bond for $550? for $600? (5.5%; 6.16%; 5.24%)

Microsoft earned $0.33 per share in 1997. Ten years later in 2007 it earned $1.42. What was the growth rate in Microsoft’s earnings per share (EPS) over the 10-year period? If EPS in 2007 had been $0.90 rather than $1.42, what would the growth rate have been? (15.71%; 10.55%)

SEL F TEST How long would it take $1,000 to double if it was invested in a bank that

paid 6% per year? How long would it take if the rate was 10%? (11.9 years; 7.27 years)

Microsoft’s 2007 earnings per share were $1.42, and its growth rate during the prior 10 years was 15.71% per year. If that growth rate was maintained, how long would it take for Microsoft’s EPS to double? (4.75 years)

5-6 ANNUITIES Thus far we have dealt with single payments, or “lump sums.” However, many assets provide a series of cash infl ows over time; and many obligations, such as auto, student, and mortgage loans, require a series of payments. When the pay- ments are equal and are made at fi xed intervals, the series is an annuity. For exam- ple, $100 paid at the end of each of the next 3 years is a 3-year annuity. If the pay- ments occur at the end of each year, the annuity is an ordinary (or deferred)

Annuity A series of equal payments at fixed intervals for a specified number of periods.

135Chapter 5 Time Value of Money

annuity. If the payments are made at the beginning of each year, the annuity is an annuity due. Ordinary annuities are more common in fi nance; so when we use the term annuity in this book, assume that the payments occur at the ends of the peri- ods unless otherwise noted.

Here are the time lines for a $100, 3-year, 5% ordinary annuity and for the same annuity on an annuity due basis. With the annuity due, each payment is shifted to the left by one year. A $100 deposit will be made each year, so we show the pay- ments with minus signs:

Ordinary Annuity: Periods

Payments !$100 !$100 !$100

0 15% 2 3

Annuity Due: Periods

Payments !$100 !$100 !$100

0 15% 2 3

As we demonstrate in the following sections, we can fi nd an annuity’s future and present values, the interest rate built into annuity contracts, and the length of time it takes to reach a fi nancial goal using an annuity. Keep in mind that annuities must have constant payments and a fi xed number of periods. If these conditions don’t hold, we don’t have an annuity.

Ordinary (Deferred) Annuity An annuity whose payments occur at the end of each period.

Annuity Due An annuity whose payments occur at the beginning of each period.

Ordinary (Deferred) Annuity An annuity whose payments occur at the end of each period.

Annuity Due An annuity whose payments occur at the beginning of each period.

SEL F TEST What’s the diff erence between an ordinary annuity and an annuity due?

Why would you prefer to receive an annuity due for $10,000 per year for 10 years than an otherwise similar ordinary annuity?

5-7 FUTURE VALUE OF AN ORDINARY ANNUITY The future value of an annuity can be found using the step-by-step approach or using a formula, a fi nancial calculator, or a spreadsheet. As an illustration, con- sider the ordinary annuity diagrammed earlier, where you deposit $100 at the end of each year for 3 years and earn 5% per year. How much will you have at the end of the third year? The answer, $315.25, is defi ned as the future value of the annuity, FVAN ; it is shown in Table 5-3.

As shown in the step-by-step section of the table, we compound each payment out to Time 3, then sum those compounded values to fi nd the annuity’s FV, FVA3 ! $315.25. The fi rst payment earns interest for two periods, the second payment earns interest for one period, and the third payment earns no interest at all because it is made at the end of the annuity’s life. This approach is straightforward; but if the annuity extends out for many years, the approach is cumbersome and time-consuming.

As you can see from the time line diagram, with the step-by-step approach, we apply the following equation, with N ! 3 and I ! 5%:

FVAN ! PMT(1 " I) N#1 " PMT(1 " I)N#2 " PMT(1 " I)N#3

! $100(1.05)2 " $100(1.05)1 " $100(1.05)0 ! $315.25

FVAN The future value of an annuity over N periods.

136 Part 2 Fundamental Concepts in Financial Management

A B C D E F G 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155

Payment amount Interest rate No. of periods

= = =

$100.00 5.00%

PMT I N

Periods:

Cash Flow Time Line:

!$100 !$100 !$100

!$100.00 !$105.00 !$110.25 !$315.25

Step-by-Step Approach. Multiply each payment by (1"I)N!t and sum these FVs to find FVAN:

1 2 3

$315.25 Formula Approach:

FVAN = PMT # ! "

Calculator Approach:

Excel entries correspond with these calculator keys:

Excel Function Approach: Fixed inputs: Cell references:

N I/YR PV PMT 3 5 $0 !$100.00

FV $315.25

$315.25=FV(0.05,3,!100,0) = =FV(C132,C133,!C131,0) = $315.25

I/YR N PMT PV FV

FVAN = FVAN =

=!1 " I" N ! 1 I

Summary: Future Value of an Ordinary AnnuityT a b l e 5 - 3

We can generalize and streamline the equation as follows:

FVAN ! PMT(1 " I) N#1 " PMT(1 " I)N#2

" PMT(1 " I)N#3 " . . . " PMT(1 " I)0

5-3 ! PMT # (1 " I)N # 1 __________ I $ The fi rst line shows the equation in its long form. It can be transformed to the sec- ond form, which can be used to solve annuity problems with a nonfi nancial calcu- lator.5 This equation is also built into fi nancial calculators and spreadsheets. With an annuity, we have recurring payments; hence, the PMT key is used. Here’s the calculator setup for our illustrative annuity:

FVPVI/YRN PMT

–100 End Mode053

315.25

We enter PV ! 0 because we start off with nothing, and we enter PMT ! $100 because we plan to deposit this amount in the account at the end of each year. When we press the FV key, we get the answer, FVA3 ! 315.25.

Because this is an ordinary annuity, with payments coming at the end of each year, we must set the calculator appropriately. As noted earlier, calculators “come out of the box” set to assume that payments occur at the end of each period, that is, to deal with ordinary annuities. However, there is a key that enables us to switch between ordinary annuities and annuities due. For ordinary annuities, the desig- nation is “End Mode” or something similar, while for annuities due, the designator

5 The long form of the equation is a geometric progression that can be reduced to the second form.

137Chapter 5 Time Value of Money

is “Begin” or “Begin Mode” or “Due” or something similar. If you make a mistake and set your calculator on Begin Mode when working with an ordinary annuity, each payment will earn interest for one extra year. That will cause the compounded amounts, and thus the FVA, to be too large.

The last approach in Table 5-3 shows the spreadsheet solution using Excel’s built-in function. We can put in fi xed values for N, I, and PMT or set up an Input Section, where we assign values to those variables, and then input values into the function as cell references. Using cell references makes it easy to change the inputs to see the effects of changes on the output.

SEL F TEST For an ordinary annuity with fi ve annual payments of $100 and a 10% inter-

est rate, how many years will the fi rst payment earn interest? What will this payment’s value be at the end? Answer this same question for the fi fth pay- ment. (4 years, $146.41; 0 years, $100)

Assume that you plan to buy a condo 5 years from now, and you estimate that you can save $2,500 per year. You plan to deposit the money in a bank that pays 4% interest, and you will make the fi rst deposit at the end of the year. How much will you have after 5 years? How will your answer change if the interest rate is increased to 6% or lowered to 3%? ($13,540.81; $14,092.73; $13,272.84)

5-8 FUTURE VALUE OF AN ANNUITY DUE Because each payment occurs one period earlier with an annuity due, all of the payments earn interest for one additional period. Therefore, the FV of an annuity due will be greater than that of a similar ordinary annuity. If you went through the step-by-step procedure, you would see that our illustrative annuity due has an FV of $331.01 versus $315.25 for the ordinary annuity.

With the formula approach, we fi rst use Equation 5-3; but since each payment occurs one period earlier, we multiply the Equation 5-3 result by (1 # I):

FVAdue ! FVAordinary(1 " I) 5-4

Thus, for the annuity due, FVAdue = $315.25(1.05) = $331.01, which is the same result when the period-by-period approach is used. With a calculator, we input the variables just as we did with the ordinary annuity; but now we set the calculator to Begin Mode to get the answer, $331.01.

SEL F TEST Why does an annuity due always have a higher future value than an ordinary

annuity?

If you calculated the value of an ordinary annuity, how could you fi nd the value of the corresponding annuity due?

Assume that you plan to buy a condo 5 years from now and you need to save for a down payment. You plan to save $2,500 per year (with the fi rst deposit made immediately), and you will deposit the funds in a bank account that pays 4% interest. How much will you have after 5 years? How much will you have if you make the deposits at the end of each year? ($14,082.44; $13,540.81)

138 Part 2 Fundamental Concepts in Financial Management

5-9 PRESENT VALUE OF AN ORDINARY ANNUITY The present value of an annuity, PVAN, can be found using the step-by-step, for- mula, calculator, or spreadsheet method. Look back at Table 5-3. To fi nd the FV of the annuity, we compounded the deposits. To fi nd the PV, we discount them, dividing each payment by (1 + I). The step-by-step procedure is diagrammed as follows:

210 5%Periods

Payments

!$100 !$100 !$100

$ 95.24 $ 90.70 $ 86.38 $272.32 = Present value of the annuity (PVAN)

Equation 5-5 expresses the step-by-step procedure in a formula. The bracketed form of the equation can be used with a scientifi c calculator, and it is helpful if the annuity extends out for a number of years:

PVAN ! PMT/(1 " I) 1 " PMT/(1 " I)2 " . . . " PMT/(1 " I)N

5-5 ! PMT # 1 # 1 _______ (1 " I)N __________ I $ ! $100 $ [1 # 1/(1.05)3]/0.05 ! $272.32

Calculators are programmed to solve Equation 5-5; so we merely input the vari- ables and press the PV key, making sure the calculator is set to End Mode. The cal- culator setup follows for both an ordinary annuity and an annuity due. Note that the PV of the annuity due is larger because each payment is discounted back one less year. Note too that you can fi nd the PV of the ordinary annuity and then multiply by (1 # I) ! 1.05, getting $272.32(1.05) ! $285.94, the PV of the annuity due.

FVPVI/YRN PMT

–100 0 End Mode (Ordinary Annuity)

272.32

FVPVI/YRN PMT

–100 0 Begin Mode (Annuity Due)

285.94

PVAN The present value of an annuity of N periods.

139Chapter 5 Time Value of Money

5-10 FINDING ANNUITY PAYMENTS, PERIODS, AND INTEREST RATES

We can fi nd payments, periods, and interest rates for annuities. Here fi ve variables come into play: N, I, PMT, FV, and PV. If we know any four, we can fi nd the fi fth.

5-10a Finding Annuity Payments, PMT Suppose we need to accumulate $10,000 and have it available 5 years from now. Suppose further that we can earn a return of 6% on our savings, which are cur- rently zero. Thus, we know that FV ! 10,000, PV ! 0, N ! 5, and I/YR ! 6. We can enter these values in a fi nancial calculator and press the PMT key to fi nd how large our deposits must be. The answer will, of course, depend on whether we make deposits at the end of each year (ordinary annuity) or at the beginning (annuity due). Here are the results for each type of annuity:

FVPVI/YRN PMT

100000 End Mode (Ordinary Annuity)

–1,773.96

FVPVI/YRN PMT

100000 Begin Mode (Annuity Due)

–1,673.55

Thus, you must save $1,773.96 per year if you make payments at the end of each year, but only $1,673.55 if the payments begin immediately. Note that the required payment for the annuity due is the ordinary annuity payment divided by (1 # I): $1,773.96/1.06 ! $1,673.55. Spreadsheets can also be used to fi nd annuity payments.

5-10b Finding the Number of Periods, N Suppose you decide to make end-of-year deposits, but you can save only $1,200 per year. Again assuming that you would earn 6%, how long would it take to reach your $10,000 goal? Here is the calculator setup:

SEL F TEST Compared to an ordinary annuity, why does an annuity due have a higher

present value?

If you know the present value of an ordinary annuity, how can you fi nd the PV of the corresponding annuity due?

What is the PVA of an ordinary annuity with 10 payments of $100 if the appropriate interest rate is 10%? What would the PVA be if the interest rate was 4%? What if the interest rate was 0%? How would the PVA values diff er if we were dealing with annuities due? ($614.46; $811.09; $1,000.00; $675.90; $843.53; $1,000.00)

Assume that you are off ered an annuity that pays $100 at the end of each year for 10 years. You could earn 8% on your money in other investments with equal risk. What is the most you should pay for the annuity? If the payments began immediately, how much would the annuity be worth? ($671.01; $724.69)

140 Part 2 Fundamental Concepts in Financial Management

FVPVI/YRN PMT

10000–12000 End Mode6

6.96

With these smaller deposits, it would take 6.96 years to reach the $10,000 target. If you began the deposits immediately, you would have an annuity due and N would be a bit less, 6.63 years.

5-10c Finding the Interest Rate, I Now suppose you can save only $1,200 annually, but you still want to have the $10,000 in 5 years. What rate of return would enable you to achieve your goal? Here is the calculator setup:

FVPVI/YRN PMT

10000–12000 End Mode5

25.78

You would need to earn a whopping 25.78%. About the only way to earn such a high return would be to invest in speculative stocks or head to the casinos in Las Vegas. Of course, investing in speculative stocks and gambling aren’t like making deposits in a bank with a guaranteed rate of return, so there’s a good chance you’d end up with nothing. You might consider changing your plans—save more, lower your $10,000 target, or extend your time horizon. It might be appropriate to seek a somewhat higher return, but trying to earn 25.78% in a 6% market would require taking on more risk than would be prudent.

It’s easy to fi nd rates of return using a fi nancial calculator or a spreadsheet. However, without one of these tools, you would have to go through a trial-and- error process, which would be very time-consuming if many years were involved.

SEL F TEST Suppose you inherited $100,000 and invested it at 7% per year. How much

could you withdraw at the end of each of the next 10 years? How would your answer change if you made withdrawals at the beginning of each year? ($14,237.75; $13,306.31)

If you had $100,000 that was invested at 7% and you wanted to withdraw $10,000 at the end of each year, how long would your funds last? How long would they last if you earned 0%? How long would they last if you earned the 7% but limited your withdrawal to $7,000 per year? (17.8 years; 10 years; forever)

Your rich uncle named you benefi ciary of his life insurance policy. The insur- ance company gives you a choice of $100,000 today or a 12-year annuity of $12,000 at the end of each year. What rate of return is the insurance company off ering? (6.11%)

Assume that you just inherited an annuity that will pay you $10,000 per year for 10 years, with the fi rst payment being made today. A friend of your mother of- fers to give you $60,000 for the annuity. If you sell it, what rate of return would your mother’s friend earn on his investment? If you think a “fair” return would be 6%, how much should you ask for the annuity? (13.70%; $78,016.92)

141Chapter 5 Time Value of Money

5-11 PERPETUITIES In the last section, we dealt with annuities whose payments continue for a specifi c number of periods—for example, $100 per year for 10 years. However, some secu- rities promise to make payments forever. For example, in 1749, the British govern- ment issued bonds whose proceeds were used to pay off other British bonds; and since this action consolidated the government’s debt, the new bonds were called consols. Because consols promise to pay interest forever, they are “perpetuities.” The interest rate on the consols was 2.5%, so a bond with a face value of $1,000 would pay $25 per year in perpetuity.6

A perpetuity is simply an annuity with an extended life. Because the pay- ments go on forever, you can’t apply the step-by-step approach. However, it’s easy to fi nd the PV of a perpetuity with a formula found by solving Equation 5-5 with N set at infi nity:7

PV of a perpetuity ! PMT ____ I 5-6

Now we can use Equation 5-6 to fi nd the value of a British consol with a face value of $1,000 that pays $25 per year in perpetuity. The answer depends on the interest rate. In 1888, the “going rate” as established in the fi nancial marketplace was 2.5%; so at that time, the consol’s value was $1,000:

Consol value1888 ! $25/0.025 ! $1,000

In 2008, 120 years later, the annual payment was still $25, but the going interest rate had risen to 4.3%, causing the consol’s value to fall to $581.40:

Consol value2008 ! $25/0.043 ! $581.40

Note, though, that if interest rates decline in the future (say, to 2%), the value of the consol will rise:

Consol value if rates decline to 2% ! $25/0.02 ! $1,250.00

These examples demonstrate an important point: When interest rates change, the prices of outstanding bonds also change. Bond prices decline when rates rise and increase when rates fall. We will discuss this point in more detail in Chapter 7, where we cover bonds in depth.

Figure 5-3 gives a graphic picture of how much each payment contributes to the value of an annuity. Here we analyze an annuity that pays $100 per year when the market interest rate is 10%. We found the PV of each payment for the fi rst 100 years and graphed those PVs. We also found the value of the annuity with a 25-year, 50-year, 100-year, and infi nite life. Here are some points to note: 1. The value of an ordinary annuity is the sum of the present values of its

payments. 2. We can construct graphs for annuities of any length—for 3 years or 25 years or

50 years or any other period. The fewer the years, the fewer the bars in the graph. 3. As the years increase, the PV of each additional payment—which represents

the amount the payment contributes to the annuity’s value—decreases. This occurs because each payment is divided by (1 + I)t, and that term increases exponentially with t. Indeed, in our graph, the payments after 62 years are too small to be noticed.

Consol A perpetual bond issued by the British government to consolidate past debts; in general, any perpetual bond.

Perpetuity A stream of equal payments at fixed intervals expected to continue forever.

6 The consols actually pay interest in pounds, but we discuss them in dollar terms for simplicity. 7 Equation 5-6 was found by letting N in Equation 5-5 approach infi nity. The result is Equation 5-6.

142 Part 2 Fundamental Concepts in Financial Management

4. The data to the right of the graph show the value of a $100 annuity when the interest rate is 10% and the annuity lasts for 25, 50, and 100 years and forever. The difference between these values shows how much the additional years contribute to the annuity’s value. The payments for distant years are worth very little today, so the value of the annuity is determined largely by the pay- ments to be received in the near term. Note, though, that the discount rate affects the values of distant cash fl ows and thus the graph. The higher the dis- count rate, the steeper the decline and thus the smaller the values of the dis- tant fl ows.

Figure 5-3 highlights some important implications for fi nancial issues. For ex- ample, if you win a $10 million lottery that pays $500,000 per year for 20 years be- ginning immediately, the lottery is really worth much less than $10 million. Each cash fl ow must be discounted, and the sum of the cash fl ows is much less than $10 million. At a 10% discount rate, the “$10 million” is worth only $4,682,460; and that’s before taxes. Not bad, but not $10 million.

81 9171615141312111 Years

PV of Each $100 Payment; Addition to Annuity’s Value

$50

$0 1

$100

Bars indicate PV of each payment. Sum of PVs from 0 to N = Value of the Annuity

Value of 25-Year Annuity: $907.70 Value of 50-Year Annuity: $991.48 Value of 100-Year Annuity: $999.93 Value of Perpetuity: $1,000.00

Contribution of Payments to Value of $100 Annuity at 10% Interest RateFIGURE 5-3

SEL F TEST What’s the present value of a perpetuity that pays $1,000 per year beginning one

year from now if the appropriate interest rate is 5%? What would the value be if payments on the annuity began immediately? ($20,000, $21,000. Hint: Just add the $1,000 to be received immediately to the value of the annuity.)

Would distant payments contribute more to the value of an annuity if interest rates were high or low? (Hint: When answering conceptual questions, it often helps to make up an example and use it to formulate your answer. PV of $100 at 5% after 25 years ! $29.53; PV at 20% ! $1.05. So distant pay- ments contribute more at low rates.)

143Chapter 5 Time Value of Money

5-12 UNEVEN CASH FLOWS The defi nition of an annuity includes the words constant payment—in other words, annuities involve payments that are equal in every period. Although many fi nancial decisions involve constant payments, many others involve uneven, or nonconstant, cash fl ows. For example, the dividends on common stocks typically increase over time, and investments in capital equipment almost always generate uneven cash fl ows. Throughout the book, we reserve the term payment (PMT) for annuities with their equal payments in each period and use the term cash fl ow (CFt) to denote uneven cash fl ows, where t designates the period in which the cash fl ow occurs.

There are two important classes of uneven cash fl ows: (1) a stream that con- sists of a series of annuity payments plus an additional fi nal lump sum and (2) all other uneven streams. Bonds represent the best example of the fi rst type, while stocks and capital investments illustrate the second type. Here are numerical ex- amples of the two types of fl ows:

4210 I = 12%Periods

Cash flows

3 5

$0 $100 $100$100$100 $ 100 $ 1,000 $1,100

1. Annuity plus additional final payment:

4210 I = 12%Periods

Cash flows

3 5

$0 $100 $300$300$300 $500

2. Irregular cash flows:

We can fi nd the PV of either stream by using Equation 5-7 and following the step- by-step procedure, where we discount each cash fl ow and then sum them to fi nd the PV of the stream:

PV ! CF1 ______ (1 # I)1 #

CF2 ______ (1 # I)2 # . . . #

CFN _______ (1 # I)N ! ∑ t!1 N

CFt ______ (1 # I)t 5-7

If we did this, we would fi nd the PV of Stream 1 to be $927.90 and the PV of Stream 2 to be $1,016.35.

The step-by-step procedure is straightforward; but if we have a large number of cash fl ows, it is time-consuming. However, fi nancial calculators speed up the process considerably. First, consider Stream 1; notice that we have a 5-year, 12% or- dinary annuity plus a fi nal payment of $1,000. We could fi nd the PV of the annuity, then fi nd the PV of the fi nal payment and sum them to obtain the PV of the stream. Financial calculators do this in one simple step—use the fi ve TVM keys, enter the data as shown below, and press the PV key to obtain the answer, $927.90.

FVPVI/YRN PMT

10001005 12

–927.90

The solution procedure is different for the second uneven stream. Here we must use the step-by-step approach as shown in Figure 5-4. Even calculators and spreadsheets solve the problem using the step-by-step procedure, but they do it

Payment (PMT) This term designates equal cash flows coming at regular intervals.

Uneven (Nonconstant) Cash Flows A series of cash flows where the amount varies from one period to the next.

Cash Flow (CFt) This term designates a cash flow that’s not part of an annuity.

144 Part 2 Fundamental Concepts in Financial Management

quickly and effi ciently. First, you enter all of the cash fl ows and the interest rate; then the calculator or computer discounts each cash fl ow to fi nd its present value and sums these PVs to produce the PV of the stream. You must enter the cash fl ows in the calculator’s “cash fl ow register,” enter the interest rate, and then press the NPV key to fi nd the PV of the stream. NPV stands for “net present value.” We cover the calculator mechanics in the tutorial, and we discuss the process in more detail in Chapters 9 and 11, where we use the NPV calculation to analyze stocks and proposed capital budgeting projects. If you don’t know how to do the calculation with your calculator, it would be worthwhile to go to the tutorial or your calculator manual, learn the steps, and make sure you can do this calculation. Since you will have to learn to do it eventually, now is a good time to begin.

$ 89.29 $ 239.16 $ 213.53 $ 190.66 $ 283.71 $1,016.35 = PV of cash flow stream = Value of the asset

4210 I = 12%Periods

Cash flows PV of CFs

3 5

$0 $100 $300$300$300 $500

PV of an Uneven Cash Flow StreamFIGURE 5-4

SEL F TEST How could you use Equation 5-2 to fi nd the PV of an uneven stream of cash

fl ows?

What’s the present value of a 5-year ordinary annuity of $100 plus an addi- tional $500 at the end of Year 5 if the interest rate is 6%? What is the PV if the $100 payments occur in Years 1 through 10 and the $500 comes at the end of Year 10? ($794.87; $1,015.21)

What’s the present value of the following uneven cash fl ow stream: $0 at Time 0, $100 in Year 1 (or at Time 1), $200 in Year 2, $0 in Year 3, and $400 in Year 4 if the interest rate is 8%? ($558.07)

Would a typical common stock provide cash fl ows more like an annuity or more like an uneven cash fl ow stream? Explain.

5-13 FUTURE VALUE OF AN UNEVEN CASH FLOW STREAM We fi nd the future value of uneven cash fl ow streams by compounding rather than discounting. Consider Cash Flow Stream 2 in the preceding section. We discounted those cash fl ows to fi nd the PV, but we would compound them to fi nd the FV. Figure 5-5 illustrates the procedure for fi nding the FV of the stream using the step- by-step approach.

145Chapter 5 Time Value of Money

The values of all fi nancial assets—stocks, bonds, and business capital invest- ments—are found as the present values of their expected future cash fl ows. There- fore, we need to calculate present values very often, far more often than future val- ues. As a result, all fi nancial calculators provide automated functions for fi nding PVs, but they generally do not provide automated FV functions. On the relatively few occasions when we need to fi nd the FV of an uneven cash fl ow stream, we gen- erally use the step-by-step procedure shown in Figure 5-5. That approach works for all cash fl ow streams, even those for which some cash fl ows are zero or negative.

$ 500.00 $ 336.00 $ 376.32 $ 421.48 $ 157.35 $ 0.00 $1,791.15

4210 I = 12%Periods

Cash flows

3 5

$0 $100 $300$300$300 $500

FV of an Uneven Cash Flow StreamFIGURE 5-5 SEL

F TEST Why are we more likely to need to calculate the PV of cash fl ow streams than the FV of streams?

What is the future value of this cash fl ow stream: $100 at the end of 1 year, $150 due after 2 years, and $300 due after 3 years if the appropriate interest rate is 15%? ($604.75)

5-14 SOLVING FOR I WITH UNEVEN CASH FLOWS8 Before fi nancial calculators and spreadsheets existed, it was extremely diffi cult to fi nd I when the cash fl ows were uneven. With spreadsheets and fi nancial calcula- tors, though, it’s relatively easy to fi nd I. If you have an annuity plus a fi nal lump sum, you can input values for N, PV, PMT, and FV into the calculator’s TVM regis- ters and then press the I/YR key. Here is the setup for Stream 1 from Section 5-12, assuming we must pay $927.90 to buy the asset. The rate of return on the $927.90 investment is 12%.

FVPVI/YRN PMT

1000100–927.905

12.00

8 This section is relatively technical. It can be deferred at this point, but the calculations will be required in Chapter 11.

146 Part 2 Fundamental Concepts in Financial Management

Finding the interest rate for an uneven cash fl ow stream such as Stream 2 is a bit more complicated. First, note that there is no simple procedure—fi nding the rate requires a trial-and-error process, which means that a fi nancial calculator or a spreadsheet is needed. With a calculator, we enter the CFs into the cash fl ow regis- ter and then press the IRR key to get the answer. IRR stands for “internal rate of re- turn,” and it is the rate of return the investment provides. The investment is the cash fl ow at Time 0, and it must be entered as a negative. As an illustration, con- sider the cash fl ows given here, where CF0 ! $$1,000 is the cost of the asset.

4210Periods

Cash flows

3 5

!$1,000

IRR $ I $ 12.55%

$100 $300$300$300 $500

When we enter those cash fl ows into the calculator’s cash fl ow register and press the IRR key, we get the rate of return on the $1,000 investment, 12.55%. You get the same answer using Excel’s IRR function. The process is covered in the calculator tutorial; it is also discussed in Chapter 11, where we study capital budgeting.

SEL F TEST An investment costs $465 and is expected to produce cash fl ows of $100 at

the end of each of the next 4 years, then an extra lump sum payment of $200 at the end of the fourth year. What is the expected rate of return on this in- vestment? (9.05%)

An investment costs $465 and is expected to produce cash fl ows of $100 at the end of Year 1, $200 at the end of Year 2, and $300 at the end of Year 3. What is the expected rate of return on this investment? (11.71%)

5-15 SEMIANNUAL AND OTHER COMPOUNDING PERIODS In all of our examples thus far, we assumed that interest was compounded once a year, or annually. This is called annual compounding. Suppose, however, that you deposit $100 in a bank that pays a 5% annual interest rate but credits interest each 6 months. So in the second 6-month period, you earn interest on your original $100 plus interest on the interest earned during the fi rst 6 months. This is called semiannual compounding. Note that banks generally pay interest more than once a year; virtually all bonds pay interest semiannually; and most mortgages, student loans, and auto loans require monthly payments. Therefore, it is important to understand how to deal with nonannual compounding.

For an illustration of semiannual compounding, assume that we deposit $100 in an account that pays 5% and leave it there for 10 years. First, consider again what the future value would be under annual compounding:

FVN ! PV(1 " I) N ! $100(1.05)10 ! $162.89

We would, of course, get the same answer using a fi nancial calculator or a spreadsheet.

How would things change in this example if interest was paid semiannually rather than annually? First, whenever payments occur more than once a year, you must make two conversions: (1) Convert the stated interest rate into a “periodic rate” and (2) convert the number of years into “number of periods.” The

Semiannual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added twice a year.

Annual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added once a year.

147Chapter 5 Time Value of Money

conversions are done as follows, where I is the stated annual rate, M is the number of compounding periods per year, and N is the number of years:

Periodic rate (IPER) ! Stated annual rate __________________________ Number of payments per year ! I/M 5-8

With a stated annual rate of 5% compounded semiannually, the periodic rate is 2.5%:

Periodic rate ! 5%/2 ! 2.5%

The number of compounding periods per year is found with Equation 5-9:

Number of periods ! (Number of years)(Periods per year) ! NM 5-9

With 10 years and semiannual compounding, there are 20 periods:

Number of periods ! 10(2) ! 20 periods

Under semiannual compounding, our $100 investment will earn 2.5% every 6 months for 20 semiannual periods, not 5% per year for 10 years. The periodic rate and number of periods, not the annual rate and number of years, must be shown on time lines and entered into the calculator or spreadsheet whenever you are working with nonannual compounding.9

With this background, we can fi nd the value of $100 after 10 years if it is held in an account that pays a stated annual rate of 5.0% but with semiannual com- pounding. Here’s the time line and the future value:

19210Periods

Cash flows

I = 2.5% 20

!$100 PV (1 + I)N = $100(1.025)20 = FV20 = $163.86

With a fi nancial calculator, we get the same result using the periodic rate and num- ber of periods:

FVPVI/YRN PMT

0–1002.520

163.86

The future value under semiannual compounding, $163.86, exceeds the FV under annual compounding, $162.89, because interest starts accruing sooner; thus, you earn more interest on interest.

How would things change in our example if interest was compounded quarterly or monthly or daily? With quarterly compounding, there would be NM ! 10(4) ! 40 periods and the periodic rate would be I/M ! 5%/4 ! 1.25% per quarter. Using those values, we would fi nd FV ! $164.36. If we used monthly compounding, we would have 10(12) ! 120 periods, the monthly rate would be 5%/12 ! 0.416667%, and the FV would rise to $164.70. If we went to daily compounding, we would have 10(365) ! 3,650 periods, the daily rate would be 5%/365 ! 0.0136986% per day, and the FV would be $164.87 (based on a 365-day year).

9 With some fi nancial calculators, you can enter the annual (nominal) rate and the number of compounding peri- ods per year rather than make the conversions we recommend. We prefer the conversions because they must be used on time lines and because it is easy to forget to reset your calculator after you change its settings, which may lead to an error on your next problem.

148 Part 2 Fundamental Concepts in Financial Management

The same logic applies when we fi nd present values under semiannual compounding. Again, we use Equation 5-8 to convert the stated annual rate to the periodic (semiannual) rate and Equation 5-9 to fi nd the number of semiannual pe- riods. We then use the periodic rate and number of periods in the calculations. For example, we can fi nd the PV of $100 due after 10 years when the stated annual rate is 5%, with semiannual compounding:

Periodic rate ! 5%/2 ! 2.5% per period Number of periods ! 10(2) ! 20 periods PV of $100 ! $100/(1.025)20 ! $61.03

We would get this same result with a fi nancial calculator:

FVPVI/YRN PMT

0 –1002.520

61.03

If we increased the number of compounding periods from 2 (semiannual) to 12 (monthly), the PV would decline to $60.72; and if we went to daily compounding, the PV would fall to $60.66.

5-16 COMPARING INTEREST RATES Different compounding periods are used for different types of investments. For example, bank accounts generally pay interest daily; most bonds pay interest semiannually; stocks pay dividends quarterly; and mortgages, auto loans, and other instruments require monthly payments.10 If we are to compare investments or loans with different compounding periods properly, we need to put them on a common basis. Here are some terms you need to understand: • The nominal interest rate (INOM), also called the annual percentage rate (APR)

(or quoted or stated rate), is the rate that credit card companies, student loan offi cers, auto dealers, and so forth, tell you they are charging on loans. Note that if two banks offer loans with a stated rate of 8% but one requires monthly payments and the other quarterly payments, they are not charging the same “true” rate—the one that requires monthly payments is charging more than

Nominal (Quoted, or Stated) Interest Rate, INOM The contracted (or quoted or stated) interest rate.

Annual Percentage Rate (APR) The periodic rate times the number of periods per year.

SEL F TEST Would you rather invest in an account that pays 7% with annual compound-

ing or 7% with monthly compounding? Would you rather borrow at 7% and make annual or monthly payments? Why?

What’s the future value of $100 after 3 years if the appropriate interest rate is 8% compounded annually? compounded monthly? ($125.97; $127.02)

What’s the present value of $100 due in 3 years if the appropriate interest rate is 8% compounded annually? compounded monthly? ($79.38; $78.73)

10 Some banks even pay interest compounded continuously. Continuous compounding is discussed in Web Appendix 5A.

149Chapter 5 Time Value of Money

the one with quarterly payments because it will get your money sooner. So to compare loans across lenders, or interest rates earned on different securities, you should calculate effective annual rates as described here.11

• The effective annual rate, abbreviated EFF%, is also called the equivalent annual rate (EAR). This is the rate that would produce the same future value under annual compounding as would more frequent compounding at a given nominal rate.

• If a loan or an investment uses annual compounding, its nominal rate is also its effective rate. However, if compounding occurs more than once a year, the EFF% is higher than INOM.

• To illustrate, a nominal rate of 10% with semiannual compounding is equiva- lent to a rate of 10.25% with annual compounding because both rates will cause $100 to grow to the same amount after 1 year. The top line in the follow- ing diagram shows that $100 will grow to $110.25 at a nominal rate of 10.25%. The lower line shows the situation if the nominal rate is 10% but semiannual compounding is used.

0 Nom = EFF% = 10.25% 1

$100.00 $110.25

0 Nom = 10.00% semi; EFF% = 10.25% 1 2

$100.00 $105 $110.25

Given the nominal rate and the number of compounding periods per year, we can fi nd the effective annual rate with this equation:

Effective annual rate (EFF%) ! ( 1 " INOM ____ M ) M # 1.0 5-10 Here INOM is the nominal rate expressed as a decimal and M is the number of compounding periods per year. In our example, the nominal rate is 10%; but with semiannual compounding, INOM ! 10% ! 0.10 and M ! 2. This results in EFF% ! 10.25%:12

Eff ective annual rate (EFF%) ! ( 1 " 0.10 ____ 2 ) 2 # 1 ! 0.1025 ! 10.25% Thus, if one investment promises to pay 10% with semiannual compounding and an equally risky investment promises 10.25% with annual compounding, we would be indifferent between the two.

Effective (Equivalent) Annual Rate (EFF% or EAR) The annual rate of interest actually being earned, as opposed to the quoted rate. Also called the “equivalent annual rate.”

11 Note, though, that if you are comparing two bonds that both pay interest semiannually, it’s OK to compare their nominal rates. Similarly, you can compare the nominal rates on two money funds that pay interest daily. But don’t compare the nominal rate on a semiannual bond with the nominal rate on a money fund that compounds daily because that will make the money fund look worse than it really is. 12 Most fi nancial calculators are programmed to fi nd the EFF% or, given the EFF%, to fi nd the nominal rate. This is called interest rate conversion. You enter the nominal rate and the number of compounding periods per year and then press the EFF% key to fi nd the eff ective annual rate. However, we generally use Equation 5-10 because it’s as easy to use as the interest conversion feature and the equation reminds us of what we are really doing. If you use the interest rate conversion feature on your calculator, don’t forget to reset your calculator settings. Inter- est rate conversion is discussed in the calculator tutorials. Interest rate conversion is also very easy using Excel. For details, look at the spreadsheet model that accompanies this chapter.

150 Part 2 Fundamental Concepts in Financial Management

5-17 FRACTIONAL TIME PERIODS Thus far we have assumed that payments occur at the beginning or the end of periods but not within periods. However, we often encounter situations that require compound- ing or discounting over fractional periods. For example, suppose you deposited $100 in a bank that pays a nominal rate of 10% but adds interest daily, based on a 365-day year. How much would you have after 9 months? The answer is $107.79, found as follows:13

Periodic rate ! IPER ! 0.10/365 ! 0.000273973 per day Number of days ! (9/12)(365) ! 0.75(365) ! 273.75 rounded to 274 Ending amount ! $100(1.000273973)274 ! $107.79

Now suppose you borrow $100 from a bank whose nominal rate is 10% per year simple interest, which means that interest is not earned on interest. If the loan is outstanding for 274 days, how much interest would you have to pay? Here we would calculate a daily interest rate, IPER, as just shown, but multiply it by 274 rather than use the 274 as an exponent:

Interest owed ! $100(0.000273973)(274) ! $7.51

You would owe the bank a total of $107.51 after 274 days. This is the procedure that most banks use to calculate interest on loans, except that they require borrow- ers to pay the interest on a monthly basis rather than after 274 days.

SEL F TEST Defi ne the terms annual percentage rate (APR), eff ective annual rate (EFF%),

and nominal interest rate (INOM ).

A bank pays 5% with daily compounding on its savings accounts. Should it advertise the nominal or eff ective rate if it is seeking to attract new deposits?

By law, credit card issuers must print their annual percentage rate on their monthly statements. A common APR is 18% with interest paid monthly. What is the EFF% on such a loan? [EFF% ! (1 " 0.18/12)12 # 1 ! 0.1956 ! 19.56%]

Some years ago banks didn’t have to reveal the rates they charged on credit cards. Then Congress passed the Truth in Lending Act that required banks to publish their APRs. Is the APR really the “most truthful” rate, or would the EFF% be “more truthful”? Explain.

13 Bank loan contracts specifi cally state whether they are based on a 360- or a 365-day year. If a 360-day year is used, the daily rate is higher, which means that the eff ective rate is also higher. Here we assumed a 365-day year. Also note that in real-world calculations, banks’ computers have built-in calendars. So they can calculate the exact number of days, taking account of 30-day, 31-day, and 28- or 29-day months.

SEL F TEST Suppose a company borrowed $1 million at a rate of 9%, simple interest, with

interest paid at the end of each month. The bank uses a 360-day year. How much interest would the fi rm have to pay in a 30-day month? What would the interest be if the bank used a 365-day year? [(0.09/360)(30)($1,000,000) ! $7,500 interest for the month. For the 365-day year, (0.09/365)(30) ($1,000,000) ! $7,397.26 of interest. The use of a 360-day year raises the interest cost by $102.74, which is why banks like to use it on loans.]

Suppose you deposited $1,000 in a credit union that pays 7% with daily com- pounding and a 365-day year. What is the EFF%, and how much could you withdraw after seven months, assuming this is seven-twelfths of a year? [EFF% ! (1 " 0.07/365)365 # 1 ! 0.07250098 ! 7.250098%. Thus, your account would grow from $1,000 to $1,000(1.07250098)0.583333 ! $1,041.67, and you could withdraw that amount.]

151Chapter 5 Time Value of Money

5-18 AMORTIZED LOANS14 An important application of compound interest involves loans that are paid off in installments over time. Included are automobile loans, home mortgage loans, stu- dent loans, and many business loans. A loan that is to be repaid in equal amounts on a monthly, quarterly, or annual basis is called an amortized loan.15

Table 5-4 illustrates the amortization process. A homeowner borrows $100,000 on a mortgage loan, and the loan is to be repaid in fi ve equal payments at the end of each of the next 5 years.16 The lender charges 6% on the balance at the beginning of each year.

Our fi rst task is to determine the payment the homeowner must make each year. Here’s a picture of the situation:

0 I = 6% 3 4

PMTPMTPMTPMTPMT$100,000

521

The payments must be such that the sum of their PVs equals $100,000:

$100,000 ! PMT ______ (1.06)1 " PMT ______ (1.06)2 "

PMT ______ (1.06)3 " PMT ______ (1.06)4 "

PMT ______ (1.06)5 ! ∑ t ! 1 5

PMT ______ (1.06)t

We could insert values into a calculator as follows to get the required payments, $23,739.64:17

FVPVI/YRN PMT

100000 065

–23,739.64

Amortized Loan A loan that is repaid in equal payments over its life.

14 Amortized loans are important, but this section can be omitted without loss of continuity. 15 The word amortized comes from the Latin mors, meaning “death”; so an amortized loan is one that is “killed off ”

over time. 16 Most mortgage loans call for monthly payments over 10 to 30 years, but we use a shorter period to reduce the

calculations. 17 You could also factor out the PMT term; fi nd the value of the remaining summation term (4.212364); and divide

it into the $100,000 to fi nd the payment, $23,739.64.

Amount borrowed: $100,000 Years: 5 Rate: 6% PMT: $$23,739.64

Year

Beginning Amount

(1) Payment

(2) Interesta

(3)

Repayment of Principalb

(4)

Ending Balance

(5) 1 $100,000.00 $23,739.64 $6,000.00 $17,739.64 $82,260.36 2 82,260.36 23,739.64 4,935.62 18,804.02 63,456.34 3 63,456.34 23,739.64 3,807.38 19,932.26 43,524.08 4 43,524.08 23,739.64 2,611.44 21,128.20 22,395.89 5 22,395.89 23,739.64 1,343.75 22,395.89 0.00

a Interest in each period is calculated by multiplying the loan balance at the beginning of the year by the interest rate. Therefore, interest in Year 1 is $100,000.00(0.06) ! $6,000; in Year 2, it is $4,935.62; and so forth.

bRepayment of principal is equal to the payment of $23,739.64 minus the interest charge for the year.

Loan Amortization Schedule, $100,000 at 6% for 5 YearsT a b l e 5 - 4

152 Part 2 Fundamental Concepts in Financial Management

Therefore, the borrower must pay the lender $23,739.64 per year for the next 5 years.

Each payment will consist of two parts—interest and repayment of principal. This breakdown is shown on an amortization schedule such as the one in Table 5-4. The interest component is relatively high in the fi rst year, but it declines as the loan balance decreases. For tax purposes, the borrower would deduct the interest com- ponent while the lender would report the same amount as taxable income.

Amortization Schedule A table showing precisely how a loan will be repaid. It gives the required payment on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment of principal.

SEL F TEST Suppose you borrowed $30,000 on a student loan at a rate of 8% and must

repay it in three equal installments at the end of each of the next 3 years. How large would your payments be, how much of the fi rst payment would represent interest, how much would be principal, and what would your end- ing balance be after the fi rst year? (PMT ! $11,641.01; Interest ! $2,400; Principal ! $9,241.01; Balance at end of Year 1 ! $20,758.99)

In this chapter, we worked with single payments, ordinary annuities, annuities due, perpetuities, and uneven cash fl ow streams. One fundamental equation, Equa- tion 5-1, is used to calculate the future value of a given amount. The equation can be transformed to Equation 5-2 and then used to fi nd the present value of a given future amount. We used time lines to show when cash fl ows occur; and we saw that time value problems can be solved in a step-by-step manner when we work with individ- ual cash fl ows, with formulas that streamline the approach, with fi nancial calcula- tors, and with spreadsheets.

As we noted at the outset, TVM is the single most important concept in fi nance and the procedures developed in Chapter 5 are used throughout this book. Time value analysis is used to fi nd the values of stocks, bonds, and capital budgeting proj- ects. It is also used to analyze personal fi nance problems, such as the retirement issue set forth in the opening vignette. You will become more familiar with time value analysis as you go through the book, but we strongly recommend that you get a good handle on Chapter 5 before you continue.

KEY TERMS Define each of the following terms: a. Time line b. FVN ; PV; I; INT; N; FVAN ; PMT; PVAN c. Compounding; discounting d. Simple interest; compound interest e. Opportunity cost f. Annuity; ordinary (deferred) annuity; annuity due g. Consol; perpetuity

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

T YING I T ALL TO GETHER

153Chapter 5 Time Value of Money

h. Uneven cash flow; payment; cash flow (CFt) i. Annual compounding; semiannual compounding j. Nominal (quoted) interest rate; annual percentage rate (APR); effective (equivalent)

annual rate (EAR or EFF%) k. Amortized loan; amortization schedule

FUTURE VALUE It is now January 1, 2009. Today you will deposit $1,000 into a savings account that pays 8%. a. If the bank compounds interest annually, how much will you have in your account on

January 1, 2012? b. What will your January 1, 2012, balance be if the bank uses quarterly compounding? c. Suppose you deposit $1,000 in three payments of $333.333 each on January 1 of 2010,

2011, and 2012. How much will you have in your account on January 1, 2012, based on 8% annual compounding?

d. How much will be in your account if the three payments begin on January 1, 2009? e. Suppose you deposit three equal payments into your account on January 1 of 2010,

2011, and 2012. Assuming an 8% interest rate, how large must your payments be to have the same ending balance as in Part a?

TIME VALUE OF MONEY It is now January 1, 2009; and you will need $1,000 on January 1, 2013, in 4 years. Your bank compounds interest at an 8% annual rate. a. How much must you deposit today to have a balance of $1,000 on January 1, 2013? b. If you want to make four equal payments on each January 1 from 2010 through 2013

to accumulate the $1,000, how large must each payment be? (Note that the payments begin a year from today.)

c. If your father offers to make the payments calculated in Part b ($221.92) or to give you $750 on January 1, 2010 (a year from today), which would you choose? Explain.

d. If you have only $750 on January 1, 2010, what interest rate, compounded annually for 3 years, must you earn to have $1,000 on January 1, 2013?

e. Suppose you can deposit only $200 each January 1 from 2010 through 2013 (4 years). What interest rate, with annual compounding, must you earn to end up with $1,000 on January 1, 2013?

f. Your father offers to give you $400 on January 1, 2010. You will then make six addi- tional equal payments each 6 months from July 2010 through January 2013. If your bank pays 8% compounded semiannually, how large must each payment be for you to end up with $1,000 on January 1, 2013?

g. What is the EAR, or EFF%, earned on the bank account in Part f? What is the APR earned on the account?

EFFECTIVE ANNUAL RATES Bank A offers loans at an 8% nominal rate (its APR) but requires that interest be paid quarterly; that is, it uses quarterly compounding. Bank B wants to charge the same effective rate on its loans but it wants to collect interest on a monthly basis, that is, use monthly compounding. What nominal rate must Bank B set?

What is an opportunity cost? How is this concept used in TVM analysis, and where is it shown on a time line? Is a single number used in all situations? Explain.

Explain whether the following statement is true or false: $100 a year for 10 years is an an- nuity; but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not consti- tute an annuity. However, the second series contains an annuity.

If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain. (Hint: If you aren’t sure, plug in some numbers and check it out.)

Would you rather have a savings account that pays 5% interest compounded semiannu- ally or one that pays 5% interest compounded daily? Explain.

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To find the present value of an uneven series of cash flows, you must find the PVs of the individual cash flows and then sum them. Annuity procedures can never be of use, even when some of the cash flows constitute an annuity because the entire series is not an annuity. True or false? Explain.

The present value of a perpetuity is equal to the payment on the annuity, PMT, divided by the interest rate, I: PV ! PMT/I. What is the future value of a perpetuity of PMT dollars per year? (Hint: The answer is infinity, but explain why.)

Banks and other lenders are required to disclose a rate called the APR. What is this rate? Why did Congress require that it be disclosed? Is it the same as the effective annual rate? If you were comparing the costs of loans from different lenders, could you use their APRs to determine the loan with the lowest effective interest rate? Explain.

What is a loan amortization schedule, and what are some ways these schedules are used?

FUTURE VALUE If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?

PRESENT VALUE What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?

FINDING THE REQUIRED INTEREST RATE Your parents will retire in 18 years. They cur- rently have $250,000, and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?

TIME FOR A LUMP SUM TO DOUBLE If you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money?

TIME TO REACH A FINANCIAL GOAL You have $42,180.53 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $250,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal?

FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE What’s the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this was an annuity due, what would its fu- ture value be?

PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 8% annually, what is its present value? its future value?

LOAN AMORTIZATION AND EAR You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized over 5 years (60 months), and the nominal inter- est rate will be 12% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR?

PRESENT AND FUTURE VALUES FOR DIFFERENT PERIODS Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. a. An initial $500 compounded for 1 year at 6% b. An initial $500 compounded for 2 years at 6% c. The present value of $500 due in 1 year at a discount rate of 6% d. The present value of $500 due in 2 years at a discount rate of 6%

PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST RATES Find the following val- ues. Compounding/discounting occurs annually. a. An initial $500 compounded for 10 years at 6% b. An initial $500 compounded for 10 years at 12% c. The present value of $500 due in 10 years at 6% d. The present value of $1,552.90 due in 10 years at 12% and at 6% e. Define present value and illustrate it using a time line with data from Part d. How are

present values affected by interest rates?

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GROWTH RATES Shalit Corporation’s 2008 sales were $12 million. Its 2003 sales were $6 million. a. At what rate have sales been growing? b. Suppose someone made this statement: “Sales doubled in 5 years. This represents a

growth of 100% in 5 years; so dividing 100% by 5, we find the growth rate to be 20% per year.” Is that statement correct?

EFFECTIVE RATE OF INTEREST Find the interest rates earned on each of the following: a. You borrow $700 and promise to pay back $749 at the end of 1 year. b. You lend $700 and the borrower promises to pay you $749 at the end of 1 year. c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years. d. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each year

for 5 years.

TIME FOR A LUMP SUM TO DOUBLE How long will it take $200 to double if it earns the following rates? Compounding occurs once a year. a. 7% b. 10% c. 18% d. 100%

FUTURE VALUE OF AN ANNUITY Find the future values of these ordinary annuities. Compounding occurs once a year. a. $400 per year for 10 years at 10% b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0% d. Rework Parts a, b, and c assuming they are annuities due.

PRESENT VALUE OF AN ANNUITY Find the present values of these ordinary annuities. Discounting occurs once a year. a. $400 per year for 10 years at 10% b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0% d. Rework Parts a, b, and c assuming they are annuities due.

PRESENT VALUE OF A PERPETUITY What is the present value of a $100 perpetuity if the interest rate is 7%? If interest rates doubled to 14%, what would its present value be?

EFFECTIVE INTEREST RATE You borrow $85,000; the annual loan payments are $8,273.59 for 30 years. What interest rate are you being charged?

UNEVEN CASH FLOW STREAM a. Find the present values of the following cash flow streams at 8% compounded

annually.

0 2 3

$300 $100

$400 $400

$100 $300

$0 $0

Stream A Stream B

4 51

b. What are the PVs of the streams at 0% compounded annually?

FUTURE VALUE OF AN ANNUITY Your client is 40 years old; and she wants to begin sav- ing for retirement, with the first payment to come one year from now. She can save $5,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future. a. If she follows your advice, how much money will she have at 65? b. How much will she have at 70? c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If

her investments continue to earn the same rate, how much will she be able to with- draw at the end of each year after retirement at each retirement age?

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PV OF A CASH FLOW STREAM A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:

1 2 3

$3,000,000 $5,000,000 $1,000,000

$3,000,000 $4,000,000 $1,000,000

$3,000,000 $3,000,000 $1,000,000

$3,000,000 $2,000,000 $7,000,000

Contract 1 Contract 2 Contract 3

As his adviser, which contract would you recommend that he accept?

EVALUATING LUMP SUMS AND ANNUITIES Crissie just won the lottery, and she must choose between three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million. a. If she thinks she can earn 7% annually, which should she choose? b. If she expects to earn 8% annually, which is the best choice? c. If she expects to earn 9% annually, which option would you recommend? d. Explain how interest rates influence the optimal choice.

LOAN AMORTIZATION Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year. a. What is the dollar amount of each payment Jan receives? b. How much interest was included in the first payment? How much repayment of prin-

cipal was included? How do these values change for the second payment? c. How much interest must Jan report on Schedule B for the first year? Will her interest

income be the same next year? d. If the payments are constant, why does the amount of interest income change over time?

FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount to which $500 will grow under each of these conditions: a. 12% compounded annually for 5 years b. 12% compounded semiannually for 5 years c. 12% compounded quarterly for 5 years d. 12% compounded monthly for 5 years e. 12% compounded daily for 5 years f. Why does the observed pattern of FVs occur?

PRESENT VALUE FOR VARIOUS DISCOUNTING PERIODS Find the present value of $500 due in the future under each of these conditions: a. 12% nominal rate, semiannual compounding, discounted back 5 years b. 12% nominal rate, quarterly compounding, discounted back 5 years c. 12% nominal rate, monthly compounding, discounted back 1 year d. Why do the differences in the PVs occur?

FUTURE VALUE OF AN ANNUITY Find the future values of the following ordinary annuities: a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded

semiannually b. FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded

quarterly c. These annuities receive the same amount of cash during the 5-year period and earn

interest at the same nominal rate, yet the annuity in Part b ends up larger than the one in Part a. Why does this occur?

PV AND LOAN ELIGIBILITY You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $350. The loan will have a 12% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? for 60 months?

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157Chapter 5 Time Value of Money

EFFECTIVE VERSUS NOMINAL INTEREST RATES Bank A pays 4% interest compounded annually on deposits, while Bank B pays 3.5% compounded daily. a. Based on the EAR (or EFF%), which bank should you use? b. Could your choice of banks be influenced by the fact that you might want to with-

draw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest.

NOMINAL INTEREST RATE AND EXTENDING CREDIT As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receiv- ables, you must borrow funds from your bank at a nominal 6%, monthly compounding. To offset your overhead, you want to charge your customers an EAR (or EFF%) that is 2% more than the bank is charging you. What APR rate should you charge your customers?

BUILDING CREDIT COST INTO PRICES Your firm sells for cash only; but it is thinking of offering credit, allowing customers 90 days to pay. Customers understand the time value of money, so they would all wait and pay on the 90th day. To carry these receivables, you would have to borrow funds from your bank at a nominal 12%, daily compounding based on a 360-day year. You want to increase your base prices by exactly enough to offset your bank interest cost. To the closest whole percentage point, by how much should you raise your product prices?

REACHING A FINANCIAL GOAL Erika and Kitty, who are twins, just received $30,000 each for their 25th birthday. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her “early retirement fund” on her birthday, begin- ning a year from today. Erika opened an account with the Safety First Bond Fund, a mu- tual fund that invests in high-quality bonds whose investors have earned 6% per year in the past. Kitty invested in the New Issue Bio-Tech Fund, which invests in small, newly is- sued bio-tech stocks and whose investors have earned an average of 20% per year in the fund’s relatively short history. a. If the two women’s funds earn the same returns in the future as in the past, how old

will each be when she becomes a millionaire? b. How large would Erika’s annual contributions have to be for her to become a million-

aire at the same age as Kitty, assuming their expected returns are realized? c. Is it rational or irrational for Erika to invest in the bond fund rather than in stocks?

REQUIRED LUMP SUM PAYMENT Starting next year, you will need $10,000 annually for 4 years to complete your education. (One year from today you will withdraw the first $10,000.) Your uncle deposits an amount today in a bank paying 5% annual interest, which will provide the needed $10,000 payments. a. How large must the deposit be? b. How much will be in the account immediately after you make the first withdrawal?

REACHING A FINANCIAL GOAL Six years from today you need $10,000. You plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays an 8% effective annual rate. Your last deposit, which will occur at the end of Year 6, will be for less than $1,500 if less is needed to reach $10,000. How large will your last payment be?

FV OF UNEVEN CASH FLOW You want to buy a house within 3 years, and you are cur- rently saving for the down payment. You plan to save $5,000 at the end of the first year, and you anticipate that your annual savings will increase by 10% annually thereafter. Your expected annual return is 7%. How much will you have for a down payment at the end of Year 3?

AMORTIZATION SCHEDULE a. Set up an amortization schedule for a $25,000 loan to be repaid in equal installments

at the end of each of the next 3 years. The interest rate is 10% compounded annually. b. What percentage of the payment represents interest and what percentage represents

principal for each of the 3 years? Why do these percentages change over time?

AMORTIZATION SCHEDULE WITH A BALLOON PAYMENT You want to buy a house that costs $100,000. You have $10,000 for a down payment, but your credit is such that mort- gage companies will not lend you the required $90,000. However, the realtor persuades the seller to take a $90,000 mortgage (called a seller take-back mortgage) at a rate of 7%, provided the loan is paid off in full in 3 years. You expect to inherit $100,000 in 3 years; but right now all you have is $10,000, and you can afford to make payments of no more

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158 Part 2 Fundamental Concepts in Financial Management

than $7,500 per year given your salary. (The loan would call for monthly payments, but assume end-of-year annual payments to simplify things.) a. If the loan was amortized over 3 years, how large would each annual payment be?

Could you afford those payments? b. If the loan was amortized over 30 years, what would each payment be? Could you

afford those payments? c. To satisfy the seller, the 30-year mortgage loan would be written as a balloon note,

which means that at the end of the third year, you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3, and what would the balloon payment be?

NONANNUAL COMPOUNDING a. You plan to make five deposits of $1,000 each, one every 6 months, with the first pay-

ment being made in 6 months. You will then make no more deposits. If the bank pays 4% nominal interest, compounded semiannually, how much will be in your account after 3 years?

b. One year from today you must make a payment of $10,000. To prepare for this payment, you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 4% nominal interest compounded quarterly. How large must each of the two payments be?

PAYING OFF CREDIT CARDS Simon recently received a credit card with an 18% nominal interest rate. With the card, he purchased a new stereo for $350. The minimum payment on the card is only $10 per month. a. If Simon makes the minimum monthly payment and makes no other charges, how

many months will it be before he pays off the card? Round to the nearest month. b. If Simon makes monthly payments of $30, how many months will it be before he pays

off the debt? Round to the nearest month. c. How much more in total payments will Simon make under the $10-a-month plan

than under the $30-a-month plan? Make sure you use three decimal places for N.

PV AND A LAWSUIT SETTLEMENT It is now December 31, 2008 (t = 0), and a jury just found in favor of a woman who sued the city for injuries sustained in a January 2007 accident. She requested recovery of lost wages plus $100,000 for pain and suffering plus $20,000 for legal expenses. Her doctor testified that she has been unable to work since the accident and that she will not be able to work in the future. She is now 62, and the jury decided that she would have worked for another 3 years. She was scheduled to have earned $34,000 in 2007. (To simplify this problem, assume that the entire annual salary amount would have been received on December 31, 2007.) Her employer testified that she probably would have received raises of 3% per year. The actual payment will be made on December 31, 2009. The judge stipulated that all dollar amounts are to be adjusted to a present value basis on December 31, 2009, using a 7% annual interest rate and using compound, not simple, interest. Furthermore, he stipulated that the pain and suffering and legal expenses should be based on a December, 31, 2008, date. How large a check must the city write on December 31, 2009?

REQUIRED ANNUITY PAYMENTS Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today. (The real value of his retirement income will decline annually after he retires.) His retire- ment income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 5%. He currently has $100,000 saved, and he expects to earn 8% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal?

REQUIRED ANNUITY PAYMENTS A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate in 4 years. Currently, the annual cost (for everything—food, clothing, tuition, books, transportation, and so forth) is $15,000, but these costs are expected to increase by 5% annually. The college requires that this amount be paid at the start of the year. She now has $7,500 in a college savings account that pays 6% annually. Her father will make six equal annual deposits into her account; the first deposit today and the sixth on the day she starts college. How large must each of the six payments be? [Hint: Calculate the cost (inflated at 5%) for each year of college and find the total present value of those costs, discounted at 6%, as of the day she enters college. Then find the compounded value of her initial $7,500 on that same day. The difference between the PV costs and the amount that would be in the savings account must be made up by the father’s deposits, so find the six equal payments (starting immediately) that will compound to the required amount.]

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TIME VALUE OF MONEY Answer the following questions: a. Assuming a rate of 10% annually, find the FV of $1,000 after 5 years. b. What is the investment’s FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years? c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5 years? e. Suppose California’s population is 30 million people and its population is expected to

grow by 2% annually. How long will it take for the population to double? f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the

interest rate is 15%. What is the annuity’s FV? g. How will the PV and FV of the annuity in (f) change if it is an annuity due? h. What will the FV and the PV be for $1,000 due in 5 years if the interest rate is 10%,

semiannual compounding? i. What will the annual payments be for an ordinary annuity for 10 years with a PV of

$1,000 if the interest rate is 8%? What will the payments be if this is an annuity due? j. Find the PV and the FV of an investment that pays 8% annually and makes the fol-

lowing end-of-year payments:

10 2 3

$400$200$100

k. Five banks offer nominal rates of 6% on deposits; but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily.

(1) What effective annual rate does each bank pay? If you deposit $5,000 in each bank today, how much will you have at the end of 1 year? 2 years?

(2) If all of the banks are insured by the government (the FDIC) and thus are equally risky, will they be equally able to attract funds? If not (and the TVM is the only consideration), what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A?

(3) Suppose you don’t have the $5,000 but need it at the end of 1 year. You plan to make a series of deposits—annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E—with payments beginning today. How large must the payments be to each bank?

(4) Even if the five banks provided the same effective annual rate, would a rational investor be indifferent between the banks? Explain.

l. Suppose you borrow $15,000. The loan’s annual interest rate is 8%, and it requires four equal end-of-year payments. Set up an amortization schedule that shows the annual pay- ments, interest payments, principal repayments, and beginning and ending loan balances.

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TIME VALUE OF MONEY ANALYSIS You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money analysis covering the following questions:

a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2; (2) an ordinary annuity of $100 per year for 3 years; and (3) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of Years 0 through 3.

b. (1) What’s the future value of $100 after 3 years if it earns 10%, annual compounding? (2) What’s the present value of $100 to be received in 3 years if the interest rate is 10%, annual compounding? c. What annual interest rate would cause $100 to grow to $125.97 in 3 years? d. If a company’s sales are growing at a rate of 20% annually, how long will it take sales to double?

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160 Part 2 Fundamental Concepts in Financial Management

e. What’s the difference between an ordinary annuity and an annuity due? What type of annuity is shown here? How would you change it to the other type of annuity?

0 1 2 3

0 $100$100$100

f. (1) What is the future value of a 3-year, $100 ordinary annuity if the annual interest rate is 10%? (2) What is its present value? (3) What would the future and present values be if it was an annuity due? g. A 5-year $100 ordinary annuity has an annual interest rate of 10%. (1) What is its present value? (2) What would the present value be if it was a 10-year annuity? (3) What would the present value be if it was a 25-year annuity? (4) What would the present value be if this was a perpetuity? h. A 20-year-old student wants to save $3 a day for her retirement. Every day she places $3 in a drawer. At the

end of each year, she invests the accumulated savings ($1,095) in a brokerage account with an expected an- nual return of 12%.

(1) If she keeps saving in this manner, how much will she have accumulated at age 65? (2) If a 40-year-old investor began saving in this manner, how much would he have at age 65? (3) How much would the 40-year-old investor have to save each year to accumulate the same amount at 65

as the 20-year-old investor? i. What is the present value of the following uneven cash flow stream? The annual interest rate is 10%.

0 1 2 3

0 !$50$300$300$100

4 Years

j. (1) Will the future value be larger or smaller if we compound an initial amount more often than annually (e.g., semiannually, holding the stated (nominal) rate constant)? Why?

(2) Define (a) the stated (or quoted or nominal) rate, (b) the periodic rate, and (c) the effective annual rate (EAR or EFF%).

(3) What is the EAR corresponding to a nominal rate of 10% compounded semiannually? compounded quarterly? compounded daily?

(4) What is the future value of $100 after 3 years under 10% semiannual compounding? quarterly compounding?

k. When will the EAR equal the nominal (quoted) rate? l. (1) What is the value at the end of Year 3 of the following cash flow stream if interest is 10% compounded

semiannually? (Hint: You can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually.)

0 2 4 6 Periods

$100$100$1000 (2) What is the PV? (3) What would be wrong with your answer to Parts l(1) and l(2) if you used the nominal rate, 10%, rather

than the EAR or the periodic rate, INOM/2 = 10%/2 = 5%, to solve the problems? m. (1) Construct an amortization schedule for a $1,000, 10% annual interest loan with three equal installments. (2) What is the annual interest expense for the borrower and the annual interest income for the lender

during Year 2?

FINANCIAL ASSETS

6 Interest Rates

7 Bonds and Their Valuation

8 Risk and Rates of Return

9 Stocks and Their Valuation

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TY IM

AG ES

The U.S. economy performed well from the early 1990s through 2007. Economic growth was posi- tive, unemployment was fairly low, and inflation remained under control. One reason for the economy’s good performance was the low level of interest rates over most of that period, with the rate on 10-year Treasury bonds generally at or below 5%, a level last seen in the 1960s, and rates on most other bonds correspondingly low. These low interest rates reduced the cost of capi- tal for businesses, which encouraged corporate investment. They also stimulated consumer spending and helped produce a massive growth in the housing market.

The drop in interest rates was due to a num- ber of factors—low inflation, foreign investors’ purchases of U.S. securities (which drove their rates down), and effective management of the economy by the Federal Reserve and other gov- ernment policy makers. However, some shocks hit the system in 2007, including $100 per barrel oil and massive write-offs by banks and other institutions that resulted from the subprime mort-

gage debacle. Higher oil prices and a weakening dollar could lead to higher inflation, which, in turn, would push interest rates up. Likewise, the growing federal budget deficit, combined with the weakening dollar, could cause foreigners to sell U.S. bonds, which would put more upward pressure on rates. At the same time, though, the economy seems to be weakening, which has led the Federal Reserve to lower its key short-term rate in hopes of staving off a general recession. So some forces are trying to drive rates higher, but other forces are operating to keep rates low.

Because corporations and individuals are greatly affected by interest rates, this chapter takes a closer look at the major factors that deter- mine those rates. As we will see, there is no single interest rate—various factors determine the rate that each borrower pays—and in some cases, rates on different types of debt move in different directions. For example, in the aftermath of the recent subprime mortgage crisis, investors rushed to put their money in liquid securities with little or no default risk. This “flight to quality”

Companies raise capital in two main forms: debt and equity. In a free economy, capi- tal, like other items, is allocated through a market system, where funds are trans- ferred and prices are established. The interest rate is the price that lenders receive and borrowers pay for debt capital. Similarly, equity investors expect to receive divi- dends and capital gains, the sum of which represents the cost of equity. We will take up the cost of equity in a later chapter, but our focus in this chapter is on the cost of debt. We begin by examining the factors that aff ect the supply of and demand for capital, which, in turn, aff ects the cost of money. We will see that there is no single interest rate—interest rates on diff erent types of debt vary depending on the bor- rower’s risk, the use of the funds borrowed, the type of collateral used to back the loan, and the length of time the money is needed. In this chapter, we concentrate mainly on how these various factors aff ect the cost of debt for individuals; but in later chapters, we delve into cost of debt for a business and its role in investment decisions. As you will see in Chapters 7 and 9, the cost of debt is a key determinant of bond and stock prices; it is also an important component of the cost of corporate capital, which we take up in Chapter 10.

When you fi nish this chapter, you should be able to: • List the various factors that infl uence the cost of money. • Discuss how market interest rates are aff ected by borrowers’ need for capital,

expected infl ation, diff erent securities’ risks, and securities’ liquidity. • Explain what the yield curve is, what determines its shape, and how you can use

the yield curve to help forecast future interest rates.

led to a decline in the rate the government had to pay when it borrowed. At the same time, investors demanded much higher rates from corporate borrowers—particularly those thought to be especially risky.

The subprime mortgage crisis demonstrates how major shocks to the economy can have profound effects on inter-

est rates in a wide number of markets, all of which are interconnected. Looking ahead, it will be interesting to see if interest rates can continue to remain low and if not, whether the economy can continue to perform as well as it has in the past.

PU T TING THINGS IN PER SPECTIVE

Chapter 6 Interest Rates 163

6-1 THE COST OF MONEY The four most fundamental factors affecting the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) infl ation. To see how these factors operate, visualize an isolated island community where people live on fi sh. They have a stock of fi shing gear that permits them to survive reasonably well, but they would like to have more fi sh. Now suppose one of the island’s inhabitants, Mr. Crusoe, had a bright idea for a new type of fi shnet that would enable him to double his daily catch. However, it would take him a year to perfect the design, build the net, and learn to use it effi ciently. Mr. Crusoe would probably starve before he could put his new net into operation. Therefore, he might suggest to Ms. Robinson, Mr. Friday, and several others that if they would give him one fi sh each day for a year, he would return two fi sh a day the next year. If someone accepted the offer, the fi sh that Ms. Robinson and the others gave

Production Opportunities The investment opportunities in productive (cash-generating) assets.

Time Preferences for Consumption The preferences of consumers for current consumption as opposed to saving for future consumption.

Production Opportunities The investment opportunities in productive (cash-generating) assets.

Time Preferences for Consumption The preferences of consumers for current consumption as opposed to saving for future consumption.

Risk In a financial market context, the chance that an investment will provide a low or negative return.

Inflation The amount by which prices increase over time.

Risk In a financial market context, the chance that an investment will provide a low or negative return.

Inflation The amount by which prices increase over time.

164 Part 3 Financial Assets

to Mr. Crusoe would constitute savings, these savings would be invested in the fi shnet, and the extra fi sh the net produced would constitute a return on the investment.

Obviously, the more productive Mr. Crusoe thought the new fi shnet would be, the more he could afford to offer potential investors for their savings. In this example, we assume that Mr. Crusoe thought he would be able to pay (and thus he offered) a 100% rate of return—he offered to give back two fi sh for every one he received. He might have tried to attract savings for less—for example, he might have offered only 1.5 fi sh per day next year for every one he received this year, which would represent a 50% rate of return to Ms. Robinson and the other potential savers.

How attractive Mr. Crusoe’s offer appeared to a potential saver would de- pend in large part on the saver’s time preference for consumption. For example, Ms. Robinson might be thinking of retirement, and she might be willing to trade fi sh today for fi sh in the future on a one-for-one basis. On the other hand, Mr. Friday might have a wife and several young children and need his current fi sh; so he might be unwilling to “lend” a fi sh today for anything less than three fi sh next year. Mr. Friday would be said to have a high time preference for current consumption; Ms. Robinson, a low time preference. Note also that if the entire population was living right at the subsistence level, time preferences for current consumption would necessarily be high, aggregate savings would be low, interest rates would be high, and capital formation would be diffi cult.

The risk inherent in the fi shnet project (and thus in Mr. Crusoe’s ability to repay the loan) also affects the return that investors require: The higher the per- ceived risk, the higher the required rate of return. Also, in a more complex society, there are many businesses like Mr. Crusoe’s, many goods other than fi sh, and many savers like Ms. Robinson and Mr. Friday. Therefore, people use money as a medium of exchange rather than barter with fi sh. When money is used, its value in the future, which is affected by infl ation, comes into play: The higher the ex- pected rate of infl ation, the larger the required dollar return. We discuss this point in detail later in the chapter.

Thus, we see that the interest rate paid to savers depends (1) on the rate of return that producers expect to earn on invested capital, (2) on savers’ time preferences for current versus future consumption, (3) on the riskiness of the loan, and (4) on the expected future rate of infl ation. Producers’ expected returns on their business investments set an upper limit to how much they can pay for savings, while consumers’ time prefer- ences for consumption establish how much consumption they are willing to defer and, hence, how much they will save at different interest rates.1 Higher risk and higher infl ation also lead to higher interest rates.

SEL F TEST What is the price paid to borrow debt capital called?

What are the two items whose sum is the cost of equity?

What four fundamental factors aff ect the cost of money?

1 The term producers is too narrow. A better word might be borrowers, which would include corporations, home purchasers, people borrowing to go to college, and even people borrowing to buy autos or to pay for vacations. Also, the wealth of a society and its demographics infl uence its people’s ability to save and thus their time prefer- ences for current versus future consumption.

165Chapter 6 Interest Rates

6-2 INTEREST RATE LEVELS Borrowers bid for the available supply of debt capital using interest rates: The fi rms with the most profi table investment opportunities are willing and able to pay the most for capital, so they tend to attract it away from ineffi cient fi rms and fi rms whose products are not in demand. Of course, the economy is not completely free in the sense of being infl uenced only by market forces. For example, the fed- eral government has agencies that help designated individuals or groups obtain credit on favorable terms. Among those eligible for this kind of assistance are small businesses, certain minorities, and fi rms willing to build plants in areas with high unemployment. Still, most capital in the United States is allocated through the price system, where the interest rate is the price.

Figure 6-1 shows how supply and demand interact to determine interest rates in two capital markets. Markets L and H represent two of the many capital mar- kets in existence. The supply curve in each market is upward-sloping, which indi- cates that investors are willing to supply more capital the higher the interest rate they receive on their capital. Likewise, the downward-sloping demand curve indi- cates that borrowers will borrow more if interest rates are lower. The interest rate in each market is the point where the supply and demand curves intersect. The going interest rate, designated as r, is initially 5% for the low-risk securities in Mar- ket L. Borrowers whose credit is strong enough to participate in this market can obtain funds at a cost of 5%, and investors who want to put their money to work without much risk can obtain a 5% return. Riskier borrowers must obtain higher- cost funds in Market H, where investors who are more willing to take risks expect to earn a 7% return but also realize that they might receive much less. In this sce- nario, investors are willing to accept the higher risk in Market H in exchange for a risk premium of 7% ! 5% " 2%.

Now let’s assume that because of changing market forces, investors perceive that Market H has become relatively more risky. This changing perception will in- duce many investors to shift toward safer investments—along the lines of the re- cent “fl ight to quality” discussed in the opening vignette to this chapter. As inves- tors move their money from Market H to Market L, this supply of funds is increased in Market L from S1 to S2; and the increased availability of capital will push down interest rates in this market from 5% to 4%. At the same time, as investors move their money out of Market H, there will be a decreased supply in that market; and tighter credit in that market will force interest rates up from 7% to 8%. In this new

Interest Rate, r (%)

rL = 5 4

Dollars0 0

Market L: Low-Risk Securities Market H: High-Risk Securities

S1 S2

Interest Rate, r (%)

rH = 7 8

Dollars

S2 S1

Interest Rates as a Function of Supply and Demand for FundsFIGURE 6-1

166 Part 3 Financial Assets

environment, money is transferred from Market H to Market L and the risk pre- mium rises from 2% to 8% ! 4% " 4%.

There are many capital markets in the United States, and Figure 6-1 highlights the fact that they are interconnected. U.S. fi rms also invest and raise capital throughout the world, and foreigners both borrow and lend in the United States. There are markets for home loans; farm loans; business loans; federal, state, and local government loans; and consumer loans. Within each category, there are re- gional markets as well as different types of submarkets. For example, in real estate, there are separate markets for fi rst and second mortgages and for loans on single- family homes, apartments, offi ce buildings, shopping centers, and vacant land. And, of course, there are separate markets for prime and subprime mortgage loans. Within the business sector, there are dozens of types of debt securities and there are several different markets for common stocks.

There is a price for each type of capital, and these prices change over time as supply and demand conditions change. Figure 6-2 shows how long- and short- term interest rates to business borrowers have varied since the early 1970s. Notice that short-term interest rates are especially volatile, rising rapidly during booms and falling equally rapidly during recessions. (The shaded areas of the chart indi- cate recessions.) When the economy is expanding, fi rms need capital; and this de- mand pushes rates up. Also, infl ationary pressures are strongest during business booms, also exerting upward pressure on rates. Conditions are reversed during recessions: Slack business reduces the demand for credit, infl ation falls, and the Federal Reserve increases the supply of funds to help stimulate the economy. The result is a decline in interest rates.

Interest Rate (%)

1971 1975 1979 1983 1987 1991 1995 1999 2003 2007

Years

Long-Term Rates

Short-Term Rates

Long- and Short-Term Interest Rates, 1971–2007FIGURE 6-2

Notes: a. The shaded areas designate business recessions. b. Short-term rates are measured by 3- to 6-month loans to very large, strong corporations; and long-term rates

are measured by AAA corporate bonds. Source: St. Louis Federal Reserve web site, FRED database, http://research.stlouisfed.org/fred2.

http://research.stlouisfed.org/fred2

167Chapter 6 Interest Rates

These tendencies do not hold exactly, as demonstrated by the period after 1984. Oil prices fell dramatically in 1985 and 1986, reducing infl ationary pressures on other prices and easing fears of serious long-term infl ation. Earlier these fears had pushed interest rates to record levels. The economy from 1984 to 1987 was strong, but the declining fears of infl ation more than offset the normal tendency for interest rates to rise during good economic times; the net result was lower interest rates.2

The relationship between infl ation and long-term interest rates is highlighted in Figure 6-3, which plots infl ation over time along with long-term interest rates. In the early 1960s, infl ation averaged 1% per year and interest rates on high-quality long-term bonds averaged 4%. Then the Vietnam War heated up, leading to an in- crease in infl ation; and interest rates began an upward climb. When the war ended in the early 1970s, infl ation dipped a bit; but then the 1973 Arab oil embargo led to rising oil prices, much higher infl ation rates, and sharply higher interest rates.

Infl ation peaked at about 13% in 1980. But interest rates continued to increase into 1981 and 1982, and they remained quite high until 1985 because people feared another increase in infl ation. Thus, the “infl ationary psychology” created during the 1970s persisted until the mid-1980s. People gradually realized that the Federal Reserve was serious about keeping infl ation down, that global competition was keeping U.S. auto producers and other corporations from raising prices as they had in the past, and that constraints on corporate price increases were diminishing

Long-Term Interest Rates

0 1972 1977 1982 1987 1992 1997 2007

Years 2002

Inflation

Interest Rate (%)

Relationship between Annual Inf lation Rates and Long-Term Interest Rates, 1972–2007FIGURE 6-3

Notes: a. Interest rates are rates on AAA long-term corporate bonds. b. Infl ation is measured as the annual rate of change in the consumer price index (CPI). Source: St. Louis Federal Reserve web site, FRED database, http://research.stlouisfed.org/fred2.

2 Short-term rates are responsive to current economic conditions, whereas long-term rates primarily refl ect long-run expectations for infl ation. As a result, short-term rates are sometimes above and sometimes below long-term rates. The relationship between long-term and short-term rates is called the term structure of interest rates, and it is discussed later in this chapter.

http://research.stlouisfed.org/fred2

168 Part 3 Financial Assets

labor unions’ ability to push through cost-increasing wage hikes. As these realiza- tions set in, interest rates declined.

The current interest rate minus the current infl ation rate (which is also the gap between the infl ation bars and the interest rate curve in Figure 6-3) is defi ned as the “current real rate of interest.” It is called a “real rate” because it shows how much investors really earned after the effects of infl ation were removed. The real rate was extremely high during the mid-1980s, but it has generally been in the range of 3% to 4% since 1987.

In recent years, infl ation has been about 2% a year. However, long-term interest rates have been volatile because investors are not sure if infl ation is truly under control or is about to jump back to the higher levels of the 1980s. In the years ahead, we can be sure of two things: (1) Interest rates will vary, and (2) they will increase if infl ation appears to be headed higher or decrease if infl ation is expected to decline. We don’t know where interest rates will go, but we do know they will vary.

SEL F TEST What role do interest rates play in allocating capital to diff erent potential

borrowers?

What happens to market-clearing, or equilibrium, interest rates in a capital market when the supply of funds declines? What happens when expected infl ation increases or decreases?

How does the price of capital tend to change during a boom? during a recession?

How does risk aff ect interest rates?

If infl ation during the last 12 months was 2% and the interest rate during that period was 5%, what was the real rate of interest? If infl ation is expected to average 4% during the next year and the real rate is 3%, what should the cur- rent rate of interest be? (3%; 7%)

6-3 THE DETERMINANTS OF MARKET INTEREST RATES In general, the quoted (or nominal) interest rate on a debt security, r, is composed of a real risk-free rate, r*, plus several premiums that refl ect infl ation, the security’s risk, its liquidity (or marketability), and the years to its maturity. This relationship can be expressed as follows:

6-1 Quoted interest rate ! r ! r* " IP " DRP " LP " MRP

3 The term nominal as it is used here means the stated rate as opposed to the real rate, where the real rate is adjusted to remove infl ation’s eff ects. If you had bought a 10-year Treasury bond in January 2008, the quoted, or nominal, rate would have been about 3.7%; but if infl ation averages 2.5% over the next 10 years, the real rate would turn out to be about 3.7% ! 2.5% " 1.2%.

Also note that in later chapters, when we discuss both debt and equity, we use the subscripts d and s to des- ignate returns on debt and stock, that is, rd and rs.

Here

r " the quoted, or nominal, rate of interest on a given security.3 r* " the real risk-free rate of interest. r* is pronounced “r-star,” and it is the rate

that would exist on a riskless security in a world where no infl ation was expected.

169Chapter 6 Interest Rates

Because rRF " r* # IP, we can rewrite Equation 6-1 as follows:

Nominal, or quoted, rate ! r ! rRF " DRP " LP " MRP

We discuss the components whose sum makes up the quoted, or nominal, rate on a given security in the following sections.

6-3a The Real Risk-Free Rate of Interest, r* The real risk-free rate of interest, r*, is the interest rate that would exist on a riskless security if no infl ation were expected. It may be thought of as the rate of interest on short-term U.S. Treasury securities in an infl ation-free world. The real risk-free rate is not static—it changes over time depending on economic condi- tions, especially on (1) the rate of return that corporations and other borrowers expect to earn on productive assets and (2) people’s time preferences for current versus future consumption. Borrowers’ expected returns on real assets set an upper limit on how much borrowers can afford to pay for funds, while savers’ time preferences for consumption establish how much consumption savers will defer—hence, the amount of money they will lend at different interest rates. It is diffi cult to measure the real risk-free rate precisely, but most experts think that r* has fl uctuated in the range of 1% to 5% in recent years.4 The best estimate of r* is the rate of return on indexed Treasury bonds, which are discussed later in the chapter.

Real Risk-Free Rate of Interest, r* The rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected.

4 The real rate of interest as discussed here is diff erent from the current real rate as discussed in connection with Figure 6-3. The current real rate is the current interest rate minus the current (or latest past) infl ation rate, while the real rate (without the word current) is the current interest rate minus the expected future infl ation rate over the life of the security. For example, suppose the current quoted rate for a one-year Treasury bill is 2.7%, infl ation dur- ing the latest year was 1.2%, and infl ation expected for the coming year is 2.2%. The current real rate would be 2.7% ! 1.2% " 1.5%, but the expected real rate would be 2.7% ! 2.2% " 0.5%. The rate on a 10-year bond would be related to the average expected infl ation rate over the next 10 years, and so on. In the press, the term real rate generally means the current real rate; but in economics and fi nance (hence, in this book unless otherwise noted), the real rate means the one based on expected infl ation rates.

rRF " r* # IP. It is the quoted rate on a risk-free security such as a U.S. Treasury bill, which is very liquid and is free of most types of risk. Note that the premium for expected infl ation, IP, is included in rRF .

IP " infl ation premium. IP is equal to the average expected rate of infl ation over the life of the security. The expected future infl ation rate is not neces- sarily equal to the current infl ation rate, so IP is not necessarily equal to current infl ation as shown in Figure 6-3.

DRP " default risk premium. This premium refl ects the possibility that the issuer will not pay the promised interest or principal at the stated time. DRP is zero for U.S. Treasury securities, but it rises as the riskiness of the issuer increases.

LP " liquidity (or marketability) premium. This is a premium charged by lend- ers to refl ect the fact that some securities cannot be converted to cash on short notice at a “reasonable” price. LP is very low for Treasury securities and for securities issued by large, strong fi rms; but it is relatively high on securities issued by small, privately held fi rms.

MRP " maturity risk premium. As we will explain later, longer-term bonds, even Treasury bonds, are exposed to a signifi cant risk of price declines due to increases in infl ation and interest rates; and a maturity risk premium is charged by lenders to refl ect this risk.

170 Part 3 Financial Assets

6-3b The Nominal, or Quoted, Risk-Free Rate of Interest, rRF ! r* " IP

The nominal, or quoted, risk-free rate, rRF , is the real risk-free rate plus a premium for expected infl ation: rRF " r* # IP. To be strictly correct, the risk-free rate should be the interest rate on a totally risk-free security—one that has no default risk, no maturity risk, no liquidity risk, no risk of loss if infl ation increases, and no risk of any other type. There is no such security; hence, there is no observable truly risk- free rate. However, one security is free of most risks—a Treasury Infl ation Pro- tected Security (TIPS), whose value increases with infl ation. TIPS are free of default, maturity, and liquidity risks and of risk due to changes in the general level of inter- est rates. However, they are not free of changes in the real rate.5

If the term risk-free rate is used without the modifi ers real or nominal, people generally mean the quoted (or nominal) rate; and we follow that convention in this book. Therefore, when we use the term risk-free rate, rRF , we mean the nominal risk- free rate, which includes an infl ation premium equal to the average expected infl a- tion rate over the remaining life of the security. In general, we use the T-bill rate to approximate the short-term risk-free rate and the T-bond rate to approximate the long-term risk-free rate. So whenever you see the term risk-free rate, assume that we are referring to the quoted U.S. T-bill rate or to the quoted T-bond rate.

6-3c Inflation Premium (IP) Infl ation has a major impact on interest rates because it erodes the real value of what you receive from the investment. To illustrate, suppose you saved $1,000 and invested it in a Treasury bill that pays a 3% interest rate and matures in one year. At the end of the year, you will receive $1,030—your original $1,000 plus $30 of interest. Now suppose the infl ation rate during the year turned out to be 3.5%, and it affected all goods equally. If heating oil had cost $1 per gallon at the beginning of the year, it would cost $1.035 at the end of the year. Therefore, your $1,000 would have bought $1,000/$1 " 1,000 gallons at the beginning of the year, but only $1,030/$1.035 " 995 gallons at the end. In real terms, you would be worse off—you would receive $30 of interest, but it would not be suffi cient to offset infl ation. You would thus be better off buying 1,000 gallons of heating oil (or some other storable asset such as land, timber, apartment buildings, wheat, or gold) than buying the Treasury bill.

Investors are well aware of all this; so when they lend money, they build an infl ation premium (IP) equal to the average expected infl ation rate over the life of the security into the rate they charge. As discussed previously, the actual interest rate on a short-term default-free U.S. Treasury bill, rT-bill, would be the real risk-free rate, r*, plus the infl ation premium (IP):

rT-bill ! rRF ! r* " IP

Therefore, if the real risk-free rate was r* " 1.7% and if infl ation was expected to be 1.5% (and hence IP " 1.5%) during the next year, the quoted rate of interest on one-year T-bills would be 1.7% # 1.5% " 3.2%.

It is important to note that the infl ation rate built into interest rates is the infl a- tion rate expected in the future, not the rate experienced in the past. Thus, the latest

Nominal (Quoted) Risk-Free Rate, rRF The rate of interest on a security that is free of all risk; rRF is proxied by the T-bill rate or the T-bond rate. rRF includes an inflation premium.

Inflation Premium (IP) A premium equal to expected inflation that investors add to the real risk-free rate of return.

5 Indexed Treasury securities are the closest thing we have to a riskless security, but even they are not totally risk- less because r* can change and cause a decline in the prices of these securities. For example, between its issue date in February 1998 and December 2004, the TIPS that matures on February 15, 2028 fi rst declined from 100 to 89, or by almost 10%, but it then rose; and in February 2008, the bond sold for 130. The cause of the initial price decline was an increase in the real rate on long-term securities from 3.625% to 4.4%, and the cause of the subsequent price increase was a decline in real rates to 2.039%.

USER

171Chapter 6 Interest Rates

reported fi gures might show an annual infl ation rate of 3% over the past 12 months, but that is for the past year. If people, on average, expect a 4% infl ation rate in the future, 4% would be built into the current interest rate. Note also that the infl ation rate refl ected in the quoted interest rate on any security is the average infl ation rate expected over the security’s life. Thus, the infl ation rate built into a 1-year bond is the

Investors who purchase bonds must constantly worry about infl ation. If infl ation turns out to be greater than expected, bonds will provide a lower-than-expected real return. To protect themselves against expected increases in infl ation, investors build an infl ation risk premium into their required rate of return. This raises borrowers’ costs. To provide investors with an infl ation-protected bond and to reduce the cost of debt to the government, the U.S. Treasury issues Treasury Infl ation Protected Securities (TIPS), which are bonds that are indexed to infl ation. For example, in 2004, the Treasury issued 10-year TIPS with a 2% coupon. These bonds pay an interest rate of 2% plus an additional amount that is just suffi cient to off set infl ation. At the end of each 6-month period, the principal (originally set at par or $1,000) is adjusted by the infl ation rate. To understand how TIPS work, consider that during the fi rst 6-month interest period, infl ation (as measured by the CPI) was 2.02%. The infl ation-adjusted principal was then calculated as $1,000(1 # Infl ation) " $1,000 $ 1.0202 " $1,020.20. So on July 15, 2004, each bond paid interest of 0.02/2 $ $1,020.20 " $10.202. Note that the interest rate is divided by 2 because interest on Treasury (and most other) bonds is paid twice a year. This same adjustment process will continue each year until the bonds mature on January 15, 2014, at which time they will pay the adjusted maturity value. Thus, the cash income provided by the bonds rises by exactly enough to cover infl ation, producing a real infl ation-adjusted rate of 2%

for those who hold the bond from the beginning to the end. Further, since the principal also rises by the infl ation rate, it too is protected from infl ation. Both the annual interest received and the increase in principal are taxed each year as interest income even though cash from the appreciation will not be received until the bond matures. Therefore, these bonds are not good for accounts subject to current income taxes; but they are excel- lent for individual retirement accounts (IRAs) and 401(k) plans, which are not taxed until funds are withdrawn. The Treasury regularly conducts auctions to issue indexed bonds. The 2% rate was based on the relative supply and demand for the issue, and it will remain fi xed over the life of the bond. However, after the bonds are issued, they con- tinue to trade in the open market; and their price will vary as investors’ perceptions of the real rate of interest changes. Indeed, as we can see in the following graph, the real rate of interest on this bond has varied quite a bit since it was issued; and as the real rate changes, so does the price of the bond. Real rates fell in 2005, causing the bond’s price to rise; rates then rose to a peak in 2007, at which point the bond sold below its par value. They fell again in late 2007 and 2008 as investors sought safety in Treasury securities. Thus, despite their protection against infl ation, indexed bonds are not com- pletely riskless. The real rate can change; and if r* rises, the prices of indexed bonds will decline. This confi rms again that there is no such thing as a free lunch or a riskless security.

Source: St. Louis Federal Reserve web site, FRED database, http://research.stlouisfed.org/fred2.

AN ALMOST RISKLESS TREASURY BOND

r* (%) 10-Yr. 2% Treasury Inflation-Indexed Note, Due 1/15/2014

3.00

0.00 1-12-04 1-12-05 1-12-06 1-12-07 1-12-08

0.50

1.00

1.50

2.00

2.50

http://research.stlouisfed.org/fred2

172 Part 3 Financial Assets

expected infl ation rate for the next year, but the infl ation rate built into a 30-year bond is the average infl ation rate expected over the next 30 years.6

Expectations for future infl ation are closely, but not perfectly, correlated with rates experienced in the recent past. Therefore, if the infl ation rate reported for last month increased, people would tend to raise their expectations for future infl ation; and this change in expectations would cause an increase in current rates. Also, consumer prices change with a lag following changes at the producer level. Thus, if the price of oil increases this month, gasoline prices are likely to increase in the coming months. This lagged situation between fi nal product and producer goods prices exists throughout the economy.

Note that Germany, Japan, and Switzerland have, over the past several years, had lower infl ation rates than the United States; hence, their interest rates have generally been lower than those of the United States. Italy and most South Ameri- can countries have experienced higher infl ation, so their rates have been higher than those of the United States.

6-3d Default Risk Premium (DRP) The risk that a borrower will default, which means the borrower will not make scheduled interest or principal payments, also affects the market interest rate on a bond: The greater the bond’s risk of default, the higher the market rate. Treasury securities have no default risk; hence, they carry the lowest interest rates on tax- able securities in the United States. For corporate bonds, the higher the bond’s rat- ing, the lower its default risk and, consequently, the lower its interest rate.7 Here are some representative interest rates on long-term bonds in January 2008:

Rate DRP U.S. Treasury 4.28% — AAA corporate 4.83 0.55 AA corporate 4.93 0.65 A corporate 5.18 0.90 BBB corporate 6.03 1.75

The difference between the quoted interest rate on a T-bond and that on a corporate bond with similar maturity, liquidity, and other features is the default risk premium (DRP). Therefore, if the bonds previously listed have the same maturity, liquidity, and so forth, the default risk premium will be DRP " 4.83% ! 4.28% " 0.55% for AAAs, 4.93% ! 4.28% " 0.65% for AAs, 5.18% ! 4.28% " 0.90% for A corporate bonds, and so forth. If we had gone down into “junk bond” territory, we would have seen DRPs of as much as 8%. Default risk premiums vary somewhat over time, but the January 2008 fi gures are representative of levels in recent years.

6-3e Liquidity Premium (LP) A “liquid” asset can be converted to cash quickly at a “fair market value.” Real assets are generally less liquid than fi nancial assets, but different fi nancial assets

Default Risk Premium (DRP) The difference between the interest rate on a U.S. Treasury bond and a corporate bond of equal maturity and marketability.

6 To be theoretically precise, we should use a geometric average. Also, since millions of investors are active in the market, it is impossible to determine exactly the consensus-expected infl ation rate. Survey data are available, however, that give us a reasonably good idea of what investors expect over the next few years. For example, in 1980, the University of Michigan’s Survey Research Center reported that people expected infl ation during the next year to be 11.9% and that the average rate of infl ation expected over the next 5 to 10 years was 10.5%. Those expectations led to record-high interest rates. However, the economy cooled thereafter; and as Figure 6-3 showed, actual infl ation dropped sharply. This led to a gradual reduction in the expected future infl ation rate; and as infl ationary expectations dropped, so did quoted market interest rates. 7 Bond ratings and bonds’ riskiness in general are discussed in detail in Chapter 7. For now, merely note that bonds rated AAA are judged to have less default risk than bonds rated AA, while AA bonds are less risky than A bonds, and so forth. Ratings are designated AAA or Aaa, AA or Aa, and so forth, depending on the rating agency. In this book, the designations are used interchangeably.

Students should go to www .bloomberg.com/markets/ rates to find current interest rates in the United States as well as in Australia, Brazil, Germany, Japan, and Great Britain.

www.bloomberg.com/markets/rates

173Chapter 6 Interest Rates

Since the yield curve is normally upward-sloping, short-term debt is normally less expensive than long-term debt. However, it’s dangerous to fi nance long-term assets with short-term debt. To get around this problem, investment bankers created a new instrument, auction rate securities (ARS), which are long-term bonds with this wrinkle: Weekly (or monthly for some) auctions are held. The borrower buys back at par the bonds of holders who want to get out and simultaneously sells those reclaimed bonds to new lenders. Potential new lenders indicate the lowest interest rate they will accept, and the actual rate paid on the entire issue is the lowest rate that causes the auction to clear. Most of the bonds were insured by AAA insurance companies, which gave them a AAA rating. To illustrate, the total issue might be for $100 million and the initial rate might be 3%. One week later holders of $5 million of bonds might turn in their bonds, which would then be off ered in an auction to potential buyers. To get the bonds resold, an annual rate of 3.1% might be required. Then for the next week, all $100 million of the bonds would earn 3.1%. There was a cap on the interest rate tied to an index of rates on regular long-term bonds.

Investors liked the ARS because they paid a somewhat higher rate than money market funds and they were equally safe and almost as liquid. They were underwritten by major fi nancial institutions such as Goldman Sachs, Merrill Lynch, and Citigroup, which would buy the excess if more bonds were turned in than were bid for at rates below the cap. The institutions would hold repurchased bonds in inventory and then sell them to their customers. Everything worked fine until the credit market melt- down of 2008. The banks who back-stopped the auction had lost billions in the subprime mortgage debacle, and they didn’t have the capital to step in. After a couple of failed auctions, many ARS holders became concerned about liquidity and tried to turn in their bonds. That rush to the exits caused the whole market to freeze up. Highly liquid securities suddenly became totally illiquid. Penalty rates for frozen securities kicked in, some as high as 20%. That’s much higher than “normal” liquidity premiums, but it does demonstrate that liquidity is valuable and that high liquidity premiums are built into illiquid securities’ rates.

Source: Stan Rosenberg and Romy Varghese, “Auction-Rate Bonds May Come to Rescue,” The Wall Street Journal, February 15, 2008, p. C2.

A 20% LIQUIDITY PREMIUM ON A HIGH-GRADE BOND

vary in their liquidity. Because liquidity is important, investors include a liquidity premium (LP) in the rates charged on different debt securities. Although it is diffi - cult to measure liquidity premiums accurately, a differential of at least two and probably four or fi ve percentage points exists between the least liquid and the most liquid fi nancial assets of similar default risk and maturity.

6-3f Interest Rate Risk and the Maturity Risk Premium (MRP)

U.S. Treasury securities are free of default risk in the sense that one can be virtu- ally certain that the federal government will pay interest on its bonds and pay them off when they mature. Therefore, the default risk premium on Treasury securities is essentially zero. Further, active markets exist for Treasury securities, so their liquidity premiums are close to zero. Thus, as a fi rst approximation, the rate of interest on a Treasury security should be the risk-free rate, rRF , which is the real risk-free rate plus an infl ation premium, rRF " r* # IP. However, the prices of long-term bonds decline whenever interest rates rise; and because interest rates can and do occasionally rise, all long-term bonds, even Treasury bonds, have an element of risk called interest rate risk. As a general rule, the bonds of any orga- nization, from the U.S. government to Delta Airlines, have more interest rate risk the longer the maturity of the bond.8 Therefore, a maturity risk premium (MRP),

Liquidity Premium (LP) A premium added to the equilibrium interest rate on a security if that security cannot be converted to cash on short notice and at close to its “fair market value.”

Interest Rate Risk The risk of capital losses to which investors are exposed because of changing interest rates.

Maturity Risk Premium (MRP) A premium that reflects interest rate risk.

Interest Rate Risk The risk of capital losses to which investors are exposed because of changing interest rates.

Maturity Risk Premium (MRP) A premium that reflects interest rate risk.

8 For example, if someone had bought a 20-year Treasury bond for $1,000 in October 1998, when the long-term interest rate was 5.3%, and sold it in May 2002, when long-term T-bond rates were about 5.8%, the value of the bond would have declined to about $942. That would represent a loss of 5.8%; and it demonstrates that long- term bonds, even U.S. Treasury bonds, are not riskless. However, had the investor purchased short-term T-bills in 1998 and subsequently reinvested the principal each time the bills matured, he or she would still have had the original $1,000. This point is discussed in detail in Chapter 7.

USER

174 Part 3 Financial Assets

which is higher the greater the years to maturity, is included in the required interest rate.

The effect of maturity risk premiums is to raise interest rates on long-term bonds relative to those on short-term bonds. This premium, like the others, is diffi - cult to measure; but (1) it varies somewhat over time, rising when interest rates are more volatile and uncertain, then falling when interest rates are more stable and (2) in recent years, the maturity risk premium on 20-year T-bonds has generally been in the range of one to two percentage points.9

We should also note that although long-term bonds are heavily exposed to in- terest rate risk, short-term bills are heavily exposed to reinvestment rate risk. When short-term bills mature and the principal must be reinvested, or “rolled over,” a decline in interest rates would necessitate reinvestment at a lower rate, which would result in a decline in interest income. To illustrate, suppose you had $100,000 invested in T-bills and you lived on the income. In 1981, short-term Trea- sury rates were about 15%, so your income would have been about $15,000. How- ever, your income would have declined to about $9,000 by 1983 and to just $2,700 by January 2008. Had you invested your money in long-term T-bonds, your in- come (but not the value of the principal) would have been stable.10 Thus, although “investing short” preserves one’s principal, the interest income provided by short- term T-bills is less stable than that on long-term bonds.

Reinvestment Rate Risk The risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested.

SEL F TEST Write an equation for the nominal interest rate on any security.

Distinguish between the real risk-free rate of interest, r*, and the nominal, or quoted, risk-free rate of interest, rRF .

How do investors deal with infl ation when they determine interest rates in the fi nancial markets?

Does the interest rate on a T-bond include a default risk premium? Explain.

Distinguish between liquid and illiquid assets and list some assets that are liquid and some that are illiquid.

Briefl y explain the following statement: Although long-term bonds are heav- ily exposed to interest rate risk, short-term T-bills are heavily exposed to rein- vestment rate risk. The maturity risk premium refl ects the net eff ects of those two opposing forces.

Assume that the real risk-free rate is r* " 2% and the average expected infl a- tion rate is 3% for each future year. The DRP and LP for Bond X are each 1%, and the applicable MRP is 2%. What is Bond X’s interest rate? Is Bond X (1) a Treasury bond or a corporate bond and (2) more likely to have a 3-month or a 20-year maturity? (9%, corporate, 20-year)

9 The MRP for long-term bonds has averaged 1.4% over the last 82 years. See Stocks, Bonds, Bills, and Infl ation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar Inc., 2008). 10 Most long-term bonds also have some reinvestment rate risk. If a person is saving and investing for some future purpose (say, to buy a house or to retire), to actually earn the quoted rate on a long-term bond, each interest payment must be reinvested at the quoted rate. However, if interest rates fall, the interest payments would be reinvested at a lower rate; so the realized return would be less than the quoted rate. Note, though, that reinvestment rate risk is lower on long-term bonds than on short-term bonds because only the interest payments (rather than interest plus principal) on a long-term bond are exposed to reinvestment rate risk. Non-callable zero coupon bonds, which are discussed in Chapter 7, are completely free of reinvestment rate risk during their lifetime.

175Chapter 6 Interest Rates

6-4 THE TERM STRUCTURE OF INTEREST RATES The term structure of interest rates describes the relationship between long- and short-term rates. The term structure is important to corporate treasurers deciding whether to borrow by issuing long- or short-term debt and to investors who are deciding whether to buy long- or short-term bonds. Therefore, both borrowers and lenders should understand (1) how long- and short-term rates relate to each other and (2) what causes shifts in their relative levels.

Interest rates for bonds with different maturities can be found in a variety of publications, including The Wall Street Journal and the Federal Reserve Bulletin, and on a number of web sites, including Bloomberg, Yahoo!, CNN Financial, and the Federal Reserve Board. Using interest rate data from these sources, we can determine the term structure at any given point in time. For example, the tabular section below Figure 6-4 presents interest rates for different maturities on three different dates. The set of data for a given date, when plotted on a graph such as Figure 6-4, is called the yield curve for that date.

Term Structure of Interest Rates The relationship between bond yields and maturities.

Yield Curve A graph showing the relationship between bond yields and maturities.

U.S. Treasury Bond Interest Rates on Diff erent DatesFIGURE 6-4

INTEREST RATE

Term to Maturity March 1980 February 2000 January 2008

1 year 14.0% 6.2% 2.7%

5 years 13.5 6.7 3.0

10 years 12.8 6.7 3.7

30 years 12.3 6.3 4.3

0 0

Short Term

Intermediate Term

Long Term

10 20 30

Yield Curve for January 2008

Yield Curve for February 2000

Yield Curve for March 1980

Years to Maturity

Interest Rate (%)

176 Part 3 Financial Assets

As the fi gure shows, the yield curve changes in position and in slope over time. In March 1980, all rates were quite high because high infl ation was expected. How- ever, the rate of infl ation was expected to decline; so short-term rates were higher than long-term rates, and the yield curve was thus downward-sloping. By February 2000, infl ation had indeed declined; thus, all rates were lower, and the yield curve had become humped—medium-term rates were higher than either short- or long-term rates. By January 2008, all rates had fallen below the 2000 levels; and because short- term rates had dropped below long-term rates, the yield curve was upward-sloping.

Figure 6-4 shows yield curves for U.S. Treasury securities; but we could have constructed curves for bonds issued by GE, IBM, Delta Air Lines, or any other company that borrows money over a range of maturities. Had we constructed such corporate yield curves and plotted them on Figure 6-4, they would have been above those for Treasury securities because corporate yields include default risk premiums and somewhat higher liquidity premiums. Even so, the corporate yield curves would have had the same general shape as the Treasury curves. Also, the riskier the corporation, the higher its yield curve; so Delta, which has been fl irting with bankruptcy, would have a higher yield curve than GE or IBM.

Historically, long-term rates are generally above short-term rates because of the maturity risk premium; so all yield curves usually slope upward. For this rea- son, people often call an upward-sloping yield curve a “normal” yield curve and a yield curve that slopes downward an inverted or “abnormal” curve. Thus, in Figure 6-4, the yield curve for March 1980 was inverted, while the one for January 2008 was normal. However, the February 2000 curve was humped, which means that interest rates on medium-term maturities were higher than rates on both short- and long-term maturities. We will explain in detail why an upward slope is the normal situation. Briefl y, however, the reason is that short-term securities have less interest rate risk than longer-term securities; hence, they have smaller MRPs. So short-term rates are normally lower than long-term rates.

“Normal” Yield Curve An upward-sloping yield curve.

Inverted (“Abnormal”) Yield Curve A downward-sloping yield curve.

Humped Yield Curve A yield curve where interest rates on medium- term maturities are higher than rates on both short- and long-term maturities.

“Normal” Yield Curve An upward-sloping yield curve.

Inverted (“Abnormal”) Yield Curve A downward-sloping yield curve.

Humped Yield Curve A yield curve where interest rates on medium- term maturities are higher than rates on both short- and long-term maturities.

SEL F TEST What is a yield curve, and what information would you need to draw this curve?

Distinguish among the shapes of a “normal” yield curve, an “abnormal” curve, and a “humped” curve.

If the interest rates on 1-, 5-, 10-, and 30-year bonds are 4%, 5%, 6%, and 7%, respectively, how would you describe the yield curve? If the rates were re- versed, how would you describe it?

6-5 WHAT DETERMINES THE SHAPE OF THE YIELD CURVE? Because maturity risk premiums are positive, if other things were held constant, long-term bonds would always have higher interest rates than short-term bonds. However, market interest rates also depend on expected infl ation, default risk, and liquidity, each of which can vary with maturity.

Expected infl ation has an especially important effect on the yield curve’s shape, especially the curve for U.S. Treasury securities. Treasuries have essentially no default or liquidity risk, so the yield on a Treasury bond that matures in t years can be expressed as follows:

T-bond yield ! r*t " IPt " MRPt

While the real risk-free rate, r*, varies somewhat over time because of changes in the economy and demographics, these changes are random rather than predictable.

177Chapter 6 Interest Rates

Therefore, the best forecast for the future value of r* is its current value. However, the infl ation premium, IP, varies signifi cantly over time and in a somewhat pre- dictable manner. Recall that the infl ation premium is the average level of expected infl ation over the life of the bond. Thus, if the market expects infl ation to increase in the future (say, from 3% to 4% to 5% over the next 3 years), the infl ation pre- mium will be higher on a 3-year bond than on a 1-year bond. On the other hand, if the market expects infl ation to decline in the future, long-term bonds will have a smaller infl ation premium than will short-term bonds. Finally, since investors con- sider long-term bonds to be riskier than short-term bonds because of interest rate risk, the maturity risk premium always increases with maturity.

Panel a of Figure 6-5 shows the yield curve when infl ation is expected to in- crease. Here long-term bonds have higher yields for two reasons: (1) Infl ation is expected to be higher in the future, and (2) there is a positive maturity risk pre- mium. Panel b shows the yield curve when infl ation is expected to decline. Such a downward-sloping yield curve often foreshadows an economic downturn because

Illustrative Treasury Yield CurvesFIGURE 6-5

WITH INFLATION EXPECTED TO INCREASE

WITH INFLATION EXPECTED TO DECREASE

Maturity r* IP MRP Yield Maturity r* IP MRP Yield

1 year 2.50% 3.00% 0.00% 5.50% 1 year 2.50% 5.00% 0.00% 7.50%

5 years 2.50 3.40 0.18 6.08 5 years 2.50 4.60 0.18 7.28

10 years 2.50 4.00 0.28 6.78 10 years 2.50 4.00 0.28 6.78

20 years 2.50 4.50 0.42 7.42 20 years 2.50 3.50 0.42 6.42

30 years 2.50 4.67 0.53 7.70 30 years 2.50 3.33 0.53 6.36

Interest Rate (%)

a. When Inflation Is Expected to Increase

Interest Rate (%)

b. When Inflation Is Expected to Decrease

Years to Maturity

Maturity Risk Premium

Inflation Premium

Real Risk- Free Rate

Years to Maturity

Maturity Risk Premium

Inflation Premium

Real Risk- Free Rate

0 2010 30 0 2010 30

178 Part 3 Financial Assets

weaker economic conditions generally lead to declining infl ation, which, in turn, results in lower long-term rates.11

Now let’s consider the yield curve for corporate bonds. Recall that corporate bonds include a default risk premium (DRP) and a liquidity premium (LP). Therefore, the yield on a corporate bond that matures in t years can be expressed as follows:

Corporate bond yield ! r*t " IPt " MRPt " DRPt " LPt

Corporate bonds’ default and liquidity risks are affected by their maturities. For example, the default risk on Coca-Cola’s short-term debt is very small since there is

11 Note that yield curves tend to rise or fall relatively sharply over the fi rst 5 to 10 years and then fl atten out. One reason this occurs is that when forecasting future interest rates, people often predict relatively high or low infl ation for the next few years, after which they assume an average long-run infl ation rate. Consequently, the short end of the yield curve tends to have more curvature and the long end of the yield curve tends to be more stable.

Throughout the text, we use the following equation to describe the link between expected infl ation and the nomi- nal risk-free rate of interest, rRF:

rRF ! r* " IP

Recall that r* is the real risk-free interest rate and IP is the cor- responding infl ation premium. This equation suggests that there is a simple link between expected infl ation and nomi- nal interest rates. It turns out, however, that this link is a bit more complex. To fully understand this relationship, fi rst recognize that indi- viduals get utility through the consumption of real goods and services such as bread, water, haircuts, pizza, and textbooks. When we save money, we are giving up the opportunity to consume these goods today in return for being able to con- sume more of them in the future. Our gain from waiting is measured by the real rate of interest, r*. To illustrate this point, consider the following example. Assume that a loaf of bread costs $1 today. Also assume that the real rate of interest is 3% and that infl ation is expected to be 5% over the next year. The 3% real rate indicates that the average consumer is willing to trade 100 loaves of bread today for 103 loaves next year. If a “bread bank” were avail- able, consumers who wanted to defer consumption until next year could deposit 100 loaves today and withdraw 103 loaves next year. In practice, most of us do not directly trade real goods such as bread—instead, we purchase these goods with money because in a well-functioning economy, it is more effi cient to exchange money than goods. However, when we lend money over time, we worry that borrowers might pay us back with dollars that aren’t worth as much due to infl ation. To compensate for this risk, lenders build in a premium for expected infl ation.

With these concerns in mind, let’s compare the dollar cost of 100 loaves of bread today to the cost of 103 loaves next year. Given the current price, 100 loaves of bread today would cost $100. Since expected infl ation is 5%, this means that a loaf of bread is expected to cost $1.05 next year. Conse- quently, 103 loaves of bread are expected to cost $108.15 next year (103 $ $1.05). So if consumers were to deposit $100 in a bank today, they would need to earn 8.15% to realize a real return of 3%. Putting this all together, we see that the 1-year nominal interest rate can be calculated as follows:

rRF ! (1 " r*)(1 " I) # 1 ! (1.03)(1.05) # 1 ! 0.0815 ! 8.15%

Note that this expression can be rewritten as follows:

rRF ! r* " I " (r* $ I)

That equation is identical to our original expression for the nominal risk-free rate except that it includes a “cross-term,” r* $ I. When real interest rates and expected infl ation are relatively low, the cross-term turns out to be quite small and thus is often ignored. Because it is normally insignifi cant we disregard the cross-term in the text unless stated otherwise. One last point—you should recognize that while it may be reasonable to ignore the cross-term when interest rates are low (as they are in the United States today), it is a mistake to do so when investing in a market where interest rates and infl ation are quite high, as is often the case in many emerging markets. In these markets, the cross-term can be signifi cant and thus should not be disregarded.

THE LINKS BETWEEN EXPECTED INFLATION AND INTEREST RATES: A CLOSER LOOK

179Chapter 6 Interest Rates

Interest Rate (%)

0 2010 30

Years to Maturity

BBB-Rated Bond

AA-Rated Bond

Treasury Bond

Illustrative Corporate and Treasury Yield CurvesFIGURE 6-6

INTEREST RATE

Term to Maturity Treasury Bond AA-Rated Bond BBB-Rated Bond

1 year 5.5% 6.7% 7.4%

5 years 6.1 7.4 8.1

10 years 6.8 8.2 9.1

20 years 7.4 9.2 10.2

30 years 7.7 9.8 11.1

almost no chance that Coca-Cola will go bankrupt over the next few years. However, Coke has some bonds that have a maturity of almost 100 years; and while the odds of Coke defaulting on those bonds might not be very high, there is still a higher probability of default risk on Coke’s long-term bonds than its short-term bonds.

Longer-term corporate bonds also tend to be less liquid than shorter-term bonds. Since short-term debt has less default risk, someone can buy a short-term bond with- out doing as much credit checking as would be necessary for a long-term bond. Thus, people can move in and out of short-term corporate debt relatively rapidly. As a result, a corporation’s short-term bonds are typically more liquid and thus have lower liquidity premiums than its long-term bonds.

Figure 6-6 shows yield curves for two hypothetical corporate bonds—an AA- rated bond with minimal default risk and a BBB-rated bond with more default risk— along with the yield curve for Treasury securities taken from Panel a of Figure 6-5. Here we assume that infl ation is expected to increase, so the Treasury yield curve is upward-sloping. Because of their additional default and liquidity risk, corporate bonds yield more than Treasury bonds with the same maturity and BBB-rated bonds yield more than AA-rated bonds. Finally, note that the yield spread between corporate and Treasury bonds is larger the longer the maturity. This occurs because longer-term

180 Part 3 Financial Assets

6-6 USING THE YIELD CURVE TO ESTIMATE FUTURE INTEREST RATES12

In the last section, we saw that the slope of the yield curve depends primarily on two factors: (1) expectations about future infl ation and (2) effects of maturity on bonds’ risk. We also saw how to calculate the yield curve, given infl ation and maturity-related risks. Note, though, that people can reverse the process: They can look at the yield curve and use information embedded in it to estimate the mar- ket’s expectations regarding future infl ation, risk, and short-term interest rates. For example, suppose a company is in the midst of a 5-year expansion program and the treasurer knows that she will need to borrow short-term funds a year from now. She knows the current cost of 1-year money, read from the yield curve, but she wants to know the cost of 1-year money next year. That information can be “backed out” by analyzing the current yield curve, as will be discussed.

The estimation process is straightforward provided we (1) focus on Treasury bonds and (2) assume that Treasury bonds contain no maturity risk premiums.13 This position has been called the pure expectations theory of the term structure of interest rates, often simply referred to as the “expectations theory.” The expecta- tions theory assumes that bond traders establish bond prices and interest rates strictly on the basis of expectations for future interest rates and that they are indif- ferent to maturity because they do not view long-term bonds as being riskier than short-term bonds. If this were true, the maturity risk premium (MRP) would be zero and long-term interest rates would simply be a weighted average of current and expected future short-term interest rates.

To illustrate the pure expectations theory, assume that a 1-year Treasury bond currently yields 5.00% while a 2-year bond yields 5.50%. Investors who want to in- vest for a 2-year horizon have two primary options:

Option 1: Buy a two-year security and hold it for 2 years.

Pure Expectations Theory A theory that states that the shape of the yield curve depends on investors’ expectations about future interest rates.

SEL F TEST How do maturity risk premiums aff ect the yield curve?

If the infl ation rate is expected to increase, would this increase or decrease the slope of the yield curve?

If the infl ation rate is expected to remain constant at the current level in the future, would the yield curve slope up, slope down, or be horizontal? Con- sider all factors that aff ect the yield curve, not just infl ation.

Explain why corporate bonds’ default and liquidity premiums are likely to increase with their maturity.

Explain why corporate bonds always yield more than Treasury bonds and why BBB-rated bonds always yield more than AA-rated bonds.

12 This section is relatively technical, but instructors can omit it without loss of continuity. 13 Although most evidence suggests that there is a positive maturity risk premium, some academics and practitioners contend that this second assumption is reasonable, at least as an approximation. They argue that the market is domi- nated by large bond traders who buy and sell securities of diff erent maturities each day, that these traders focus only on short-term returns, and that they are not concerned with maturity risk. According to this view, a bond trader is just as willing to buy a 20-year bond to pick up a short-term profi t as he or she is to buy a 3-month security. Proponents of this view argue that the shape of the Treasury yield curve is therefore determined only by market expectations about future interest rates. Later we show what happens when we include the eff ects of maturity risk premiums.

corporate bonds have more default and liquidity risk than shorter-term bonds, and both of these premiums are absent in Treasury bonds.

181Chapter 6 Interest Rates

Option 2: Buy a 1-year security; hold it for 1 year; and then at the end of the year, reinvest the proceeds in another 1-year security.

If they select Option 1, for every dollar they invest today, they will have accumu- lated $1.113025 by the end of Year 2:

Funds at end of Year 2 ! $1 $ (1.055)2 ! $1.113025

If they select Option 2, they should end up with the same amount; but this equa- tion is used to fi nd the ending amount:

Funds at end of Year 2 ! $1 $ (1.05) $ (1 " X)

Here X is the expected interest rate on a 1-year Treasury security 1 year from now.

If the expectations theory is correct, each option must provide the same amount of cash at the end of 2 years, which implies the following:

(1.05)(1 " X) ! (1.055)2

We can rearrange this equation and then solve for X:

1 " X ! (1.055)2/1.05 X ! (1.055)2/1.05 # 1 ! 0.0600238 ! 6.00238%

Therefore, X, the 1-year rate 1 year from today, must be 6.00238%; otherwise, one option will be better than the other and the market will not be in equilibrium. However, if the market is not in equilibrium, buying and selling will quickly bring about equilibrium. For example, suppose investors expect the 1-year Treasury rate to be 6.00238% a year from now but a 2-year bond now yields 5.25%, not the 5.50% rate required for equilibrium. Bond traders could earn a profi t by adopting the fol- lowing strategy: 1. Borrow money for 2 years at the 2-year rate, 5.25% per year. 2. Invest the money in a series of 1-year securities, expecting to earn 5.00% this

year and 6.00238% next year, for an overall expected return over the 2 years of [(1.05) $ (1.0600238)]1/2 ! 1 " 5.50%.

Borrowing at 5.25% and investing to earn 5.50% is a good deal, so bond traders would rush to borrow money (demand funds) in the 2-year market and invest (or supply funds) in the 1-year market.

Recall from Figure 6-1 that a decline in the supply of funds raises interest rates, while an increase in the supply lowers rates. Likewise, an increase in the demand for funds raises rates, while a decline in demand lowers rates. Therefore, bond traders would push up the 2-year yield and simultaneously lower the yield on 1-year bonds. This buying and selling would cease when the 2-year rate becomes a weighted average of expected future 1-year rates.14

The preceding analysis was based on the assumption that the maturity risk premium is zero. However, most evidence suggests that a positive maturity risk premium exists. For example, assume once again that 1- and 2-year matur- ities yield 5.00% and 5.50%, respectively; so we have a rising yield curve.

14 In our calculations, we used the geometric average of the current and expected 1-year rates: [(1.05) $ (1.0600238)]1/2 ! 1 " 0.055 or 5.50%. The arithmetic average of the two rates is (5% # 6.00238%)/2 " 5.50119%. The geometric average is theoretically correct, but the diff erence is only 0.00119%. With interest rates at the levels they have been in the United States and most other nations in recent years, the geometric and arithmetic averages are so close that many people use the arithmetic average, especially given the other assumptions that underlie the estimation of future 1-year rates.

182 Part 3 Financial Assets

However, now assume that the maturity risk premium on the 2-year bond is 0.20% versus zero for the 1-year bond. This premium means that in equilibrium, the expected annual return on a 2-year bond (5.50%) must be 0.20% higher than the expected return on a series of two 1-year bonds (5.00% and X%). Therefore, the expected return on the series must be 5.50% ! 0.20% " 5.30%:

Expected return on 2-year series ! Rate on 2-year bond # MRP ! 0.055 # 0.002 ! 0.053 ! 5.30%

Now recall that the annual expected return from the series of two 1-year bonds can be expressed as follows, where X is the 1-year rate next year:

(1.05)(1 " X) ! (1 " Expected return on 2-year series)2 ! (1.053)2

1.05X ! (1.053)2 # 1.05

X ! 0.0588090 __________ 1.05 ! 0.0560086 ! 5.60086%

Under these conditions, equilibrium requires that market participants expect the 1-year rate next year to be 5.60086%.

Note that the rate read from the yield curve rises by 0.50% when the years to maturity increase from one to two: 5.50% ! 5.00% " 0.50%. Of this 0.50% increase, 0.20% is attributable to the MRP and the remaining 0.30% is due to the increase in expected 1-year rates next year.

Putting all of this together, we see that one can use the yield curve to estimate what the market expects the short-term rate to be next year. However, this requires an estimate of the maturity risk premium; and if our estimated MRP is incorrect, then so will our yield-curve-based interest rate forecast. Thus, while the yield curve can be used to obtain insights into what the market thinks future interest rates will be, we calculate out these expectations with precision unless the pure ex- pectations theory holds or we know with certainty the exact maturity risk pre- mium. Since neither of these conditions holds, it is diffi cult to know for sure what the market is forecasting.

Note too that even if we could determine the market’s consensus fore- cast for future rates, the market is not always right. So a forecast of next year’s rate based on the yield curve could be wrong. Therefore, obtaining an accu- rate forecast of rates for next year—or even for next month—is extremely difficult.

SEL F TEST What key assumption underlies the pure expectations theory?

Assuming that the pure expectations theory is correct, how are expected short-term rates used to calculate expected long-term rates?

According to the pure expectations theory, what would happen if long-term rates were not an average of expected short-term rates?

Most evidence suggests that a positive maturity risk premium exists. How would this aff ect your calculations when determining interest rates?

Assume that the interest rate on a 1-year T-bond is currently 7% and the rate on a 2-year bond is 9%. If the maturity risk premium is zero, what is a reason- able forecast of the rate on a 1-year bond next year? What would the forecast be if the maturity risk premium on the 2-year bond was 0.5% versus zero for the 1-year bond? (11.04%; 10.02%)

183Chapter 6 Interest Rates

6-7 MACROECONOMIC FACTORS THAT INFLUENCE INTEREST RATE LEVELS

We described how key components such as expected infl ation, default risk, matu- rity risk, and liquidity concerns infl uence the level of interest rates over time and across different markets. On a day-to-day basis, a variety of macroeconomic fac- tors may infl uence one or more of these components; hence, macroeconomic factors have an important effect on both the general level of interest rates and the shape of the yield curve. The primary factors are (1) Federal Reserve policy; (2) the federal budget defi cit or surplus; (3) international factors, including the foreign trade balance and interest rates in other countries; and (4) the level of business activity.

6-7a Federal Reserve Policy As you probably learned in your economics courses, (1) the money supply has a signifi cant effect on the level of economic activity, infl ation, and interest rates, and (2) in the United States, the Federal Reserve Board controls the money supply. If the Fed wants to stimulate the economy, it increases the money supply. The Fed buys and sells short-term securities, so the initial effect of a monetary easing would be to cause short-term rates to decline. However, a larger money supply might lead to an increase in expected future infl ation, which would cause long-term rates to rise even as short-term rates fell. The reverse holds if the Fed tightens the money supply.

As you can see from Figure 6-2, interest rates in recent years have been rela- tively low, with short-term rates especially low in 2003 and 2004. Those low rates enabled mortgage banks to write adjustable rate mortgage loans with very favor- able rates, and that helped stimulate a huge housing boom along with growth of the economy. The Fed became concerned that the economy would overheat; so from 2004 to 2006, it raised its target rate 17 times, going from 2.0% to 5.25% in 2006. Long-term rates remained relatively stable during those years.

The Fed left its target rate unchanged from June 2006 to September 2007, but the subprime credit crunch that began in 2007 caused increasing concerns about a possi- ble recession. Those fears led the Fed to cut rates fi ve times from September 2007 to February 2008, taking the target rate down from 5.25% to 3.00%. The Fed also signaled that more cuts were likely in the coming few months.

Actions that lower short-term rates won’t necessarily lower long-term rates. This point was made in the following quote from the online edition of Investors’ Business Daily on February 15, 2008:

U.S. government debt prices ended mostly lower Thursday, led by long-dated issues, as traders turned their focus to potential infl ation risks resulting from additional interest rate cuts signaled by the Federal Reserve.

It was a rough day for the Treasuries market, as traders concluded that more Fed rate cuts and the government’s fi scal stimulus program would come at the ex- pense of higher long-term infl ation.

“Fiscal and monetary stimuli are focused on the current strain in the fi nancial markets and its effect on the economy, but there are fears about what these actions may do to infl ation down the road,” said Tom Sapio, a managing director at Cantor Fitzgerald in New York.

Lower rates could also cause foreigners to sell their holdings of U.S. bonds. These investors would be paid with dollars, which they would then sell to buy their own currencies. The sale of dollars and the purchase of other currencies

The home page for the Board of Governors of the Federal Reserve System can be found at www.federalreserve .gov. You can access general information about the Federal Reserve, including press releases, speeches, and monetary policy.

www.federalreserve.gov

184 Part 3 Financial Assets

would lower the value of the dollar relative to other currencies, which would make U.S. goods less expensive, which would help manufacturers and thus lower the trade defi cit. Note also that during periods when the Fed is actively intervening in the markets, the yield curve may be temporarily distorted. Short-term rates may be driven below the long-run equilibrium level if the Fed is easing credit and above the equilibrium rate if the Fed is tightening credit. Long-term rates are not affected as much by Fed intervention.

6-7b Federal Budget Deficits or Surpluses If the federal government spends more than it takes in as taxes, it runs a defi cit; and that defi cit must be covered by additional borrowing (selling more Treasury bonds) or by printing money. If the government borrows, this increases the demand for funds and thus pushes up interest rates. If the government prints money, inves- tors recognize that with “more money chasing a given amount of goods,” the result will be increased infl ation, which will also increase interest rates. So the larger the federal defi cit, other things held constant, the higher the level of interest rates.

Over the past several decades, the federal government has generally run large budget defi cits. There were some surpluses in the late 1990s; but the September 11, 2001, terrorist attacks, the subsequent recession, and the Iraq war all boosted gov- ernment spending and caused the defi cits to return. It is diffi cult to tell where fi scal policy will go and consequently what effect it will have on interest rates.

6-7c International Factors Businesses and individuals in the United States buy from and sell to people and fi rms all around the globe. If they buy more than they sell (that is, if there are more imports than exports), they are said to be running a foreign trade defi cit. When trade defi cits occur, they must be fi nanced; and this generally means borrowing from nations with export surpluses. Thus, if the United States imported $200 bil- lion of goods but exported only $100 billion, it would run a trade defi cit of $100 billion while other countries would have a $100 billion trade surplus. The United States would probably borrow the $100 billion from the surplus nations.15 At any rate, the larger the trade defi cit, the higher the tendency to borrow. Note that foreigners will hold U.S. debt if and only if the rates on U.S. securities are competitive with rates in other countries. This causes U.S. interest rates to be highly dependent on rates in other parts of the world.

All this interdependency limits the ability of the Federal Reserve to use mone- tary policy to control economic activity in the United States. For example, if the Fed attempts to lower U.S. interest rates and this causes rates to fall below rates abroad, foreigners will begin selling U.S. bonds. Those sales will depress bond prices, which will push up rates in the United States. Thus, the large U.S. trade defi cit (and foreigners’ holdings of U.S. debt that resulted from many years of defi - cits) hinders the Fed’s ability to combat a recession by lowering interest rates.

For about 25 years following World War II, the United States ran large trade surpluses and the rest of the world owed it many billions of dollars. However, the situation changed, and the United States has been running trade defi cits since the mid-1970s. The cumulative effect of these defi cits has been to change the United States from being the largest creditor nation to being the largest debtor nation of all time. As a result, interest rates are very much infl uenced by interest rates in other

Foreign Trade Deficit The situation that exists when a country imports more than it exports.

15 The defi cit could also be fi nanced by selling assets, including gold, corporate stocks, entire companies, and real estate. The United States has fi nanced its massive trade defi cits by all of these means in recent years. Although the primary method has been by borrowing from foreigners, in recent years, there has been a sharp increase in foreign purchases of U.S. assets, especially oil exporters’ purchases of U.S. businesses.

185Chapter 6 Interest Rates

countries—higher or lower rates abroad lead to higher or lower U.S. rates. Because of all of this, U.S. corporate treasurers and everyone else who is affected by interest rates should keep up with developments in the world economy.

6-7d Business Activity You can examine Figure 6-2 to see how business conditions infl uence interest rates. Here are the key points revealed by the graph: 1. Because infl ation increased from 1972 to 1981, the general tendency during

that period was toward higher interest rates. However, since the 1981 peak, the trend has generally been downward.

2. The shaded areas in the graph represent recessions, during which (a) the demand for money and the rate of infl ation tended to fall and (b) the Federal Reserve tended to increase the money supply in an effort to stimulate the economy. As a result, there is a tendency for interest rates to decline during recessions. For example, the economy began to slow down in 2000, and the country entered a mild recession in 2001. In response, the Federal Reserve cut interest rates. In 2004, the economy began to rebound; so the Fed began to raise rates. However, the subprime debacle hit in 2007; so the Fed began low- ering rates in September 2007. By February, the Fed’s target rate had fallen from 5.25% to 3.00%, with indications that more reductions were likely.

3. During recessions, short-term rates decline more sharply than long-term rates. This occurs for two reasons: (a) The Fed operates mainly in the short- term sector, so its intervention has the strongest effect there. (b) Long-term rates refl ect the average expected infl ation rate over the next 20 to 30 years; and this expectation generally does not change much, even when the current infl ation rate is low because of a recession or high because of a boom. So short-term rates are more volatile than long-term rates. Taking another look at Figure 6-2, we see that short-term rates did decline recently by much more than long-term rates.

6-8 INTEREST RATES AND BUSINESS DECISIONS The yield curve for January 2008 shown earlier in Figure 6-4 indicates how much the U.S. government had to pay in January 2008 to borrow money for 1 year, 5 years, 10 years, and so forth. A business borrower would have paid somewhat more, but assume for the moment that it is January 2008 and the yield curve shown for that year applies to your company. Now suppose you decide to build a new plant with a 30-year life that will cost $1 million and you will raise the $1 million by borrowing rather than by issuing new stock. If you borrowed in January 2008 on a short-term basis—say for 1 year—your annual interest cost would be only 2.7%, or $27,000. On the other hand, if you used long-term fi nancing, your annual cost would be 4.3%, or $43,000. Therefore, at fi rst glance, it would seem that you should use short-term debt.

SEL F TEST Identify some macroeconomic factors that infl uence interest rates and ex-

plain the eff ects of each.

How does the Fed stimulate the economy? How does the Fed aff ect interest rates?

Does the Fed have complete control over U.S. interest rates? That is, can it set rates at any level it chooses? Why or why not?

186 Part 3 Financial Assets

However, this could prove to be a horrible mistake. If you use short-term debt, you will have to renew your loan every 6 months; and the rate charged on each new loan will refl ect the then-current short-term rate. Interest rates could return to their previous highs, in which case you would be paying 14%, or $140,000, per year. Those high interest payments would cut into and perhaps eliminate your profi ts. Your reduced profi tability could increase your fi rm’s risk to the point where your bond rating was lowered, causing lenders to increase the risk premium built into your interest rate. That would further increase your interest payments, which would further reduce your profi tability, worry lend- ers still more, and make them reluctant to renew your loan. If your lenders re- fused to renew the loan and demanded its repayment, as they would have every right to do, you might have to sell assets at a loss, which could result in bankruptcy.

On the other hand, if you used long-term fi nancing in 2008, your interest costs would remain constant at $43,000 per year; so an increase in interest rates in the economy would not hurt you. You might even be able to acquire some of your bankrupt competitors at bargain prices—bankruptcies increase dramatically when interest rates rise, primarily because many fi rms use so much short-term debt.

Does all of this suggest that fi rms should avoid short-term debt? Not at all. If infl ation falls over the next few years, so will interest rates. If you had borrowed on a long-term basis for 4.3% in January 2008, your company would be at a disad- vantage if it was locked into 4.3% debt while its competitors (who used short-term debt in 2008) had a borrowing cost of only 2.7%.

Financing decisions would be easy if we could make accurate forecasts of future interest rates. Unfortunately, predicting interest rates with consistent ac- curacy is nearly impossible. However, although it is diffi cult to predict future interest rate levels, it is easy to predict that interest rates will fl uctuate—they al- ways have, and they always will. That being the case, sound fi nancial policy calls for using a mix of long- and short-term debt as well as equity to position the fi rm so that it can survive in any interest rate environment. Further, the op- timal fi nancial policy depends in an important way on the nature of the fi rm’s assets—the easier it is to sell off assets to generate cash, the more feasible it is to use more short-term debt. This makes it logical for a fi rm to fi nance current as- sets such as inventories and receivables with short-term debt and to fi nance fi xed assets such as buildings and equipment with long-term debt. We will re- turn to this issue later in the book when we discuss capital structure and fi nanc- ing policy.

Changes in interest rates also have implications for savers. For example, if you had a 401(k) plan—and someday most of you will—you would probably want to invest some of your money in a bond mutual fund. You could choose a fund that had an average maturity of 25 years, 20 years, on down to only a few months (a money market fund). How would your choice affect your investment results and hence your retirement income? First, your decision would affect your annual interest income. For example, if the yield curve was upward- sloping, as it normally is, you would earn more interest if you chose a fund that held long-term bonds. Note, though, that if you chose a long-term fund and interest rates then rose, the market value of your fund would decline. For exam- ple, as we will see in Chapter 7, if you had $100,000 in a fund whose average bond had a maturity of 25 years and a coupon rate of 6% and if interest rates then rose from 6% to 10%, the market value of your fund would decline from $100,000 to about $63,500. On the other hand, if rates declined, your fund would increase in value. If you invested in a short-term fund, its value would be stable, but it would probably provide less interest per year. In any event, your choice of maturity would have a major effect on your investment performance and hence on your future income.

187Chapter 6 Interest Rates

In this chapter, we discussed the way interest rates are determined, the term struc- ture of interest rates, and some of the ways interest rates aff ect business decisions. We saw that the interest rate on a given bond, r, is based on this equation:

r ! r* " IP " DRP " LP " MRP

Here r* is the real risk-free rate, IP is the premium for expected infl ation, DRP is the premium for potential default risk, LP is the premium for lack of liquidity, and MRP is the premium to compensate for the risk inherent in bonds with long maturities. Both r* and the various premiums can and do change over time depending on economic conditions, Federal Reserve actions, and the like. Since changes in these factors are diffi cult to predict, it is hard to forecast the future direction of interest rates.

The yield curve, which relates bonds’ interest rates to their maturities, usually has an upward slope; but it can slope up or down, and both its slope and level change over time. The main determinants of the slope of the curve are expectations for fu- ture infl ation and the MRP. We can analyze yield curve data to estimate what market participants think future interest rates are likely to be.

We will use the insights gained from this chapter in later chapters, when we ana- lyze the values of bonds and stocks and when we examine various corporate invest- ment and fi nancing decisions.

T Y I N G I T A L L T O GET H E R

KEY TERMS Define each of the following terms: a. Production opportunities; time preferences for consumption; risk; inflation b. Real risk-free rate of interest, r*; nominal (quoted) risk-free rate of interest, rRF c. Inflation premium (IP) d. Default risk premium (DRP) e. Liquidity premium (LP); maturity risk premium (MRP) f. Interest rate risk; reinvestment rate risk g. Term structure of interest rates; yield curve h. “Normal” yield curve; inverted (“abnormal”) yield curve; humped yield curve i. Pure expectations theory

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SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

SEL F TEST If short-term interest rates are lower than long-term rates, why might a bor-

rower still choose to fi nance with long-term debt?

Explain the following statement: The optimal fi nancial policy depends in an important way on the nature of the fi rm’s assets.

188 Part 3 Financial Assets

INFLATION AND INTEREST RATES The real risk-free rate of interest, r*, is 3%; and it is expected to remain constant over time. Inflation is expected to be 2% per year for the next 3 years and 4% per year for the next 5 years. The maturity risk premium is equal to 0.1 (t ! 1)%, where t " the bond’s maturity. The default risk premium for a BBB-rated bond is 1.3%. a. What is the average expected inflation rate over the next 4 years? b. What is the yield on a 4-year Treasury bond? c. What is the yield on a 4-year BBB-rated corporate bond with a liquidity premium of

0.5%? d. What is the yield on an 8-year Treasury bond? e. What is the yield on an 8-year BBB-rated corporate bond with a liquidity premium of

0.5%? f. If the yield on a 9-year Treasury bond is 7.3%, what does that imply about expected

inflation in 9 years?

PURE EXPECTATIONS THEORY The yield on 1-year Treasury securities is 6%, 2-year secu- rities yield 6.2%, and 3-year securities yield 6.3%. There is no maturity risk premium. Using expectations theory, forecast the yields on the following securities: a. A 1-year security, 1 year from now b. A 1-year security, 2 years from now c. A 2-year security, 1 year from now

Suppose interest rates on residential mortgages of equal risk are 5.5% in California and 7.0% in New York. Could this differential persist? What forces might tend to equalize rates? Would differentials in borrowing costs for businesses of equal risk located in California and New York be more or less likely to exist than differentials in residential mortgage rates? Would differentials in the cost of money for New York and California firms be more likely to exist if the firms being compared were very large or if they were very small? What are the implications of all of this with respect to nationwide branching?

Which fluctuate more—long-term or short-term interest rates? Why?

Suppose you believe that the economy is just entering a recession. Your firm must raise capital immediately, and debt will be used. Should you borrow on a long-term or a short- term basis? Why?

Suppose the population of Area Y is relatively young and the population of Area O is rela- tively old but everything else about the two areas is the same. a. Would interest rates likely be the same or different in the two areas? Explain. b. Would a trend toward nationwide branching by banks and the development of na-

tionwide diversified financial corporations affect your answer to part a? Explain.

Suppose a new process was developed that could be used to make oil out of seawater. The equipment required is quite expensive; but it would, in time, lead to low prices for gaso- line, electricity, and other types of energy. What effect would this have on interest rates?

Suppose a new and more liberal Congress and administration are elected. Their first order of business is to take away the independence of the Federal Reserve System and to force the Fed to greatly expand the money supply. What effect will this have: a. On the level and slope of the yield curve immediately after the announcement? b. On the level and slope of the yield curve that would exist two or three years in the

future?

It is a fact that the federal government (1) encouraged the development of the savings and loan industry, (2) virtually forced the industry to make long-term fixed-interest-rate mort- gages, and (3) forced the savings and loans to obtain most of their capital as deposits that were withdrawable on demand.

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QUESTIONSQUESTIONS

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189Chapter 6 Interest Rates

a. Would the savings and loans have higher profits in a world with a “normal” or an inverted yield curve?

b. Would the savings and loan industry be better off if the individual institutions sold their mortgages to federal agencies and then collected servicing fees or if the institu- tions held the mortgages that they originated?

Suppose interest rates on Treasury bonds rose from 5% to 9% as a result of higher interest rates in Europe. What effect would this have on the price of an average company’s com- mon stock?

What does it mean when it is said that the United States is running a trade deficit? What impact will a trade deficit have on interest rates?

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YIELD CURVES The following yields on U.S. Treasury securities were taken from a recent financial publication:

Term Rate 6 months 5.1% 1 year 5.5 2 years 5.6 3 years 5.7 4 years 5.8 5 years 6.0 10 years 6.1 20 years 6.5 30 years 6.3

a. Plot a yield curve based on these data. b. What type of yield curve is shown? c. What information does this graph tell you? d. Based on this yield curve, if you needed to borrow money for longer than 1 year,

would it make sense for you to borrow short-term and renew the loan or borrow long-term? Explain.

REAL RISK-FREE RATE You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums: • Inflation premium " 3.25% • Liquidity premium " 0.6% • Maturity risk premium " 1.8% • Default risk premium " 2.15%

On the basis of these data, what is the real risk-free rate of return?

EXPECTED INTEREST RATE The real risk-free rate is 3%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?

DEFAULT RISK PREMIUM A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 8%. Assume that the liquidity premium on the cor- porate bond is 0.5%. What is the default risk premium on the corporate bond?

MATURITY RISK PREMIUM The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.2%. What is the maturity risk premium for the 2-year security?

INFLATION CROSS-PRODUCT An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result, the analyst has been warned not to ignore

PROBLEMS PROBLEMS

6-16-1Easy Problems 1–7 Easy Problems 1–7

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190 Part 3 Financial Assets

the cross-product between the real rate and inflation. If the real risk-free rate is 5% and in- flation is expected to be 16% each of the next 4 years, what is the yield on a 4-year security with no maturity, default, or liquidity risk? (Hint: Refer to “The Links between Expected Inflation and Interest Rates: A Closer Look” on page 178.)

EXPECTATIONS THEORY One-year Treasury securities yield 5%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities?

EXPECTATIONS THEORY Interest rates on 4-year Treasury securities are currently 7%, while 6-year Treasury securities yield 7.5%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now?

EXPECTED INTEREST RATE The real risk-free rate is 3%. Inflation is expected to be 3% this year, 4% next year, and 3.5% thereafter. The maturity risk premium is estimated to be 0.05 $ (t ! 1)%, where t " number of years to maturity. What is the yield on a 7-year Treasury note?

INFLATION Due to a recession, expected inflation this year is only 3%. However, the in- flation rate in Year 2 and thereafter is expected to be constant at some level above 3%. As- sume that the expectations theory holds and the real risk-free rate is r* " 2%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2%, what inflation rate is expected after Year 1?

DEFAULT RISK PREMIUM A company’s 5-year bonds are yielding 7.75% per year. Trea- sury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r*) is 2.3%. The average inflation premium is 2.5%; and the maturity risk premium is esti- mated to be 0.1 $ (t ! 1)%, where t " number of years to maturity. If the liquidity pre- mium is 1%, what is the default risk premium on the corporate bonds?

MATURITY RISK PREMIUM An investor in Treasury securities expects inflation to be 2.5% in Year 1, 3.2% in Year 2, and 3.6% each year thereafter. Assume that the real risk-free rate is 2.75% and that this rate will remain constant. Three-year Treasury securities yield 6.25%, while 5-year Treasury securities yield 6.80%. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is MRP5 ! MRP3?

DEFAULT RISK PREMIUM The real risk-free rate, r*, is 2.5%. Inflation is expected to aver- age 2.8% a year for the next 4 years, after which time inflation is expected to average 3.75% a year. Assume that there is no maturity risk premium. An 8-year corporate bond has a yield of 8.3%, which includes a liquidity premium of 0.75%. What is its default risk premium?

EXPECTATIONS THEORY AND INFLATION Suppose 2-year Treasury bonds yield 4.5%, while 1-year bonds yield 3%. r* is 1%, and the maturity risk premium is zero. a. Using the expectations theory, what is the yield on a 1-year bond 1 year from now? b. What is the expected inflation rate in Year 1? Year 2?

EXPECTATIONS THEORY Assume that the real risk-free rate is 2% and that the maturity risk premium is zero. If the 1-year bond yield is 5% and a 2-year bond (of similar risk) yields 7%, what is the 1-year interest rate that is expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year pe- riod differs from the 1-year interest rate expected for Year 2.

INFLATION CROSS-PRODUCT An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result, the analyst has been warned not to ignore the cross-product between the real rate and inflation. A 6-year security with no maturity, default, or liquidity risk has a yield of 20.84%. If the real risk-free rate is 6%, what average rate of inflation is expected in this country over the next 6 years? (Hint: Refer to “The Links between Expected Inflation and Interest Rates: A Closer Look” on page 178.)

INTEREST RATE PREMIUMS A 5-year Treasury bond has a 5.2% yield. A 10-year Treasury bond yields 6.4%, and a 10-year corporate bond yields 8.4%. The market expects that inflation will average 2.5% over the next 10 years (IP10 " 2.5%). Assume that there is no maturity risk premium (MRP " 0) and that the annual real risk-free rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP " LP " 0.) A 5-year corporate

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191Chapter 6 Interest Rates

bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. What is the yield on this 5-year corporate bond?

YIELD CURVES Suppose the inflation rate is expected to be 7% next year, 5% the following year, and 3% thereafter. Assume that the real risk-free rate, r*, will remain at 2% and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) to 0.2% for 1-year securities. Furthermore, maturity risk premiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer- term T-bonds. a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities and

plot the yield curve. b. Suppose a AAA-rated company (which is the highest bond rating a firm can have)

had bonds with the same maturities as the Treasury bonds. Estimate and plot what you believe a AAA-rated company’s yield curve would look like on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on its long-term versus its short-term bonds.)

c. On the same graph, plot the approximate yield curve of a much riskier lower-rated company with a much higher risk of defaulting on its bonds.

INFLATION AND INTEREST RATES In late 1980, the U.S. Commerce Department released new data showing inflation was 15%. At the time, the prime rate of interest was 21%, a re- cord high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter administration had been. Moreover, many observers believed that the extremely high interest rates and generally tight credit, which resulted from the Federal Reserve System’s attempts to curb the inflation rate, would lead to a recession, which, in turn, would lead to a decline in inflation and interest rates. As- sume that at the beginning of 1981, the expected inflation rate for 1981 was 13%; for 1982, 9%; for 1983, 7%; and for 1984 and thereafter, 6%. a. What was the average expected inflation rate over the 5-year period 1981!1985? (Use

the arithmetic average.) b. Over the 5-year period, what average nominal interest rate would be expected to

produce a 2% real risk-free return on 5-year Treasury securities? Assume MRP " 0. c. Assuming a real risk-free rate of 2% and a maturity risk premium that equals 0.1 $ (t)%,

where t is the number of years to maturity, estimate the interest rate in January 1981 on bonds that mature in 1, 2, 5, 10, and 20 years. Draw a yield curve based on these data.

d. Describe the general economic conditions that could lead to an upward-sloping yield curve.

e. If investors in early 1981 expected the inflation rate for every future year to be 10% (that is, It " It#1 " 10% for t " 1 to ∞), what would the yield curve have looked like? Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c?

COMPREHENSIVE/SPREADSHEET PROBLEM

INTEREST RATE DETERMINATION AND YIELD CURVES a. What effect would each of the following events likely have on the level of nominal

interest rates? (1) Households dramatically increase their savings rate. (2) Corporations increase their demand for funds following an increase in invest-

ment opportunities. (3) The government runs a larger-than-expected budget deficit. (4) There is an increase in expected inflation. b. Suppose you are considering two possible investment opportunities: a 12-year Treasury

bond and a 7-year, A-rated corporate bond. The current real risk-free rate is 4%; and in- flation is expected to be 2% for the next 2 years, 3% for the following 4 years, and 4% thereafter. The maturity risk premium is estimated by this formula: MRP " 0.1(t ! 1)%.

6-186-18

6-196-19

6-206-20

192 Part 3 Financial Assets

The liquidity premium for the corporate bond is estimated to be 0.7%. Finally, you may determine the default risk premium, given the company’s bond rating, from the default risk premium table in the text. What yield would you predict for each of these two investments?

c. Given the following Treasury bond yield information from a recent financial publica- tion, construct a graph of the yield curve.

Maturity Yield 1 year 5.37% 2 years 5.47 3 years 5.65 4 years 5.71 5 years 5.64 10 years 5.75 20 years 6.33 30 years 5.94

d. Based on the information about the corporate bond provided in part b, calculate yields and then construct a new yield curve graph that shows both the Treasury and the corporate bonds.

e. Which part of the yield curve (the left side or right side) is likely to be most volatile over time?

f. Using the Treasury yield information in part c, calculate the following rates: (1) The 1-year rate 1 year from now (2) The 5-year rate 5 years from now (3) The 10-year rate 10 years from now (4) The 10-year rate 20 years from now

INTEREST RATE DETERMINATION Maria Juarez is a professional tennis player, and your firm manages her money. She has asked you to give her information about what determines the level of various interest rates. Your boss has prepared some questions for you to consider.

a. What are the four most fundamental factors that affect the cost of money, or the general level of interest rates, in the economy?

b. What is the real risk-free rate of interest (r*) and the nominal risk-free rate (rRF)? How are these two rates measured?

c. Define the terms inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP). Which of these premiums is included in determining the interest rate on (1) short-term U.S. Treasury securities, (2) long-term U.S. Treasury securities, (3) short-term corporate securities, and (4) long- term corporate securities? Explain how the premiums would vary over time and among the different securi- ties listed.

d. What is the term structure of interest rates? What is a yield curve? e. Suppose most investors expect the inflation rate to be 5% next year, 6% the following year, and 8% thereaf-

ter. The real risk-free rate is 3%. The maturity risk premium is zero for bonds that mature in 1 year or less and 0.1% for 2-year bonds; then the MRP increases by 0.1% per year thereafter for 20 years, after which it is stable. What is the interest rate on 1-, 10-, and 20-year Treasury bonds? Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward-sloping?

f. At any given time, how would the yield curve facing a AAA-rated company compare with the yield curve for U.S. Treasury securities? At any given time, how would the yield curve facing a BB-rated company com- pare with the yield curve for U.S. Treasury securities? Draw a graph to illustrate your answer.

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IN TEGRATED C ASE MORTON HANDLEY & COMPANY

193Chapter 6 Interest Rates

g. What is the pure expectations theory? What does the pure expectations theory imply about the term struc- ture of interest rates?

h. Suppose you observe the following term structure for Treasury securities:

Maturity Yield 1 year 6.0% 2 years 6.2 3 years 6.4 4 years 6.5 5 years 6.5

Assume that the pure expectations theory of the term structure is correct. (This implies that you can use the yield curve provided to “back out” the market’s expectations about future interest rates.) What does the market expect will be the interest rate on 1-year securities 1 year from now? What does the market expect will be the interest rate on 3-year securities 2 years from now?

S i z i n g U p R i s k i n t h e B o n d M a r ke t

Bonds and Their Valuation

H N

C LA

RK /S

H U

TT ER

ST O

7 CHAPTER

194

Many people view Treasury securities as a lack- luster but ultra-safe investment. From a default standpoint, Treasuries are indeed our safest investments; but their prices can still decline in any given year if interest rates increase. This is especially true for long-term bonds, which lost nearly 9% in 1999. However, bonds can perform well—in fact, they outgained stocks in 5 of the 8 years between 2000 and 2007.

All bonds aren’t alike, and they don’t neces- sarily all move in the same direction. For exam- ple, corporate bonds are callable and they can default, whereas Treasury bonds are not exposed to these risks. This results in higher nominal yields on corporates, but the spread between corporate and Treasury yields differs widely depending on the risk of the particular corporate bond. Moreover, yield spreads vary substantially over time, especially for lower-rated securities. For example, as information about WorldCom’s deteriorating condition began coming out in 2002, the spread on its 5-year bonds jumped from 1.67% to over 20% in mid-2002. These

bonds subsequently defaulted, so greedy people who bought them expecting a high return ended up with a large loss.

When the economy is strong, corporate bonds generally produce higher returns than Treasuries— their promised returns are higher, and most make their promised payments because few go into default. However, when the economy weakens, concerns about defaults rise, which leads to declines in corporate bond prices. For example, from the beginning of 2000 to the end of 2002, a sluggish economy and a string of accounting scandals led to some major corporate defaults, which worried investors. All corporate bond prices then declined relative to Treasuries, and the result was an increase in yield spreads. As the economy rebounded in 2003, yield spreads declined to their former levels, which resulted in good gains in cor- porate bond prices. The situation is once again worrisome in 2008. The subprime mortgage crisis has led to fears of recession; and this has caused spreads to rise dramatically, especially for lower- rated bonds. For example, the spread on junk

In previous chapters, we noted that companies raise capital in two main forms: debt and equity. In this chapter, we examine the characteristics of bonds and discuss the various factors that infl uence bond prices. In Chapter 9, we will turn our attention to stocks and their valuation.

If you skim through The Wall Street Journal, you will see references to a wide vari- ety of bonds. This variety may seem confusing; but in actuality, only a few character- istics distinguish the various types of bonds.

When you fi nish this chapter, you should be able to: • Identify the diff erent features of corporate and government bonds. • Discuss how bond prices are determined in the market, what the relationship is

between interest rates and bond prices, and how a bond’s price changes over time as it approaches maturity.

• Calculate a bond’s yield to maturity and its yield to call if it is callable and deter- mine the “true” yield.

• Explain the diff erent types of risk that bond investors and issuers face and the way a bond’s terms and collateral can be changed to aff ect its interest rate.

7-1 WHO ISSUES BONDS? A bond is a long-term contract under which a borrower agrees to make payments of interest and principal on specifi c dates to the holders of the bond. Bonds are issued by corporations and government agencies that are looking for long-term debt capital. For example, on January 3, 2009, Allied Food Products borrowed $50 million by issuing $50 million of bonds. For convenience, we assume that Allied sold 50,000 individual bonds for $1,000 each. Actually, it could have sold one $50 million bond, 10 bonds each with a $5 million face value, or any other combination that totaled $50 million. In any event, Allied received the $50 million; and in exchange, it promised to make annual interest payments and to repay the $50 million on a specifi ed maturity date.

Bond A long-term debt instrument.

bonds over Treasuries rose from 2.4% to 7.5% the 6 months from mid-2007 in January 2008.

Bond investors are rightly worried today. If a recession does occur, this will lead to increased defaults on corporate bonds. A recession might benefit investors in Treasury bonds. However, because there have already been several rounds of Federal Reserve rate cuts, Treasury rates may not have much room to fall. Also, there is concern that recent Fed easing is sewing the seeds for higher inflation down the road, which would lead to higher rates and lower bond prices.

In the face of similar risks in 2001, a BusinessWeek Online article gave investors the following advice, which is still applicable today:

Take the same diversified approach to bonds as you do with stocks. Blend in U.S. government, corporate— both high-quality and high-yield—and perhaps even some foreign government debt. If you’re investing tax- able dollars, consider tax-exempt municipal bonds. And it doesn’t hurt to layer in some inflation-indexed bonds.

PU T TING THINGS IN PER SPECTIVE

Chapter 7 Bonds and Their Valuation 195

Sources: Scott Patterson, “Ahead of the Tape: Junk Yields Flashing Back to ’01 Slump,” The Wall Street Journal, January 30, 2008, p. C1; Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008); and Susan Scherreik, “Getting the Most Bang Out of Your Bonds,” BusinessWeek Online, November 12, 2001.

196 Part 3 Financial Assets

Until the 1970s, most bonds were beautifully engraved pieces of paper and their key terms, including their face values, were spelled out on the bonds. Today, though, virtually all bonds are represented by electronic data stored in secure com- puters, much like the “money” in a bank checking account.

Bonds are grouped in several ways. One grouping is based on the issuer: the U.S. Treasury, corporations, state and local governments, and foreigners. Each bond differs with respect to risk and consequently its expected return.

Treasury bonds, generally called Treasuries and sometimes referred to as gov- ernment bonds, are issued by the federal government.1 It is reasonable to assume that the U.S. government will make good on its promised payments, so Treasuries have no default risk. However, these bonds’ prices do decline when interest rates rise; so they are not completely riskless.

Corporate bonds are issued by business fi rms. Unlike Treasuries, corporates are exposed to default risk—if the issuing company gets into trouble, it may be unable to make the promised interest and principal payments and bondholders may suffer losses. Different corporate bonds have different levels of default risk depending on the issuing company’s characteristics and the terms of the specifi c bond. Default risk is often referred to as “credit risk”; and as we saw in Chapter 6, the larger this risk, the higher the interest rate investors demand.

Municipal bonds, or munis, is the term given to bonds issued by state and local governments. Like corporates, munis are exposed to some default risk; but they have one major advantage over all other bonds: As we discussed in Chapter 3, the interest earned on most munis is exempt from federal taxes and from state taxes if the holder is a resident of the issuing state. Consequently, the market inter- est rate on a muni is considerably lower than on a corporate of equivalent risk.

Foreign bonds are issued by a foreign government or a foreign corporation. All foreign corporate bonds are exposed to default risk, as are some foreign gov- ernment bonds. An additional risk exists when the bonds are denominated in a currency other than that of the investor’s home currency. Consider, for example, a U.S. investor who purchases a corporate bond denominated in Japanese yen. At some point, the investor will want to close out his investment and convert the yen back to U.S. dollars. If the Japanese yen unexpectedly falls relative to the dollar, the investor will have fewer dollars than he originally expected to receive. Conse- quently, the investor could still lose money even if the bond does not default.

Treasury Bonds Bonds issued by the federal government, sometimes referred to as government bonds.

Corporate Bonds Bonds issued by corporations.

Municipal Bonds Bonds issued by state and local governments.

Foreign Bonds Bonds issued by foreign governments or by foreign corporations.

1 The U.S. Treasury actually calls its debt “bills,” “notes,” or “bonds.” T-bills generally have maturities of 1 year or less at the time of issue, notes generally have original maturities of 2 to 7 years, and bonds originally mature in 8 to 30 years. There are technical diff erences between bills, notes, and bonds; but they are not important for our purposes. So we generally call all Treasury securities “bonds.” Note too that a 30-year T-bond at the time of issue becomes a 29-year bond the next year, and it is a 1-year bond after 29 years.

SEL F TEST What is a bond?

What are the four main issuers of bonds?

Why are U.S. Treasury bonds not completely riskless?

In addition to default risk, what key risk do investors in foreign bonds face?

7-2 KEY CHARACTERISTICS OF BONDS Although all bonds have some common characteristics, different bonds can have different contractual features. For example, most corporate bonds have provisions that allow the issuer to pay them off early (“call” features), but the specifi c call

197Chapter 7 Bonds and Their Valuation

provisions vary widely among different bonds. Similarly, some bonds are backed by specifi c assets that must be turned over to the bondholders if the issuer defaults, while other bonds have no such collateral backup. Differences in contractual pro- visions (and in the fundamental underlying fi nancial strength of the companies backing the bonds) lead to differences in bonds’ risks, prices, and expected returns. To understand bonds, it is essential that you understand the following terms.

7-2a Par Value The par value is the stated face value of the bond; for illustrative purposes, we generally assume a par value of $1,000, although any multiple of $1,000 (e.g., $5,000 or $5 million) can be used. The par value generally represents the amount of money the fi rm borrows and promises to repay on the maturity date.

7-2b Coupon Interest Rate Allied Food Products’ bonds require the company to pay a fi xed number of dollars of interest each year. This payment, generally referred to as the coupon payment, is set at the time the bond is issued and remains in force during the bond’s life.2 Typically, at the time a bond is issued, its coupon payment is set at a level that will induce investors to buy the bond at or near its par value. Most of the examples and problems throughout this text will focus on bonds with fi xed coupon rates.

When this annual coupon payment is divided by the par value, the result is the coupon interest rate. For example, Allied’s bonds have a $1,000 par value, and they pay $100 in interest each year. The bond’s coupon payment is $100, so its cou- pon interest rate is $100/$1,000 ! 10%. In this regard, the $100 is the annual income that an investor receives when he or she invests in the bond.

Allied’s bonds are fi xed-rate bonds because the coupon rate is fi xed for the life of the bond. In some cases, however, a bond’s coupon payment is allowed to vary over time. These fl oating-rate bonds work as follows: The coupon rate is set for an initial period, often 6 months, after which it is adjusted every 6 months based on some open market rate. For example, the bond’s rate may be adjusted so as to equal the 10-year Treasury bond rate plus a “spread” of 1.5 percentage points. Other provisions can be included in corporate bonds. For example, some can be converted at the holders’ option into fi xed-rate debt, and some fl oaters have upper limits (caps) and lower limits (fl oors) on how high or low the rate can go.

Some bonds pay no coupons at all, but are offered at a discount below their par values and hence provide capital appreciation rather than interest income. These securities are called zero coupon bonds (zeros). Other bonds pay some cou- pon interest, but not enough to induce investors to buy them at par. In general, any bond originally offered at a price signifi cantly below its par value is called an original issue discount (OID) bond. Some of the details associated with issuing or investing in zero coupon bonds are discussed more fully in Web Appendix 7A.

7-2c Maturity Date Bonds generally have a specifi ed maturity date on which the par value must be repaid. Allied’s bonds, which were issued on January 3, 2009, will mature on

Par Value The face value of a bond. Par Value The face value of a bond.

Coupon Payment The specified number of dollars of interest paid each year.

Coupon Interest Rate The stated annual interest rate on a bond.

Floating-Rate Bond A bond whose interest rate fluctuates with shifts in the general level of interest rates.

Fixed-Rate Bond A bond whose interest rate is fixed for its entire life.

Zero Coupon Bond A bond that pays no annual interest but is sold at a discount below par, thus compensating investors in the form of capital appreciation.

Original Issue Discount (OID) Bond Any bond originally offered at a price below its par value.

Maturity Date A specified date on which the par value of a bond must be repaid.

2 Back when bonds were ornate, they were engraved pieces of paper rather than electronic information stored on a computer. Each bond had a number of small (1/2- by 2-inch) dated coupons attached to them; and on each interest payment date, the owner would “clip the coupon” for that date, send it to the company’s paying agent, and receive a check for the interest. A 30-year semiannual bond would start with 60 coupons, whereas a 5-year annual payment bond would start with only 5 coupons. Today no physical coupons are involved, and interest checks are mailed or deposited automatically to the bonds’ registered owners on the payment date. Even so, people continue to use the terms coupon and coupon interest rate when discussing bonds. You can think of the coupon interest rate as the promised rate.

198 Part 3 Financial Assets

January 2, 2024; thus, they had a 15-year maturity at the time they were issued. Most bonds have original maturities (the maturity at the time the bond is issued) ranging from 10 to 40 years, but any maturity is legally permissible.3 Of course, the effective maturity of a bond declines each year after it has been issued. Thus, Allied’s bonds had a 15-year original maturity. But in 2010, a year later, they will have a 14-year maturity; a year after that, they will have a 13-year maturity; and so forth.

7-2d Call Provisions Most corporate and municipal bonds, but not Treasuries, contain a call provision that gives the issuer the right to call the bonds for redemption.4 The call provision generally states that the issuer must pay the bondholders an amount greater than the par value if they are called. The additional sum, which is termed a call premium, is often equal to one year’s interest. For example, the call premium on a 10-year bond with a 10% annual coupon and a par value of $1,000 might be $100, which means that the issuer would have to pay investors $1,100 (the par value plus the call premium) if it wanted to call the bonds. In most cases, the provisions in the bond contract are set so that the call premium declines over time as the bonds approach maturity. Also, while some bonds are immediately callable, in most cases, bonds are often not callable until several years after issue, generally 5 to 10 years. This is known as a deferred call, and such bonds are said to have call protection.

Companies are not likely to call bonds unless interest rates have declined sig- nifi cantly since the bonds were issued. Suppose a company sold bonds when inter- est rates were relatively high. Provided the issue is callable, the company could sell a new issue of low-yielding securities if and when interest rates drop, use the proceeds of the new issue to retire the high-rate issue, and thus reduce its interest expense. This process is called a refunding operation. Thus, the call privilege is valu- able to the fi rm but detrimental to long-term investors, who will need to reinvest the funds they receive at the new and lower rates. Accordingly, the interest rate on a new issue of callable bonds will exceed that on the company’s new noncallable bonds. For example, on February 29, 2008, Pacifi c Timber Company sold a bond issue yielding 8% that was callable immediately. On the same day, Northwest Milling Company sold an issue with similar risk and maturity that yielded only 7.5%; but its bonds were noncallable for 10 years. Investors were willing to accept a 0.5% lower coupon interest rate on Northwest’s bonds for the assurance that the 7.5% interest rate would be earned for at least 10 years. Pacifi c, on the other hand, had to incur a 0.5% higher annual interest rate for the option of calling the bonds in the event of a decline in rates.

Note that the refunding operation is similar to a homeowner refi nancing his or her home mortgage after a decline in rates. Consider, for example, a homeowner with an outstanding mortgage at 8%. If mortgage rates have fallen to 5%, the home- owner will probably fi nd it benefi cial to refi nance the mortgage. There may be

Original Maturity The number of years to maturity at the time a bond is issued.

Call Provision A provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date.

3 In July 1993, The Walt Disney Company, attempting to lock in a low interest rate, stretched the meaning of “long-term bond” by issuing the fi rst 100-year bonds sold by any borrower in modern times. Soon after, Coca- Cola became the second company to sell 100-year bonds. A number of other companies have followed. 4 The number of new corporate issues with call provisions has declined somewhat in recent years. In the 1980s, nearly 80% of new issues contained call provisions; but in recent years, this number has fallen to about 35%. The use of call provisions also varies with credit quality. Roughly 25% of investment-grade bonds in recent years have call provisions versus about 75% of non-investment-grade bonds. Interest rates were historically high in the 1980s, so issuers wanted to be able to refund their debt if and when rates fell. Similarly, companies with low ratings hoped their ratings would rise, lowering their market rates and giving them an opportunity to refund. For more in- formation on the use of callable bonds, see Levent Güntay, N. R. Prabhala, and Haluk Unal, “Callable Bonds, Interest- Rate Risk, and the Supply Side of Hedging,” May 2005, a Wharton Financial Institutions Center working paper.

199Chapter 7 Bonds and Their Valuation

some fees involved in the refi nancing, but the lower rate may be more than enough to offset those fees. The analysis required is essentially the same for homeowners and corporations.

7-2e Sinking Funds Some bonds include a sinking fund provision that facilitates the orderly retire- ment of the bond issue. Years ago fi rms were required to deposit money with a trustee, which invested the funds and then used the accumulated sum to retire the bonds when they matured. Today, though, sinking fund provisions require the issuer to buy back a specifi ed percentage of the issue each year. A failure to meet the sinking fund requirement constitutes a default, which may throw the company into bankruptcy. Therefore, a sinking fund is a mandatory payment.

Suppose a company issued $100 million of 20-year bonds and it is required to call 5% of the issue, or $5 million of bonds, each year. In most cases, the issuer can handle the sinking fund requirement in either of two ways: 1. It can call in for redemption, at par value, the required $5 million of bonds. The

bonds are numbered serially, and those called for redemption would be deter- mined by a lottery administered by the trustee.

2. The company can buy the required number of bonds on the open market.

The fi rm will choose the least-cost method. If interest rates have fallen since the bond was issued, the bond will sell for more than its par value. In this case, the fi rm will use the call option. However, if interest rates have risen, the bonds will sell at a price below par; so the fi rm can and will buy $5 million par value of bonds in the open market for less than $5 million. Note that a call for sinking fund pur- poses is generally different from a refunding call because most sinking fund calls require no call premium. However, only a small percentage of the issue is nor- mally callable in a given year.

Although sinking funds are designed to protect investors by ensuring that the bonds are retired in an orderly fashion, these funds work to the detriment of bond- holders if the bond’s coupon rate is higher than the current market rate. For exam- ple, suppose the bond has a 10% coupon but similar bonds now yield only 7.5%. A sinking fund call at par would require a long-term investor to give up a bond that pays $100 of interest and then to reinvest in a bond that pays only $75 per year. This is an obvious disadvantage to those bondholders whose bonds are called. On balance, however, bonds that have a sinking fund are regarded as being safer than those without such a provision; so at the time they are issued, sinking fund bonds have lower coupon rates than otherwise similar bonds without sinking funds.

7-2f Other Features Several other types of bonds are used suffi ciently often to warrant mention.5 First, convertible bonds are bonds that are exchangeable into shares of common stock at a fi xed price at the option of the bondholder. Convertibles offer investors the chance for capital gains if the stock increases, but that feature enables the issuing company to set a lower coupon rate than on nonconvertible debt with similar credit risk. Bonds issued with warrants are similar to convertibles; but instead of giving the investor an option to exchange the bonds for stock, warrants give the holder an option to buy stock for a stated price, thereby providing a capital gain if the stock’s price rises. Because of this factor, bonds issued with warrants, like con- vertibles, carry lower coupon rates than otherwise similar nonconvertible bonds.

Sinking Fund Provision A provision in a bond contract that requires the issuer to retire a portion of the bond issue each year.

Convertible Bond A bond that is exchangeable at the option of the holder for the issuing firm’s common stock.

Warrant A long-term option to buy a stated number of shares of common stock at a specified price.

5 A recent article by John D. Finnerty and Douglas R. Emery reviews new types of debt (and other) securities that have been created in recent years. See “Corporate Securities Innovations: An Update,” Journal of Applied Finance: Theory, Practice, Education, Vol. 12, no. 1 (Spring/Summer 2002), pp. 21–47.

200 Part 3 Financial Assets

Whereas callable bonds give the issuer the right to retire the debt prior to ma- turity, putable bonds allow investors to require the company to pay in advance. If interest rates rise, investors will put the bonds back to the company and reinvest in higher coupon bonds. Yet another type of bond is the income bond, which pays interest only if the issuer has earned enough money to pay the interest. Thus, in- come bonds cannot bankrupt a company; but from an investor’s standpoint, they are riskier than “regular” bonds. Yet another bond is the indexed, or purchasing power, bond. The interest rate is based on an infl ation index such as the consumer price index; so the interest paid rises automatically when the infl ation rate rises, thus protecting bondholders against infl ation. As we mentioned in Chapter 6, the U.S. Treasury is the main issuer of indexed bonds. Recall that these Treasury Infl a- tion Protected Securities (TIPS) generally pay a real return varying from 1% to 3%, plus the rate of infl ation during the past year.

Putable Bond A bond with a provision that allows its investors to sell it back to the company prior to maturity at a prearranged price.

Income Bond A bond that pays interest only if it is earned.

Indexed (Purchasing Power) Bond A bond that has interest payments based on an inflation index so as to protect the holder from inflation.

SEL F TEST Defi ne fl oating-rate bonds, zero coupon bonds, callable bonds, putable

bonds, income bonds, convertible bonds, and infl ation-indexed bonds (TIPS).

Which is riskier to an investor, other things held constant—a callable bond or a putable bond?

In general, how is the rate on a fl oating-rate bond determined?

What are the two ways sinking funds can be handled? Which alternative will be used if interest rates have risen? if interest rates have fallen?

7-3 BOND VALUATION The value of any fi nancial asset—a stock, a bond, a lease, or even a physical asset such as an apartment building or a piece of machinery—is the present value of the cash fl ows the asset is expected to produce.

The cash fl ows for a standard coupon-bearing bond, like those of Allied Foods, consist of interest payments during the bond’s 15-year life plus the amount bor- rowed (generally the par value) when the bond matures. In the case of a fl oating- rate bond, the interest payments vary over time. For zero coupon bonds, there are no interest payments; so the only cash fl ow is the face amount when the bond ma- tures. For a “regular” bond with a fi xed coupon, like Allied’s, here is the situation:

3210

Bond’s value

rd% N

INT INT INT M

INT

Here

rd ! the market rate of interest on the bond, 10%. This is the discount rate used to calculate the present value of the cash fl ows, which is also the bond’s price. In Chapter 6, we discussed in detail the various factors that deter- mine market interest rates. Note that rd is not the coupon interest rate. However, rd is equal to the coupon rate at times, especially the day the bond is issued; and when the two rates are equal, as in this case, the bond sells at par.

201Chapter 7 Bonds and Their Valuation

We can now redraw the time line to show the numerical values for all variables except the bond’s value (and price, assuming an equilibrium exists), VB:

3210

Bond’s value

10% 15

100 100 100100 1,000 1,100

The following general equation can be solved to fi nd the value of any bond:

Bond’s value ! VB ! INT _______ (1 " rd)

1 " INT _______ (1 " rd)

2 " . . . " INT _______ (1 " rd)

N " M _______ (1 " rd)

! ∑ t!1

INT _______ (1 " rd) t "

M _______ (1 " rd) N 7-1

Inserting values for the Allied bond, we have

VB ! ∑ t!1

$100 ______ (1.10)t " $1,000 _______ (1.10)15

The cash fl ows consist of an annuity of N years plus a lump sum payment at the end of Year N, and this fact is refl ected in Equation 7-1.

We could simply discount each cash fl ow back to the present and sum those PVs to fi nd the bond’s value; see Figure 7-1 for an example. However, this proce- dure is not very effi cient, especially when the bond has many years to maturity. Therefore, we use a fi nancial calculator to solve the problem. Here is the setup:

FVPVI/YRN PMT

10001001015

= –1,000Output:

Inputs:

Simply input N ! 15, rd ! I/YR ! 10, INT ! PMT ! 100, and M ! FV ! 1000; then press the PV key to fi nd the bond’s value, $1,000.6 Since the PV is an outfl ow to the

N ! the number of years before the bond matures ! 15. N declines over time after the bond has been issued; so a bond that had a maturity of 15 years when it was issued (original maturity ! 15) will have N ! 14 after 1 year, N ! 13 after 2 years, and so forth. At this point, we assume that the bond pays interest once a year, or annually; so N is measured in years. Later on we will analyze semiannual payment bonds, which pay interest every 6 months.

INT ! dollars of interest paid each year ! Coupon rate " Par value ! 0.10($1,000) ! $100. In calculator terminology, INT ! PMT ! 100. If the bond had been a semiannual payment bond, the payment would have been $50 every 6 months. The payment would have been zero if Allied had issued zero coupon bonds, and it would have varied over time if the bond had been a “fl oater.”

M ! the par, or maturity, value of the bond ! $1,000. This amount must be paid at maturity. Back in the 1970s and before, when paper bonds with paper cou- pons were used, most bonds had a $1,000 value. Now with computer-entry bonds, the par amount purchased can vary; but we use $1,000 for simplicity.

6 Spreadsheets can also be used to solve for the bond’s value, as we show in the Excel model for this chapter.

202 Part 3 Financial Assets

investor, it is shown with a negative sign. The calculator is programmed to solve Equation 7-1: It fi nds the PV of an annuity of $100 per year for 15 years discounted at 10%; then it fi nds the PV of the $1,000 maturity payment; then it adds those two PVs to fi nd the bond’s value.

In this example, the bond is selling at a price equal to its par value. Whenever the bond’s market, or going, rate, rd, is equal to its coupon rate, a fi xed-rate bond will sell at its par value. Normally, the coupon rate is set at the going rate in the market the day a bond is issued, causing it to sell at par initially.

The coupon rate remains fi xed after the bond is issued, but interest rates in the market move up and down. Looking at Equation 7-1, we see that an increase in the market interest rate (rd) causes the price of an outstanding bond to fall, whereas a decrease in the rate causes the bond’s price to rise. For example, if the market inter- est rate on Allied’s bond increased to 15% immediately after it was issued, we would recalculate the price with the new market interest rate as follows:

FVPVI/YRN PMT

10001001515

= –707.63Output:

Inputs:

The bond’s price would fall to $707.63, well below par, as a result of the increase in interest rates. Whenever the going rate of interest rises above the coupon rate, a fi xed-rate bond’s price will fall below its par value; this type of bond is called a discount bond.

Discount Bond A bond that sells below its par value; occurs whenever the going rate of interest is above the coupon rate.

100Payments

Present !Value

100 1,000

1,000.00 when rd ! 10%

100 100 100 100 100 100 100 100 100 100 100 100 100

1/3/10 1/2/20241/11 1/12 1/13 1/14 1/15 1/16 1/17 1/18 1/19 1/20 1/21 1/22 1/23

90.91 82.64 75.13 68.30 62.09 56.45 51.32 46.65 42.41 38.55 35.05 31.86 28.97 26.33 23.94

239.39

Time Line for Allied Food Products’ Bonds, 10% Interest RateFIGURE 7-1

203Chapter 7 Bonds and Their Valuation

On the other hand, bond prices rise when market interest rates fall. For exam- ple, if the market interest rate on Allied’s bond decreased to 5% immediately after it was issued, we would once again recalculate its price as follows:

FVPVI/YRN PMT

1000100515

= –1,518.98Output:

Inputs:

In this case, the price rises to $1,518.98. In general, whenever the going interest rate falls below the coupon rate, a fi xed-rate bond’s price will rise above its par value; this type of bond is called a premium bond.

To summarize, here is the situation:

rd ! coupon rate, fi xed-rate bond sells at par; hence, it is a par bond rd > coupon rate, fi xed-rate bond sells below par; hence, it is a discount bond rd < coupon rate, fi xed-rate bond sells above par; hence, it is a premium bond

Premium Bond A bond that sells above its par value; occurs whenever the going rate of interest is below the coupon rate.

SEL F TEST A bond that matures in 8 years has a par value of $1,000 and an annual coupon

payment of $70; its market interest rate is 9%. What is its price? ($889.30)

A bond that matures in 12 years has a par value of $1,000 and an annual cou- pon of 10%; the market interest rate is 8%. What is its price? ($1,150.72)

Which of those two bonds is a discount bond, and which is a premium bond?

7-4 BOND YIELDS If you examine the bond market table of The Wall Street Journal or a price sheet put out by a bond dealer, you will typically see information regarding each bond’s maturity date, price, and coupon interest rate. You will also see a reported yield. Unlike the coupon interest rate, which is fi xed, the bond’s yield varies from day to day depending on current market conditions.

To be most useful, the bond’s yield should give us an estimate of the rate of re- turn we would earn if we bought the bond today and held it over its remaining life. If the bond is not callable, its remaining life is its years to maturity. If it is call- able, its remaining life is the years to maturity if it is not called or the years to the call if it is called. In the following sections, we explain how to calculate those two possible yields and which one is likely to occur.

7-4a Yield to Maturity Suppose you were offered a 14-year, 10% annual coupon, $1,000 par value bond at a price of $1,494.93. What rate of interest would you earn on your investment if you bought the bond, held it to maturity, and received the promised interest and maturity payments? This rate is called the bond’s yield to maturity (YTM), and it is the interest rate generally discussed by investors when they talk about rates of return and the rate reported by The Wall Street Journal and other

Yield to Maturity (YTM) The rate of return earned on a bond if it is held to maturity.

204 Part 3 Financial Assets

publications. To fi nd the YTM, all you need to do is solve Equation 7-1 for rd as follows:

VB ! INT _______ (1 " rd)

1 " INT _______ (1 " rd)

2 " . . . " INT _______ (1 " rd)

N " M _______ (1 " rd)

$1,494.93 ! $100 _______ (1 # rd) 1 " . . . "

$100 ________ (1 # rd) 14 "

$1,000 ________ (1 # rd) 14

You can substitute values for rd until you fi nd a value that “works” and force the sum of the PVs in the equation to equal $1,494.93. However, fi nding rd ! YTM by trial and error would be a tedious, time-consuming process. However, as you might guess, the calculation is easy with a fi nancial calculator.7 Here is the setup:

FVPVI/YRN PMT

1000100–1494.9314

= 5Output:

Inputs:

Simply enter N ! 14, PV ! $1494.93, PMT ! 100, and FV ! 1000; then press the I/YR key. The answer, 5%, will appear.

The yield to maturity can also be viewed as the bond’s promised rate of return, which is the return that investors will receive if all of the promised payments are made. However, the yield to maturity equals the expected rate of return only when (1) the probability of default is zero and (2) the bond cannot be called. If there is some default risk or the bond may be called, there is some chance that the prom- ised payments to maturity will not be received, in which case the calculated yield to maturity will exceed the expected return.

Note also that a bond’s calculated yield to maturity changes whenever interest rates in the economy change, which is almost daily. An investor who purchases a bond and holds it until it matures will receive the YTM that existed on the pur- chase date, but the bond’s calculated YTM will change frequently between the purchase date and the maturity date.

7-4b Yield to Call If you purchase a bond that is callable and the company calls it, you do not have the option of holding it to maturity. Therefore, the yield to maturity would not be earned. For example, if Allied’s 10% coupon bonds were callable and if interest rates fell from 10% to 5%, the company could call in the 10% bonds, replace them with 5% bonds, and save $100 $ $50 ! $50 interest per bond per year. This would be benefi cial to the company but not to its bondholders.

If current interest rates are well below an outstanding bond’s coupon rate, a callable bond is likely to be called; and investors will estimate its most likely rate of return as the yield to call (YTC) rather than the yield to maturity. To calculate the YTC, we modify Equation 7-1, using years to call as N and the call price rather than the maturity value as the ending payment. Here’s the modifi ed equation:

7-2 Price of bond ! ∑ t!1

INT _______ (1 " rd) t "

Call price ________ (1 " rd) N

Here N is the number of years until the company can call the bond; call price is the price the company must pay in order to call the bond (it is often set equal to the par value plus one year’s interest); and rd is the YTC.

Yield to Call (YTC) The rate of return earned on a bond when it is called before its maturity date.

7 You can also fi nd the YTM with a spreadsheet. In Excel, you use the Rate function, inputting Nper ! 14, Pmt ! 100, Pv ! $1494.93, Fv ! 1000, and 0 for Type and leaving Guess blank.

205Chapter 7 Bonds and Their Valuation

To illustrate, suppose Allied’s bonds had a provision that permitted the com- pany, if it desired, to call them 10 years after their issue date at a price of $1,100. Suppose further that interest rates had fallen and that 1 year after issuance, the going interest rate had declined, causing their price to rise to $1,494.93. Here is the time line and the setup for fi nding the bonds’ YTC with a fi nancial calculator:

8210

#1,494.93

YTC = ? 9

100 100 100100 1,100

FVPVI/YRN PMT

1100100–1494.939

4.21 = YTCOutput:

Inputs:

The YTC is 4.21%—this is the return you would earn if you bought an Allied bond at a price of $1,494.93 and it was called 9 years from today. (It could not be called until 10 years after issuance. One year has gone by, so there are 9 years left until the fi rst call date.)

Do you think Allied will call its 10% bonds when they become callable? Allied’s action will depend on what the going interest rate is when they become callable. If the going rate remains at rd ! 5%, Allied could save 10% $ 5% ! 5%, or $50 per bond per year; so it would call the 10% bonds and replace them with a new 5% issue. There would be some cost to the company to refund the bonds; but because the interest savings would most likely be worth the cost, Allied would probably refund them. Therefore, you should expect to earn the YTC ! 4.21% rather than the YTM ! 5% if you bought the bond under the indicated conditions.

In the balance of this chapter, we assume that bonds are not callable unless otherwise noted. However, some of the end-of-chapter problems deal with yield to call.8

8 Brokerage houses occasionally report a bond’s current yield, defi ned as the annual interest payment divided by the current price. For example, if Allied’s 10% coupon bonds were selling for $985, the current yield would be $100/$985 ! 10.15%. Unlike the YTM or YTC, the current yield does not represent the actual return that investors should expect because it does not account for the capital gain or loss that will be realized if the bond is held until it matures or is called. The current yield was popular before calculators and computers came along because it was easy to calculate. However, it can be misleading, and now it’s easy enough to calculate the YTM and YTC.

SEL F TEST Explain the diff erence between yield to maturity and yield to call.

Halley Enterprises’ bonds currently sell for $975. They have a 7-year maturity, an annual coupon of $90, and a par value of $1,000. What is their yield to maturity? (9.51%)

The Henderson Company’s bonds currently sell for $1,275. They pay a $120 annual coupon and have a 20-year maturity, but they can be called in 5 years at $1,120. What are their YTM and their YTC, and which is “more relevant” in the sense that investors should expect to earn it? (8.99%; 7.31%; YTC)

206 Part 3 Financial Assets

7-5 CHANGES IN BOND VALUES OVER TIME When a coupon bond is issued, the coupon is generally set at a level that causes the bond’s market price to equal its par value. If a lower coupon were set, investors would not be willing to pay $1,000 for the bond; but if a higher coupon were set, investors would clamor for it and bid its price up over $1,000. Investment bankers can judge quite precisely the coupon rate that will cause a bond to sell at its $1,000 par value.

A bond that has just been issued is known as a new issue. Once it has been is- sued, it is an outstanding bond, also called a seasoned issue. Newly issued bonds gen- erally sell at prices very close to par, but the prices of outstanding bonds can vary widely from par. Except for fl oating-rate bonds, coupon payments are constant; so when economic conditions change, a bond with a $100 coupon that sold at its $1,000 par value when it was issued will sell for more or less than $1,000 thereafter.

Among its outstanding bonds, Allied currently has three equally risky issues that will mature in 15 years: • Allied’s just-issued 15-year bonds have a 10% annual coupon. They were

issued at par, which means that the market interest rate on their issue date was also 10%. Because the coupon rate equals the market interest rate, these bonds are trading at par, or $1,000.

• Five years ago Allied issued 20-year bonds with a 7% annual coupon. These bonds currently have 15 years remaining until maturity. They were originally issued at par, which means that 5 years ago the market interest rate was 7%. Currently, this bond’s coupon rate is less than the 10% market rate, so they sell at a discount. Using a fi nancial calculator or spreadsheet, we can quickly fi nd that they have a price of $771.82. (Set N ! 15, I/YR ! 10, PMT ! 70, and FV ! 1000 and solve for the PV to get the price.)

• Ten years ago Allied issued 25-year bonds with a 13% coupon rate. These bonds currently have 15 years remaining until maturity. They were originally issued at par, which means that 10 years ago the market interest rate must have been 13%. Because their coupon rate is greater than the current market rate, they sell at a premium. Using a fi nancial calculator or spreadsheet, we can fi nd that their price is $1,228.18. (Set N ! 15, I/YR ! 10, PMT ! 130, and FV ! 1000 and solve for the PV to get the price.)

Each of these three bonds has a 15-year maturity; each has the same credit risk; and thus each has the same market interest rate, 10%. However, the bonds have differ- ent prices because of their different coupon rates.

Now let’s consider what would happen to the prices of these three bonds over the 15 years until they mature, assuming that market interest rates remain constant at 10% and Allied does not default on its payments. Table 7-1 demonstrates how the prices of each of these bonds will change over time if market interest rates re- main at 10%. One year from now each bond will have a maturity of 14 years—that is, N ! 14. With a fi nancial calculator, override N ! 15 with N ! 14 and press the PV key; that gives you the value of each bond 1 year from now. Continuing, set N ! 13, N ! 12, and so forth, to see how the prices change over time.

Table 7-1 also shows the current yield (which is the coupon interest divided by the bond’s price), the capital gains yield, and the total return over time. For any given year, the capital gains yield is calculated as the bond’s annual change in price divided by the beginning-of-year price. For example, if a bond was selling for $1,000 at the beginning of the year and $1,035 at the end of the year, its capital gains yield for the year would be $35/$1,000 ! 3.5%. (If the bond was selling at a premium, its price would decline over time. Then the capital gains yield would be negative, but it would be offset by a high current yield.) A bond’s total return is

Calculation of Current Yields, Capital Gains Yields, and Total Returns for 7%, 10%, and 13% Coupon Bonds When the Market Rate Remains Constant at 10%

T a b l e 7 - 1

7% COUPON BOND 10% COUPON BOND 13% COUPON BOND

Number of Years Until

Maturity Pricea

Expected Current Yieldb

Expected Capital Gains Yieldc

Expected Total

Returnd Pricea

Expected Current Yieldb

Expected Capital Gains Yieldc

Expected Total

Returnd Pricea

Expected Current Yieldb

Expected Capital Gains Yieldc

Expected Total

Returnd

15 $ 771.82 9.1% 0.9% 10.0% $1,000.00 10.0% 0.0% 10.0% $1,228.18 10.6% $0.6% 10.0% 14 779.00 9.0 1.0 10.0 1,000.00 10.0 0.0 10.0 1,221.00 10.6 $0.6 10.0 13 786.90 8.9 1.1 10.0 1,000.00 10.0 0.0 10.0 1,213.10 10.7 $0.7 10.0 12 795.59 8.8 1.2 10.0 1,000.00 10.0 0.0 10.0 1,204.41 10.8 $0.8 10.0 11 805.15 8.7 1.3 10.0 1,000.00 10.0 0.0 10.0 1,194.85 10.9 $0.9 10.0 10 815.66 8.6 1.4 10.0 1,000.00 10.0 0.0 10.0 1,184.34 11.0 $1.0 10.0

9 827.23 8.5 1.5 10.0 1,000.00 10.0 0.0 10.0 1,172.77 11.1 $1.1 10.0 8 839.95 8.3 1.7 10.0 1,000.00 10.0 0.0 10.0 1,160.05 11.2 $1.2 10.0 7 853.95 8.2 1.8 10.0 1,000.00 10.0 0.0 10.0 1,146.05 11.3 $1.3 10.0 6 869.34 8.1 1.9 10.0 1,000.00 10.0 0.0 10.0 1,130.66 11.5 $1.5 10.0 5 886.28 7.9 2.1 10.0 1,000.00 10.0 0.0 10.0 1,113.72 11.7 $1.7 10.0 4 904.90 7.7 2.3 10.0 1,000.00 10.0 0.0 10.0 1,095.10 11.9 $1.9 10.0 3 925.39 7.6 2.4 10.0 1,000.00 10.0 0.0 10.0 1,074.61 12.1 $2.1 10.0 2 947.93 7.4 2.6 10.0 1,000.00 10.0 0.0 10.0 1,052.07 12.4 $2.4 10.0 1 972.73 7.2 2.8 10.0 1,000.00 10.0 0.0 10.0 1,027.27 12.7 $2.7 10.0 0 1,000.00 1,000.00 1,000.00

Notes: aUsing a financial calculator, the price of each bond is calculated by entering the data for N, I/YR, PMT, and FV, then solving for PV ! the bond’s value. bThe expected current yield is calculated as the annual interest divided by the price of the bond. c The expected capital gains yield is calculated as the differece between the end-of-year bond price and the beginning - of - year bond price divided by the beginning-of-year price. dThe expected total return is the sum of the expected current yield and the expected capital gains yield.

207

208 Part 3 Financial Assets

equal to the current yield plus the capital gains yield. In the absence of default risk and assuming market equilibrium, the total return is also equal to YTM and the market interest rate, which in our example is 10%.

Figure 7-2 plots the three bonds’ predicted prices as calculated in Table 7-1. Notice that the bonds have very different price paths over time but that at matu- rity, all three will sell at their par value of $1,000. Here are some points about the prices of the bonds over time: • The price of the 10% coupon bond trading at par will remain at $1,000 if the

market interest rate remains at 10%. Therefore, its current yield will remain at 10% and its capital gains yield will be zero each year.

• The 7% bond trades at a discount; but at maturity, it must sell at par because that is the amount the company will give to its holders. Therefore, its price must rise over time.

• The 13% coupon bond trades at a premium. However, its price must be equal to its par value at maturity; so the price must decline over time.

While the prices of the 7% and 13% coupon bonds move in opposite directions over time, each bond provides investors with the same total return, 10%, which is also the total return on the 10% coupon bond that sells at par. The discount bond has a low coupon rate (and therefore a low current yield), but it provides a capital gain each year. In contrast, the premium bond has a high current yield, but it has an expected capital loss each year.9

9 In this example (and throughout the text), we ignore the tax eff ects associated with purchasing diff erent types of bonds. For coupon bonds, under the current Tax Code, coupon payments are taxed as ordinary income, whereas capital gains are taxed at the capital gains tax rate. As we mentioned in Chapter 3, for most investors, the capital gains tax rate is lower than the personal tax rate. Moreover, while coupon payments are taxed each year, capital gains taxes are deferred until the bond is sold or matures. Consequently, all else equal, investors end up paying lower taxes on discount bonds because a greater percentage of their total return comes in the form of capital gains. For details on the tax treatment of zero coupon bonds, see Web Appendix 7A.

15 12 9 6 3 0 0

1,000

1,250

1,500

500

750

Coupon = 10%

Coupon = 7%

Coupon = 13%

Bond Value ($)

Years Remaining until Maturity

Time Paths of 7%, 10%, and 13% Coupon Bonds When the Market Rate Remains Constant at 10%FIGURE 7-2

209Chapter 7 Bonds and Their Valuation

7-6 BONDS WITH SEMIANNUAL COUPONS Although some bonds pay interest annually, the vast majority actually make pay- ments semiannually. To evaluate semiannual bonds, we must modify the valu ation model (Equation 7-1) as follows: 1. Divide the annual coupon interest payment by 2 to determine the dollars of

interest paid each six months. 2. Multiply the years to maturity, N, by 2 to determine the number of semiannual

periods. 3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic

(semiannual) interest rate.

On a time line, there would be twice as many payments, but each would be half as large as with an annual payment bond. Making the indicated changes re- sults in the following equation for fi nding a semiannual bond’s value:

VB ! ∑ t!1

INT/2 __________ (1 " rd / 2) t "

M ___________ (1 " rd / 2) 2N 7-1a

To illustrate, assume that Allied Food’s 15-year bonds as discussed in Section 7-3 pay $50 of interest each 6 months rather than $100 at the end of each year. Thus, each interest payment is only half as large but there are twice as many of them. We would describe the coupon rate as “10% with semiannual payments.”10

When the going (nominal) rate is rd ! 5% with semiannual compounding, the value of a 15-year, 10% semiannual coupon bond that pays $50 interest every 6 months is found as follows:

FVPVI/YRN PMT

1000502.5

= –1,523.26

Output:

Inputs:

Enter N ! 30, rd ! I/YR ! 2.5, PMT ! 50, and FV ! 1000; then press the PV key to obtain the bond’s value, $1,523.26. The value with semiannual interest payments is slightly larger than $1,518.98, the value when interest is paid annually as we

SEL F TEST What is meant by the terms new issue and seasoned issue?

Last year a fi rm issued 20-year, 8% annual coupon bonds at a par value of $1,000.

(1) Suppose that one year later the going rate drops to 6%. What is the new price of the bonds assuming they now have 19 years to maturity? ($1,223.16)

(2) Suppose that one year after issue, the going interest rate is 10% (rather than 6%). What would the price have been? ($832.70)

Why do the prices of fi xed-rate bonds fall if expectations for infl ation rise?

10 In this situation, the coupon rate of “10% paid semiannually” is the rate that bond dealers, corporate treasurers, and investors generally discuss. Of course, if this bond were issued at par, its eff ective annual rate would be higher than 10%.

EAR ! EFF% ! ( 1 # rNOM ____ M ) M $1 ! ( 1 # 0.10 ____ 2 ) 2 $1 ! (1.05)2 $ 1 ! 10.25% Since 10% with annual payments is quite diff erent from 10% with semiannual payments, we have assumed a change in eff ective rates in this section from the situation in Section 7-3, where we assumed 10% with annual payments.

210 Part 3 Financial Assets

calculated in Section 7-3. This higher value occurs because each interest payment is received somewhat faster under semiannual compounding.

Alternatively, when we know the price of a semiannual bond, we can easily back out the bond’s nominal yield to maturity. In the previous example, if you were told that a 15-year bond with a 10% semiannual coupon was selling for $1,523.26, you could solve for the bond’s periodic interest rate as follows:

FVPVI/YRN PMT

100050

= 2.5

–1,523.2630

Output:

Inputs:

In this case, enter N = 30, PV = $1523.26, PMT = 50, and FV = 1000; then press the I/YR key to obtain the interest rate per semiannual period, 2.5%. Multiplying by 2, we calculate the bond’s nominal yield to maturity to be 5%.11

SEL F TEST Describe how the annual payment bond valuation formula is changed to

evaluate semiannual coupon bonds and write the revised formula.

Hartwell Corporation’s bonds have a 20-year maturity, an 8% semiannual coupon, and a face value of $1,000. The going interest rate (rd) is 7% based on semiannual compounding. What is the bond’s price? ($1,106.78)

11 We can use a similar process to calculate the nominal yield to call for a semiannual bond. The only diff erence would be that N should represent the number of semiannual periods until the bond is callable and FV should be the bond’s call price rather than its par value. 12 An immediate increase in rates from 10% to 15% would be quite unusual, and it would occur only if something quite bad were revealed about the company or happened in the economy. Smaller but still signifi cant rate increases that adversely aff ect bondholders do occur fairly often. 13 You would have an accounting (and tax) loss only if you sold the bond; if you held it to maturity, you would not have such a loss. However, even if you did not sell, you would still have suff ered a real economic loss in an opportunity cost sense because you would have lost the opportunity to invest at 15% and would be stuck with a 10% bond in a 15% market. In an economic sense, “paper losses” are just as bad as realized accounting losses.

7-7 ASSESSING A BOND’S RISKINESS In this section, we identify and explain the two key factors that impact a bond’s riskiness. Once those factors are identifi ed, we differentiate between them and discuss how you can minimize these risks.

7-7a Interest Rate Risk As we saw in Chapter 6, interest rates fl uctuate over time and when they rise, the value of outstanding bonds decline. This risk of a decline in bond values due to an increase in interest rates is called interest rate risk (or interest rate price risk). To illustrate, refer back to Allied’s bonds; assume once more that they have a 10% annual coupon; and assume that you bought one of these bonds at its par value, $1,000. Shortly after your purchase, the going interest rate rises from 10 to 15%.12 As we saw in Section 7-3, this interest rate increase would cause the bond’s price to fall from $1,000 to $707.63; so you would have a loss of $292.37 on the bond.13 Since interest rates can and do rise, rising rates cause losses to bondholders; people or fi rms who invest in bonds are exposed to risk from increasing interest rates.

Interest Rate (Price) Risk The risk of a decline in a bond’s price due to an increase in interest rates.

211Chapter 7 Bonds and Their Valuation

Interest rate risk is higher on bonds that have long maturities than on bonds that will mature in the near future.14 This follows because the longer the maturity, the longer before the bond will be paid off and the bondholder can replace it with another bond with a higher coupon. This point can be demonstrated by showing how the value of a 1-year bond with a 10% annual coupon fl uctuates with changes in rd and then comparing those changes with changes on a 15-year bond. The 1-year bond’s values at different interest rates are shown here:

Value of a 1-year bond at

FVPVI/YRN PMT

10001005

–1,047.62

Output (Bond Value):

Inputs:rd = 5%:

FVPVI/YRN PMT

100010010

–1,000.00

Output (Bond Value):

Inputs:rd = 10%:

FVPVI/YRN PMT

100010015

–956.52

Output (Bond Value):

Inputs:rd = 15%:

You would obtain the fi rst value with a fi nancial calculator by entering N ! 1, I/YR ! 5, PMT ! 100, and FV ! 1000 and then pressing PV to get $1,047.62. With everything still in your calculator, enter I/YR ! 10 to override the old I/YR ! 5 and press PV to fi nd the bond’s value at a 10% rate; it drops to $1,000. Then enter I/YR ! 15 and press the PV key to fi nd the last bond value, $956.52.

The effects of increasing rates on the 15-year bond as found earlier can be com- pared with the just-calculated effects for the 1-year bond. This comparison is shown in Figure 7-3, where we show bond prices at several rates and then plot those prices on the graph. Compared to the 1-year bond, the 15-year bond is far more sensitive to changes in rates. At a 10% interest rate, both the 15-year and 1-year bonds are valued at $1,000. When rates rise to 15%, the 15-year bond falls to $707.63, but the 1-year bond falls only to $956.52. The price decline for the 1-year bond is only 4.35%, while that for the 15-year bond is 29.24%.

For bonds with similar coupons, this differential interest rate sensitivity always holds true—the longer its maturity, the more its price changes in response to a given change in interest rates. Thus, even if the risk of default on two bonds is exactly the same, the

14 Actually, a bond’s maturity and coupon rate both aff ect interest rate risk. Low coupons mean that most of the bond’s return will come from repayment of principal, whereas on a high-coupon bond with the same maturity, more of the cash fl ows will come in during the early years due to the relatively large coupon payments. A measurement called duration, which fi nds the average number of years the bond’s PV of cash fl ows remain outstanding, has been developed to combine maturity and coupons. A zero coupon bond, which has no interest payments and whose payments all come at maturity, has a duration equal to its maturity. All coupon bonds have durations that are shorter than their maturity; and the higher the coupon rate, the shorter the duration. Bonds with longer duration are exposed to more interest rate risk. A discussion of duration would go beyond the scope of this book, but see any investments text for a discussion of the concept.

212 Part 3 Financial Assets

one with the longer maturity is typically exposed to more risk from a rise in inter- est rates.15

The logical explanation for this difference in interest rate risk is simple. Sup- pose you bought a 15-year bond that yielded 10%, or $100 a year. Now suppose in- terest rates on comparable-risk bonds rose to 15%. You would be stuck with only $100 of interest for the next 15 years. On the other hand, had you bought a 1-year bond, you would have had a low return for only 1 year. At the end of the year, you would have received your $1,000 back; then you could have reinvested it and earned 15%, or $150 per year, for the next 14 years.

Values of Long- and Short-Term 10% Annual Coupon Bonds at Diff erent Market Interest RatesFIGURE 7-3

VALUE OF

Current Market Interest Rate, rd

1-Year Bond

15-Year Bond

5% $1,047.62 $1,518.98

10 1,000.00 1,000.00

15 956.52 707.63

20 916.67 532.45

25 880.00 421.11

Note: Bond values were calculated using a fi nancial calculator assuming annual, or once-a-year, compounding.

500

1,000

1,500

2,000

2,500

5 10 15 20 250

Bond Value ($)

15-Year Bond

1-Year Bond

Interest Rate (%)

15 If a 10-year bond were plotted on the graph in Figure 7-3, its curve would lie between those of the 15-year and the 1-year bonds. The curve of a 1-month bond would be almost horizontal, indicating that its price would change very little in response to an interest rate change; but a 100-year bond would have a very steep slope, and the slope of a perpetuity would be even steeper. Also, a zero coupon bond’s price is quite sensitive to interest rate changes; and the longer its maturity, the greater its price sensitivity. Therefore, a 30-year zero coupon bond would have a huge amount of interest rate risk.

213Chapter 7 Bonds and Their Valuation

7-7b Reinvestment Rate Risk As we saw in the preceding section, an increase in interest rates hurts bondholders because it leads to a decline in the current value of a bond portfolio. But can a decrease in interest rates also hurt bondholders? Actually, the answer is yes because if interest rates fall, long-term investors will suffer a reduction in income. For example, consider a retiree who has a bond portfolio and lives off the income it produces. The bonds in the portfolio, on average, have coupon rates of 10%. Now suppose interest rates decline to 5%. Many of the bonds will mature or be called; as this occurs, the bondholder will have to replace 10% bonds with 5% bonds. Thus, the retiree will suffer a reduction of income.

The risk of an income decline due to a drop in interest rates is called reinvestment rate risk, and its importance has been demonstrated to all bond- holders in recent years as a result of the sharp drop in rates since the mid-1980s. Reinvestment rate risk is obviously high on callable bonds. It is also high on short- term bonds because the shorter the bond’s maturity, the fewer the years before the relatively high old-coupon bonds will be replaced with the new low-coupon is- sues. Thus, retirees whose primary holdings are short-term bonds or other debt securities will be hurt badly by a decline in rates, but holders of noncallable long- term bonds will continue to enjoy the old high rates.

7-7c Comparing Interest Rate and Reinvestment Rate Risk

Note that interest rate risk relates to the current market value of the bond portfolio, while reinvestment rate risk relates to the income the portfolio produces. If you hold long-term bonds, you will face signifi cant interest rate price risk because the value of your portfolio will decline if interest rates rise, but you will not face much reinvestment rate risk because your income will be stable. On the other hand, if you hold short-term bonds, you will not be exposed to much interest rate price risk, but you will be exposed to signifi cant reinvestment rate risk.

Which type of risk is “more relevant” to a given investor depends critically on how long the investor plans to hold the bonds—this is often referred to as his or her investment horizon. To illustrate, consider an investor who has a relatively short 1-year investment horizon—say, the investor plans to go to graduate school a year from now and needs money for tuition and expenses. Reinvestment rate risk is of minimal concern to this investor because there is little time for reinvest- ment. The investor could eliminate interest rate risk by buying a 1-year Treasury security since he would be assured of receiving the face value of the bond 1 year from now (the investment horizon). However, if this investor were to buy a long- term Treasury security, he would bear a considerable amount of interest rate risk because, as we have seen, long-term bond prices decline when interest rates rise. Consequently, investors with shorter investment horizons should view long-term bonds as being more risky than short-term bonds.

By contrast, the reinvestment risk inherent in short-term bonds is especially relevant to investors with longer investment horizons. Consider a retiree who is living on income from her portfolio. If this investor buys 1-year bonds, she will have to “roll them over” every year; and if rates fall, her income in subse- quent years will likewise decline. A younger couple saving for their retirement or their children’s college costs, for example, would be affected similarly be- cause if they buy short-term bonds, they too will have to roll over their portfo- lio at possibly much lower rates. Since there is uncertainty today about the rates that will be earned on these reinvested cash fl ows, long-term investors should be especially concerned about the reinvestment rate risk inherent in short-term bonds.

Reinvestment Rate Risk The risk that a decline in interest rates will lead to a decline in income from a bond portfolio.

Investment Horizon The period of time an investor plans to hold a particular investment.

214 Part 3 Financial Assets

One way to manage both interest rate and reinvestment rate risk is to buy a zero coupon Treasury bond with a maturity that matches the investor’s invest- ment horizon. For example, assume your investment horizon is 10 years. If you buy a 10-year zero, you will receive a guaranteed payment in 10 years equal to the bond’s face value.16 Moreover, as there are no coupons to reinvest, there is no rein- vestment rate risk. This explains why investors with specifi c goals often invest in zero coupon bonds.17

Recall from Chapter 6 that maturity risk premiums are generally positive. Moreover, a positive maturity risk premium implies that investors, on average, re- gard longer-term bonds as being riskier than shorter-term bonds. That, in turn, suggests that the average investor is most concerned with interest rate price risk. Still, it is appropriate for each investor to consider his or her own situation, to rec- ognize the risks inherent in bonds with different maturities, and to construct a portfolio that deals best with the investor’s most relevant risk.

16 Note that in this example, the 10-year zero technically has a considerable amount of interest rate risk since its current price is highly sensitive to changes in interest rates. However, the year-to year movements in price should not be of great concern to an investor with a 10-year horizon. The reason is that the investor knows that regardless of what happens to interest rates, the bond’s price will still be $1,000 when it matures. 17 Two words of caution about zeros are in order. First, as we show in Web Appendix 7A, investors in zeros must pay taxes each year on their accrued gain in value even though the bonds don’t pay any cash until they mature. Second, buying a zero coupon with a maturity equal to your investment horizon enables you to lock in a nominal cash payoff , but the real value of that payment still depends on what happens to infl ation during your investment horizon. What we need is an infl ation-indexed zero coupon Treasury bond; but to date, no such bond exists.

Also, the fact that maturity risk premiums are positive suggests that most investors have relatively short in- vestment horizons, or at least worry about short-term changes in their net worth. See Stocks, Bonds, Bills, and In- fl ation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008), which fi nds that the maturity risk pre- mium for long-term bonds has averaged 1.4% over the past 2 years.

SEL F TEST Diff erentiate between interest rate risk and reinvestment rate risk.

To which type of risk are holders of long-term bonds more exposed? short- term bondholders?

What type of security can be used to minimize both interest rate and reinvestment rate risk for an investor with a fi xed investment horizon?

7-8 DEFAULT RISK Potential default is another important risk that bondholders face. If the issuer defaults, investors will receive less than the promised return. Recall from Chapter 6 that the quoted interest rate includes a default risk premium—the higher the probability of default, the higher the premium and thus the yield to maturity. Default risk on Treasuries is zero, but this risk is substantial for lower-grade corpo- rate and municipal bonds.

To illustrate, suppose two bonds have the same promised cash fl ows—their coupon rates, maturities, liquidity, and infl ation exposures are identical; but one has more default risk than the other. Investors will naturally pay more for the one with less chance of default. As a result, bonds with higher default risk have higher market rates: rd ! r* # IP # DRP # LP # MRP. If a bond’s default risk changes, rd and thus the price will be affected. Thus, if the default risk on Allied’s bonds increases, their price will fall and the yield to maturity (YTM ! rd) will increase.

215Chapter 7 Bonds and Their Valuation

7-8a Various Types of Corporate Bonds Default risk is infl uenced by the fi nancial strength of the issuer and the terms of the bond contract, including whether collateral has been pledged to secure the bond. The characteristics of some key types of bonds are described in this section.

Mortgage Bonds Under a mortgage bond, the corporation pledges specifi c assets as security for the bond. To illustrate, in 2008, Billingham Corporation needed $10 million to build a regional distribution center. Bonds in the amount of $4 million, secured by a fi rst mortgage on the property, were issued. (The remaining $6 million was fi nanced with equity capital.) If Billingham defaults on the bonds, the bondholders can fore- close on the property and sell it to satisfy their claims.

If Billingham had chosen to, it could have issued second mortgage bonds secured by the same $10 million of assets. In the event of liquidation, the holders of the sec- ond mortgage bonds would have a claim against the property, but only after the fi rst mortgage bondholders had been paid off in full. Thus, second mortgages are sometimes called junior mortgages because they are junior in priority to the claims of senior mortgages, or fi rst mortgage bonds.

All mortgage bonds are subject to an indenture, which is a legal document that spells out in detail the rights of the bondholders and the corporation. The indentures of many major corporations were written 20, 30, 40, or more years ago. These indentures are generally “open-ended,” meaning that new bonds can be issued from time to time under the same indenture. However, the amount of new bonds that can be issued is usually limited to a specifi ed percentage of the fi rm’s total “bondable property,” which generally includes all land, plant, and equip- ment. And, of course, the coupon interest rate on the newly issued bonds changes over time, along with the market rate on the older bonds.

Debentures A debenture is an unsecured bond; and as such, it provides no specifi c collateral as security for the obligation. Therefore, debenture holders are general creditors whose claims are protected by property not otherwise pledged. In practice, the use of debentures depends on the nature of the fi rm’s assets and on its general credit strength. Extremely strong companies such as General Electric and ExxonMobil can use debentures because they do not need to put up property as security for their debt. Debentures are also issued by weak companies that have already pledged most of their assets as collateral for mortgage loans. In this case, the debentures are quite risky and that risk will be refl ected in their interest rates.

Subordinated Debentures The term subordinate means “below” or “inferior to”; and in the event of bank- ruptcy, subordinated debt has a claim on assets only after senior debt has been paid in full. Subordinated debentures may be subordinated to designated notes payable (usually bank loans) or to all other debt. In the event of liquidation or reorganization, holders of subordinated debentures receive nothing until all senior debt, as named in the debentures’ indenture, has been paid. Precisely how subor- dination works and how it strengthens the position of senior debtholders are explained in detail in Web Appendix 7B.

7-8b Bond Ratings Since the early 1900s, bonds have been assigned quality ratings that refl ect their probability of going into default. The three major rating agencies are Moody’s Investors Service (Moody’s), Standard & Poor’s Corporation (S&P), and Fitch

Mortgage Bond A bond backed by fixed assets. First mortgage bonds are senior in priority to claims of second mortgage bonds.

Indenture A formal agreement between the issuer and the bondholders.

Debenture A long-term bond that is not secured by a mortgage on specific property.

Subordinated Debenture A bond having a claim on assets only after the senior debt has been paid off in the event of liquidation.

216 Part 3 Financial Assets

Investor’s Service. Moody’s and S&P’s rating designations are shown in Table 7-2.18 The triple- and double-A bonds are extremely safe. Single-A and triple-B bonds are also strong enough to be called investment-grade bonds, and they are the lowest- rated bonds that many banks and other institutional investors are permitted by law to hold. Double-B and lower bonds are speculative, or junk, bonds; and they have a signifi cant probability of going into default.

Bond Rating Criteria Bond ratings are based on fi nancial ratios such as those discussed in Chapter 4 and on various qualitative factors. The ratios, especially the debt and interest coverage ratios, are generally the most important ratings determinants; but at times, other factors that are expected to affect the ratios in the future take center stage. In 2008, fi rms’ exposures to subprime mortgages are leading to downgrades of fi rms whose ratios still look “reasonable.” Published ratios are, of course, historical—they show the fi rm’s condition in the past, whereas bond investors are more interested in the fi rm’s condition in the future. The qualitative factors can be divided into two groups: factors that are related to the bond contract and all other factors. Follow- ing is an outline of the determinants of bond ratings: 1. Financial Ratios. All of the ratios are potentially important, but the debt and

interest coverage ratios are key. The rating agencies’ analysts go through a fi nancial analysis along the lines discussed in Chapter 4 and forecast future ratios along the lines described in the fi nancial planning and forecasting chap- ter. For the forecasts, the qualitative factors discussed next are important.

2. Qualitative Factors: Bond Contract Terms. Every bond is covered by a contract, often called an indenture, between the issuer and the bondholders. The inden- ture spells out all the terms related to the bond. Included in the indenture are the maturity, the coupon interest rate, a statement of whether the bond is secured by a mortgage on specifi c assets, any sinking fund provisions, and a statement of whether the bond is guaranteed by some other party with a high credit ranking. Other provisions might include restrictive covenants such as requirements that the fi rm not let its debt ratio exceed a stated level and that it keep its times-interest-earned ratio at or above a given level. Some bond inden- tures are hundreds of pages long, while others are quite short and cover just the terms of the loan.

3. Miscellaneous Qualitative Factors. Included here are issues like the sensitivity of the fi rm’s earnings to the strength of the economy, the way it is affected by infl ation, a statement of whether it is having or likely to have labor problems, the extent of its international operations (including the stability of the coun- tries in which it operates), potential environmental problems, and potential antitrust problems. Today the most important factor is exposure to subprime loans, including the diffi culty to determine the extent of this exposure as a result of the complexity of the assets backed by such loans.

Investment-Grade Bond Bonds rated triple-B or higher; many banks and other institutional investors are permitted by law to hold only investment-grade bonds.

Junk Bond A high-risk, high-yield bond.

18 In the discussion to follow, reference to the S&P rating is intended to imply the Moody’s and Fitch’s ratings as well. Thus, triple-B bonds mean both BBB and Baa bonds; double-B bonds mean both BB and Ba bonds; and so forth.

Moody’s and S&P Bond RatingsT a b l e 7 - 2

INVESTMENT GRADE JUNK BONDS Moody’s Aaa Aa A Baa Ba B Caa C S&P AAA AA A BBB BB B CCC C

Note: Both Moody’s and S&P use “modifiers” for bonds rated below triple A. S&P uses a plus and minus system. Thus, A+ designates the strongest A-rated bonds; A-, the weakest. Moody’s uses a 1, 2, or 3 designation, with 1 denoting the strongest and 3 denoting the weakest; thus, within the double-A category, Aa1 is the best, Aa2 is average, and Aa3 is the weakest.

217Chapter 7 Bonds and Their Valuation

We see that bond ratings are determined by a great many factors, some quantita- tive and some qualitative (or subjective). Also, the rating process is dynamic—at times, one factor is of primary importance; at other times, some other factor is key. Nevertheless, as we can see from Table 7-3, there is a strong correlation between bond ratings and many of the ratios that we described in Chapter 4. Not surpris- ingly, companies with lower debt ratios, higher free cash fl ow to debt, higher returns on invested capital, higher EBITDA coverage ratios, and higher TIE ratios typically have higher bond ratings.

Importance of Bond Ratings Bond ratings are important to both fi rms and investors. First, because a bond’s rat- ing is an indicator of its default risk, the rating has a direct, measurable infl uence on the bond’s interest rate and the fi rm’s cost of debt. Second, most bonds are pur- chased by institutional investors rather than individuals and many institutions are restricted to investment-grade securities. Thus, if a fi rm’s bonds fall below BBB, it will have a diffi cult time selling new bonds because many potential purchasers will not be allowed to buy them.

As a result of their higher risk and more restricted market, lower-grade bonds have higher required rates of return, rd, than high-grade bonds. Figure 7-4 illus- trates this point. In each of the years shown on the graph, U.S. government bonds have had the lowest yields, AAA bonds have been next, and BBB bonds have had the highest yields. The fi gure also shows that the gaps between yields on the three types of bonds vary over time, indicating that the cost differentials, or yield spreads, fl uctuate from year to year. This point is highlighted in Figure 7-5, which gives the yields on the three types of bonds and the yield spreads for AAA and BBB bonds over Treasuries in January 1994 and January 2008.19 Note fi rst from

Bond Rating Criteria: Three-Year (2002–2004) Median Financial Ratios for Different Bond Rating Classifications of Industrial Companiesa

T a b l e 7 - 3

AAA AA A BBB BB B CCC Times interest earned (EBIT/Interest)

23.8" 19.5" 8.0" 4.7" 2.5" 1.2" 0.4"

EBITDA interest coverage (EBITDA/Interest)

25.5 24.6 10.2 6.5 3.5 1.9 0.9

Net cash flow/Total debt 203.3% 79.9% 48.0% 35.9% 22.4% 11.5% 5.0% Free cash flow/Total debt 127.6 44.5 25.0 17.3 8.3 2.8 (2.1) Return on capital 27.6 27.0 17.5 13.4 11.3 8.7 3.2 Total debt/EBITDA 0.4 0.9 1.6 2.2 3.5 5.3 7.9 Total debt/Total capital 12.4 28.3 37.5 42.5 53.7 75.9 113.5 a Somewhat different criteria are applied to firms in different industries, such as utilities and financial corporations. This table pertains to industrial companies, which include manufacturers, retailers, and service firms.

Source: Adapted from “CreditStats Adjusted Key Industrial Financial Ratios,” Standard & Poor’s 2006 Corporate Ratings Criteria, September 10, 2007, p. 43.

19 A yield spread is related to but not identical to risk premiums on corporate bonds. The true risk premium refl ects only the diff erence in expected (and required) returns between two securities that results from diff erences in their risk. However, yield spreads refl ect (1) a true risk premium; (2) a liquidity premium, which refl ects the fact that U.S. Treasury bonds are more readily marketable than most corporate bonds; (3) a call premium because most Treasury bonds are not callable whereas corporate bonds are; and (4) an expected loss diff erential, which refl ects the probability of loss on the corporate bonds. As an example of the last point, suppose the yield to maturity on a BBB bond was 6.0% versus 4.8% on government bonds but there was a 5% probability of total default loss on the corporate bond. In this case, the expected return on the BBB bond would be 0.95(6.0%) # 0.05(0%) ! 5.7% and the yield spread would be 0.9%, not the full 1.2 percentage points diff erence in “promised” yields to maturity.

218 Part 3 Financial Assets

Figure 7-5 that the risk-free rate, or vertical axis intercept, was lower in January 2008 than it was in January 1994, primarily refl ecting the decline in both rates and expected infl ation over the past few years. Second, the slope of the line has in- creased, indicating an increase in investors’ risk aversion largely due to the sub- prime mortgage problem and growing fears of a possible recession. Thus, the pen- alty for having a low credit rating varies over time. Occasionally, as in 2008, the penalty is quite large; but at times, as in 1994 (shown in Figures 7-4 and 7-5), it is small. These spread differences refl ect investors’ risk aversion and their optimism or pessimism regarding the economy and corporate profi ts. In 2008, as more and more homeowners default on their loans and poor economic news continues, in- vestors were both pessimistic and risk-averse; so spreads were quite high.

Changes in Ratings Changes in a fi rm’s bond rating affect its ability to borrow funds capital and its cost of that capital. Rating agencies review outstanding bonds on a periodic basis, occasionally upgrading or downgrading a bond as a result of its issuer’s changed circumstances. For example, on March 4, 2008, S&P upgraded Reliant Energy’s secured debt facilities from B to BB–; however, the fi rm’s “B” corporate credit rat- ing remained unchanged. The secured debt’s upgrade was due to the fi rm’s refi - nancing the secured debt with unsecured debt, reducing the size of its secured revolving loan, and paying down the senior secured notes. On the other hand, on March 6, 2008, S&P downgraded Airborne Health Inc.’s corporate credit rating from B– to CCC+. The downgrade was largely due to S&P’s concern about the company’s future sales following negative publicity from its recent settlement of a class action lawsuit. (The lawsuit came about from the company’s claims that its product helped prevent the common cold, a fact that was proved to be untrue.)

1994 1995 1996 1997 1998 1999 2000

U.S. Government

Wide Spread

Corporate AAA

Narrow Spread

Corporate BBB

Yield (%)

Years 2001 2002 2003 2004 2005 2006 2007 2008

Yields on Selected Long-Term Bonds, 1994–2008FIGURE 7-4

Source: Federal Reserve Statistical Release, Selected Interest Rates (Historical Data), www.federalreserve.gov/releases/H15/data.htm.

www.federalreserve.gov/releases/H15/data.htm

219Chapter 7 Bonds and Their Valuation

Over the long run, rating agencies have done a reasonably good job of measur- ing the average credit risk of bonds and of changing ratings whenever there is a signifi cant change in credit quality. However, it is important to understand that ratings do not adjust immediately to changes in credit quality; and in some cases, there can be a considerable lag between a change in credit quality and a change in rating. For example, Enron’s bonds still carried an investment-grade rating on a Friday in December 2001, but the company declared bankruptcy 2 days later, on Sunday. Many other abrupt downgrades occurred in 2007 and 2008, leading to calls by Congress and the SEC for changes in rating agencies and the way they rate bonds. Improvements can clearly be made, but there will always be surprises when we learn that supposedly strong bonds were in fact quite weak.

7-8c Bankruptcy and Reorganization When a business becomes insolvent, it doesn’t have enough cash to meet its interest and principal payments. A decision must then be made whether to dissolve the fi rm through liquidation or to permit it to reorganize and thus continue to operate. These issues are addressed in Chapters 7 and 11 of the federal bankruptcy statutes, and the fi nal decision is made by a federal bankruptcy court judge.

The decision to force a fi rm to liquidate versus permitting it to reorganize de- pends on whether the value of the reorganized business is likely to be greater than the value of its assets if they were sold off piecemeal. In a reorganization, the fi rm’s creditors negotiate with management on the terms of a potential reorganization. The reorganization plan may call for restructuring the debt, in which case the

AAA BBBTreasury

Yield (%)

Yield SpreadBBB = 2.2%Yield SpreadAAA = 1.0%

Yield SpreadBBB = 1.3% Yield SpreadAAA = 0.5%

January 1994 January 2008

Relationship between Bond Ratings and Bond Yields, 1994 and 2008FIGURE 7-5

Long-Term Government

Bonds (Default-Free)

(1)

AAA Corporate

Bonds (2)

BBB Corporate

Bonds (3)

YIELD SPREADS

AAA (4) ! (2) # (1)

BBB (5) ! (3) # (1)

January 1994 6.4% 6.9% 7.7% 0.5% 1.3%

January 2008 4.3 5.3 6.5 1.0 2.2

Source: Federal Reserve Statistical Release, Selected Interest Rates (Historical Data), www.federalreserve.gov/releases/H15/data.htm.

www.federalreserve.gov/releases/H15/data.htm

220 Part 3 Financial Assets

interest rate may be reduced, the term to maturity lengthened, or some of the debt exchanged for equity. The point of the restructuring is to reduce the fi nancial charges to a level that is supportable by the fi rm’s projected cash fl ows. Of course, the common stockholders also have to “take a haircut”—they generally see their position diluted as a result of additional shares being given to debtholders in ex- change for accepting a reduced amount of debt principal and interest. A trustee may be appointed by the court to oversee the reorganization, but the existing man- agement generally is allowed to retain control.

Liquidation occurs if the company is deemed to be worth more “dead” than “alive.” If the bankruptcy court orders a liquidation, assets are auctioned off and the cash obtained is distributed as specifi ed in Chapter 7 of the Bankruptcy Act. Web Appendix 7B provides an illustration of how a fi rm’s assets are distributed after liq- uidation. For now, you should know that (1) the federal bankruptcy statutes govern reorganization and liquidation, (2) bankruptcies occur frequently, (3) a priority of the specifi ed claims must be followed when the assets of a liquidated fi rm are distributed, (4) bondholders’ treatment depends on the terms of the bond, and (5) stockholders generally receive little in reorganizations and nothing in liquidations because the as- sets are usually worth less than the amount of debt outstanding.

SEL F TEST Diff erentiate between mortgage bonds and debentures.

Name the major rating agencies and list some factors that aff ect bond ratings.

Why are bond ratings important to fi rms and investors?

Do bond ratings adjust immediately to changes in credit quality? Explain.

Diff erentiate between Chapter 7 liquidations and Chapter 11 reorganiza- tions. In general, when should each be used?

7-9 BOND MARKETS Corporate bonds are traded primarily in the over-the-counter market. Most bonds are owned by and traded among large fi nancial institutions (for example, life insurance companies, mutual funds, hedge funds, and pension funds, all of which deal in very large blocks of securities), and it is relatively easy for over-the-counter bond dealers to arrange the transfer of large blocks of bonds among the relatively few holders of the bonds. It would be more diffi cult to conduct similar operations in the stock market among the literally millions of large and small stockholders, so a higher percentage of stock trades occur on the exchanges.

The Wall Street Journal routinely reports key developments in the Treasury, cor- porate, and municipal bond markets. The online edition of The Wall Street Journal also lists for each trading day the most actively traded investment-grade bonds, high-yield bonds, and convertible bonds. Table 7-4 reprints portions of the online edition’s “Corporate Bonds Data” section which shows the most active issues that traded on March 6, 2008, in descending order of sales volume.

Looking at Table 7-4, you will see the coupon rate, maturity date, bond rating, high and low prices for the day, closing (last) price, change in price, and yield to maturity. The table assumes that each bond has a par value of $100. Not surprisingly, the high- yield bonds have much higher yields to maturity because of their higher default risk and the convertible bonds have much lower yields because investors are willing to ac- cept lower yields in return for the option to convert their bonds to common stock.

If you examine the table closely, you will also see that the bonds with a yield to maturity above their coupon rate trade at a discount, whereas bonds with a

221Chapter 7 Bonds and Their Valuation

CORPORATE BONDS

Market Breadth Last updated: 3/6/2008 at 6:35 PM ET

Total Issues Traded Advances Declines Unchanged 52 Week High 52 Week Low Dollar Volume *

3,774 1,457 1,873

126 170 344

15,640

MERRlLL LYNCH BANK OF AMERICA CORP JPMORGAN CHASE & CO SPRINT CAPITAL GOLDMAN SACHS GP GENERAL ELECTRIC CAPITAL SPRINT CAPITAL TELECOM ITALIA CAPITAL UNITED PARCEL SERVICE SPRINT CAPITAL

MER.GDW BAC.HBM JPM.JPF S.GJ GS.YL GE.HEE S.HK Tl.GK UPS.QE S.GM

2,587 1,083 1,187

53 161 191

7,350

942 299 532

68 8

117 4,989

245 75

154 5 1

36 3,301

About This Information: End of Day data. Activity as reported to FINRA TRACE (Trade Reporting and Compliance Engine). The Market breadth information represents activity in all TRACE eligible publicly traded securities. The most active information represent the most active fixed- coupon bonds (ranked by par value traded). Inclusion in Investment Grade or High Yield tables based on TRACE dissemination criteria. ”C” indicates yield is unavailable because of issues call criteria.

Most Active Investment Grade Bonds

All Issues

Issuer Name Symbol

4.125% 5.750% 6.000% 6.875% 5.950% 5.250% 8.750% 5.250% 4.500% 6.900%

Jan 2009 Dec 2017 Jan 2018

Nov 2028 Jan 2018 Dec 2017 Mar 2032 Nov 2013 Jan 2013

May 2019

100.886 103.143 104.566

74.000 100.516 101.750

81.120 100.834 103.964

76.313

99.500 99.280

100.632 69.000 95.956 97.678 76.063 95.908

103.617 73.950

100.886 99.280

101.587 72.563 98.520 98.770 80.000 95.908

103.734 76.313

3.051 5.847 5.784

10.048 6.151 5.413

11.159 6.112 3.651

10.565

0.910 –1.339 –0.413

0.063 0.576

–0.335 0.000

–1.949 1.053 0.563

A1/A+/A+ Aa1/AA/AA

Aa2/AA–/AA– Baa3/BBB–/BB+ Aa3/AA–/AA–

Aaa/AAA/-- Baa3/BBB–/BB+

Baa2/BBB+/BBB+ Aa2/AA–/--

Baa3/BBB–/BB+

Coupon Maturity Rating

Moody’s/S&P/ Fitch

High Low Last Change Yield %

Issuer Name Symbol Coupon Maturity Rating

Moody’s/S&P/ Fitch

High Low Last Change Yield %

Issuer Name Symbol Coupon Maturity Rating

Moody’s/S&P/ Fitch

High Low Last Change Yield %

THORNBURG MORTGAGE GENERAL MOTORS E TRADE FINANClAL CCH I BLOCKBUSTER COMMUNITY HEALTH SYSTEMS HERTZ CORP GENERAL MOTORS ACCEPTANCE NEIMAN MARCUS GP INTELSAT(BERMUDA)

TMA.GB GM.HB ET.GF CHTR.HM BBI.GB CYH.GI F.GRY GMA.HE NMGA.GD INTEL.GR

Most Active High Yield Bonds

8.000% 8.375% 8.000% 11.000% 9.000% 8.875% 8.875% 6.875% 9.000% 9.250%

May 2013 Jul 2033

Jun 2011 Oct 2015 Sep 2012 Jul 2015

Jan 2014 Sep 2011 Oct 2015 Jun 2016

49.000 79.750 86.000 70.125 87.500 99.500 99.000 81.710 98.250

101.250

35.500 74.000 85.000 69.688 83.000 98.750 94.750 79.000 97.000

100.875

40.000 75.938 86.000 70.070 83.500 98.750 97.086 80.516 97.250

100.875

32.807 11.262 13.429 18.517 14.096

9.108 9.535

14.099 9.511 9.093

–23.750 –1.063

0.500 –0.430

1.625 –0.750

0.586 –0.484 –0.688

0.000

Caa2/CCC+/CCC– Caa1/B–/B–

Ba3/B/-- Caa2/CCC/CCC Caa2/CCC/CC B3/B–/CCC+

B1/B/BB– B1/B+/BB B2/B/B–

B3/B–/BB–

AMGEN SANDISK CORP NABORS INDUSTRlES PROTEIN DESIGN LABS AMGEN

AMGN.GM SNDK.GC NBR.GP PDLI.GF AMGN.GN

Most Active Convertible Bonds

Source: FINRA TRACE data. Reference information from Reuters DataScope Data. Credit ratings from Moody’s, Standard & Poor’s, and Fitch Ratings.

0.125% 1.000% 0.940% 2.000% 0.375%

Feb 2011 May 2013 May 2011 Feb 2012 Feb 2013

92.438 74.000

100.500 80.608 88.467

91.813 72.690 96.000 78.882 87.000

91.883 74.000

100.000 79.443 87.587

3.083 7.086 0.940 8.231 3.133

–0.745 –0.116 –0.750

0.203 –0.663

A2/--/-- --/BB–/--

--/BBB+/A– --/--/--

A2/--/--

Investment Grade High Yield Convertibles

* Par value in millions.

Most Active Investment-Grade, High-Yield, and Convertible Corporate Bonds, March 6, 2008

T a b l e 7 - 4

Source: http://online.wsj.com, “Corporate Bonds,” The Wall Street Journal Online, March 7, 2008.

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222 Part 3 Financial Assets

yield below their coupon rate trade at a premium above par. We see that the large majority of high-yield bonds trade at a discount to par, which suggests that be- cause of increased default risk, most of these bonds now trade at higher yields relative to when they were issued. (Recall that most bonds are issued at par, so the coupon rate tells us what the bond’s yield was at the time it was issued.) You should also note that when bonds with similar ratings are compared, bonds with longer maturities tend to have higher yields, which is consistent with the upward- sloping yield curve during this time period.

SEL F TEST Why do most bond trades occur in the over-the-counter market?

If a bond issue is to be sold at par, at what rate must its coupon rate be set? Explain.

This chapter described the diff erent types of bonds governments and corporations issue, explained how bond prices are established, and discussed how investors esti- mate rates of return on bonds. It also discussed various types of risks that investors face when they purchase bonds.

When an investor purchases a company’s bonds, the investor is providing the company with capital. Moreover, when a fi rm issues bonds, the return that investors require on the bonds represents the cost of debt capital to the fi rm. This point is ex- tended in Chapter 10, where the ideas developed in this chapter are used to help de- termine a company’s overall cost of capital, which is a basic component of the capital budgeting process.

In recent years, many companies have used zero coupon bonds to raise billions of dollars, while bankruptcy is an important consideration for companies that issue debt and for investors. Therefore, these two related issues are discussed in detail in Web Appendixes 7A and 7B. Go to the textbook’s web site to access these appendixes.

KEY TERMS Define each of the following terms: a. Bond; treasury bond; corporate bond; municipal bond; foreign bond b. Par value; maturity date; original maturity c. Coupon payment; coupon interest rate d. Fixed-rate bond; floating-rate bond; zero coupon bond; original issue discount (OID)

bond e. Call provision; sinking fund provision f. Convertible bond; warrant; putable bond; income bond; indexed, or purchasing

power, bond

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

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223Chapter 7 Bonds and Their Valuation

g. Discount bond; premium bond h. Yield to maturity (YTM); yield to call (YTC); total return; yield spread i. Interest rate risk; reinvestment rate risk; investment horizon; default risk j. Mortgage bond; indenture; debenture; subordinated debenture k. Investment-grade bond; junk bond

BOND VALUATION The Pennington Corporation issued a new series of bonds on January 1, 1985. The bonds were sold at par ($1,000); had a 12% coupon; and mature in 30 years, on December 31, 2014. Coupon payments are made semiannually (on June 30 and December 31). a. What was the YTM on January 1, 1985? b. What was the price of the bonds on January 1, 1990, 5 years later, assuming that

interest rates had fallen to 10%? c. Find the current yield, capital gains yield, and total return on January 1, 1990, given

the price as determined in Part b. d. On July 1, 2008, 6½ years before maturity, Pennington’s bonds sold for $916.42. What

were the YTM, the current yield, the capital gains yield, and the total return at that time? e. Now assume that you plan to purchase an outstanding Pennington bond on March 1,

2008, when the going rate of interest given its risk was 15.5%. How large a check must you write to complete the transaction? This is a difficult question.

SINKING FUND The Vancouver Development Company (VDC) is planning to sell a $100 million, 10-year, 12%, semiannual payment bond issue. Provisions for a sinking fund to retire the issue over its life will be included in the indenture. Sinking fund payments will be made at the end of each year, and each payment must be sufficient to retire 10% of the original amount of the issue. The last sinking fund payment will retire the last of the bonds. The bonds to be retired each period can be purchased on the open market or obtained by calling up to 5% of the original issue at par, at VDC’s option. a. How large must each sinking fund payment be if the company (1) uses the option to

call bonds at par or (2) decides to buy bonds on the open market? For Part (2), you can only answer in words.

b. What will happen to debt service requirements per year associated with this issue over its 10-year life?

c. Now consider an alternative plan where VDC sets up its sinking fund so that equal annual amounts are paid into a sinking fund trust held by a bank, with the proceeds being used to buy government bonds that are expected to pay 7% annual interest. The payments, plus accumulated interest, must total $100 million at the end of 10 years, when the proceeds will be used to retire the issue. How large must the annual sinking fund payments be? Is this amount known with certainty, or might it be higher or lower?

d. What are the annual cash requirements for covering bond service costs under the trusteeship arrangement described in Part c? (Note: Interest must be paid on Vancouver’s outstanding bonds but not on bonds that have been retired.) Assume level interest rates for purposes of answering this question.

e. What would have to happen to interest rates to cause the company to buy bonds on the open market rather than call them under the plan where some bonds are retired each year?

A sinking fund can be set up in one of two ways: a. The corporation makes annual payments to the trustee, who invests the proceeds in

securities (frequently government bonds) and uses the accumulated total to retire the bond issue at maturity.

b. The trustee uses the annual payments to retire a portion of the issue each year, calling a given percentage of the issue by a lottery and paying a specified price per bond or buying bonds on the open market, whichever is cheaper.

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QUESTIONS QUESTIONS

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224 Part 3 Financial Assets

What are the advantages and disadvantages of each procedure from the viewpoint of (a) the firm and (b) the bondholders?

Is it true that the following equation can be used to find the value of a bond with N years to maturity that pays interest once a year? Assume that the bond was issued several years ago.

VB ! ∑ t!1

Annual interest ______________ (1 # rd) t #

Par value ________ (1 # rd) N

The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices. Is that statement true or false? Explain. (Hint: Make up a “reasonable” example based on a 1-year and a 20-year bond to help answer the question.)

If interest rates rise after a bond issue, what will happen to the bond’s price and YTM? Does the time to maturity affect the extent to which interest rate changes affect the bond’s price? (Again, an example might help you answer this question.)

If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain.

Assume that you have a short investment horizon (less than 1 year). You are considering two investments: a 1-year Treasury security and a 20-year Treasury security. Which of the two investments would you view as being riskier? Explain.

Indicate whether each of the following actions will increase or decrease a bond’s yield to maturity: a. The bond’s price increases. b. The bond is downgraded by the rating agencies. c. A change in the bankruptcy code makes it more difficult for bondholders to receive

payments in the event the firm declares bankruptcy. d. The economy seems to be shifting from a boom to a recession. Discuss the effects of

the firm’s credit strength in your answer. e. Investors learn that the bonds are subordinated to another debt issue.

Why is a call provision advantageous to a bond issuer? When would the issuer be likely to initiate a refunding call?

Are securities that provide for a sinking fund more or less risky from the bondholder’s perspective than those without this type of provision? Explain.

What’s the difference between a call for sinking fund purposes and a refunding call?

Why are convertibles and bonds with warrants typically offered with lower coupons than similarly rated straight bonds?

Explain whether the following statement is true or false: Only weak companies issue debentures.

Would the yield spread on a corporate bond over a Treasury bond with the same maturity tend to become wider or narrower if the economy appeared to be heading toward a recession? Would the change in the spread for a given company be affected by the firm’s credit strength? Explain.

A bond’s expected return is sometimes estimated by its YTM and sometimes by its YTC. Under what conditions would the YTM provide a better estimate, and when would the YTC be better?

BOND VALUATION Callaghan Motors’ bonds have 10 years remaining to maturity. Inter- est is paid annually, they have a $1,000 par value, the coupon interest rate is 8%, and the yield to maturity is 9%. What is the bond’s current market price?

YIELD TO MATURITY AND FUTURE PRICE A bond has a $1,000 par value, 10 years to ma- turity, and a 7% annual coupon and sells for $985.

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225Chapter 7 Bonds and Their Valuation

a. What is its yield to maturity (YTM)? b. Assume that the yield to maturity remains constant for the next 3 years. What will the

price be 3 years from today?

BOND VALUATION Nungesser Corporation’s outstanding bonds have a $1,000 par value, a 9% semiannual coupon, 8 years to maturity, and an 8.5% YTM. What is the bond’s price?

YIELD TO MATURITY A firm’s bonds have a maturity of 10 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their nominal yield to maturity and their nominal yield to call? What return should investors expect to earn on these bonds?

BOND VALUATION An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%?

Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

b. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

BOND VALUATION An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.6%. Bond C pays a 10% annual coupon, while Bond Z is a zero coupon bond. a. Assuming that the yield to maturity of each bond remains at 9.6% over the next 4

years, calculate the price of the bonds at each of the following years to maturity:

Years to Maturity Price of Bond C Price of Bond Z

b. Plot the time path of prices for each bond.

INTEREST RATE SENSITIVITY An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell and each then had a new YTM of 7%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table:

Price @ 8%

Price @ 7%

Percentage Change

10-year, 10% annual coupon

10-year zero

5-year zero

30-year zero

$100 perpetuity

YIELD TO CALL Six years ago the Singleton Company issued 20-year bonds with a 14% annual coupon rate at their $1,000 par value. The bonds had a 9% call premium, with 5 years of call protection. Today Singleton called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Explain why the investor should or should not be happy that Singleton called them.

YIELD TO MATURITY Heymann Company bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 9%. a. What is the yield to maturity at a current market price of (1) $829 and (2) $1,104? b. Would you pay $829 for each bond if you thought that a “fair” market interest rate for

such bonds was 12%—that is, if rd ! 12%? Explain your answer.

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226 Part 3 Financial Assets

CURRENT YIELD, CAPITAL GAINS YIELD, AND YIELD TO MATURITY Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8% annual coupon rate and were issued 1 year ago at their par value of $1,000. However, due to changes in interest rates, the bond’s market price has fallen to $901.40. The capital gains yield last year was $9.86%. a. What is the yield to maturity? b. For the coming year, what are the expected current and capital gains yields? (Hint:

Refer to Footnote 8 for the definition of the current yield and to Table 7-1.) c. Will the actual realized yields be equal to the expected yields if interest rates change?

If not, how will they differ?

BOND YIELDS Last year Clark Company issued a 10-year, 12% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 4 years at a price of $1,060 and it sells for $1,100. a. What are the bond’s nominal yield to maturity and its nominal yield to call? Would

an investor be more likely to earn the YTM or the YTC? b. What is the current yield? Is this yield affected by whether the bond is likely to be

called? (Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1.) c. What is the expected capital gains (or loss) yield for the coming year? Is this yield

dependent on whether the bond is expected to be called?

YIELD TO CALL It is now January 1, 2009, and you are considering the purchase of an outstanding bond that was issued on January 1, 2007. It has a 9.5% annual coupon and had a 30-year original maturity. (It matures on December 31, 2036.) There is 5 years of call protection (until December 31, 2011), after which time it can be called at 109—that is, at 109% of par, or $1,090. Interest rates have declined since it was issued; and it is now selling at 116.575% of par, or $1,165.75. a. What is the yield to maturity? What is the yield to call? b. If you bought this bond, which return would you actually earn? Explain your reasoning. c. Suppose the bond had been selling at a discount rather than a premium. Would the

yield to maturity have been the most likely return, or would the yield to call have been most likely?

PRICE AND YIELD An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.21%. What are the bond’s price and YTM? (Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1.)

EXPECTED INTEREST RATE Lloyd Corporation’s 14% coupon rate, semiannual payment, $1,000 par value bonds, which mature in 30 years, are callable 5 years from today at $1,050. They sell at a price of $1,353.54, and the yield curve is flat. Assume that interest rates are expected to remain at their current level. a. What is the best estimate of these bonds’ remaining life? b. If Lloyd plans to raise additional capital and wants to use debt financing, what

coupon rate would it have to set in order to issue new bonds at par?

BOND VALUATION Bond X is noncallable and has 20 years to maturity, a 9% annual coupon, and a $1,000 par value. Your required return on Bond X is 10%; and if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 8.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.)

BOND VALUATION You are considering a 10-year, $1,000 par value bond. Its coupon rate is 9%, and interest is paid semiannually. If you require an “effective” annual interest rate (not a nominal rate) of 8.16%, how much should you be willing to pay for the bond?

BOND RETURNS Last year Joan purchased a $1,000 face value corporate bond with an 11% annual coupon rate and a 10-year maturity. At the time of the purchase, it had an expected yield to maturity of 9.79%. If Joan sold the bond today for $1,060.49, what rate of return would she have earned for the past year?

BOND REPORTING Look back at Table 7-4 and examine United Parcel Service and Telecom Italia Capital bonds that mature in 2013. a. If these companies were to sell new $1,000 par value long-term bonds, approximately

what coupon interest rate would they have to set if they wanted to bring them out at par? b. If you had $10,000 and wanted to invest in United Parcel Service bonds, what return

would you expect to earn? What about Telecom Italia Capital bonds? Based just on

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7-157-15Challenging Problems 15–19 Challenging Problems 15–19

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227Chapter 7 Bonds and Their Valuation

the data in the table, would you have more confidence about earning your expected rate of return if you bought United Parcel Service or Telecom Italia Capital bonds? Explain.

YIELD TO MATURITY AND YIELD TO CALL Kaufman Enterprises has bonds outstanding with a $1,000 face value and 10 years left until maturity. They have an 11% annual coupon payment, and their current price is $1,175. The bonds may be called in 5 years at 109% of face value (Call price ! $1,090). a. What is the yield to maturity? b. What is the yield to call if they are called in 5 years? c. Which yield might investors expect to earn on these bonds? Why? d. The bond’s indenture indicates that the call provision gives the firm the right to call

the bonds at the end of each year beginning in Year 5. In Year 5, the bonds may be called at 109% of face value; but in each of the next 4 years, the call percentage will decline by 1%. Thus, in Year 6, they may be called at 108% of face value; in Year 7, they may be called at 107% of face value; and so forth. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?

BOND VALUATION Clifford Clark is a recent retiree who is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds: • Bond A has a 7% annual coupon, matures in 12 years, and has a $1,000 face value. • Bond B has a 9% annual coupon, matures in 12 years, and has a $1,000 face value. • Bond C has an 11% annual coupon, matures in 12 years, and has a $1,000 face value.

Each bond has a yield to maturity of 9%. a. Before calculating the prices of the bonds, indicate whether each bond is trading at a

premium, at a discount, or at par. b. Calculate the price of each of the three bonds. c. Calculate the current yield for each of the three bonds. (Hint: Refer to Footnote 8 for

the definition of the current yield and to Table 7-1.) d. If the yield to maturity for each bond remains at 9%, what will be the price of each

bond 1 year from now? What is the expected capital gains yield for each bond? What is the expected total return for each bond?

e. Mr. Clark is considering another bond, Bond D. It has an 8% semiannual coupon and a $1,000 face value (i.e., it pays a $40 coupon every 6 months). Bond D is scheduled to mature in 9 years and has a price of $1,150. It is also callable in 5 years at a call price of $1,040.

(1) What is the bond’s nominal yield to maturity? (2) What is the bond’s nominal yield to call? (3) If Mr. Clark were to purchase this bond, would he be more likely to receive the

yield to maturity or yield to call? Explain your answer. f. Explain briefly the difference between interest rate (or price) risk and reinvestment

rate risk. Which of the following bonds has the most interest rate risk? • A 5-year bond with a 9% annual coupon • A 5-year bond with a zero coupon • A 10-year bond with a 9% annual coupon • A 10-year bond with a zero coupon

g. Only do this part if you are using a spreadsheet. Calculate the price of each bond (A, B, and C) at the end of each year until maturity, assuming interest rates remain constant. Create a graph showing the time path of each bond’s value similar to Figure 7-2.

(1) What is the expected interest yield for each bond in each year? (2) What is the expected capital gains yield for each bond in each year? (3) What is the total return for each bond in each year?

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228 Part 3 Financial Assets

BOND VALUATION Robert Black and Carol Alvarez are vice presidents of Western Money Management and codirectors of the company’s pension fund management division. A major new client, the California League of Cities, has requested that Western present an investment seminar to the mayors of the represented cities. Black and Alvarez, who will make the presentation, have asked you to help them by answering the following questions.

a. What are a bond’s key features? b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? c. How is the value of any asset whose value is based on expected future cash flows determined? d. How is a bond’s value determined? What is the value of a 10-year, $1,000 par value bond with a 10% annual

coupon if its required return is 10%? e. (1) What is the value of a 13% coupon bond that is otherwise identical to the bond described in Part d?

Would we now have a discount or a premium bond? (2) What is the value of a 7% coupon bond with these characteristics? Would we now have a discount or

premium bond? (3) What would happen to the values of the 7%, 10%, and 13% coupon bonds over time if the required

return remained at 10%? [Hint: With a financial calculator, enter PMT, I/YR, FV, and N; then change (override) N to see what happens to the PV as it approaches maturity.]

f. (1) What is the yield to maturity on a 10-year, 9%, annual coupon, $1,000 par value bond that sells for $887.00? that sells for $1,134.20? What does the fact that it sells at a discount or at a premium tell you about the relationship between rd and the coupon rate?

(2) What are the total return, the current yield, and the capital gains yield for the discount bond? Assume that it is held to maturity and the company does not default on it. (Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1.)

g. What is interest rate (or price) risk? Which has more interest rate risk, an annual payment 1-year bond or a 10-year bond? Why?

h. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond? i. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a

10-year, semiannual payment, 10% coupon bond if nominal rd ! 13%. j. Suppose for $1,000 you could buy a 10%, 10-year, annual payment bond or a 10%, 10-year, semiannual pay-

ment bond. They are equally risky. Which would you prefer? If $1,000 is the proper price for the semiannual bond, what is the equilibrium price for the annual payment bond?

k. Suppose a 10-year, 10%, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a nominal yield to maturity of 8%. However, it can be called after 4 years for $1,050.

(1) What is the bond’s nominal yield to call (YTC)? (2) If you bought this bond, would you be more likely to earn the YTM or the YTC? Why? l. Does the yield to maturity represent the promised or expected return on the bond? Explain. m. These bonds were rated AA- by S&P. Would you consider them investment-grade or junk bonds? n. What factors determine a company’s bond rating? o. If this firm were to default on the bonds, would the company be immediately liquidated? Would the bond-

holders be assured of receiving all of their promised payments? Explain.

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IN TEGRATED C ASE WESTERN MONEY MANAGEMENT INC.

A Ta l e o f T h r e e M a r ke t s — o r I s I t Fo u r ?

Risk and Rates of Return

RA N

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H O

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8 CHAPTER

229

The purpose of this vignette is to give you some additional perspective on the stock market. Refer to Figure 8-1 on page 232 as you read the following paragraphs.

Market 1: 1975–2000. These were great years, especially the last five. Only 3 years saw losses; and toward the end of the run, most investors and money managers had never experienced a really bad market and acted as though bad mar- kets had been banished and would never re appear again. However, Alan Greenspan, Chair- man of the Federal Reserve Board at that time, knew the wild ride couldn’t continue. In 1995, he stated that investors were exhibiting “irrational exuberance”; but the market ignored him and kept roaring ahead.

Market 2: 2000–2003. Greenspan was right. In 2000, the bubble started to leak and the market fell by 10%. Then in 2001, the 9/11 terrorist attacks on the World Trade Center knocked stocks down another 14%. Finally, in 2002, fears of another attack in addition to a recession led to

a gut-wrenching 24% decline. Those 3 years cost the average investor almost 50% of his or her beginning-of-2000 market value. People plan- ning to retire rich and young had to rethink those plans.

Market 3: 2003–2007. Investors had overre- acted; so in 2003, the market rebounded, rising by just over 25%. The market remained strong through 2007—the economy was robust, prof- its were rising rapidly, and the Federal Reserve encouraged a bull market by cutting interest rates 11 times. In 2007, the Dow Jones and other stock averages hit all-time highs. But the debt markets were suffering from the subprime mortgage debacle, and institutions such as Merrill Lynch and Citigroup were writing off tens of billions of dollars of bad loans. Oil prices hit $100 per barrel, gasoline prices hit new highs, and unemployment rates were creeping up. With this backdrop, some observers won- dered if we were again suffering from irrational exuberance.

230 Part 3 Financial Assets

We start this chapter from the basic premise that investors like returns and dislike risk; hence, they will invest in risky assets only if those assets off er higher expected returns. We defi ne what risk means as it relates to investments, examine procedures that are used to measure risk, and discuss the relationship between risk and return. Investors should understand these concepts, as should corporate managers as they develop the plans that will shape their fi rms’ futures. Risk can be measured in diff erent ways, and diff erent conclusions about an asset’s riskiness can be reached depending on the measure used. Risk analysis can be confusing, but it will help if you keep the following points in mind: 1. All business assets are expected to produce cash fl ows, and the riskiness of an

asset is based on the riskiness of its cash fl ows. The riskier the cash fl ows, the risk- ier the asset.

2. Assets can be categorized as fi nancial assets, especially stocks and bonds, and as real assets, such as trucks, machines, and whole businesses. In theory, risk analysis for all types of assets is similar and the same fundamental concepts apply to all assets. However, in practice, diff erences in the types of available data lead to dif- ferent procedures for stocks, bonds, and real assets. Our focus in this chapter is on fi nancial assets, especially stocks. We considered bonds in Chapter 7; and we take up real assets in the capital budgeting chapters, especially Chapter 12.

3. A stock’s risk can be considered in two ways: (a) on a stand-alone, or single-stock, basis, or (b) in a portfolio context, where a number of stocks are combined and their consolidated cash fl ows are analyzed.1 There is an important diff erence between stand-alone and portfolio risk, and a stock that has a great deal of risk held by itself may be much less risky when held as part of a larger portfolio.

4. In a portfolio context, a stock’s risk can be divided into two components: (a) diver- sifi able risk, which can be diversifi ed away and is thus of little concern to diversi- fi ed investors, and (b) market risk, which refl ects the risk of a general stock market decline and cannot be eliminated by diversifi cation (hence, does concern inves- tors). Only market risk is relevant to rational investors because diversifi able risk can and will be eliminated.

5. A stock with high market risk must off er a relatively high expected rate of return to attract investors. Investors in general are averse to risk, so they will not buy risky assets unless they are compensated with high expected returns.

6. If investors, on average, think a stock’s expected return is too low to compensate for its risk, they will start selling it, driving down its price and boosting its expected return. Conversely, if the expected return on a stock is more than enough to

Market 4: 2008 and Thereafter: Bull or Bear? In early 2008, the big question is this: Will the bull market continue; or are we entering another bear market, with a possible decline of

50% or so? We wish we knew! By the time you read this, you will know; but it will be too late to profit from that knowledge.

1 A portfolio is a collection of investment securities. If you owned stock in General Motors, ExxonMobil, and IBM, you would be holding a three-stock portfolio. Because diversifi cation lowers risk without sacrifi cing much if any expected return, most stocks are held in portfolios.

PU T TING THINGS IN PER SPECTIVE

231Chapter 8 Risk and Rates of Return

2 The graph refl ects stock prices; dividends are not included. If dividends were included, the percentage gains would be somewhat higher.

compensate for the risk, people will start buying it, raising its price and thus lower- ing its expected return. The stock will be in equilibrium, with neither buying nor selling pressure, when its expected return is exactly suffi cient to compensate for its risk.

7. Stand-alone risk, the topic of Section 8-2, is important in stock analysis primarily as a lead-in to portfolio risk analysis. However, stand-alone risk is extremely important when analyzing real assets such as capital budgeting projects.

When you fi nish this chapter, you should be able to: • Explain the diff erence between stand-alone risk and risk in a portfolio context. • Explain how risk aversion aff ects a stock’s required rate of return. • Discuss the diff erence between diversifi able risk and market risk, and explain how

each type of risk aff ects well-diversifi ed investors. • Explain what the CAPM is and how it can be used to estimate a stock’s required

rate of return. • Discuss how changes in the general stock and the bond markets could lead to

changes in the required rate of return on a fi rm’s stock. • Discuss how changes in a fi rm’s operations might lead to changes in the required

rate of return on the fi rm’s stock.

8-1 STOCK PRICES OVER THE LAST 20 YEARS Figure 8-1 gives you an idea about how stocks have performed over the period from 1988 through 2007.2 The top graph compares General Electric (GE), the broad stock market as measured by the S&P 500, and General Motors (GM). GE illustrates companies that have done well, GM illustrates those that have not done well, and the S&P 500 shows how an average company has performed. Most stocks climbed sharply until 2000 (Market 1 in the vignette), then dropped equally sharply during Market 2, then rose nicely through most of Market 3. Since there are thousands of stocks, we could have shown many different pic- tures, with some rising much faster than GE and others falling much faster than GM—with some going to zero and vanishing. Most of the indexes rise and fall together; but if we had shown the Nasdaq index, it would have looked a great deal like GE, rising much faster than the S&P but then falling faster later on. Also note that the beginning and ending dates can lead to totally different “pictures” of stocks’ performances. If we had started in 1990 and ended in 2000, it would have looked as though stocks were wonderful investments. On the other hand, if we had started in 2000 and ended in 2003, it would have looked as though stocks were a terrible place to put our money. It would be great if we knew when to get in and out of the market.

The lower graph shows GE’s P/E ratio. The P/E ratio depends on a number of factors, including fundamental factors such as interest rates and earnings growth rates; but it also refl ects investors’ optimism or pessimism—or in Alan Greenspan’s words, their “irrational exuberance or pessimism.” Security analysts and investors forecast the future, but they seem to be overly optimistic at certain times and overly pessimistic at other times. Looking back, we can see that they were overly optimistic in 2000. But what about in 1997? There had been a sharp run-up to that time, and some “experts” thought the market was at a top and rec- ommended getting out. Those experts turned out to be wrong, and they “left a lot of money on the table.”

232 Part 3 Financial Assets

Note also that if you had bought and held GE stock you would have done quite well; but if you had bought GM stock, you wouldn’t have done well at all. If you had formed a portfolio with some GM and some GE stocks, you would have had “average” performance. The portfolio would have limited your potential gain but also would have limited your low-end returns. We will have more to say about portfolios later, but keep this in mind as you go through the chapter.

8-2 STAND-ALONE RISK Risk is defi ned by Webster as “a hazard; a peril; exposure to loss or injury.” Thus, risk refers to the chance that some unfavorable event will occur. If you engage in skydiving, you are taking a chance with your life—skydiving is risky. If you bet on the horses, you are risking your money.

As we saw in previous chapters, individuals and fi rms invest funds today with the expectation of receiving additional funds in the future. Bonds offer relatively low returns, but with relatively little risk—at least if you stick to Treasury and high- grade corporate bonds. Stocks offer the chance of higher returns, but stocks are generally riskier than bonds. If you invest in speculative stocks (or, really, any stock), you are taking a signifi cant risk in the hope of making an appreciable return.

Risk The chance that some unfavorable event will occur.

88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 © BigCharts.com

88 89 90 91 92 93 94

P/E Ratio

GE Daily 6/18/07 SP500 GM

95 96 97 98 99 00 01 02 03 04 05 06 07

+1,600%

+1,400%

+1,200%

+1,000%

+800%

+600%

+400%

+200%

+0%

–200%

Stock Performance, 1988–2007FIGURE 8-1

Source: http://online.wsj.com, The Wall Street Journal Online, January 12, 2008.

http://online.wsj.com

233Chapter 8 Risk and Rates of Return233

An asset’s risk can be analyzed in two ways: (1) on a stand-alone basis, where the asset is considered by itself, and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio. Thus, an asset’s stand-alone risk is the risk an investor would face if he or she held only this one asset. Most fi nancial as- sets, and stocks in particular, are held in portfolios; but it is necessary to under- stand stand-alone risk to understand risk in a portfolio context.

To illustrate stand-alone risk, suppose an investor buys $100,000 of short-term Treasury bills with an expected return of 5%. In this case, the investment’s return, 5%, can be estimated quite precisely; and the investment is defi ned as being essen- tially risk-free. This same investor could also invest the $100,000 in the stock of a company just being organized to prospect for oil in the mid-Atlantic. Returns on the stock would be much harder to predict. In the worst case, the company would go bankrupt and the investor would lose all of his or her money, in which case the return would be !100%. In the best-case scenario, the company would discover huge amounts of oil and the investor would receive a 1,000% return. When evaluat- ing this investment, the investor might analyze the situation and conclude that the expected rate of return, in a statistical sense, is 20%; but the actual rate of return could range from, say, "1,000% to !100%. Because there is a signifi cant danger of earning much less than the expected return, such a stock would be relatively risky.

No investment should be undertaken unless the expected rate of return is high enough to compensate for the perceived risk. In our example, it is clear that few if any investors would be willing to buy the oil exploration stock if its expected return didn’t ex- ceed that of the T-bill. This is an extreme example. Generally, things are much less obvious; and we need to measure risk in order to decide whether a potential in- vestment should be undertaken. Therefore, we need to defi ne risk more precisely.

As you will see, the risk of an asset is different when the asset is held by itself versus when it is held as a part of a group, or portfolio, of assets. We look at stand- alone risk in this section, then at portfolio risk in later sections. It’s necessary to know something about stand-alone risk in order to understand portfolio risk. Also, stand-alone risk is important to the owners of small businesses and in our exami- nation of physical assets in the capital budgeting chapters. For stocks and most fi - nancial assets, though, it is portfolio risk that is most important. Still, you need to understand the key elements of both types of risk.

8-2a Statistical Measures of Stand-Alone Risk This is not a statistics book, and we won’t spend a great deal of time on statistics. However, you do need an intuitive understanding of the relatively simple statis- tics presented in this section. All of the calculations can be done easily with a cal- culator or with Excel; and while we show pictures of the Excel setup, Excel is not needed for the calculations.

Here are the fi ve key items that are covered: • Probability distributions • Expected rates of return, r̂ (“r hat”) • Historical, or past realized, rates of return, r- (“r bar”) • Standard deviation, # (sigma) • Coeffi cient of variation (CV)

Table 8-1 gives the probability distributions for Martin Products, which makes engines for long-haul trucks (18-wheelers), and for U.S. Water, which supplies an es- sential product and thus has very stable sales and profi ts. Three possible states of the economy are shown in Column 1; and the probabilities of these outcomes, expressed as decimals rather than percentages, are given in Column 2 and then repeated in Column 5. There is a 30% chance of a strong economy and thus strong demand, a 40% probability of normal demand, and a 30% probability of weak demand.

Stand-Alone Risk The risk an investor would face if he or she held only one asset.

Probability Distribution A listing of possible outcomes or events with a probability (chance of occurrence) assigned to each outcome.

234 Part 3 Financial Assets

3 It is completely unrealistic to think that any stock has no chance of a loss. Only in hypothetical examples could this occur. To illustrate, the price of Countrywide Financial’s stock dropped from $45.26 to $4.43 in the 12 months ending January 2008. 4 The expected return can also be calculated with an equation that does the same thing as the table:

Expected rate of return $ r̂ $ P1r1 " P2r2 " . . . " PNrN

8-1 $ ∑ i$1

Piri The second form of the equation is a shorthand expression in which sigma ( ∑ ) means “sum up,” or add the values of n factors. If i $ 1, then Piri $ P1r1; if i $ 2, then Piri $ P2r2; and so forth; until i $ N, the last possible outcome.

The symbol ∑ i$1

simply says, “Go through the following process: First, let i $ 1 and fi nd the fi rst product; then let

i $ 2 and fi nd the second product; then continue until each individual product up to N has been found. Add these individual products to fi nd the expected rate of return.”

A B C D E F G 3 4 5 6 7 8 9

10 11 12 13 14 15 16

Economy, Which Affects

Demand (1)

Strong Normal Weak

Probability of This

Demand Occurring

(2)

Rate of Return If This

Demand Occurs

(3)

Probability of This

Demand Occurring

(5)

Rate of Return If This

Demand Occurs

(6)

Product (2)!(3)

(4)

Product (5)!(6)

(7)

Martin Products U.S. Water

0.30 0.40 0.30 1.00 10%

80% 10

-60

24% 4

-18 Expected return = 10.0%Expected return =

0.30 0.40 0.30 1.00

15% 10

4.5% 4.0 1.5

Probability Distributions and Expected ReturnsT a b l e 8 - 1

Columns 3 and 6 show the returns for the two companies under each state of the economy. Returns are relatively high when demand is strong and low when demand is weak. Notice, though, that Martin’s rate of return could vary far more widely than U.S. Water’s. Indeed, there is a fairly high probability that Martin’s stock will suffer a 60% loss, while at worst, U.S. Water should have a 5% return.3

Columns 4 and 7 show the products of the probabilities times the returns under the different demand levels. When we sum these products, we obtain the expected rates of return, r̂ “r-hat,” for the stocks. Both stocks have an expected re- turn of 10%.4

We can graph the data in Table 8-1 as we do in Figure 8-2. The height of each bar indicates the probability that a given outcome will occur. The range of possible returns for Martin is from !60% to "80%, and the expected return is 10%. The ex- pected return for U.S. Water is also 10%, but its possible range (and thus maximum loss) is much narrower.

In Figure 8-2, we assumed that only three economic states could occur: strong, normal, and weak. Actually, the economy can range from a deep depression to a fantastic boom; and there are an unlimited number of possibilities in between. Suppose we had the time and patience to assign a probability to each possible level of demand (with the sum of the probabilities still equaling 1.0) and to assign a rate of return to each stock for each level of demand. We would have a table similar to Table 8-1 except that it would have many more demand levels. This table could be used to calculate expected rates of return as shown previously, and the probabili- ties and outcomes could be represented by continuous curves such as those shown in Figure 8-3. Here we changed the assumptions so that there is essentially no chance that Martin’s return will be less than –60% or more than 80% or that

Expected Rate of Return, r̂ The rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results.

235Chapter 8 Risk and Rates of Return

Probability Distributions of Martin Products’ and U.S. Water’s Rates of ReturnFIGURE 8-2

Probability of Occurrence

a. Martin Products

Rate of Return (%)

80100–60

0.4

0.3

0.2

0.1

Expected Rate of Return

Probability of Occurrence

b. U.S. Water

Rate of Return (%)

15100 5

0.4

0.3

0.2

0.1

Expected Rate of Return

Continuous Probability Distributions of Martin Products’ and U.S. Water’s Rates of ReturnFIGURE 8-3

Note: The assumptions regarding the probabilities of various outcomes have been changed from those in Figure 8-2. There the probability of obtaining exactly 10% was 40%; here it is much smaller because there are many possible outcomes instead of just three. With continuous distributions, it is more appropriate to ask what the probability is of obtaining at least some specifi ed rate of return than to ask what the probability is of obtaining exactly that rate. This topic is covered in detail in statistics courses.

Probability Density

U.S. Water

Martin Products

80100–60

Expected Rate of Return

Rate of Return (%)

236 Part 3 Financial Assets

U.S. Water’s return will be less than 5% or more than 15%. However, virtually any return within these limits is possible.

The tighter (or more peaked) the probability distributions shown in Figure 8-3, the more likely the actual outcome will be close to the expected value and, conse- quently, the less likely the actual return will end up far below the expected return. Thus, the tighter the probability distribution, the lower the risk. Since U.S. Water has a relatively tight distribution, its actual return is likely to be closer to its 10% ex- pected return than is true for Martin; so U.S. Water is less risky.5

8-2b Measuring Stand-Alone Risk: The Standard Deviation6

It is useful to measure risk for comparative purposes, but risk can be defi ned and measured in several ways. A common defi nition that is simple and is satisfactory for our purpose is based on probability distributions such as those shown in Fig- ure 8-3: The tighter the probability distribution of expected future returns, the smaller the risk of a given investment. According to this defi nition, U.S. Water is less risky than Martin Products because there is a smaller chance that the actual return of U.S. Water will end up far below its expected return.

We can use the standard deviation (#, pronounced “sigma”) to quantify the tightness of the probability distribution.7 The smaller the standard deviation, the tighter the probability distribution and, accordingly, the lower the risk. We calcu- late Martin’s # in Table 8-2. We picked up Columns 1, 2, and 3 from Table 8-1. Then in Column 4, we fi nd the deviation of the return in each demand state from the ex- pected return: Actual return – Expected 10% return. The deviations are squared and shown in Column 5. Each squared deviation is then multiplied by the relevant probability and shown in Column 6. The sum of the products in Column 6 is the variance of the distribution. Finally, we fi nd the square root of the variance—this is

5 In this example, we implicitly assume that the state of the economy is the only factor that aff ects returns. In reality, many factors, including labor, materials, and development costs, infl uence returns. This is discussed at greater length in the chapters on capital budgeting. 6 This section is relatively technical, but it can be omitted without loss of continuity. 7 There are actually two types of standard deviations, one for complete distributions and one for situations that involve only a sample. Diff erent formulas and notations are used. Also, the standard deviation should be modifi ed if the distribution is not normal, or bell-shaped. Since our purpose is simply to get the general idea across, we leave the refi nements to advanced fi nance and statistics courses.

A B C D E F 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Economy, Which Affects

Demand (1)

Strong Normal Weak

Rate of Return If This

Demand Occurs

(3)

Deviation Squared

(5)

Squared Deviation

x Prob. (6)

Deviation: Actual -

10% Expected

Return (4)

0.30 0.40 0.30 1.00

Probability of This

Demand Occurring

(2) 80% 10

-60

70% 0

-70 " = Variance:

Standard deviation = square root of variance: # = Standard deviation expressed as a percentage: # =

0.2940 0.5422

0.4900 0.0000 0.4900

0.1470 0.0000 0.1470

54.22%

Calculating Martin Products’ Standard DeviationT a b l e 8 - 2

237Chapter 8 Risk and Rates of Return

the standard deviation, and it is shown at the bottom of Column 6 as a fraction and a percentage.8

The standard deviation is a measure of how far the actual return is likely to deviate from the expected return. Martin’s standard deviation is 54.2%, so its actual return is likely to be quite different from the expected 10%.9 U.S. Water’s standard deviation is 3.9%, so its actual return should be much closer to the ex- pected return of 10%. The average publicly traded fi rm’s # has been in the range of 20% to 30% in recent years; so Martin is more risky than most stocks, while U.S. Water is less risky.

8-2c Using Historical Data to Measure Risk10

In the last section, we found the mean and standard deviation based on a subjective probability distribution. If we had actual historical data instead, the standard devi- ation of returns could be found as shown in Table 8-3.11 Because past results are often repeated in the future, the historical # is often used as an estimate of future risk.12 A key question that arises when historical data is used to forecast the future is how far back in time should we go. Unfortunately, there is no simple answer. Using a longer historical time series has the benefi t of giving more information, but some of that information may be misleading if you believe that the level of risk in the future is likely to be very different than the level of risk in the past.

Standard Deviation, ! (sigma) A statistical measure of the variability of a set of observations.

8 This formula summarizes what we did in Table 8-2:

Standard deviation $ # $ √ ______________

∑ i$1

(ri ! r̂)2 Pi 8-2

9 With a normal (bell-shaped) distribution, the actual return should be within one # about 68% of the time. 10 Again, this section is relatively technical, but it can be omitted without loss of continuity. 11 The 4 years of historical data are considered to be a “sample” of the full (but unknown) set of data, and the pro- cedure used to fi nd the standard deviation is diff erent from the one used for probabilistic data. Here is the equa- tion for sample data, and it is the basis for Table 8-3:

Estimated # $

√ __________

∑ t$1

(r-t ! r-Avg)2 ___________ N ! 1 8-2a

Here r-t (“r bar t”) denotes the past realized rate of return in Period t, and r -

Avg is the average annual return earned over the last N years. 12 The average return for the past period (10.3% in our example) may also be used as an estimate of future returns, but this is problematic because the average historical return varies widely depending on the period examined. In our example, if we went from 2005 to 2007, we would get a diff erent average from the 10.3%. The average historical return stabilizes with more years of data, but that brings into question whether data from many years ago is still relevant today.

Finding ! Based On Historical DataT a b l e 8 - 3

A B C D E F 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Year (1)

2005 2006 2007 2008

30.0% -10.0 -19.0 40.0 10.3%Average

Return (2)

Deviation from

average (3)

Squared Deviation

(4) 19.8%

-20.3 -29.3 29.8

Variance = ": 25.4% Variance/(N–1) = Variance/3:

Standard deviation = Square root of variance: # = 8.5%

3.9% 4.1 8.6 8.9

29.1%

238 Part 3 Financial Assets

13 See our tutorials on the text’s web site (http://academic.cengage.com/finance/brigham) or your calculator manual for instructions on calculating historical standard deviations.

All fi nancial calculators (and Excel) have easy-to-use functions for fi nding # based on historical data.13 Simply enter the rates of return and press the key marked S (or Sx) to obtain the standard deviation. However, neither calculators nor Excel have a built-in formula for fi nding # where probabilistic data are involved. In those cases, you must go through the process outlined in Table 8-2.

8-2d Measuring Stand-Alone Risk: The Coefficient of Variation

If a choice has to be made between two investments that have the same expected returns but different standard deviations, most people would choose the one with the lower standard deviation and, therefore, the lower risk. Similarly, given a choice between two investments with the same risk (standard deviation) but dif- ferent expected returns, investors would generally prefer the investment with the higher expected return. To most people, this is common sense—return is “good” and risk is “bad”; consequently, investors want as much return and as little risk as possible. But how do we choose between two investments if one has the higher expected return but the other has the lower standard deviation? To help answer that question, we use another measure of risk, the coeffi cient of variation (CV), which is the standard deviation divided by the expected return:

8-3 Coeffi cient of variation " CV " ! __ r̂

The coeffi cient of variation shows the risk per unit of return, and it provides a more mean- ingful risk measure when the expected returns on two alternatives are not the same. Since U.S. Water and Martin Products have the same expected return, the coeffi cient of variation is not necessary in this case. Here the fi rm with the larger standard deviation, Martin, must have the larger coeffi cient of variation. In fact, the coeffi - cient of variation for Martin is 54.22/10 $ 5.42 and the coeffi cient of variation for U.S. Water is 3.87/10 $ 0.39. Thus, Martin is about 14 times riskier than U.S. Water on the basis of this criterion.

8-2e Risk Aversion and Required Returns Suppose you inherited $1 million, which you plan to invest and then retire on the income. You can buy a 5% U.S. Treasury bill, and you will be sure of earning $50,000 of interest. Alternatively, you can buy stock in R&D Enterprises. If R&D’s research programs are successful, your stock will increase to $2.1 million. However, if the research is a failure, the value of your stock will be zero and you will be penniless. You regard R&D’s chances of success or failure as 50-50, so the expected value of the stock a year from now is 0.5($0) " 0.5($2,100,000) $ $1,050,000. Subtracting the $1 million cost leaves an expected $50,000 profi t and a 5% rate of return, the same as for the T-bill:

Expected rate of return " Expected ending value # Cost

___________________________ Cost

" $1,050,000 # $1,000,000 ______________________ $1,000,000

" $50,000 __________ $1,000,000 " 5%

Given the choice of the sure $50,000 profi t (and 5% rate of return) and the risky expected $50,000 profi t and 5% return, which one would you choose? If you choose the

Coefficient of Variation (CV) The standardized measure of the risk per unit of return; calculated as the standard deviation divided by the expected return.

http://academic.cengage.com/finance/brigham

239Chapter 8 Risk and Rates of Return

less risky investment, you are risk-averse. Most investors are risk-averse, and certainly the av- erage investor is with regard to his or her “serious money.” Because this is a well-documented fact, we assume risk aversion in our discussions throughout the remainder of the book.

What are the implications of risk aversion for security prices and rates of re- turn? The answer is that, other things held constant, the higher a security’s risk, the higher its required return; and if this situation does not hold, prices will change to bring about the required condition. To illustrate this point, look back at Figure 8-3 and consider again the U.S. Water and Martin Products stocks. Suppose each stock sells for $100 per share and each has an expected rate of return of 10%. Investors are averse to risk; so under those conditions, there would be a general preference for U.S. Water. People with money to invest would bid for U.S. Water, and Martin’s stockholders would want to sell and use the money to buy U.S. Water. Buying pressure would quickly drive U.S. Water’s stock up, and selling pressure would simultaneously cause Martin’s price to fall.

These price changes, in turn, would change the expected returns of the two se- curities. Suppose, for example, that U.S. Water’s stock were bid up from $100 to $125 and Martin’s stock declined from $100 to $77. These price changes would cause U.S. Water’s expected return to fall to 8% and Martin’s return to rise to 13%.14 The differ- ence in returns, 13% ! 8% $ 5%, would be a risk premium (RP), which represents the additional compensation investors require for bearing Martin’s higher risk.

This example demonstrates a very important principle: In a market dominated by risk-averse investors, riskier securities compared to less risky securities must have higher expected returns as estimated by the marginal investor. If this situation does not exist, buying and selling will occur until it does exist. Later in the chapter we will con- sider the question of how much higher the returns on risky securities must be, after we see how diversifi cation affects the way risk should be measured.

Risk Aversion Risk-averse investors dislike risk and require higher rates of return as an inducement to buy riskier securities.

Risk Premium (RP) The difference between the expected rate of return on a given risky asset and that on a less risky asset.

14 We assume that each stock is expected to pay shareholders $10 a year in perpetuity. The price of this perpetuity can be found by dividing the annual cash fl ow by the stock’s return. Thus, if the stock’s expected return is 10%, the price must be $10/0.10 $ $100. Likewise, an 8% expected return would be consistent with a $125 stock price ($10/0.08 $ $125) and a 13% return with a $77 stock price ($10/0.13 $ $77).

The table accompanying this box summarizes the histori- cal trade-off between risk and return for diff erent classes of investments from 1926 through 2007. As the table shows, those assets that produced the highest average returns also had the highest standard deviations and the widest ranges of returns. For example, small-company stocks had the highest average annual return, 17.1%, but the standard deviation of their returns, 32.6%, was also the highest. By contrast, U.S. Treasury bills had the lowest standard devia- tion, 3.1%, but they also had the lowest average return, 3.8%. While there is no guarantee that history will repeat itself, the returns and standard deviations observed in the past are often used as a starting point for estimating future returns.

Selected Realized Returns, 1926–2007

Average Return

Standard Deviation

Small-company stocks 17.1% 32.6%

Large-company stocks 12.3 20.0

Long-term corporate bonds 6.2 8.4

Long-term government bonds 5.8 9.2

U.S. Treasury bills 3.8 3.1

Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008), p. 28.

THE TRADE-OFF BETWEEN RISK AND RETURN

240 Part 3 Financial Assets

8-3 RISK IN A PORTFOLIO CONTEXT: THE CAPM In this section, we discuss the risk of stocks when they are held in portfolios rather than as stand-alone assets. Our discussion is based on an extremely important the- ory, the Capital Asset Pricing Model, or CAPM, that was developed in the 1960s.15 We do not attempt to cover the CAPM in detail—rather, we simply use its intuition to explain how risk should be considered in a world where stocks and other assets are held in portfolios. If you go on to take a course in investments, you will cover the CAPM in detail.

Thus far in the chapter we have considered the riskiness of assets when they are held in isolation. This is generally appropriate for small businesses, many real estate investments, and capital budgeting projects. However, the risk of a stock held in a portfolio is typically lower than the stock’s risk when it is held alone. Since investors dislike risk and since risk can be reduced by holding portfolios, most stocks are held in portfolios. Banks, pension funds, insurance companies, mutual funds, and other fi nancial institutions are required by law to hold diversi- fi ed portfolios. Most individual investors—at least those whose security holdings constitute a signifi cant part of their total wealth—also hold portfolios. Therefore, the fact that one particular stock’s price goes up or down is not important—what is important is the return on the portfolio and the portfolio’s risk. Logically, then, the risk and return of an individual stock should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held.

To illustrate, Pay Up Inc. is a collection agency that operates nationwide through 37 offi ces. The company is not well known, its stock is not very liquid, and its earn- ings have experienced sharp fl uctuations in the past. This suggests that Pay Up is risky and that its required rate of return, r, should be relatively high. However, Pay Up’s required return in 2008 (and all other years) was quite low in comparison to most other companies. This indicates that investors think Pay Up is a low-risk com- pany in spite of its uncertain profi ts. This counterintuitive fi nding has to do with diversi- fi cation and its effect on risk. Pay Up’s earnings rise during recessions, whereas most other companies’ earnings decline when the economy slumps. Thus, Pay Up’s stock is like insurance—it pays off when other things go bad—so adding Pay Up to a port- folio of “regular” stocks stabilizes the portfolio’s returns and makes it less risky.

Capital Asset Pricing Model (CAPM) A model based on the proposition that any stock’s required rate of return is equal to the risk- free rate of return plus a risk premium that reflects only the risk remaining after diversification.

15 The CAPM was originated by Professor William F. Sharpe in his article “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 1964. Literally thousands of articles exploring various aspects of the CAPM have been published subsequently, and it is very widely used in investment analysis.

SEL F TEST What does investment risk mean?

Set up an illustrative probability distribution table for an investment with probabilities for diff erent conditions, returns under those conditions, and the expected return.

Which of the two stocks graphed in Figure 8-3 is less risky? Why?

Explain why you agree or disagree with this statement: Most investors are risk-averse.

How does risk aversion aff ect rates of return?

An investment has a 50% chance of producing a 20% return, a 25% chance of producing an 8% return, and a 25% chance of producing a !12% return. What is its expected return? (9%)

241Chapter 8 Risk and Rates of Return

8-3a Expected Portfolio Returns, r̂p The expected return on a portfolio, r̂p, is the weighted average of the expected returns of the individual assets in the portfolio, with the weights being the per- centage of the total portfolio invested in each asset:

r̂p " w1r̂1 + w2r̂2 $ . . . $ wN r̂N

" ∑ i=1

wir̂i 8-4

Here r̂i is the expected return on the ith stock; the wi’s are the stocks’ weights, or the percentage of the total value of the portfolio invested in each stock; and N is the number of stocks in the portfolio.

Table 8-4 can be used to implement the equation. Here we assume that an ana- lyst estimated returns on the four stocks shown in Column 1 for the coming year, as shown in Column 2. Suppose further that you had $100,000 and you planned to in- vest $25,000, or 25% of the total, in each stock. You could multiply each stock’s per- centage weight as shown in Column 4 by its expected return; get the product terms in Column 5; and then sum Column 5 to get the expected portfolio return, 10.75%.

If you added a fi fth stock with a higher expected return, the portfolio’s ex- pected return would increase, and vice versa if you added a stock with a lower expected return. The key point to remember is that the expected return on a portfolio is a weighted average of expected returns on the stocks in the portfolio.

Several additional points should be made: 1. The expected returns in Column 2 would be based on a study of some type,

but they would still be essentially subjective and judgmental because different analysts could look at the same data and reach different conclusions. There- fore, this type of analysis must be viewed with a critical eye. Nevertheless, it is useful, indeed necessary, if one is to make intelligent investment decisions.

2. If we added companies such as Delta Airlines and Ford, which are generally considered to be relatively risky, their expected returns as estimated by the marginal investor would be relatively high; otherwise, investors would sell them, drive down their prices, and force the expected returns above the returns on safer stocks.

3. After the fact and a year later, the actual realized rates of return, r-i, on the individual stocks—the r-i, or “r-bar,” values—would almost certainly be differ- ent from the initial expected values. That would cause the portfolio’s actual return, r-p, to differ from the expected return, r̂p $ 10.75%. For example, Micro- soft’s price might double and thus provide a return of "100%, whereas IBM might have a terrible year, fall sharply, and have a return of !75%. Note, though, that those two events would be offsetting; so the portfolio’s return still might be close to its expected return even though the returns on the individual stocks were far from their expected values.

Expected Return on a Portfolio, r̂p The weighted average of the expected returns on the assets held in the portfolio.

Realized Rate of Return, r-

The return that was actually earned during some past period. The actual return (r-) usually turns out to be different from the expected return (r̂) except for riskless assets.

Realized Rate of Return, r-

The return that was actually earned during some past period. The actual return (r-) usually turns out to be different from the expected return (r̂) except for riskless assets.

Expected Return On a Portfolio, r̂p T a b l e 8 - 4

A B C D E F 52 53 54 55 56 57 58 59 60 61 62

Product: (2)!(4)

(5) Stock

(1)

100.0%$100,00010.75%

Microsoft IBM GE

Exxon

Expected Return

(2) 12.00% 11.50 10.00

9.50

Dollars Invested

(3) $ 25,000

25,000 25,000 25,000

Percent of Total (wi)

(4) 25.0% 25.0 25.0 25.0

3.000% 2.875 2.500 2.375

= Expected rp10.750%

242 Part 3 Financial Assets

8-3b Portfolio Risk Although the expected return on a portfolio is simply the weighted average of the expected returns on its individual stocks, the portfolio’s risk, #p, is not the weighted average of the individual stocks’ standard deviations. The portfolio’s risk is gen- erally smaller than the average of the stocks’ #s because diversifi cation lowers the portfolio’s risk.

To illustrate this point, consider the situation in Figure 8-4. The bottom section gives data on Stocks W and M individually and data on a portfolio with 50% in each stock. The left graph plots the data in a time series format, and it shows that the returns on the individual stocks vary widely from year to year. Therefore, the individual stocks are risky. However, the portfolio’s returns are constant at 15%, indicating that it is not risky at all. The probability distribution graphs to the right show the same thing—the two stocks would be quite risky if they were held in iso- lation; but when they are combined to form Portfolio WM, they have no risk whatsoever.

If you invested all of your money in Stock W, you would have an expected re- turn of 15%, but you would face a great deal of risk. The same thing would hold if you invested entirely in Stock M. However, if you invested 50% in each stock, you would have the same expected return of 15%, but with no risk whatsoever. Being rational and averse to risk, you and all other rational investors would choose to hold the portfolio, not the stocks individually.

A B C D E F G 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108

Portfolio WMStock MStock WYear

Rate of Return (%) -20% 15% 40%

2004 2005 2006 2007 2008

Avg return = Estimated ! =

40.00% -10.00 40.00

-10.00 15.00

-10.00% 40.00

-10.00 40.00 15.00

15.00% 15.00 15.00 15.00 15.00

15.00% 25.00%

15.00% 0.00%

Correlation coefficient = -1.00

Portfolio WM

Stocks W and M, held separately

2004 2005 2006 2007 2008

W M

Rate of Return

-15%

15%

30%

45%

Returns With Perfect Negative Correlation, % $ !1.0FIGURE 8-4

243Chapter 8 Risk and Rates of Return

Stocks W and M can be combined to form a riskless portfolio because their re- turns move countercyclically to each other—when W’s fall, M’s rise, and vice versa. The tendency of two variables to move together is called correlation, and the correlation coeffi cient, % (pronounced “rho”), measures this tendency.16 In sta- tistical terms, we say that the returns on Stocks W and M are perfectly negatively correlated, with % $ !1.0. The opposite of perfect negative correlation is perfect posi- tive correlation, with % $ "1.0. If returns are not related to one another at all, they are said to be independent and % $ 0.

The returns on two perfectly positively correlated stocks with the same ex- pected return would move up and down together, and a portfolio consisting of these stocks would be exactly as risky as the individual stocks. If we drew a graph like Figure 8-4, we would see just one line because the two stocks and the portfolio would have the same return at each point in time. Thus, diversifi cation is completely useless for reducing risk if the stocks in the portfolio are perfectly positively correlated.

We see then that when stocks are perfectly negatively correlated (% $ !1.0), all risk can be diversifi ed away; but when stocks are perfectly positively correlated (% $ "1.0), diversifi cation does no good. In reality, most stocks are positively cor- related but not perfectly so. Past studies have estimated that on average, the corre- lation coeffi cient between the returns of two randomly selected stocks is about 0.30.17 Under this condition, combining stocks into portfolios reduces risk but does not completely eliminate it.18 Figure 8-5 illustrates this point using two stocks whose cor- relation coeffi cient is % $ "0.35. The portfolio’s average return is 15%, which is the same as the average return for the two stocks; but its standard deviation is 18.62%, which is below the stocks’ standard deviations and their average #. Again, a ratio- nal, risk-averse investor would be better off holding the portfolio rather than just one of the individual stocks.

In our examples, we considered portfolios with only two stocks. What would happen if we increased the number of stocks in the portfolio?

As a rule, portfolio risk declines as the number of stocks in a portfolio increases.

If we added enough partially correlated stocks, could we completely eliminate risk? In general, the answer is no. For an illustration, see Figure 8-6 on page 246, which shows that a portfolio’s risk declines as stocks are added. Here are some points to keep in mind about the fi gure: 1. The portfolio’s risk declines as stocks are added, but at a decreasing rate; and

once 40 to 50 stocks are in the portfolio, additional stocks do little to reduce risk. 2. The portfolio’s total risk can be divided into two parts, diversifi able risk and

market risk.19 Diversifi able risk is the risk that is eliminated by adding stocks.

Correlation The tendency of two variables to move together.

Correlation Coefficient, % A measure of the degree of relationship between two variables.

Correlation The tendency of two variables to move together.

Correlation Coefficient, % A measure of the degree of relationship between two variables.

Diversifiable Risk That part of a security’s risk associated with random events; it can be eliminated by proper diversification. This risk is also known as company- specific, or unsystematic, risk.

Market Risk The risk that remains in a portfolio after diversification has eliminated all company- specific risk. This risk is also known as non- diversifiable or systematic or beta risk.

Diversifiable Risk That part of a security’s risk associated with random events; it can be eliminated by proper diversification. This risk is also known as company- specific, or unsystematic, risk.

Market Risk The risk that remains in a portfolio after diversification has eliminated all company- specific risk. This risk is also known as non- diversifiable or systematic or beta risk.

16 The correlation coeffi cient, ρ, can range from +1.0, denoting that the two variables move up and down in per- fect synchronization, to !1.0, denoting that the variables move in exactly opposite directions. A correlation coef- fi cient of zero indicates that the two variables are not related to each other—that is, changes in one variable are independent of changes in the other. It is easy to calculate correlation coeffi cients with a fi nancial calculator. Sim- ply enter the returns on the two stocks and press a key labeled “r.” For W and M, ρ $ !1.0. See our tutorial on the text’s web site or your calculator manual for the exact steps. Also note that the correlation coeffi cient is often de- noted by the term r. We use ρ here to avoid confusion with r used to denote the rate of return. 17 A study by Chan, Karceski, and Lakonishok (1999) estimated that the average correlation coeffi cient between two randomly selected stocks was 0.28, while the average correlation coeffi cient between two large-company stocks was 0.33. The time period of their sample was 1968 to 1998. See Louis K. C. Chan, Jason Karceski, and Josef Lakonishok, “On Portfolio Optimization: Forecasting Covariance and Choosing the Risk Model,” The Review of Financial Studies, Vol. 12, no. 5 (Winter 1999), pp. 937–974. 18 If we combined a large number of stocks with ρ = 0, we could form a riskless portfolio. However, there are not many stocks with ρ = 0—stocks’ returns tend to move together, not to be independent of one another. 19 Diversifi able risk is also known as company-specifi c, or unsystematic, risk. Market risk is also known as non- diversifi able or systematic or beta risk; it is the risk that remains in the portfolio after diversifi cation has eliminated all company-specifi c risk.

244 Part 3 Financial Assets

Market risk is the risk that remains even if the portfolio holds every stock in the market. Market risk is the risk that we discussed in the opening vignette and in our discussion of Figure 8-1.

3. Diversifi able risk is caused by such random, unsystematic events as lawsuits, strikes, successful and unsuccessful marketing and R&D programs, the win- ning or losing of a major contract, and other events that are unique to the par- ticular fi rm. Because these events are random, their effects on a portfolio can be eliminated by diversifi cation—bad events for one fi rm will be offset by good events for another. Market risk, on the other hand, stems from factors that systematically affect most fi rms: war, infl ation, recessions, high interest rates, and other macro factors. Because most stocks are affected by macro fac- tors, market risk cannot be eliminated by diversifi cation.

4. If we carefully selected the stocks included in the portfolio rather than adding them randomly, the graph would change. In particular, if we chose stocks with low correlations with one another and with low stand-alone risk, the portfo- lio’s risk would decline faster than if random stocks were added. The reverse would hold if we added stocks with high correlations and high #s.

5. Most investors are rational in the sense that they dislike risk, other things held constant. That being the case, why would an investor ever hold one (or a few) stocks? Why not hold a market portfolio consisting of all stocks? There are several

Market Portfolio A portfolio consisting of all stocks.

A B C D E F G 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138

Rate of Return (%) -20% 15% 40%

Portfolio WY

Stocks W and Y, held separately

Portfolio WYStock YStock WYear 2004 2005 2006 2007 2008

Avg return = Estimated ! =

40.00% -10.00 35.00 -5.00

15.00

40.00% 15.00 -5.00

-10.00 35.00

40.00% 2.50

15.00 -7.50

25.00 15.00% 22.64%

15.00% 22.64%

15.00% 18.62%

Correlation coefficient = 0.35

2004 2005 2006 2007 2008

Rate of Return

-15%

15%

30%

45%

Returns With Partial Correlation, % $ " 0.35FIGURE 8-5

245Chapter 8 Risk and Rates of Return

reasons. First, high administrative costs and commissions would more than offset the benefi ts for individual investors. Second, index funds can diversify for inves- tors, and many individuals can and do get broad diversifi cation through these funds. Third, some people think that they can pick stocks that will “beat the mar- ket”; so they buy them rather than the broad market. And fourth, some people can, through superior analysis, beat the market; so they fi nd and buy underval- ued stocks and sell overvalued ones and, in the process, cause most stocks to be properly valued, with their expected returns consistent with their risks.

6. One key question remains: How should the risk of an individual stock be mea- sured? The standard deviation of expected returns, #, is not appropriate because it includes risk that can be eliminated by holding the stock in a portfo- lio. How then should we measure a stock’s risk in a world where most people hold portfolios? That’s the subject of the next section.

8-3c Risk in a Portfolio Context: The Beta Coefficient When a stock is held by itself, its risk can be measured by the standard deviation of its expected returns. However, # is not appropriate when the stock is held in a portfolio, as stocks generally are. So how do we measure a stock’s relevant risk in a portfolio context?

First, note that all risk except that related to broad market movements can and will be diversifi ed away by most investors—rational investors will hold enough stocks to move down the risk curve in Figure 8-6 to the point where only market risk remains in their portfolios.

The risk that remains once a stock is in a diversifi ed portfolio is its contribution to the portfolio’s market risk, and that risk can be measured by the extent to which the stock moves up or down with the market.

The tendency of a stock to move with the market is measured by its beta coeffi cient, b. Ideally, when estimating a stock’s beta, we would like to have a crystal ball that tells us how the stock is going to move relative to the overall stock market in the future. But since we can’t look into the future, we often use historical data and assume that the stock’s historical beta will give us a reasonable estimate of how the stock will move relative to the market in the future.

To illustrate the use of historical data, consider Figure 8-7, which shows the historical returns on three stocks and a market index. In Year 1, “the market,” as defi ned by a portfolio containing all stocks, had a total return (dividend yield plus capital gains yield) of 10%, as did the three individual stocks. In Year 2, the market went up sharply and its return was 20%. Stocks H (for high) soared by 30%; A (for average) returned 20%, the same as the market; and L (for low) returned 15%. In Year 3, the market dropped sharply; its return was !10%. The three stocks’ returns also fell—H’s return was !30%, A’s was !10%, and L broke even with a 0% return. In Years 4 and 5, the market returned 0% and 5%, respectively, and the three stocks’ returns were as shown in the fi gure.

A plot of the data shows that the three stocks moved up or down with the market but that H was twice as volatile as the market, A was exactly as volatile as the market, and L had only half the market’s volatility. It is apparent that the steeper a stock’s line, the greater its volatility and thus the larger its loss in a down market. The slopes of the lines are the stocks’ beta coeffi cients. We see in the fi gure that the slope coeffi cient for H is 2.0; for A, it is 1.0; and for L, it is 0.5.20 Thus, beta measures a given stock’s volatility relative to the market, and an average stock’s beta, bA $ 1.0.

Relevant Risk The risk that remains once a stock is in a diversified portfolio is its contribution to the portfolio’s market risk. It is measured by the extent to which the stock moves up or down with the market.

Beta Coefficient, b A metric that shows the extent to which a given stock’s returns move up and down with the stock market. Beta thus measures market risk.

Average Stock’s Beta, bA By definition, bA = 1 because an average-risk stock is one that tends to move up and down in step with the general market.

20 For more on calculating betas, see Brigham and Daves, Intermediate Financial Management, 9th ed., (Mason, OH: Thomson/South-Western, 2007), pp. 55–58 and pp. 89–94.

246 Part 3 Financial Assets

Stock A is defi ned as an average-risk stock because it has a beta of b $ 1.0 and thus moves up and down in step with the general market. Thus, an average stock will, in general, move up by 10% when the market moves up by 10% and fall by 10% when the market falls by 10%. A large portfolio of such b $ 1.0 stocks would (1) have all of its diversifi able risk removed but (2) would still move up and down with the broad market averages and thus have a degree of risk.

Stock H, which has b $ 2.0, is twice as volatile as an average stock, which means that it is twice as risky. The value of a portfolio consisting of b = 2.0 stocks could double—or halve—in a short time; and if you held such a portfolio, you could quickly go from being a millionaire to being a pauper. Stock L, on the other hand, with b $ 0.5, is only half as volatile as the average stock, and a portfolio of such stocks would rise and fall only half as rapidly as the market. Thus, its risk would be half that of an average-risk portfolio with b $ 1.0.

Betas for literally thousands of companies are calculated and published by Merrill Lynch, Value Line, Yahoo, Google, and numerous other organizations; and the beta coeffi cients of some well-known companies are shown in Table 8-5. Most stocks have betas in the range of 0.50 to 1.50; and the average beta for all stocks is 1.0, which indicates that the average stock moves in sync with the market.21

21 While fairly uncommon, it is possible for a stock to have a negative beta. In that case, the stock’s returns would tend to rise whenever the returns on other stocks fell.

= 20.4

101 20 30 40 2,000+ Number of Stocks

in the Portfolio

σM

Portfolio’s Total Risk:

Declines as Stocks

Are Added Portfolio’s Market Risk: Remains Constant

Portfolio’s Diversifiable Risk: Could Be Reduced by Adding More Stocks

Portfolio’s Risk, #p

Portfolio Risk, σp (%)

Minimum Attainable Risk in a Portfolio of Average Stocks

Eff ects of Portfolio Size on Risk for a Portfolio of Randomly Selected StocksFIGURE 8-6

Note: This graph assumes that stocks in the portfolio are randomly selected from the universe of large, publicly-traded stocks listed on the NYSE.

247Chapter 8 Risk and Rates of Return

A B C D E F 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182

Calculating beta: 1. Rise-Over-Run. Divide the vertical axis change that results from a given change on the horizontal axis (i.e., the change in the stock’s return divided by the changes in the market return). For Stock H, when the market rises from –10% to +20%, or by 30%, the stock’s return goes from –30% to +30%, or by 60%. Thus, beta H by the rise-over-run method is 60/30 = 2.0. In the same way, we find beta A to be 1.0 and beta L to be 0.5. This procedure is easy in our example because all of the points lie on a straight line; but if the points were scattered around the trend line, we could not calculate an exact beta. 2. Financial Calculator. Financial calculators have a built-in function that can be used to calculate beta. The procedure differs somewhat from calculator to calculator. See our tutorial on the text’s web site for instructions on several calculators. 3. Excel. Excel’s Slope function can be used to calculate betas. Here are the functions for our three stocks: BetaH 2.0 =SLOPE(C163:C164,B163:B164) BetaA 1.0 =SLOPE(D163:D164,B163:B164) BetaL 0.5 =SLOPE(E163:E164,B163:B164)

1 2 3 4 5

10.0% 20.0

-10.0 0.0 5.0

-30.0%

-20.0%

-10.0%

10.0%

20.0%

30.0%

-10.0% 10.0% 20.0% 30.0%0

Return on Market

High: b = 2.0

Average: b = 1.0

Low: b = 0.5

Return on Stocks

-20.0%

Year rM rH rA rL 10.0% 30.0

-30.0 -10.0

0.0

10.0% 20.0

-10.0 0.0 5.0

10.0% 15.0

0.0 5.0 7.5

Betas: Relative Volatility of Stocks H, A, and LFIGURE 8-7

If a stock whose beta is greater than 1.0 (say 1.5) is added to a bp $ 1.0 portfo- lio, the portfolio’s beta and consequently its risk will increase. Conversely, if a stock whose beta is less than 1.0 is added to a bp $ 1.0 portfolio, the portfolio’s beta and risk will decline. Thus, because a stock’s beta refl ects its contribution to the riskiness of a portfolio, beta is the theoretically correct measure of the stock’s riskiness.

248 Part 3 Financial Assets

We can summarize our discussion up to this point as follows: 1. A stock’s risk has two components, diversifi able risk and market risk. 2. Diversifi able risk can be eliminated; and most investors do eliminate it, either

by holding very large portfolios or by buying shares in a mutual fund. We are left, then, with market risk, which is caused by general movements in the stock market and refl ects the fact that most stocks are systematically affected by events such as wars, recessions, and infl ation. Market risk is the only risk that should matter to a rational, diversifi ed investor.

3. Investors must be compensated for bearing risk—the greater the risk of a stock, the higher its required return. However, compensation is required only for risk that cannot be eliminated by diversifi cation. If risk premiums existed on a stock due to its diversifi able risk, that stock would be a bargain to well- diversifi ed investors. They would start buying it and bid up its price, and the stock’s fi nal (equilibrium) price would be consistent with an expected return that refl ected only its market risk.

To illustrate this point, suppose half of Stock B’s risk is market risk (it occurs because the stock moves up and down with the market), while the other half is diversifi able. You are thinking of buying Stock B and holding it in a one-stock portfolio, so you would be exposed to all of its risk. As compensation for bearing so much risk, you want a risk premium of 8% over the 6% T-bond rate; so your required return is rA $ 6% " 8% $ 14%. But other investors, including your professor, are well diversifi ed. They are also looking at Stock B; but they would hold it in diversifi ed portfolios, eliminate its diversifi able risk, and thus be exposed to only half as much risk as you. Therefore, their required risk premium would be half as large as yours, and their required rate of return would be rB $ 6% " 4% $ 10%.

If the stock was priced to yield the 14% you require, those diversifi ed investors, including your professor, would buy it, push its price up and its yield down, and prevent you from getting the stock at a price low enough to provide the 14% return. In the end, you would have to accept a 10% return or keep your money in the bank.

4. The market risk of a stock is measured by its beta coeffi cient, which is an index of the stock’s relative volatility. Here are some benchmark betas:

b $ 0.5: Stock is only half as volatile, or risky, as an average stock. b $ 1.0: Stock is of average risk. b $ 2.0: Stock is twice as risky as an average stock.

Illustrative List of Beta CoefficientsT a b l e 8 - 5

Stock Beta Merrill Lynch 1.35 Best Buy 1.25 eBay 1.20 General Electric 0.95 Microsoft 0.95 ExxonMobil 0.90 Heinz 0.80 Coca-Cola 0.75 FPL Group 0.75 Procter & Gamble 0.65

Source: Adapted from Value Line, February 2008.

249Chapter 8 Risk and Rates of Return

5. A portfolio consisting of low-beta stocks will also have a low beta because the beta of a portfolio is a weighted average of its individual securities’ betas, found using this equation:

bp " w1b1 $ w2b2 $ . . . $ wNbN

" ∑ i"1

wib N. 8-5

Here bp is the beta of the portfolio, and it shows how volatile the portfolio is rela- tive to the market; wi is the fraction of the portfolio invested in the ith stock; and bi is the beta coeffi cient of the ith stock. To illustrate, if an investor holds a $100,000 portfolio consisting of $33,333.33 invested in each of three stocks and if each of the stocks has a beta of 0.70, the portfolio’s beta will be bp $ 0.70:

bp = 0.333(0.70) + 0.333(0.70) + 0.333(0.70) = 0.70.

Such a portfolio would be less risky than the market, so it should experience relatively narrow price swings and have relatively small rate-of-return fl uctu- ations. In terms of Figure 8-7, the slope of its regression line would be 0.70, which is less than that for a portfolio of average stocks.

Now suppose one of the existing stocks is sold and replaced by a stock with bi $ 2.00. This action will increase the portfolio’s beta from bp1 $ 0.70 to bp2 $ 1.13:

bp2 " 0.333(0.70) $ 0.333(0.70) $ 0.333(2.00) " 1.13.

Had a stock with bi $ 0.20 been added, the portfolio’s beta would have declined from 0.70 to 0.53. Adding a low-beta stock would therefore reduce the portfo- lio’s riskiness. Consequently, changing the stocks in a portfolio can change the riskiness of that portfolio.

6. Because a stock’s beta coeffi cient determines how the stock affects the riski- ness of a diversifi ed portfolio, beta is, in theory, the most relevant measure of a stock’s risk.

SEL F TEST Explain the following statement: An asset held as part of a portfolio is gener-

ally less risky than the same asset held in isolation.

What is meant by perfect positive correlation, perfect negative correlation, and zero correlation?

In general, can the riskiness of a portfolio be reduced to zero by increasing the number of stocks in the portfolio? Explain.

What is an average-risk stock? What is the beta of such a stock?

Why is it argued that beta is the best measure of a stock’s risk?

If you plotted a particular stock’s returns versus those on the S&P 500 Index over the past fi ve years, what would the slope of the regression line indicate about the stock’s risk?

An investor has a two-stock portfolio with $25,000 invested in Stock X and $50,000 invested in Stock Y. X’s beta is 1.50, and Y’s beta is 0.60. What is the beta of the investor’s portfolio? (0.90)

250 Part 3 Financial Assets

The increasing availability of international securities is mak- ing it possible to achieve a better risk-return trade-off than could be obtained by investing only in U.S. securities. So investing overseas might result in a portfolio with less risk but a higher expected return. This result occurs because of low correlations between the returns on U.S. and interna- tional securities, along with potentially high returns on over- seas stocks. Figure 8-6, presented earlier, demonstrated that an investor can reduce the risk of his or her portfolio by holding a number of stocks. The fi gure that follows suggests that investors may be able to reduce risk even further by holding a portfolio of stocks from all around the world, given the fact that the returns on domestic and international stocks are not perfectly correlated. Even though foreign stocks represent roughly 60% of the worldwide equity market and despite the apparent ben- efi ts from investing overseas, the typical U.S. investor still puts less than 10% of his or her money in foreign stocks. One possible explanation for this reluctance to invest overseas is

that investors prefer domestic stocks because of lower trans- actions costs. However, this explanation is questionable because recent studies reveal that investors buy and sell overseas stocks more frequently than they trade their domes- tic stocks. Other explanations for the domestic bias include the additional risks from investing overseas (for example, exchange rate risk) and the fact that the typical U.S. investor is uninformed about international investments and/or thinks that international investments are extremely risky. It has been argued that world capital markets have become more integrated, causing the correlation of returns between diff er- ent countries to increase, which reduces the benefi ts from international diversifi cation. In addition, U.S. corporations are investing more internationally, providing U.S. investors with international diversifi cation even if they purchase only U.S. stocks. Whatever the reason for their relatively small holdings of international assets, our guess is that in the future U.S. investors will shift more of their assets to overseas investments.

Source: For further reading, see also Kenneth Kasa, “Measuring the Gains from International Portfolio Diversifi cation,” Federal Reserve Bank of San Francisco Weekly Letter, Number 94–14, April 8, 1994.

THE BENEFITS OF DIVERSIFYING OVERSEAS

U.S. Stocks

U.S. and International Stocks

Number of Stocks in the Portfolio

Portfolio Risk, σp (%)

251Chapter 8 Risk and Rates of Return

8-4 THE RELATIONSHIP BETWEEN RISK AND RATES OF RETURN

The preceding section demonstrated that under the CAPM theory, beta is the most appropriate measure of a stock’s relevant risk. The next issue is this: For a given level of risk as measured by beta, what rate of return is required to compensate investors for bearing that risk? To begin, let us defi ne the following terms:

r̂i $ expected rate of return on the i th stock.

ri $ required rate of return on the i th stock. Note that if r̂i is less than ri, the typi-

cal investor will not purchase this stock or will sell it if he or she owns it. If r̂i is greater than ri, the investor will purchase the stock because it looks like a bargain. Investors will be indifferent if r̂i $ ri. Buying and selling by investors tends to force the expected return to equal the required return, although the two can differ from time to time before the adjustment is completed.

r– $ realized, after-the-fact return. A person obviously does not know r– at the time he or she is considering the purchase of a stock.

rRF $ risk-free rate of return. In this context, rRF is generally measured by the return on U.S. Treasury securities. Some analysts recommend that short- term T-bills be used; others recommend long-term T-bonds. We gener- ally use T-bonds because their maturity is closer to the average investor’s holding period of stocks.

bi $ beta coeffi cient of the ith stock. The beta of an average stock is bA $ 1.0. rM $ required rate of return on a portfolio consisting of all stocks, which is

called the market portfolio. rM is also the required rate of return on an aver- age (bA $ 1.0) stock.

RPM $ (rM – rRF) $ risk premium on “the market” and the premium on an aver- age stock. This is the additional return over the risk-free rate required to compensate an average investor for assuming an average amount of risk. Average risk means a stock where bi $ bA $ 1.0.

RPi $ (rM – rRF)bi $ (RPM)bi $ risk premium on the ith stock. A stock’s risk premium will be less than, equal to, or greater than the premium on an average stock, RPM, depending on whether its beta is less than, equal to, or greater than 1.0. If bi $ bA $ 1.0, then RPi $ RPM.

The market risk premium, RPM, shows the premium that investors require for bearing the risk of an average stock. The size of this premium depends on how risky investors think the stock market is and on their degree of risk aversion. Let us assume that at the current time, Treasury bonds yield rRF $ 6% and an average share of stock has a required rate of return of rM $ 11%. Therefore, the market risk premium is 5%, calculated as follows:

RPM " rM # rRF " 11% # 6% " 5%

It should be noted that the risk premium of an average stock, rM ! rRF , is actually hard to measure because it is impossible to obtain a precise estimate of the expected future return of the market, rM.

22 Given the diffi culty of estimating future market

Market Risk Premium, RPM The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.

22 This concept, as well as other aspects of the CAPM, is discussed in more detail in Chapter 3 of Eugene F. Brigham and Philip R. Daves, Intermediate Financial Management, 9th ed., (Mason, OH: Thomson/South-Western, 2007). That chapter also discusses the assumptions embodied in the CAPM framework. Some of those assumptions are unrealistic; and because of this, the theory does not hold exactly.

252 Part 3 Financial Assets

returns, analysts often look to historical data to estimate the market risk premium. Historical data suggest that the market risk premium varies somewhat from year to year due to changes in investors’ risk aversion but that it has generally ranged from 4% to 8%.

While historical estimates might be a good starting point for estimating the market risk premium, those estimates would be misleading if investors’ attitudes toward risk changed considerably over time. (See “Estimating the Market Risk Premium” box above.) Indeed, many analysts have argued that the market risk premium has fallen in recent years. If this claim is correct, the market risk pre- mium is considerably lower than one based on historical data.

The risk premium on individual stocks varies in a systematic manner from the market risk premium. For example, if one stock is twice as risky as another stock as measured by their beta coeffi cients, its risk premium should be twice as high. Therefore, if we know the market risk premium, RPM, and the stock’s beta, bi, we can fi nd its risk premium as the product (RPM)bi. For example, if beta for Stock L $ 0.5 and RPM $ 5%, RPL will be 2.5%:

8-6 Risk premium for Stock L " RPi " (RPM)bi " (5%)(0.5) " 2.5%

The Capital Asset Pricing Model (CAPM) is more than a theory describing the trade-off between risk and return—it is also widely used in practice. As we will see later, investors use the CAPM to determine the discount rate for valuing stocks and corporate managers use it to estimate the cost of equity capital. The market risk premium is a key component of the CAPM, and it should be the diff erence between the expected future return on the overall stock market and the expected future return on a riskless investment. However, we cannot obtain investors’ expectations; instead, academicians and practitioners often use a historical risk premium as a proxy for the expected risk premium. The historical premium is found by taking the diff erence between the actual return on the overall stock market and the risk-free rate during a num- ber of diff erent years and then averaging the annual results. Morningstar (through its recent purchase of Ibbotson Asso- ciates) may provide the most comprehensive estimates of historical risk premiums. It reports that the annual premiums have averaged 7.1% over the past 82 years. However, there are three potential problems with his- torical risk premiums. First, what is the proper number of years over which to compute the average? Morningstar goes back to 1926, when good data fi rst became available; but that is an arbitrary choice, and the starting and ending points make a major diff erence in the calculated premium.

Second, historical premiums are likely to be misleading at times when the market risk premium is changing. To illustrate, the stock market was very strong from 1995 through 1999, in part because investors were becoming less risk-averse, which means that they applied a lower risk premium when they valued stocks. The strong market resulted in stock returns of about 30% per year; and when bond yields were subtracted from the high stock returns, the calculated risk premiums averaged 22.3% a year. When those high numbers were added to data from prior years, they caused the long-run historical risk pre- mium as reported by Morningstar to increase. Thus, a declin- ing “true” risk premium led to very high stock returns, which, in turn, led to an increase in the calculated historical risk pre- mium. That’s a worrisome result, to say the least. The third concern is that historical estimates may be biased upward because they include only the returns of fi rms that have survived—they do not refl ect the losses incurred on investments in failed fi rms. Stephen Brown, William Goetzmann, and Stephen Ross discussed the implications of this “survivorship bias” in a 1995 Journal of Finance article. Putting these ideas into practice, Tim Koller, Marc Goedhart, and David Wessels recently suggested that survivorship bias increases historical returns by 1% to 2% a year. Therefore, they suggest that practitioners subtract 1% to 2% from the historical estimates to obtain the risk premium used in the CAPM.

Sources: Stocks, Bonds, Bills, and Infl ation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008); Stephen J. Brown, William N. Goetzmann, and Stephen A. Ross, “Survival,” Journal of Finance, Vol. 50, no. 3 (July 1995), pp. 853–873; and Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th edition (New York: McKinsey & Company, 2005).

ESTIMATING THE MARKET RISK PREMIUM

253Chapter 8 Risk and Rates of Return

As the discussion in Chapter 6 implied, the required return for any stock can be found as follows:

Required return on a stock " Risk-free return $ Premium for the stock’s risk

Here the risk-free return includes a premium for expected infl ation; and if we assume that the stocks under consideration have similar maturities and liquidity, the required return on Stock L can be found using the Security Market Line (SML) equation:

Required return on Stock L

" Risk-free return $ ( Market risk premium ) ( Stock L’s beta )

rL " rRF $ (rM # rRF)bL 8-7 " rRF $ (RPM)bL " 6% $ (11% # 6%)(0.5)

" 6% $ 2.5%

" 8.5%

Stock H had bH $ 2.0, so its required rate of return is 16%:

rH " 6% $ (5%)2.0 " 16%

An average stock, with b = 1.0, would have a required return of 11%, the same as the market return:

rA " 6% $ (5%)1.0 " 11% " rM

The SML equation is plotted in Figure 8-8 using the data shown below the graph on Stocks L, A, and H and assuming that rRF $ 6% and rM $ 11%. Note the following points: 1. Required rates of return are shown on the vertical axis, while risk as measured

by beta is shown on the horizontal axis. This graph is quite different from the one shown in Figure 8-7, where we calculated betas. In the earlier graph, the returns on individual stocks were plotted on the vertical axis and returns on the market index were shown on the horizontal axis. The betas found in Fig- ure 8-7 were then plotted as points on the horizontal axis of Figure 8-8.

2. Riskless securities have bi $ 0; so the return on the riskless asset, rRF $ 6.0%, is shown as the vertical axis intercept in Figure 8-8.

3. The slope of the SML in Figure 8-8 can be found using the rise-over-run proce- dure. When beta goes from 0 to 1.0, the required return goes from 6% to 11%, or 5%; so the slope is 5%/1.0 $ 5%. Thus, a 1-unit increase in beta causes a 5% increase in the required rate of return.

4. The slope of the SML refl ects the degree of risk aversion in the economy—the greater the average investor’s risk aversion, (a) the steeper the slope of the line and (b) the greater the risk premium for all stocks—hence, the higher the required rate of return on all stocks.

Both the SML and a company’s position on it change over time due to changes in interest rates, investors’ risk aversion, and individual companies’ betas. Such changes are discussed in the following sections.

8-4a The Impact of Expected Inflation As we discussed in Chapter 6, interest amounts to “rent” on borrowed money, or the price of money. Thus, rRF is the price of money to a riskless borrower. We also

Security Market Line (SML) Equation An equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities.

254 Part 3 Financial Assets

saw that the risk-free rate as measured by the rate on U.S. Treasury securities is called the nominal, or quoted, rate; and it consists of two elements: (1) a real infl ation-free rate of return, r* and (2) an infl ation premium, IP, equal to the anticipated rate of infl ation.23 Thus, rRF $ r* + IP. The real rate on long-term Treasury bonds has historically ranged from 2% to 4%, with a mean of about 3%. Therefore, if no infl ation were expected, long-term Treasury bonds would yield about 3%. How- ever, as the expected rate of infl ation increases, a premium must be added to the real risk-free rate of return to compensate investors for the loss of purchasing power that results from infl ation. Therefore, the 6% rRF shown in Figure 8-8 might be thought of as consisting of a 3% real risk-free rate of return plus a 3% infl ation premium: rRF $ r* " IP $ 3% " 3% $ 6%.

A B C D E F IHG 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225

BetaKey Inputs

0.0 0.5 1.0 1.5 2.52.0

Required Rate of Return (%)

6.0% 11.0

5.0

rRF rM

RPM = rM – rRF

Riskless asset: Stock L: Stock A: Stock H:

0.0 0.5 1.0 2.0

6.00% 8.50

11.00 16.00

rRF = 6.0%

rL = 8.5%

rA = rM = 11.0%

rH = 16.0%

H’s Risk Premium

L’s Risk Premium

Risk-Free Return, rRF

Market Risk Premium, RPM. Also Stock A’s Risk Premium

Beta Coefficient

ri = rRF + RPM(bi)

SML = rRF + RPM x bi

The Security Market Line (SML)FIGURE 8-8

23 Long-term Treasury bonds also contain a maturity risk premium, MRP. We include the MRP in r* to simplify the discussion.

255Chapter 8 Risk and Rates of Return

If the expected infl ation rate rose by 2%, to 3% " 2% $ 5%, rRF would rise to 8%. Such a change is shown in Figure 8-9. Notice that the increase in rRF leads to an equal increase in the rates of return on all risky assets because the same infl ation premium is built into required rates of return on both riskless and risky assets.24 Therefore, the rate of return on our illustrative average stock, rA, increases from 11% to 13%. Other risky securities’ returns also rise by two percentage points.

8-4b Changes in Risk Aversion The slope of the SML refl ects the extent to which investors are averse to risk—the steeper the slope of the line, the more the average investor requires as compensa- tion for bearing risk. Suppose investors were indifferent to risk; that is, they were not at all risk-averse. If rRF was 6%, risky assets would also have a required return of 6% because if there were no risk aversion, there would be no risk premium. In that case, the SML would plot as a horizontal line. However, because investors are risk-averse, there is a risk premium; and the greater the risk aversion, the steeper the slope of the SML.

24 Recall that the infl ation premium for any asset is the average expected rate of infl ation over the asset’s life. Thus, in this analysis, we must assume that all securities plotted on the SML graph have the same life or that the expected rate of future infl ation is constant.

It should also be noted that rRF in a CAPM analysis can be proxied by either a long-term rate (the T-bond rate) or a short-term rate (the T-bill rate). Traditionally, the T-bill rate was used; but in recent years, there has been a movement toward use of the T-bond rate because there is a closer relationship between T-bond yields and stocks’ returns than between T-bill yields and stocks’ returns. See Stocks, Bonds, Bills, and Infl ation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008) for a discussion.

0 0.5 1.0 1.5 2.0 Risk, b i

rA2 = rM2 = 13

rA1 = rM1 = 11

rRF2 = 8

Required Rate of Return (%)

rRF1 = 6

r* = 3

Original IP = 3%

Increase in Anticipated Inflation, $IP = 2%

Real Risk-Free Rate of Return, r*

SML2 = 8% + 5%(bi)

SML1 = 6% + 5%(bi)

Shift in the SML Caused by an Increase in Expected Inf lationFIGURE 8-9

256 Part 3 Financial Assets

Figure 8-10 illustrates an increase in risk aversion. The market risk premium rises from 5% to 7.5%, causing rM to rise from rM1 $ 11% to rM2 $ 13.5%. The returns on other risky assets also rise, and the effect of this shift in risk aversion is more pronounced on riskier securities. For example, the required return on Stock L with bA $ 0.5 increases by only 1.25 percentage points, from 8.5% to 9.75%, whereas the required return on a stock with a beta of 1.5 increases by 3.75 percentage points, from 13.5% to 17.25%.

8-4c Changes in a Stock’s Beta Coefficient As we will see later in the book, a fi rm can infl uence its market risk (hence, its beta) through changes in the composition of its assets and through changes in the amount of debt it uses. A company’s beta can also change as a result of external factors such as increased competition in its industry and expiration of basic patents. When such changes occur, the fi rm’s required rate of return also changes; and as we will see in Chapter 9, this change will affect its stock price. For example, consider Allied Food Products, with a beta of 1.48. Now suppose some action occurred that caused Allied’s beta to increase from 1.48 to 2.0. If the conditions depicted in Figure 8-8 held, Allied’s required rate of return would increase from 13.4% to 16%:

r1 " rRF $ (rM ! rRF)bi " 6% $ (11% # 6%)1.48 " 13.4%

r2 " 6% $ (11% # 6%)2.0 " 16.0%

0 0.5 1.0 1.5 2.0 Risk, b i

rA2 = rM2 = 13.5

rRF = 6

Required Rate of Return (%)

New Market Risk Premium, rM2 – rRF = RPM2 = RPA2 = 7.5%

Original Market Risk Premium, rM1 – rRF = 5%

rL1 = 8.5 rL2 = 9.75

rA1 = rM1 = 11

17.25

SML2 = 6% + 7.5%(bi)

SML1 = 6% + 5%(bi)

Shift in the SML Caused by Increased Risk AversionFIGURE 8-10

257Chapter 8 Risk and Rates of Return

As we will see in Chapter 9, this change would have a negative effect on Allied’s stock price.25

25 The concepts covered in this chapter are obviously important to investors, but they are also important for managers in two key ways. First, as we will see in the next chapter, the risk of a stock aff ects the required rate of return on its equity capital, and that feeds directly into the important subject of capital budgeting. Second, and also related to capital budgeting, the “true” risk of individual projects is impacted by their correlation with the fi rm’s other projects and with other assets that the fi rm’s stockholders might hold. We will discuss these topics in later chapters. 26 See Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance, Vol. 47 (1992), pp. 427–465; and Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, Vol. 33 (1993), pp. 3–56. They found that stock returns are re- lated to fi rm size and market/book ratios. Small fi rms and fi rms with low market/book ratios had higher returns; however, they found no relationship between returns and beta.

SEL F TEST Diff erentiate between a stock’s expected rate of return (r̂); required rate of

return (r); and realized, after-the-fact historical return ( r– ). Which would have to be larger to induce you to buy the stock, r̂ or r? At a given point in time, would r̂, r, and r– typically be the same or diff erent? Explain.

What are the diff erences between the relative volatility graph (Figure 8-7), where “betas are made,” and the SML graph (Figure 8-8), where “betas are used”? Explain how both graphs are constructed and what information they convey.

What would happen to the SML graph in Figure 8-8 if expected infl ation increased or decreased?

What happens to the SML graph when risk aversion increases or decreases?

What would the SML look like if investors were indiff erent to risk, that is, if they had zero risk aversion?

How can a fi rm infl uence the size of its beta?

A stock has a beta of 1.2. Assume that the risk-free rate is 4.5% and the mar- ket risk premium is 5%. What is the stock’s required rate of return? (10.5%)

8-5 SOME CONCERNS ABOUT BETA AND THE CAPM The Capital Asset Pricing Model (CAPM) is more than just an abstract theory described in textbooks—it has great intuitive appeal and is widely used by analysts, investors, and corporations. However, a number of recent studies have raised con- cerns about its validity. For example, a study by Eugene Fama of the University of Chicago and Kenneth French of Dartmouth found no historical relationship between stocks’ returns and their market betas, confi rming a position long held by some professors and stock market analysts.26

As an alternative to the traditional CAPM, researchers and practitioners are developing models with more explanatory variables than just beta. These multi- variable models represent an attractive generalization of the traditional CAPM model’s insight that market risk—risk that cannot be diversifi ed away—underlies the pricing of assets. In the multivariable models, risk is assumed to be caused by a number of different factors, whereas the CAPM gauges risk only relative to re- turns on the market portfolio. These multivariable models represent a potentially

Kenneth French’s web site http://mba.tuck .dartmouth .edu/pages/faculty/ken .french/index.html is an excellent resource for information regarding factors related to stock returns.

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html

258 Part 3 Financial Assets

important step forward in fi nance theory; they also have some defi ciencies when applied in practice. As a result, the basic CAPM is still the most widely used method for estimating required rates of return on stocks.

SEL F TEST Have there been any studies that question the validity of the CAPM?

Explain.

8-6 SOME CONCLUDING THOUGHTS: IMPLICATIONS FOR CORPORATE MANAGERS AND INVESTORS

The connection between risk and return is an important concept, and it has numerous implications for both corporate managers and investors. As we will see in later chapters, corporate managers spend a great deal of time assessing the risk and returns on individual projects. Indeed, given their concerns about the risk of individual projects, it might be fair to ask why we spend so much time discussing the riskiness of stocks. Why not begin by looking at the riskiness of such business assets as plant and equipment? The reason is that for management whose primary goal is stock price maximization, the overriding consideration is the riskiness of the fi rm’s stock, and the relevant risk of any physical asset must be measured in terms of its effect on the stock’s risk as seen by investors. For example, suppose Goodyear, the tire com- pany, is considering a major investment in a new product, recapped tires. Sales of recaps (hence, earnings on the new operation) are highly uncertain; so on a stand- alone basis, the new venture appears to be quite risky. However, suppose returns in the recap business are negatively correlated with Goodyear’s other operations— when times are good and people have plenty of money, they buy new cars with new tires; but when times are bad, they tend to keep their old cars and buy recaps for them. Therefore, returns would be high on regular operations and low on the recap division during good times, but the opposite would be true during reces- sions. The result might be a pattern like that shown earlier in Figure 8-4 for Stocks W and M. Thus, what appears to be a risky investment when viewed on a stand- alone basis might not be very risky when viewed within the context of the com- pany as a whole.

This analysis can be extended to the corporation’s stockholders. Because Goodyear’s stock is owned by diversifi ed stockholders, the real issue each time management makes an investment decision is this: How will this investment affect the risk of our stockholders? Again, the stand-alone risk of an individual project may look quite high; however, viewed in the context of the project’s effect on stockholder risk, it may not be very large. We will address this issue again in Chapter 12, where we examine the effects of capital budgeting on companies’ beta coeffi cients and thus on stockholders’ risks.

While these concepts are obviously important for individual investors, they are also important for corporate managers. We summarize some key ideas that all investors should consider: 1. There is a trade-off between risk and return. The average investor likes higher

returns but dislikes risk. It follows that higher-risk investments need to offer

259Chapter 8 Risk and Rates of Return

investors higher expected returns. Put another way—if you are seeking higher returns, you must be willing to assume higher risks.

2. Diversifi cation is crucial. By diversifying wisely, investors can dramatically reduce risk without reducing their expected returns. Don’t put all of your money in one or two stocks or in one or two industries. A huge mistake that many people make is to invest a high percentage of their funds in their employ- er’s stock. If the company goes bankrupt, they not only lose their job but also their invested capital. While no stock is completely riskless, you can smooth out the bumps by holding a well-diversifi ed portfolio.

3. Real returns are what matters. All investors should understand the difference between nominal and real returns. When assessing performance, the real return (what you have left over after infl ation) is what matters. It follows that as expected infl ation increases, investors need to receive higher nominal returns.

4. The risk of an investment often depends on how long you plan to hold the investment. Common stocks, for example, can be extremely risky for short- term investors. However, over the long haul, the bumps tend to even out; thus, stocks are less risky when held as part of a long-term portfolio. Indeed, in his best-selling book Stocks for the Long Run, Jeremy Siegel of the University of Pennsylvania concludes that “[t]he safest long-term investment for the preser- vation of purchasing power has clearly been stocks, not bonds.”

5. While the past gives us insights into the risk and returns on various invest- ments, there is no guarantee that the future will repeat the past. Stocks that have performed well in recent years might tumble, while stocks that have struggled may rebound. The same thing may hold true for the stock market as a whole. Even Jeremy Siegel, who has preached that stocks have historically been good long-term investments, also has argued that there is no assurance that returns in the future will be as strong as they have been in the past. More importantly, when purchasing a stock, you always need to ask, “Is this stock fairly valued, or is it currently priced too high?” We discuss this issue more completely in the next chapter.

SEL F TEST Explain the following statement: The stand-alone risk of an individual corpo-

rate project may be quite high; but viewed in the context of its eff ect on stockholders’ risk, the project’s true risk may not be very large.

How does the correlation between returns on a project and returns on the fi rm’s other assets aff ect the project’s risk?

What are some important concepts for individual investors to consider when evaluating the risk and returns of various investments?

In this chapter, we described the relationship between risk and return. We discussed how to calculate risk and return for individual assets and for portfolios. In particular, we diff erentiated between stand-alone risk and risk in a portfolio context and we ex- plained the benefi ts of diversifi cation. We also discussed the CAPM, which describes how risk should be measured and how risk aff ects rates of return. In the chapters that follow, we will give you the tools needed to estimate the required rates of return on

T YING I T ALL TO GETHER

260 Part 3 Financial Assets

a fi rm’s common stock and explain how that return and the yield on its bonds are used to develop the fi rm’s cost of capital. As you will see, the cost of capital is a key element in the capital budgeting process.

KEY TERMS Define the following terms using graphs or equations to illustrate your an- swers whenever feasible: a. Risk; stand-alone risk; probability distribution b. Expected rate of return, r̂ c. Standard deviation, #; coefficient of variation (CV) d. Risk aversion; risk premium (RP); realized rate of return, r–

e. Risk premium for Stock i, RPi; market risk premium, RPM f. Expected return on a portfolio, r̂p; market portfolio g. Correlation; correlation coefficient, % h. Market risk; diversifiable risk; relevant risk i. Capital Asset Pricing Model (CAPM) j. Beta coefficient, b; average stock’s beta, bA k. Security Market Line (SML) equation

REALIZED RATES OF RETURN Stocks A and B have the following historical returns:

Year Stock A’s Returns, rA Stock B’s Returns, rB 2004 (24.25%) 5.50% 2005 18.50 26.73 2006 38.67 48.25 2007 14.33 (4.50) 2008 39.13 43.86

a. Calculate the average rate of return for each stock during the period 2004 through 2008. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been in each year from 2004 through 2008? What would the average return on the portfolio have been during that period?

b. Calculate the standard deviation of returns for each stock and for the portfolio. Use Equation 8-2a.

c. Looking at the annual returns on the two stocks, would you guess that the correlation coefficient between the two stocks is closer to "0.8 or to !0.8?

d. If more randomly selected stocks had been included in the portfolio, which of the following is the most accurate statement of what would have happened to #p?

(1) #p would have remained constant. (2) #p would have been in the vicinity of 20%. (3) #p would have declined to zero if enough stocks had been included.

BETA AND THE REQUIRED RATE OF RETURN ECRI Corporation is a holding company with four main subsidiaries. The percentage of its capital invested in each of the subsidiar- ies (and their respective betas) are as follows:

Subsidiary Percentage of Capital Beta Electric utility 60% 0.70 Cable company 25 0.90 Real estate development 10 1.30 International/special projects 5 1.50

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

ST-3ST-3

261Chapter 8 Risk and Rates of Return

a. What is the holding company’s beta? b. If the risk-free rate is 6% and the market risk premium is 5%, what is the holding

company’s required rate of return? c. ECRI is considering a change in its strategic focus; it will reduce its reliance on

the electric utility subsidiary, so the percentage of its capital in this subsidiary will be reduced to 50%. At the same time, it will increase its reliance on the international/special projects division, so the percentage of its capital in that subsidiary will rise to 15%. What will the company’s required rate of return be after these changes?

Suppose you owned a portfolio consisting of $250,000 of long-term U.S. government bonds. a. Would your portfolio be riskless? Explain. b. Now suppose the portfolio consists of $250,000 of 30-day Treasury bills. Every

30 days your bills mature, and you will reinvest the principal ($250,000) in a new batch of bills. You plan to live on the investment income from your portfolio, and you want to maintain a constant standard of living. Is the T-bill portfolio truly riskless? Explain.

c. What is the least risky security you can think of? Explain.

The probability distribution of a less risky expected return is more peaked than that of a riskier return. What shape would the probability distribution be for (a) completely certain returns and (b) completely uncertain returns?

A life insurance policy is a financial asset, with the premiums paid representing the investment’s cost. a. How would you calculate the expected return on a 1-year life insurance policy? b. Suppose the owner of a life insurance policy has no other financial assets—the

person’s only other asset is “human capital,” or earnings capacity. What is the correlation coefficient between the return on the insurance policy and the return on the human capital?

c. Life insurance companies must pay administrative costs and sales representatives’ commissions; hence, the expected rate of return on insurance premiums is generally low or even negative. Use portfolio concepts to explain why people buy life insurance in spite of low expected returns.

Is it possible to construct a portfolio of real-world stocks that has an expected return equal to the risk-free rate?

Stock A has an expected return of 7%, a standard deviation of expected returns of 35%, a correlation coefficient with the market of !0.3, and a beta coefficient of !0.5. Stock B has an expected return of 12%, a standard deviation of returns of 10%, a 0.7 correlation with the market, and a beta coefficient of 1.0. Which security is riskier? Why?

A stock had a 12% return last year, a year when the overall stock market declined. Does this mean that the stock has a negative beta and thus very little risk if held in a portfolio? Explain.

If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock? Explain.

If a company’s beta were to double, would its required return also double?

In Chapter 7, we saw that if the market interest rate, rd, for a given bond increased, the price of the bond would decline. Applying this same logic to stocks, explain (a) how a decrease in risk aversion would affect stocks’ prices and earned rates of return, (b) how this would affect risk premiums as measured by the historical difference between returns on stocks and returns on bonds, and (c) what the implications of this would be for the use of historical risk premiums when applying the SML equation.

QUESTIONS QUESTIONS

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EXPECTED RETURN A stock’s returns have the following distribution:

Demand for the Company’s Products

Probability of This Demand Occurring

Rate of Return If This Demand Occurs

Weak 0.1 (50%) Below average 0.2 (5) Average 0.4 16 Above average 0.2 25 Strong 0.1 60

1.0

Calculate the stock’s expected return, standard deviation, and coefficient of variation.

PORTFOLIO BETA An individual has $35,000 invested in a stock with a beta of 0.8 and another $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio’s beta?

REQUIRED RATE OF RETURN Assume that the risk-free rate is 6% and the expected return on the market is 13%. What is the required rate of return on a stock with a beta of 0.7?

EXPECTED AND REQUIRED RATES OF RETURN Assume that the risk-free rate is 5% and the market risk premium is 6%. What is the expected return for the overall stock market? What is the required rate of return on a stock with a beta of 1.2?

BETA AND REQUIRED RATE OF RETURN A stock has a required return of 11%, the risk- free rate is 7%, and the market risk premium is 4%. a. What is the stock’s beta? b. If the market risk premium increased to 6%, what would happen to the stock’s re-

quired rate of return? Assume that the risk-free rate and the beta remain unchanged.

EXPECTED RETURNS Stocks X and Y have the following probability distributions of ex- pected future returns:

Probability X Y 0.1 (10%) (35%) 0.2 2 0 0.4 12 20 0.2 20 25 0.1 38 45

a. Calculate the expected rate of return, r̂Y , for Stock Y (r̂X $ 12%). b. Calculate the standard deviation of expected returns, #X , for Stock X (#Y $ 20.35%).

Now calculate the coefficient of variation for Stock Y. Is it possible that most investors will regard Stock Y as being less risky than Stock X? Explain.

PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta A $ 400,000 1.50 B 600,000 (0.50) C 1,000,000 1.25 D 2,000,000 0.75

If the market’s required rate of return is 14% and the risk-free rate is 6%, what is the fund’s required rate of return?

BETA COEFFICIENT Given the following information, determine the beta coefficient for Stock J that is consistent with equilibrium: r̂J $ 12.5%; rRF $ 4.5%; rM $ 10.5%.

PROBLEMSPROBLEMS

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REQUIRED RATE OF RETURN Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return on an average stock is 13%, and the risk-free rate of return is 7%. By how much does the required return on the riskier stock exceed the required return on the less risky stock?

CAPM AND REQUIRED RETURN Bradford Manufacturing Company has a beta of 1.45, while Farley Industries has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12.0%. The risk-free rate of interest is 5%. By how much does Bradford’s required return exceed Farley’s required return?

CAPM AND REQUIRED RETURN Calculate the required rate of return for Manning Enterprises assuming that investors expect a 3.5% rate of inflation in the future. The real risk-free rate is 2.5%, and the market risk premium is 6.5%. Manning has a beta of 1.7, and its realized rate of return has averaged 13.5% over the past 5 years.

REQUIRED RATE OF RETURN Suppose rRF $ 9%, rM $ 14%, and bi $ 1.3. a. What is ri, the required rate of return on Stock i? b. Now suppose that rRF (1) increases to 10% or (2) decreases to 8%. The slope of the

SML remains constant. How would this affect rM and ri? c. Now assume that rRF remains at 9% but rM (1) increases to 16% or (2) falls to 13%. The

slope of the SML does not remain constant. How would these changes affect ri?

CAPM, PORTFOLIO RISK, AND RETURN Consider the following information for three stocks, Stocks X, Y, and Z. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)

Stock Expected Return Standard Deviation Beta X 9.00% 15% 0.8 Y 10.75 15 1.2 Z 12.50 15 1.6

Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) a. What is the market risk premium (rM ! rRF)? b. What is the beta of Fund Q? c. What is the expected return of Fund Q? d. Would you expect the standard deviation of Fund Q to be less than 15%, equal to

15%, or greater than 15%? Explain.

PORTFOLIO BETA Suppose you held a diversified portfolio consisting of a $7,500 invest- ment in each of 20 different common stocks. The portfolio’s beta is 1.12. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 1.75. What would your portfolio’s new beta be?

CAPM AND REQUIRED RETURN HR Industries (HRI) has a beta of 1.8, while LR Industries’ (LRI) beta is 0.6. The risk-free rate is 6%, and the required rate of return on an average stock is 13%. The expected rate of inflation built into rRF falls by 1.5 percentage points, the real risk-free rate remains constant, the required return on the market falls to 10.5%, and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI?

CAPM AND PORTFOLIO RETURN You have been managing a $5 million portfolio that has a beta of 1.25 and a required rate of return of 12%. The current risk-free rate is 5.25%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.75, what will be the required return on your $5.5 million portfolio?

PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 1.5. The risk-free rate is 4.5%, and the market risk premium is 5.5%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund’s required return to be 13%. What should be the average beta of the new stocks added to the portfolio?

EXPECTED RETURNS Suppose you won the lottery and had two options: (1) receiving $0.5 million or (2) taking a gamble in which at the flip of a coin you receive $1 million if a head comes up but receive zero if a tail comes up. a. What is the expected value of the gamble?

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264 Part 3 Financial Assets

b. Would you take the sure $0.5 million or the gamble? c. If you chose the sure $0.5 million, would that indicate that you are a risk averter or a

risk seeker? d. Suppose the payoff was actually $0.5 million—that was the only choice. You now face

the choice of investing it in a U.S. Treasury bond that will return $537,500 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $1,150,000 at the end of the year.

(1) The expected profit on the T-bond investment is $37,500. What is the expected dollar profit on the stock investment?

(2) The expected rate of return on the T-bond investment is 7.5%. What is the expected rate of return on the stock investment?

(3) Would you invest in the bond or the stock? Why? (4) Exactly how large would the expected profit (or the expected rate of return) have

to be on the stock investment to make you invest in the stock, given the 7.5% return on the bond?

(5) How might your decision be affected if, rather than buying one stock for $0.5 million, you could construct a portfolio consisting of 100 stocks with $5,000 invested in each? Each of these stocks has the same return characteristics as the one stock—that is, a 50-50 chance of being worth zero or $11,500 at year-end. Would the correlation between returns on these stocks matter? Explain.

EVALUATING RISK AND RETURN Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. a. Calculate each stock’s coefficient of variation. b. Which stock is riskier for a diversified investor? c. Calculate each stock’s required rate of return. d. On the basis of the two stocks’ expected and required returns, which stock would be

more attractive to a diversified investor? e. Calculate the required return of a portfolio that has $7,500 invested in Stock X and

$2,500 invested in Stock Y. f. If the market risk premium increased to 6%, which of the two stocks would have the

larger increase in its required return?

REALIZED RATES OF RETURN Stocks A and B have the following historical returns:

Year Stock A’s Returns, rA Stock B’s Returns, rB 2004 (18.00%) (14.50%) 2005 33.00 21.80 2006 15.00 30.50 2007 (0.50) (7.60) 2008 27.00 26.30

a. Calculate the average rate of return for each stock during the period 2004 through 2008.

b. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? What would the average return on the portfolio have been during this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Calculate the coefficient of variation for each stock and for the portfolio. e. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B,

or the portfolio? Why?

SECURITY MARKET LINE You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks:

Stock Investment Stock’s Beta Coefficient A $160 million 0.5 B 120 million 1.2 C 80 million 1.8 D 80 million 1.0 E 60 million 1.6

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Kish’s beta coefficient can be found as a weighted average of its stocks’ betas. The risk-free rate is 6%, and you believe the following probability distribution for future market returns is realistic:

Probability Market Return 0.1 !28% 0.2 0 0.4 12 0.2 30 0.1 50

a. What is the equation for the Security Market Line (SML)? (Hint: First, determine the expected market return.)

b. Calculate Kish’s required rate of return. c. Suppose Rick Kish, the president, receives a proposal from a company seeking new

capital. The amount needed to take a position in the stock is $50 million, it has an ex- pected return of 15%, and its estimated beta is 1.5. Should Kish invest in the new company? At what expected rate of return should Kish be indifferent to purchasing the stock?

EVALUATING RISK AND RETURN Bartman Industries’ and Reynolds Inc.’s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 2003–2008. The Winslow 5000 data are adjusted to include dividends.

BARTMAN INDUSTRIES REYNOLDS INC. WINSLOW 5000 Year Stock Price Dividend Stock Price Dividend Includes Dividends 2008 $17.250 $1.15 $48.750 $3.00 $11,663.98 2007 14.750 1.06 52.300 2.90 8,785.70 2006 16.500 1.00 48.750 2.75 8,679.98 2005 10.750 0.95 57.250 2.50 6,434.03 2004 11.375 0.90 60.000 2.25 5,602.28 2003 7.625 0.85 55.750 2.00 4,705.97

a. Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index. Then calculate each entity’s average return over the 5-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2003 because you do not have 2002 data.)

b. Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the sample standard deviation formula, Equation 8-2a, to this chapter, which corresponds to the STDEV function in Excel.)

c. Calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000. d. Construct a scatter diagram that shows Bartman’s and Reynolds’ returns on the

vertical axis and the Winslow 5000 Index’s returns on the horizontal axis. e. Estimate Bartman’s and Reynolds’ betas by running regressions of their returns

against the index’s returns. (Hint: Refer to Web Appendix 8A.) Are these betas consistent with your graph?

f. Assume that the risk-free rate on long-term Treasury bonds is 6.04%. Assume also that the average annual return on the Winslow 5000 is not a good estimate of the market’s required return—it is too high. So use 11% as the expected return on the market. Use the SML equation to calculate the two companies’ required returns.

g. If you formed a portfolio that consisted of 50% Bartman and 50% Reynolds, what would the portfolio’s beta and required return be?

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h. Suppose an investor wants to include Bartman Industries’ stock in his portfolio. Stocks A, B, and C are currently in the portfolio; and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 25% of Bartman, 15% of Stock A, 40% of Stock B, and 20% of Stock C.

RISK AND RETURN Assume that you recently graduated with a major in finance. You just landed a job as a fi- nancial planner with Merrill Finch Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been in- structed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives in the following table, shown with their probabilities and associated outcomes. (For now, disregard the items at the bottom of the data; you will fill in the blanks later.)

RETURNS ON ALTERNATIVE INVESTMENTS Estimated Rate of Return

State of the Economy Probability T-Bills

High Tech Collections U.S. Rubber

Market Portfolio

2-Stock Portfolio

Recession 0.1 5.5% (27.0%) 27.0% 6.0%a (17.0%) 0.0% Below average 0.2 5.5 (7.0) 13.0 (14.0) (3.0) Average 0.4 5.5 15.0 0.0 3.0 10.0 7.5 Above average 0.2 5.5 30.0 (11.0) 41.0 25.0 Boom 0.1 5.5 45.0 (21.0) 26.0 38.0 12.0 r̂ 1.0% 9.8% 10.5% # 0.0 13.2 18.8 15.2 3.4 CV 13.2 1.9 1.4 0.5 b !0.87 0.88

a Note that the estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer tires than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances, we would expect U.S. Rubber’s stock price to be higher if there was a recession than if the economy was just below average.

Merrill Finch’s economic forecasting staff has developed probability estimates for the state of the economy; and its security analysts have developed a sophisticated computer program, which was used to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm, Collections Inc. collects past-due debts, and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a “market portfolio” that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio and thus obtain average stock market results. Given the situation de- scribed, answer the following questions:

a. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bills promise a completely risk-free return? Explain.

(2) Why are High Tech’s returns expected to move with the economy, whereas Collections’ are expected to move counter to the economy?

b. Calculate the expected rate of return on each alternative and fill in the blanks on the row for r̂ in the previous table.

c. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like most people, is risk-averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns.

(1) Calculate this value for each alternative and fill in the blank on the row for # in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber,

and T-bills.

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267Chapter 8 Risk and Rates of Return

d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs and fill in the blanks on the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? Explain.

e. Suppose you created a two-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. (1) Calculate the expected return (r̂p), the standard deviation (#p), and the coefficient of variation (CVp) for

this portfolio and fill in the appropriate blanks in the table. (2) How does the riskiness of this two-stock portfolio compare with the riskiness of the individual stocks if

they were held in isolation? f. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen: (1) To the riskiness and to the expected return of the portfolio as more randomly selected stocks were

added to the portfolio? (2) What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. g. (1) Should the effects of a portfolio impact the way investors think about the riskiness of individual

stocks? (2) If you decided to hold a 1-stock portfolio (and consequently were exposed to more risk than diversified

investors), could you expect to be compensated for all of your risk; that is, could you earn a risk pre- mium on the part of your risk that you could have eliminated by diversifying?

h. The expected rates of return and the beta coefficients of the alternatives supplied by Merrill Finch’s com- puter program are as follows:

Security Return (r̂) Risk (Beta) High Tech 12.4% 1.32 Market 10.5 1.00 U.S. Rubber 9.8 0.88 T-bills 5.5 0.00 Collections 1.0 (0.87)

(1) What is a beta coefficient, and how are betas used in risk analysis? (2) Do the expected returns appear to be related to each alternative’s market risk? (3) Is it possible to choose among the alternatives on the basis of the information developed thus far? Use

the data given at the start of the problem to construct a graph that shows how the T-bill’s, High Tech’s, and the market’s beta coefficients are calculated. Then discuss what betas measure and how they are used in risk analysis.

i. The yield curve is currently flat; that is, long-term Treasury bonds also have a 5.5% yield. Consequently, Merrill Finch assumes that the risk-free rate is 5.5%.

(1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and graph the relationship between the expected and required rates of return.

(2) How do the expected rates of return compare with the required rates of return? (3) Does the fact that Collections has an expected return that is less than the T-bill rate make any sense?

Explain. (4) What would be the market risk and the required return of a 50-50 portfolio of High Tech and Collec-

tions? of High Tech and U.S. Rubber? j. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as

reflected in the 5.5% risk-free rate. What effect would higher inflation have on the SML and on the re- turns required on high- and low-risk securities?

(2) Suppose instead that investors’ risk aversion increased enough to cause the market risk premium to in- crease by 3 percentage points. (Inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?

268 Part 3 Financial Assets

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions.

Using Past Information to Estimate Required Returns Chapter 8 discussed the basic trade-off between risk and return. In the Capital Asset Pricing Model (CAPM) discussion, beta was identifi ed as the correct measure of risk for diversifi ed shareholders. Recall that beta measures the extent to which the returns of a given stock move with the stock market. When using the CAPM to estimate required returns, we would like to know how the stock will move with the market in the future; but since we don’t have a crystal ball, we generally use historical data to estimate this relationship with beta.

As mentioned in the Web Appendix for this chapter, beta can be estimated by regressing the individ- ual stock’s returns against the returns of the overall market. As an alternative to running our own regres- sions, we can rely on reported betas from a variety of sources. These published sources make it easy for us to readily obtain beta estimates for most large publicly traded corporations. However, a word of cau- tion is in order. Beta estimates can often be quite sensitive to the time period in which the data are esti- mated, the market index used, and the frequency of the data used. Therefore, it is not uncommon to fi nd a wide range of beta estimates among the various published sources. Indeed, Thomson One reports multiple beta estimates. These multiple estimates refl ect the fact that Thomson One puts together data from a variety of different sources.

Discussion Questions 1. Begin by looking at the historical performance of the overall stock market. If you want to see, for example, the

performance of the S&P 500, select “INDICES” and enter S&PCOMP. Click on “PERFORMANCE.” You will see a quick summary of the market’s performance in recent months and years. How has the market performed over the past year? the past 3 years? the past 5 years? the past 10 years?

2. Now let’s take a closer look at the stocks of four companies: Colgate Palmolive (Ticker = CL), Campbell Soup (CPB), Motorola (MOT), and Tiffany & Co (TIF). Before looking at the data, which of these companies would you expect to have a relatively high beta (greater than 1.0) and which of these companies would you expect to have a relatively low beta (less than 1.0)?

3. Select one of the four stocks listed in Question 2 by selecting “COMPANY ANALYSIS,” entering the company’s ticker symbol in the blank companies box, and clicking “GO.” On the company overview page, you should see a chart that summarizes how the stock has done relative to the S&P 500 over the past 6 months. Has the stock outperformed or underperformed the overall market during this time period?

4. If you scroll down the company overview page, you should see an estimate of the company’s beta. What is the company’s beta? What was the source of the estimated beta?

5. Click on “PRICES” on the left-hand side of the screen. What is the company’s current dividend yield? What has been its total return to investors over the past 6 months? over the past year? over the past 3 years? (Remember that total return includes the dividend yield plus any capital gains or losses.)

6. Assume that the risk-free rate is 5% and the market risk premium is 6%. What is the required return on the company’s stock?

7. Repeat the same exercise for each of the 3 remaining companies. Do the reported betas confirm your earlier in- tuition? In general, do you find that the higher-beta stocks tend to do better in up markets and worse in down markets? Explain.

Discussion Questions 1. Begin by looking at the historical performance of the overall stock market. If you want to see, for example, the

4. If you scroll down the company overview page, you should see an estimate of the company’s beta. What is the company’s beta? What was the source of the estimated beta?

6. Assume that the risk-free rate is 5% and the market risk premium is 6%. What is the required return on the company’s stock?

S e a r c h i n g f o r t h e R i g h t S t o c k

Stocks and Their Valuation

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A recent study by the securities industry found that roughly half of all U.S. households have invested in common stocks. As noted in Chapter 8, over the long run, returns in the U.S. stock market have been quite strong, averaging 12% per year. However, the market’s perfor- mance recently has been less than stellar. Trying to put things in perspective, Fortune magazine’s senior editor Allan Sloan offered the following comments about the market’s performance:

When the greatest bull market in U.S. his- tory started in the summer of 1982, only a relative handful of people owned stocks, which were cheap because they were con- sidered highly risky. But by the time the Standard & Poor’s 500 peaked in March 2000 amid a fully infl ated stock bubble, the masses were in the market. Stocks were magical, a supposedly can’t-miss way to pay for your kids’ college, save for retirement, enrich employees by giving them options, and regrow hair. (Just kid- ding about the hair. Alas.)

Stocks might go down in any given year, the mantra went, but in the long term they’d produce double-digit returns. How- ever, one of the lessons of the past eight years is that the long run can be . . . really long. As I write this in late February 2008, the U.S. market—which I’m defi ning as the Standard & Poor’s 500—is well below the high that it set on March 24, 2000. Even after you include dividends, which have run a bit below 2% a year, you’ve barely broken even, according to calculations for Fortune by Aronson & Johnson & Ortiz, a Philadelphia money manager.

One month later in March 2008 the stock market fell further in the aftermath of the startling col- lapse of Wall Street giant Bear Stearns. While most experts believe the stock market will ulti- mately rebound, most doubt that investors will average double-digit returns from common stock returns in the years ahead.

As we discussed in Chapter 8, the returns of individual stocks are more volatile than the

270 Part 3 Financial Assets

In Chapter 7, we examined bonds. We now turn to stocks, both common and pre- ferred. Since the cash fl ows provided by bonds are set by contract, it is generally easy to predict their cash fl ows. Preferred stock returns are also set by contract, which makes them similar to bonds; and they are valued in much the same way. However, common stock returns are not contractual—they depend on the fi rm’s earnings, which in turn depend on many random factors, making their valuation more diffi - cult. Two fairly straightforward models are used to estimate stocks’ intrinsic (or “true”) values: (1) the discounted dividend model and (2) the corporate valuation model. A stock should, of course, be bought if its price is less than its estimated intrinsic value and sold if its price exceeds its intrinsic value. By the time you fi nish this chap- ter, you should be able to: • Discuss the legal rights of stockholders. • Explain the distinction between a stock’s price and its intrinsic value. • Identify the two models that can be used to estimate a stock’s intrinsic value: the

discounted dividend model and the corporate model. • List the key characteristics of preferred stock and explain how to estimate the

value of preferred stock. Stock valuation is interesting in its own right; but you also need to understand valu- ation when you estimate the cost of capital for use in capital budgeting, which is probably a fi rm’s most important task.

9-1 LEGAL RIGHTS AND PRIVILEGES OF COMMON STOCKHOLDERS

A corporation’s common stockholders are the owners of the corporation; and as such, they have certain rights and privileges, as discussed in this section.

returns of the overall market. For example, in 2007, the over- all market (as measured by the S&P 500 Index) was up slightly (!5.49%). That same year some individual stocks realized huge gains while others declined sharply. On the plus side, Research in Motion was up 166%, Amazon.com rose 135%, and Apple Computer climbed 133%. On the down side, E*Trade Financial plummeted 84%; Circuit City, 78%; and Starbucks, 42%. This wide range in individual stocks’ returns shows, first, that diversification is important and, second, that when it comes to picking stocks, it is not enough to simply pick a good company—the stock must also be “fairly” priced.

To determine whether a stock is fairly priced, you first need to estimate the stock’s true value, or “intrinsic value,” a concept first discussed in Chapter 1. With this objective in mind, in this chapter, we describe some models that analysts have used to estimate intrinsic values. As you will see, while it is difficult to predict stock prices, we are not completely in the dark. Indeed, after studying this chapter, you should have a reasonably good understanding of the factors that influence stock prices; and with that knowledge—plus a little luck—you should be able to successfully navigate the market’s often-treacherous ups and downs.

Sources: Allan Sloan, “The Incredible Shrinking Bull,” Fortune, March 17, 2008, p. 24 and Alexandra Twin, “Best and Worst Stocks of 2007,” CNNMoney.com, December 31, 2007.

Key trends in the securities industry are listed and explained at www.sifma. org/research/statistics/ key_industry_trends.html.

PU T TING THINGS IN PER SPECTIVE

www.sifma.org/research/statistics/key_industry_trends.html

271Chapter 9 Stocks and Their Valuation

1 In the situation described, a 1,000-share stockholder could cast 1,000 votes for each of three directors if there were three contested seats on the board. An alternative procedure that may be prescribed in the corporate charter calls for cumulative voting. There the 1,000-share stockholder would get 3,000 votes if there were three vacancies, and he or she could cast all of them for one director. Cumulative voting helps small groups obtain representation on the board.

9-1a Control of the Firm A fi rm’s common stockholders have the right to elect its directors, who, in turn, elect the offi cers who manage the business. In a small fi rm, usually the major stockholder is also the president and chair of the board of directors. In large, pub- licly owned fi rms, the managers typically have some stock, but their personal holdings are generally insuffi cient to give them voting control. Thus, the manage- ments of most publicly owned fi rms can be removed by the stockholders if the management team is not effective.

State and federal laws stipulate how stockholder control is to be exercised. First, corporations must hold elections of directors periodically, usually once a year, with the vote taken at the annual meeting. Each share of stock has one vote; thus, the owner of 1,000 shares has 1,000 votes for each director.1 Stockholders can appear at the annual meeting and vote in person, but typically they transfer their right to vote to another person by means of a proxy. Management always solicits stockholders’ proxies and usually receives them. However, if earnings are poor and stockholders are dissatisfi ed, an outside group may solicit the proxies in an ef- fort to overthrow management and take control of the business. This is known as a proxy fi ght.

The question of control has become a central issue in fi nance in recent years. The frequency of proxy fi ghts has increased, as have attempts by one corporation to take over another by purchasing a majority of the outstanding stock. These ac- tions are called takeovers. Some well-known examples of takeover battles in past years include KKR’s acquisition of RJR Nabisco, Chevron’s acquisition of Gulf Oil, and the QVC/Viacom fi ght to take over Paramount. More recently, in February 2008, Microsoft made an unsolicited offer for Yahoo; but thus far Yahoo’s manage- ment has resisted.

Managers without more than 50% of their fi rms’ stock are very much con- cerned about proxy fi ghts and takeovers, and many of them have attempted to obtain stockholder approval for changes in their corporate charters that would make takeovers more diffi cult. For example, a number of companies have gotten their stockholders to agree (1) to elect only one-third of the directors each year (rather than electing all directors each year), (2) to require 75% of the stockholders (rather than 50%) to approve a merger, and (3) to vote in a “poison pill” provision that would allow the stockholders of a fi rm that is taken over by another fi rm to buy shares in the second fi rm at a reduced price. The poison pill makes the acquisi- tion unattractive and thus helps ward off hostile takeover attempts. Managers seeking such changes generally cite a fear that the fi rm will be picked up at a bar- gain price, but it often appears that the managers’ concern about their own posi- tions is the primary consideration.

Managers’ moves to make takeovers more diffi cult have been countered by stockholders, especially large institutional stockholders, who do not like barriers erected to protect incompetent managers. To illustrate, the California Public Employees Retirement System (CalPERS), which is one of the largest institutional investors, has led proxy fi ghts with several corporations whose fi nancial perfor- mances were poor in CalPERS’ judgment. CalPERS wants companies to increase outside (non-management) directors’ ability to force managers to be more respon- sive to stockholder complaints.

Proxy A document giving one person the authority to act for another, typically the power to vote shares of common stock.

Proxy Fight An attempt by a person or group to gain control of a firm by getting its stockholders to grant that person or group the authority to vote its shares to replace the current management.

Takeover An action whereby a person or group succeeds in ousting a firm’s management and taking control of the company.

Proxy A document giving one person the authority to act for another, typically the power to vote shares of common stock.

Proxy Fight An attempt by a person or group to gain control of a firm by getting its stockholders to grant that person or group the authority to vote its shares to replace the current management.

Takeover An action whereby a person or group succeeds in ousting a firm’s management and taking control of the company.

272 Part 3 Financial Assets

Managers’ pay is another contentious issue. It has been asserted, with consid- erable support, that CEOs tend to pick other CEOs to serve on their boards, with “you-scratch-my-back-and-I’ll-scratch-yours” behavior resulting in excessive compensation packages to top managers across the board. Boards have tried to conceal the facts by making it extremely diffi cult for stockholders to know what the top managers are being paid. Investors are galled to see CEOs such as Stan O’Neil of Merrill Lynch, who was fi red because of his fi rm’s multibillion-dollar loss, walk away with stock and cash worth hundreds of millions. CalPERS and other institutional investors have weighed in on this issue, and most fi rms today have been forced to make their compensation packages more transparent.

For many years, SEC rules prohibited large investors such as CalPERS from getting together to force corporate managers to institute policy changes. However, the SEC began changing its rules in 1993, and now large investors can work to- gether to force management changes. These rulings have helped keep managers focused on stockholder concerns, which means the maximization of stock prices.

9-1b The Preemptive Right Common stockholders often have the right, called the preemptive right, to pur- chase on a pro rata basis any additional shares sold by the fi rm. In some states, the preemptive right is automatically included in every corporate charter; in other states, it must be specifi cally inserted into the charter.

The purpose of the preemptive right is twofold. First, it prevents the manage- ment of a corporation from issuing a large number of additional shares and pur- chasing those shares itself. Management could use this tactic to seize control of the corporation and frustrate the will of the current stockholders. The second, and far more important, reason for the preemptive right is to protect stockholders from a dilution of value. For example, suppose 1,000 shares of common stock, each with a price of $100, were outstanding, making the total market value of the fi rm $100,000. If an additional 1,000 shares were sold at $50 a share, or for $50,000, this would raise the fi rm’s total market value to $150,000. When the new total market value is divided by the 2,000 total shares now outstanding, a value of $75 a share is obtained. The old stockholders would thus lose $25 per share, and the new stockholders would have an instant profi t of $25 per share. Thus, selling common stock at a price below the market value would dilute a fi rm’s price and transfer wealth from its present stockholders to those who were allowed to purchase the new shares. The preemptive right prevents this.

Preemptive Right A provision in the corporate charter or bylaws that gives common stockholders the right to purchase on a pro rata basis new issues of common stock (or convertible securities).

9-2 TYPES OF COMMON STOCK Although most fi rms have only one type of common stock, in some instances, classifi ed stock is used to meet special needs. Generally, when special classifi ca- tions are used, one type is designated Class A, another Class B, and so forth. Small, new companies seeking funds from outside sources frequently use different types of common stock. For example, when Google went public, it sold Class A stock to the public while its Class B stock was retained by the company’s insiders. The key

Classified Stock Common stock that is given a special designation such as Class A or Class B to meet special needs of the company.

SEL F TEST Identify some actions that companies have taken to make takeovers more

diffi cult.

What is the preemptive right, and what are the two primary reasons for its existence?

273Chapter 9 Stocks and Their Valuation

difference is that the Class B stock has 10 votes per share while the Class A stock has 1 vote per share. Google’s Class B shares are predominantly held by the com- pany’s two founders and its current CEO. The use of classifi ed stock thus enables the company’s founders to maintain control over the company without having to own a majority of the common stock. For this reason, Class B stock of this type is sometimes called founders’ shares. Since dual-class share structures of this type give special voting privileges to key insiders, these structures are sometimes criti- cized because they may enable insiders to make decisions that are counter to the interests of the majority of stockholders.

Note that “Class A,” “Class B,” and so forth, have no standard meanings. Most fi rms have no classifi ed shares; but a fi rm that does could designate its Class B shares as founders’ shares and its Class A shares as those sold to the public, while another could reverse those designations. Still other fi rms could use stock classifi - cations for entirely different purposes. For example, when General Motors ac- quired Hughes Aircraft for $5 billion, it paid in part with a new Class H common, GMH, which had limited voting rights and whose dividends were tied to Hughes’s performance as a GM subsidiary. The reasons for the new stock were that (1) GM wanted to limit voting privileges on the new classifi ed stock because of manage- ment’s concern about a possible takeover and (2) Hughes’s employees wanted to be rewarded more directly on Hughes’s own performance than would have been possible through regular GM stock. These Class H shares disappeared in 2003 when GM decided to sell off the Hughes unit.

Founders’ Shares Stock owned by the firm’s founders that has sole voting rights but restricted dividends for a specified number of years.

SEL F TEST What are some reasons a company might use classifi ed stock?

9-3 STOCK PRICE VS. INTRINSIC VALUE We saw in Chapter 1 that a manager should seek to maximize the value of his or her fi rm’s stock. In that chapter, we also emphasized the difference between stock price and intrinsic value. The stock price is simply the current market price, and it is easily observed for publicly traded companies. By contrast, intrinsic value, which represents the “true” value of the company’s stock, cannot be directly observed and must instead be estimated. Figure 9-1 illustrates once again the con- nection between stock price and intrinsic value.

As the fi gure suggests, market equilibrium occurs when the stock’s price equals its intrinsic value. If the stock market is reasonably effi cient, gaps between the stock price and intrinsic value should not be very large and they should not persist for very long. However, in some cases, an individual stock price may be much higher or lower than its intrinsic value. During several years leading up to the credit crunch of 2007–2008, most of the large investment banks were reporting record profi ts and selling at record prices. However, much of those earnings were illusory in that they did not refl ect the huge risks that existed in the mortgage- backed securities they were buying. So with hindsight, we now know that the market prices of most fi nancial fi rms’ stocks exceeded their intrinsic values just prior to 2007. Then when the market realized what was happening, those stock prices crashed. Citigroup, Merrill Lynch, and others lost over 60% of their value in a few short months; and Bear Stearns, the fi fth largest investment bank, saw its

274 Part 3 Financial Assets

stock price drop from $171 in 2007 to $2 in mid-March 2008. It clearly pays to ques- tion market prices at times!

9-3a Why Do Investors and Companies Care About Intrinsic Value?

The remainder of this chapter focuses primarily on different approaches for esti- mating a stock’s intrinsic value. Before these approaches are described, it is worth asking why it is important for investors and companies to understand how to cal- culate intrinsic value.

When investing in common stocks, one’s goal is to purchase stocks that are undervalued (i.e., the price is below the stock’s intrinsic value) and avoid stocks that are overvalued. Consequently, Wall Street analysts, institutional investors who control mutual funds and pension funds, and many individual investors are interested in fi nding reliable models that help predict intrinsic value.

Investors obviously care about intrinsic value, but managers also need to under- stand how intrinsic value is estimated. First, managers need to know how alternative actions are likely to affect stock prices; and the models of intrinsic value that we cover help demonstrate the connection between managerial decisions and fi rm value. Sec- ond, managers should consider whether their stock is signifi cantly undervalued or overvalued before making certain decisions. For example, fi rms should consider carefully the decision to issue new shares if they believe their stock is undervalued; and an estimate of their stock’s intrinsic value is the key to such decisions.

Two basic models are used to estimate intrinsic values: the discounted dividend model and the corporate valuation model. The dividend model focuses on dividends, while the corporate model goes beyond dividends and focuses on sales, costs, and free cash fl ows. In the following sections, we describe these approaches in more detail.

Managerial Actions, the Economic Environment, Taxes, and the Political Climate

“True” Investor Returns

“True” Risk

“Perceived” Investor Returns

“Perceived” Risk

Stock’s Intrinsic Value

Stock’s Market Price

Market Equilibrium: Intrinsic Value = Stock Price

Determinants of Intrinsic Values and Stock PricesFIGURE 9-1

275Chapter 9 Stocks and Their Valuation

9-4 THE DISCOUNTED DIVIDEND MODEL The value of a share of common stock depends on the cash fl ows it is expected to provide, and those fl ows consist of two elements: (1) the dividends the investor receives each year while he or she holds the stock and (2) the price received when the stock is sold. The fi nal price includes the original price paid plus an expected capital gain. Keep in mind that there are many different investors in the market and thus many different sets of expectations. Therefore, different investors will have different opinions about a stock’s true intrinsic value and thus proper price. The analysis as performed by the marginal investor, whose actions actually deter- mine the equilibrium stock price, is critical; but every investor, marginal or not, implicitly goes through the same type of analysis.

The following terms are used in our analysis:2

Marginal Investor A representative investor whose actions reflect the beliefs of those people who are currently trading a stock. It is the marginal investor who determines a stock’s price.

SEL F TEST What is the diff erence between a stock’s price and its intrinsic value?

Why do investors and managers need to understand how to estimate a fi rm’s intrinsic value?

What are two commonly used approaches for estimating a stock’s intrinsic value?

2 Many terms are described here, and students sometimes get concerned about having to memorize all of them. We tell our students that we will provide formula sheets for use on exams, so they don’t have to try to memorize everything. With their minds thus eased, they end up learning what the terms are rather than memorizing them. 3 Stocks generally pay dividends quarterly, so theoretically we should evaluate them on a quarterly basis. However, most analysts actually work with annual data because forecasted stock data are not precise enough to warrant the use of a quarterly model. For additional information on the quarterly model, see Charles M. Linke and J. Kenton Zumwalt, “Estimation Biases in Discounted Cash Flow Analysis of Equity Capital Costs in Rate Regulation,” Financial Management, Autumn 1984, pp. 15–21.

Marginal investor " the investor (or group of investors with similar views) who is at the margin and would be willing to buy if the stock price was slightly lower or to sell if the price was slightly higher. It is this investor’s expectations about dividends, growth, and risk that are key in the valuation process.

Other investors " all except the marginal investor. Some will be more opti- mistic than the marginal investor; others, more pessimistic. These investors will place new buy or sell orders if events occur to cause them to change their current expectations.

Dt " the dividend a stockholder expects to receive at the end of each Year t. D0 is the last dividend the company paid. Since it has already been paid, a buyer of the stock will not re- ceive D0. The fi rst dividend a new buyer will receive is D1, which is paid at the end of Year 1. D2 is the dividend ex- pected at the end of Year 2; D3, at the end of Year 3; and so forth. D0 is known with certainty; but D1, D2, and all other future dividends are expected values; and different inves- tors can have different expectations.3 Our primary concern is with Dt as forecasted by the marginal investor.

276 Part 3 Financial Assets

P0 " actual market price of the stock today. P0 is known with certainty, but predicted future prices are subject to uncertainty.

P̂t " both the expected price and the expected intrinsic value of the stock at the end of each Year t (pronounced “P hat t”) as seen by the investor doing the analysis. P̂t is based on the investor’s estimates of the dividend stream and the riskiness of that stream. There are many investors in the market, so there can be many estimates for P̂t. However, for the marginal investor, P0 must equal P̂0. Otherwise, a dis- equilibrium would exist, and buying and selling in the market would soon result in P0 equaling P̂0 as seen by the marginal investor.

g " expected growth rate in dividends as predicted by an in- vestor. If dividends are expected to grow at a constant rate, g should also equal the expected growth rate in earnings and the stock’s price. Different investors use different g’s to evaluate a fi rm’s stock; but the market price, P0, is based on g as estimated by the marginal investor.

rs " required, or minimum acceptable, rate of return on the stock considering its riskiness and the returns available on other investments. Different investors typically have dif- ferent opinions, but the key is again the marginal investor. The determinants of rs include factors discussed in Chap- ter 8, including the real rate of return, expected infl ation, and risk.

r̂s " expected rate of return (pronounced “r hat s”) that an investor believes the stock will provide in the future. The expected return can be above or below the required return; but a rational investor will buy the stock if r̂s ex- ceeds rs, sell the stock if r̂s is less than rs, and simply hold the stock if these returns are equal. Again, the key is the marginal investor, whose views determine the actual stock price.

r̄s " actual, or realized, after-the-fact rate of return, pronounced “r bar s.” You can expect to obtain a return of r–s " 10% if you buy a stock today; but if the market goes down, you may end up with an actual realized return that is much lower, perhaps even negative.

D1/P0 " dividend yield expected during the coming year. If Com- pany X’s stock is expected to pay a dividend of D1 " $1 dur- ing the next 12 months and if X’s current price is P0 " $20, the expected dividend yield will be $1/$20 " 0.05 " 5%. Different investors could have different expectations for D1; but again, the marginal investor is the key.

(P̂1 – P0)/P0 " expected capital gains yield on the stock during the com- ing year. If the stock sells for $20.00 today and if it is ex- pected to rise to $21.00 by the end of the year, the expected capital gain will be P̂1 # P0 " $21.00 # $20.00 " $1.00 and the expected capital gains yield will be $1.00/$20.00 " 0.05" 5%. Different investors can have different expecta- tions for P̂1, but the marginal investor is key.

Expected total return " r̂s " expected dividend yield (D1/P0) plus expected capital gains yield [(P̂1 # P0)/P0]. In our example, the expected total return " r̂s " 5% ! 5%"10%.

Market Price, P0 The price at which a stock sells in the market.

Growth Rate, g The expected rate of growth in dividends per share.

Required Rate of Return, rs The minimum rate of return on a common stock that a stockholder considers acceptable.

Expected Rate of Return, r̂s The rate of return on a common stock that a stockholder expects to receive in the future.

Actual (Realized) Rate of Return, r̄s The rate of return on a common stock actually received by stockholders in some past period. r̄s may be greater or less than r̂ s and/or rs.

Dividend Yield The expected dividend divided by the current price of a share of stock.

Capital Gains Yield The capital gain during a given year divided by the beginning price.

Expected Total Return The sum of the expected dividend yield and the expected capital gains yield.

277Chapter 9 Stocks and Their Valuation

All active investors hope to be better than average—they hope to identify stocks whose intrinsic values exceed their current prices and whose expected re- turns (expected by this investor) exceed the required rate of return. Note, though, that about half of all investors are likely to be disappointed. A good understanding of the points made in this chapter can help you avoid being disappointed.

9-4a Expected Dividends as the Basis for Stock Values In our discussion of bonds, we used Equation 7-1 to fi nd the value of a bond; the equation is the present value of interest payments over the bond’s life plus the present value of its maturity (or par) value:

VB ! INT _______ (1 " rd)

1 " INT _______ (1 " rd)

2 " . . . " INT _______ (1 " rd)

N " M _______ (1 " rd)

Stock prices are likewise determined as the present value of a stream of cash fl ows, and the basic stock valuation equation is similar to the one for bonds. What are the cash fl ows that a corporation will provide to its stockholders? To answer that ques- tion, think of yourself as an investor who buys the stock of a company that is expected to go on indefi nitely (for example, GE). You intend to hold it (in your family) forever. In this case, all you (and your heirs) will receive is a stream of divi- dends; and the value of the stock today can be calculated as the present value of an infi nite stream of dividends:

Value of stock ! P̂0 ! PV of expected future dividends

! D1 _______ (1 " rs)

1 " D2 _______ (1 " rs)

2 " . . . " D

# _______ (1 " rs) #

! ∑ t ! 1

Dt _______ (1 " rs)

t 9-1

What about the more typical case, where you expect to hold the stock for a fi nite period and then sell it—what will be the value of P̂0 in this case? Unless the company is likely to be liquidated or sold and thus disappears, the value of the stock is again determined by Equation 9-1. To see this, recognize that for any individual investor, the expected cash fl ows consist of expected dividends plus the expected sale price of the stock. However, the sale price to the current investor depends on the dividends some future investor expects, and that investor’s expected sale price is also dependent on some future dividends, and so forth. Therefore, for all present and future investors in total, expected cash fl ows must be based on expected future dividends. Put another way, unless a fi rm is liquidated or sold to another concern, the cash fl ows it provides to its stockholders will consist only of a stream of divi- dends. Therefore, the value of a share of stock must be established as the present value of the stock’s expected dividend stream.4

4 The general validity of Equation 9-1 can also be confi rmed by asking yourself the following question: Suppose I buy a stock and expect to hold it for 1 year. I will receive dividends during the year plus the value P̂1 when I sell it at the end of the year. But what will determine the value of P̂1? The answer is that it will be determined as the present value of the dividends expected during Year 2 plus the stock price at the end of that year, which, in turn, will be determined as the present value of another set of future dividends and an even more distant stock price. This process can be continued ad infi nitum, and the ultimate result is Equation 9-1. We should note that investors periodically lose sight of the long-run nature of stocks as investments and forget that in order to sell a stock at a profi t, one must fi nd a buyer who will pay the higher price. If you analyze a stock’s value in accordance with Equation 9-1, conclude that the stock’s market price exceeds a reasonable value, and buy the stock anyway, you would be following the “bigger fool” theory of investment—you think you may be a fool to buy the stock at its excessive price; but you also believe that when you get ready to sell it, you can fi nd someone who is an even bigger fool. The bigger fool theory was widely followed in the summer of 2000, just before the stock market crashed.

278 Part 3 Financial Assets

9-5 CONSTANT GROWTH STOCKS Equation 9-1 is a generalized stock valuation model in the sense that the time pat- tern of Dt can be anything: Dt can be rising, falling, or fl uctuating randomly; or it can be zero for several years. Equation 9-1 can be applied in any of these situations; and with a computer spreadsheet, we can easily use the equation to fi nd a stock’s intrinsic value—provided we have an estimate of the future dividends. However, it is not easy to obtain accurate estimates of future dividends.

Still, for many companies it is reasonable to predict that dividends will grow at a constant rate. In this case, Equation 9-1 may be rewritten as follows:

P̂0 ! D0(1 " g)

_________ (1 " rs) 1 "

D0(1 " g) 2

_________ (1 " rs) 2 " . . . "

D0(1 " g) #

_________ (1 " rs) #

9-2 ! D0(1 " g) ________ rs $ g

! D1 _____ rs $ g

The last term of Equation 9-2 is the constant growth model, or Gordon model, named after Myron J. Gordon, who did much to develop and popularize it.5

The term rs in Equation 9-2 is the required rate of return, which is a riskless rate plus a risk premium. However, we know that if the stock is in equilibrium, the re- quired rate of return must equal the expected rate of return, which is the expected dividend yield plus an expected capital gains yield. So we can solve Equation 9-2 for rs, but now using the hat to indicate that we are dealing with an expected rate of return:6

Expected rate of return

Expected dividend yield

Expected growth rate, or capital gains yield

9-3 r̂s ! D1 __ P0

" g

We illustrate Equations 9-2 and 9-3 in the following section.

Constant Growth (Gordon) Model Used to find the value of a constant growth stock.

SEL F TEST Explain the following statement: Whereas a bond contains a promise to pay

interest, a share of common stock typically provides an expectation of, but no promise of, dividends plus capital gains.

What are the two parts of most stocks’ expected total return?

If D1 " $2.00, g " 6%, and P0 " $40.00, what are the stock’s expected dividend yield, capital gains yield, and total expected return for the coming year? (5%, 6%, 11%)

Is it necessary for all investors to have the same expectations regarding a stock for the stock to be in equilibrium? (No, but explain.) What would happen to a stock’s price if the “marginal investor” examined a stock and concluded that its intrinsic value was greater than its current market price? (P0 would rise.)

5 The last term in Equation 9-2 is derived in the Web/CD Extension of Chapter 5 of Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 9th ed. (Mason, OH: Thomson/South-Western, 2007). In essence, Equation 9-2 is the sum of a geometric progression, and the fi nal result is the solution value of the progression. 6 The rs value in Equation 9-2 is a required rate of return; but when we transform Equation 9-2 to obtain Equation 9-3, we are fi nding an expected rate of return. Obviously, the transformation requires that rs " r̂s. This equality must hold if the stock is in equilibrium, as most normally are.

279Chapter 9 Stocks and Their Valuation

9-5a Illustration of a Constant Growth Stock Table 9-1 presents an analysis of Allied Food Products’ stock as performed by a security analyst after a meeting for analysts and other investors presided over by Allied’s CFO. The table looks complicated, but it is really quite straightforward.7 Part I, in the upper left corner, provides some basic data. The last dividend, which was just paid, was $1.15; the stock’s last closing price was $23.06; and it is in equi- librium. Based on an analysis of Allied’s history and likely future, the analyst forecasts that earnings and dividends will grow at a constant rate of 8.3% per year and that the stock’s price will grow at this same rate. Moreover, the analyst believes that the most appropriate required rate of return is 13.7%. Different analysts might use different inputs; but we assume for now that since this analyst is widely fol- lowed, her results represent those of the marginal investor.

Now look at Part IV, where we show the predicted stream of dividends and stock prices along with annual values for the dividend yield, the capital gains yield, and the expected total return. Notice that the total return shown in Col- umn 6 is equal to the required rate of return shown in Part I. This indicates that the

7 You may notice some minor “errors” in the table. These are not errors—they are simply diff erences caused by rounding.

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

I. Basic Information

III. Examples:

II. Formulas Used in the Analysis: D0 P0 g rs

= = = =

$1.15 $23.06 8.30%

13.70%

Col. 2 Col. 3 Col. 4 Col. 5 Col. 6 Col. 7

At end of year:

(1) 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

$1.15 1.25 1.35 1.46 1.58 1.71 1.86 2.01 2.18 2.36 2.55

$23.06 24.98 27.05 29.30 31.73 34.36 37.21 40.30 43.65 47.27 51.19

5.40% 5.40 5.40 5.40 5.40 5.40 5.40 5.40 5.40 5.40

8.30% 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30

13.70% 13.70 13.70 13.70 13.70 13.70 13.70 13.70 13.70 13.70

$1.10 1.04 0.99 0.95 0.90 0.86 0.82 0.78 0.74 0.71

Dividend (2)

Price (3)

Dividend yield

(4)

Capital gain yield

(5)

Total returns

(6)

Sum of PVs from 1 to ! = P0 = $23.06!

PV of dividend at 13.7%

(7)

$1.25 $23.06 5.40% 8.30%

13.70% $1.10

D1 = $1.1500(1.083) P0 = $1.25/(0.137 - 0.083) Dividend yield, Year 1: $1.25/$23.06 Cap gains yield, Year 1: ($24.98 - $23.06)/$23.06 Total return, Year 1: 5.4% + 8.3% PV of D1 discounted at 13.7%

Dividend in Year t, Dt, in Col. 2 Intrinsic value (and price) in Year t, Pt, in Col. 3

Dividend yield (constant), in Col. 4 Capital gains yield (constant), in Col. 5

Total return (constant), in Col. 6 PV of dividends, discounted at 13.7% Col. 7

Dt-1(1 + g) Dt+1/(rs - g)

Dt/Pt-1 (Pt - Pt-1)/Pt-1

Div. yield + CG yield Dt/(1 + rs)t

A B C D E F G H I

IV. Table: Forecasted Results over Time

Analysis of a Constant Growth StockT a b l e 9 - 1

280 Part 3 Financial Assets

stock analyst thinks that the stock is fairly priced; hence, it is in equilibrium. She forecasted out 10 years, but she could have forecasted out to infi nity.

Part II shows the formulas used to calculate the data in Part IV, and Part III gives examples of the calculations. For example, D1, the fi rst dividend a purchaser would receive, is forecasted to be D1 " $1.15(1.083) " $1.25, and the other fore- casted dividends in Column 2 were calculated similarly.

The estimated intrinsic values shown in Column 3 are based on Equation 9-2, the constant growth model: P0 " D1/(rs # g) " $1.25/(0.137 # 0.083) " $23.06 (cor- rected for rounding), P1 " $24.98, and so forth.

Column 4 shows the dividend yield, which for 2009 is D1/P0 " 5.40%; and this number is constant thereafter. The capital gain expected during 2009 is P1 # P0 " $24.98 # $23.06 " $1.92, which when divided by P0 gives the expected capital gains yield, $1.92/$23.06 " 8.3%, again corrected for rounding. The total return is found as the dividend yield plus the capital gains yield, 13.7%; and it is both con- stant and equal to the required rate of return given in Part I.

Finally, look at Column 7 in the table. Here we fi nd the present value of each of the dividends shown in Column 2, discounted at the required rate of return. For ex- ample, the PV of D1 " $1.25/(1.137)

1 " $1.10, the PV of D2 " $1.35/(1.137) 2 " $1.04,

and so forth. If you extended the table out to about 170 years (with Excel, this is easy), then summed the PVs of the dividends, you would get the same value as that found using Equation 9-2, $23.06.8 Figure 9-2 shows graphically what’s happening. We extended the table out 20 years and then plotted dividends from Column 2 in the upper step function curve and the PV of those dividends in the lower curve. The sum of the PVs is an estimate of the stock’s forecasted intrinsic value.

Note that in Table 9-1, the forecasted intrinsic value is equal to the current stock price and the expected total return is equal to the required rate of return. In this situation, the analysis would call the stock a “Hold” and would recommend that investors not buy or sell it. However, if the analyst were somewhat more optimistic and thought the growth rate would be 10.0% rather than 8.3%, the fore- casted intrinsic value would be (by Equation 9-2) $34.19 and the analyst would call it a “Buy.” At g " 6%, the intrinsic value would be $15.83 and the stock would be a “Sell.” Changes in the required rate of return would produce similar changes in the forecasted intrinsic value and thus the equilibrium current price.

9-5b Dividends Versus Growth The discounted dividend model as expressed in Equation 9-2 shows that, other things held constant, a higher value for D1 increases a stock’s price. However, Equation 9-2 shows that a higher growth rate also increases the stock’s price. But now recognize the following: • Dividends are paid out of earnings. • Therefore, growth in dividends requires growth in earnings. • Earnings growth in the long run occurs primarily because fi rms retain earn-

ings and reinvest them in the business. • Therefore, the higher the percentage of earnings retained, the higher the growth

rate.

To illustrate all this, suppose you inherit a business that has $1,000,000 of assets, no debt, and thus $1,000,000 of equity. The expected return on equity (ROE)

8 The dividends get quite large, but the discount rate exceeds the growth rate; so the PVs of the dividends become quite small. In theory, you would have to go out to infi nity to fi nd the exact price of a constant growth stock, but the diff erence between the Equation 9-2 value and the sum of the PVs can’t be seen out to 2 decimal places if you go out about 170 periods.

281Chapter 9 Stocks and Their Valuation

equals 10.0%, so its expected earnings for the coming year are (0.10)$1,000,000 " $100,000. You could take out the entire $100,000 of earnings in dividends, or you could reinvest some or all of the $100,000 in the business. If you pay out all the earnings, you will have $100,000 of dividend income this year, but dividends will not grow because assets and therefore earnings will not grow.

However, suppose you decide to have the fi rm pay out 40% and retain 60%. Now your dividend income in Year 1 will be $40,000; but assets will rise by $60,000, and earnings and dividends will likewise increase:

Next year’s earnings ! Prior earnings " ROE(Retained earnings)

! $100,000 " 0.1($60,000)

! $106,000

Next year’s dividends ! 0.4($106,000) ! $42,400

Moreover, your dividend income will continue to grow by 6% per year thereafter:

Growth rate ! (1 $ Payout ratio)ROE 9-4

= (1 – 0.4)10.0%

= 0.6(10.0%) = 6.0%

This demonstrates that in the long run, growth in dividends depends primarily on the fi rm’s payout ratio and its ROE.

Present Values of Dividends of a Constant Growth Stock where D0 " $1.15, g " 8.3%, rs " 13.7% FIGURE 9-2

Dividend ($)

1.15 PV D1 = 1.10

0 5 10 15 20

PV of Each Dividend = D0 (1 + g) t

(1 + rs)t

= Area under PV Curve = $23.06

Dollar Amount of Each Dividend = D0 (1 + g)t

Years

PV DtP0 = Σ

t = 1

282 Part 3 Financial Assets

In our example, we assumed that other things remain constant. This is often but not always a logical assumption. For example, suppose the fi rm develops a success- ful new product or hires a better CEO or makes some other change that increased the ROE. Any of these actions could cause the ROE and thus the growth rate to in- crease. Also note that the earnings of new fi rms are often low or even negative for several years, then begin to rise rapidly; fi nally, growth levels off as the fi rm ap- proaches maturity. Such a fi rm might pay no dividends for its fi rst few years, then pay a low initial dividend but let it increase rapidly, and fi nally make regular pay- ments that grow at a constant rate once earnings have stabilized. In any such situation, the nonconstant model as discussed in a later section must be used.

9-5c Which Is Better: Current Dividends or Growth? We saw in the preceding section that a fi rm can pay a higher current dividend by increasing its payout ratio, but that will lower its dividend growth rate. So the fi rm can provide a relatively high current dividend or a high growth rate but not both. This being the case, which would stockholders prefer? The answer is not clear. As we will see in the dividend chapter, some stockholders prefer current dividends while others prefer a lower payout ratio and future growth. Empirical studies have been unable to determine which strategy is optimal in the sense of maximizing a fi rm’s stock price. So dividend policy is an issue that management must decide on the basis of its judgment, not a mathematical formula. Logically, shareholders should prefer for the company to retain more earnings (hence pay less current dividends) if the fi rm has exceptionally good investment opportunities; however, shareholders should prefer a high payout if investment opportunities are poor. In spite of this, taxes and other factors complicate the situation. We will discuss all this in detail in the dividend chapter; but for now, just assume that the fi rm’s management has decided on a payout policy and uses that policy to determine the actual dividend.

9-5d Required Conditions for the Constant Growth Model

Several conditions are necessary for Equation 9-2 to be used. First, the required rate of return, rs, must be greater than the long-run growth rate, g. If the equation is used in situations where g is greater than rs, the results will be wrong, meaningless, and misleading. For example, if the forecasted growth rate in our example was 15% and thus exceeded the 13.7% required rate of return, stock price as calculated by Equation 9-2 would be a negative $101.73. That would be nonsense—stocks can’t have negative prices. Moreover, in Table 9-1, the PV of each future dividend would exceed that of the prior year. If this situation was graphed in Figure 9-2, the step-function curve for the PV of dividends would be increasing, not decreasing; so the sum would be infi nitely high, which would indicate an infi nitely high stock price. Obviously, stock prices cannot be either infi nite or negative, so Equation 9-2 cannot be used unless rs $ g.

Second, the constant growth model as expressed in Equation 9-2 is not appro- priate unless a company’s growth rate is expected to remain constant in the future. This condition almost never holds for new start-up fi rms, but it does exist for many mature companies. Indeed, mature fi rms such as Allied and GE are generally expected to grow at about the same rate as nominal gross domestic product (that is, real GDP plus infl ation). On this basis, one might expect the dividends of an average, or “normal,” company to grow at a rate of 5% to 8% a year.

Note too that Equation 9-2 is suffi ciently general to handle the case of a zero growth stock, where the dividend is expected to remain constant over time. If g = 0, Equation 9-2 reduces to Equation 9-5:

9-5 P̂0 ! D __ rs

Zero Growth Stock A common stock whose future dividends are not expected to grow at all; that is, g " 0.

283Chapter 9 Stocks and Their Valuation

This is the same equation as the one we developed in Chapter 5 for a perpetuity, and it is simply the current dividend divided by the discount rate.

Finally, as we discuss later in the chapter, most fi rms, even rapidly growing startups and others that pay no dividends at present, can be expected to pay divi- dends at some point in the future, at which time the constant growth model will be appropriate. For such fi rms, Equation 9-2 is used as one part of a more complicated valuation equation that we discuss next.

SEL F TEST Write out and explain the valuation formula for a constant growth stock.

Explain how the formula for a zero growth stock can be derived from that for a normal constant growth stock.

Firm A is expected to pay a dividend of $1.00 at the end of the year. The required rate of return is rs " 11%. Other things held constant, what would the stock’s price be if the growth rate was 5%? What if g was 0%? ($16.67; $9.09)

Firm B has a 12% ROE. Other things held constant, what would its expected growth rate be if it paid out 25% of its earnings as dividends? 75%? (9%, 3%)

If Firm B had a 75% payout ratio but then lowered it to 25%, causing its growth rate to rise from 3% to 9%, would that action necessarily increase the price of its stock? Why or why not?

9-6 VALUING NONCONSTANT GROWTH STOCKS For many companies, it is not appropriate to assume that dividends will grow at a constant rate. Indeed, most fi rms go through life cycles where they experience dif- ferent growth rates during different parts of the cycle. In their early years, most fi rms grow much faster than the economy as a whole; then they match the econo- my’s growth; and fi nally they grow at a slower rate than the economy.9 Automo- bile manufacturers in the 1920s, computer software fi rms such as Microsoft in the 1990s, and Google in the 2000s are examples of fi rms in the early part of their cycle. These fi rms are defi ned as supernormal, or nonconstant growth, fi rms. Figure 9-3 illustrates nonconstant growth and compares it with normal growth, zero growth, and negative growth.10

In the fi gure, the dividends of the supernormal growth fi rm are expected to grow at a 30% rate for three years, after which the growth rate is expected to fall to 8%, the

Supernormal (Nonconstant) Growth The part of the firm’s life cycle in which it grows much faster than the economy as a whole.

9 The concept of life cycles could be broadened to product cycle, which would include both small start-up companies and large companies such as Microsoft and Procter & Gamble, which periodically introduce new products that give sales and earnings a boost. We should also mention business cycles, which alternately depress and boost sales and profi ts. The growth rate just after a major new product has been introduced (or just after a fi rm emerges from the depths of a recession) is likely to be much higher than the “expected long-run average growth rate,” which is the proper number for use in the discounted dividend model. 10 A negative growth rate indicates a declining company. A mining company whose profi ts are falling because of a declining ore body is an example. Someone buying such a company would expect its earnings (and consequently its dividends and stock price) to decline each year, which would lead to capital losses rather than capital gains. Obviously, a declining company’s stock price is relatively low, and its dividend yield must be high enough to off set the expected capital loss and still produce a competitive total return. Students sometimes argue that they would never be willing to buy a stock whose price was expected to decline. However, if the present value of the expected dividends exceeds the stock price, the stock is still a good investment that would provide a good return.

284 Part 3 Financial Assets

assumed average for the economy. The value of this fi rm’s stock, like any other asset, is the present value of its expected future dividends as determined by Equation 9-1. When Dt is growing at a constant rate, we can simplify Equation 9-1 to Equation 9-2, P̂0 " D1/(rs # g). In the supernormal case, however, the expected growth rate is not a constant. In our example, there are two distinctly different rates.

Because Equation 9-2 requires a constant growth rate, we obviously cannot use it to value stocks that are not growing at a constant rate. However, assuming that a company currently enjoying supernormal growth will eventually slow down and become a constant growth stock, we can combine Equations 9-1 and 9-2 to construct a new formula, Equation 9-6, for valuing the stock.

First, we assume that the dividend will grow at a nonconstant rate (generally a relatively high rate) for N periods, after which it will grow at a constant rate, g. N is often called the terminal, or horizon, date. Second, we can use the constant growth formula, Equation 9-2, to determine what the stock’s horizon, or terminal, value will be N periods from today:

Horizon Value ! P̂N ! DN"1 _____ rs $ g

The stock’s intrinsic value today, P̂0, is the present value of the dividends during the nonconstant growth period plus the present value of the horizon value:

P̂0 ! D1 _______ (1 " rs)

1 " D2 _______ (1 " rs)

2 " . . . " DN _______ (1 " rs)

N " DN"1 _________ (1 " rs)

N"1 " . . . " D# _______ (1" rs)

PV of dividends during the Horizon value ! PV of dividends nonconstant growth during the constant growth

period, t ! 1, . . . N period, t ! N " 1, . . . #

Terminal (Horizon) Date The date when the growth rate becomes constant. At this date, it is no longer necessary to forecast the individual dividends.

Horizon (Terminal) Value The value at the horizon date of all dividends expected thereafter.

Illustrative Dividend Growth RatesFIGURE 9-3

Dividend ($)

1.15

Declining Growth, –8%

Zero Growth, 0%

Normal Growth, 8%

End of Supernormal Growth Period

Supernormal Growth, 30%

0 1 2 3 4 5 Years

285Chapter 9 Stocks and Their Valuation

P̂0 ! D1 _______ (1 " rs)

1 " D2 _______ (1 " rs)

2 " . . . " DN _______ (1 " rs)

N " P̂N _______ (1 " rs)

N 9-6

PV of dividends during the PV of horizon nonconstant growth period value, P̂N:

t = 1, . . . N [(DN"1)/(rs $ g)] _____________ (1 " rs)

To implement Equation 9-6, we go through the following three steps: 1. Find the PV of each dividend during the period of nonconstant growth and

sum them. 2. Find the expected stock price at the end of the nonconstant growth period, at

which point it has become a constant growth stock so it can be valued with the constant growth model, and discount this price back to the present.

3. Add these two components to fi nd the stock’s intrinsic value, P̂0. Figure 9-4 illustrates the process for valuing nonconstant growth stocks. Here

we use a new company, Firm M, and we assume that the following fi ve facts exist:

rs " stockholders’ required rate of return " 13.4%. This rate is used to discount the cash fl ows.

N " years of nonconstant growth " 3. gs " rate of growth in both earnings and dividends during the nonconstant

growth period " 30%. This rate is shown directly on the time line. (Note: The growth rate during the nonconstant growth period could vary from year to year. Also, there could be several different nonconstant growth periods—for example, 30% for three years, 20% for the next three years, and a constant 8% thereafter).

gn " rate of normal, constant growth after the nonconstant period " 8.0%. This rate is also shown on the time line, after Period 3, when it is in effect.

D0 " last dividend the company paid " $1.15.

The valuation process diagrammed in Figure 9-4 is explained in the steps set forth below the time line. The value of the nonconstant growth stock is calculated to be $39.21.

Note that in this example, we assumed a relatively short 3-year horizon to keep things simple. When evaluating stocks, most analysts use a longer horizon (for example, 5 years) to estimate intrinsic values. This requires a few more calcu- lations; but because analysts use spreadsheets, the arithmetic is not a problem. In practice, the real limitation is obtaining reliable forecasts for future growth.

Explain how one would fi nd the value of a nonconstant growth stock.

Explain what is meant by terminal (horizon) date and horizon (terminal) value.

SEL F TEST

286 Part 3 Financial Assets

9-7 VALUING THE ENTIRE CORPORATION11 Thus far we have discussed the discounted dividend model for valuing a fi rm’s common stock. This procedure is widely used, but it is based on the assumption that the analyst can forecast future dividends reasonably well. This is often true for mature companies that have a history of steadily growing dividends. However, dividends are dependent on earnings; so a really reliable dividend forecast must be based on an underlying forecast of the fi rm’s future sales, costs, and capital requirements. This recognition has led to an alternative stock valuation approach, the corporate valuation model.

Corporate Valuation Model A valuation model used as an alternative to the discounted dividend model to determine a firm’s value, especially one with no history of dividends, or the value of a division of a larger firm. The corporate model first calculates the firm’s free cash flows, then finds their present values to determine the firm’s value.

11 The corporate valuation model presented in this section is widely used by analysts, and it is in many respects superior to the discounted dividend model. However, it is rather involved as it requires the estimation of sales, costs, and cash fl ows on out into the future before the discounting process is begun. Therefore, in the introductory course, some instructors may prefer to omit Section 9-7 and skip to Section 9-8.

Notes to Figure 9-4: Step 1. Calculate the dividends expected at the end of each year during the nonconstant growth period.

Calculate the fi rst dividend, D1 " D0(1 ! gs) " $1.15(1.30) " $1.4950. Here gs is the growth rate during the 3-year nonconstant growth period, 30%. Show the $1.4950 on the time line as the cash fl ow at Time 1. Calculate D2 " D1(1 ! gs) " $1.4950(1.30) " $1.9435, then D3 " D2(1 ! gs) " $1.9435(1.30) " $2.5266. Show these values on the time line as the cash fl ows at Times 2 and 3. Note that D0 is used only to calculate D1.

Step 2. The price of the stock is the PV of dividends from Time 1 to infi nity; so in theory, we could project each future dividend, with the normal growth rate, gn " 8%, used to calculate D4 and subsequent dividends. However, we know that after D3 has been paid at Time 3, the stock becomes a constant growth stock. Therefore, we can use the constant growth formula to fi nd P̂3, which is the PV of the dividends from Time 4 to infi nity as evaluated at Time 3.

First, we determine D4 " $2.5266(1.08) " $2.7287 for use in the formula; then we calculate P̂3 as follows:

P̂3 ! D4 ______ rs $ gn

! $2.7287 ___________ 0.134 $ 0.08 ! $50.5310

We show this $50.5310 on the time line as a second cash fl ow at Time 3. The $50.5310 is a Time 3 cash fl ow in the sense that the stockholder could sell the stock for $50.5310 at Time 3 and in the sense that $50.5310 is the present value of the dividend cash fl ows from Time 4 to infi nity. Note that the total cash fl ow at Time 3 consists of the sum of D3 ! P̂3 " $2.5266 ! $50.5310 " $53.0576.

Step 3. Now that the cash fl ows have been placed on the time line, we can discount each cash fl ow at the required rate of return, rs " 13.4%. We could discount each cash fl ow by dividing by (1.134)

t, where t " 1 for Time 1, t " 2 for Time 2, and t " 3 for Time 3. This produces the PVs shown to the left below the time line; and the sum of the PVs is the value of the nonconstant growth stock, $39.21.

With a fi nancial calculator, you can fi nd the PV of the cash fl ows as shown on the time line with the cash fl ow (CFLO) register of your calculator. Enter 0 for CF0 because you receive no cash fl ow at Time 0, CF1 " 1.495, CF2 " 1.9435, and CF3 " 2.5266 ! 50.5310 " 53.0576. Then enter I/YR " 13.4 and press the NPV key to fi nd the value of the stock, $39.21.

0 21 3 4

D3 = 2.5266D2 = 1.9435D1 = 1.4950 D4 = 2.7287

53.0576 P̂3 = 50.5310

gs = 30% 30%

13.4% 13.4% 13.4%

30% gn = 8%

1.3183

1.5113

36.3838

39.2134 = $39.21 = P̂0

Finding the Value of a Nonconstant Growth StockFIGURE 9-4

287Chapter 9 Stocks and Their Valuation

The discounted dividend model assumes that the fi rm is cur- rently paying a dividend. However, many fi rms, even highly profi table ones, including Google, Dell, and Apple, have never paid a dividend. If a fi rm is expected to begin paying dividends in the future, we can modify the equations presented in the chapter and use them to determine the value of the stock. A new business often expects to have low sales during its fi rst few years of operation as it develops its product. Then if the product catches on, sales will grow rapidly for several years. Sales growth brings with it the need for additional assets—a fi rm cannot increase sales without also increasing its assets, and asset growth requires an increase in liability and/or equity accounts. Small fi rms can generally obtain some bank credit, but they must maintain a reasonable balance between debt and equity. Thus, additional bank borrowings require increases in equity, and getting the equity capital needed to support growth can be diffi cult for small fi rms. They have limited access to the capital markets; and even when they can sell common stock, their owners are reluctant to do so for fear of losing vot- ing control. Therefore, the best source of equity for most small businesses is retained earnings; for this reason most small fi rms pay no dividends during their rapid growth years. Even- tually, though, successful small fi rms do pay dividends, and those dividends generally grow rapidly at fi rst but slow down to a sustainable constant rate once the fi rm reaches maturity. If a fi rm currently pays no dividends but is expected to pay future dividends, the value of its stock can be found as follows: 1. Estimate at what point dividends will be paid, the

amount of the fi rst dividend, the growth rate during the supernormal growth period, the length of the supernor- mal period, the long-run (constant) growth rate, and the rate of return required by investors.

2. Use the constant growth model to determine the price of the stock after the fi rm reaches a stable growth situation.

3. Set out on a time line the cash fl ows (dividends during the supernormal growth period and the stock price once the constant growth state is reached); then fi nd the pres- ent value of these cash fl ows. That present value repre- sents the value of the stock today. To illustrate this process, consider the situation for Marvel-

Lure Inc., a company that was set up in 2007 to produce and market a new high-tech fi shing lure. MarvelLure’s sales are cur- rently growing at a rate of 200% per year. The company expects to experience a high but declining rate of growth in sales and earnings during the next 10 years, after which analysts estimate that it will grow at a steady 10% per year. The fi rm’s manage- ment has announced that it will pay no dividends for 5 years but that if earnings materialize as forecasted, it will pay a dividend of $0.20 per share at the end of Year 6, $0.30 in Year 7, $0.40 in Year 8, $0.45 in Year 9, and $0.50 in Year 10. After Year 10, cur- rent plans are to increase dividends by 10% per year.

MarvelLure’s investment bankers estimate that investors require a 15% return on similar stocks. Therefore, we fi nd the value of a share of MarvelLure’s stock as follows:

P0 ! $0 ______ (1.15)1 "

. . . " $0 ______ (1.15)5 " $0.20 ______ (1.15)6 "

$0.30 ______ (1.15)7 " $0.40 ______ (1.15)8

" $0.45 ______ (1.15)9 " $0.50 _______ (1.15)10 " ( $0.50(1.10) __________ 0.15 $ 0.10 ) ( 1 _______ (1.15)10 )

! $3.30

The last term fi nds the expected stock price in Year 10 and then fi nds the present value of that price. Thus, we see that the discounted dividend model can be applied to fi rms that currently pay no dividends, provided we can estimate future dividends with a fair degree of confi dence. However, in many cases, we can have more confi dence in the forecasts of free cash fl ows; and in these situations, it is better to use the cor- porate valuation model.

EVALUATING STOCKS THAT DON’T PAY DIVIDENDS

Rather than starting with a forecast of dividends, the corporate valuation model focuses on the fi rm’s future free cash fl ows. We discussed free cash fl ow (FCF) in Chapter 3, where we developed the following equation:

FCF ! ! EBIT(1 $ T) " Depreciation and amortization " $ ! Capital expenditures " %Net working capital " EBIT is earnings before interest and taxes, and free cash fl ow represents the cash generated from current operations, less the cash that must be spent on investments in fi xed assets and working capital to support future growth. Consider the case of Home Depot (HD). The fi rst term in brackets in the preceding equation represents the amount of cash that HD is generating from its existing stores. The second term represents the amount of cash the company plans to spend this period to construct new stores. To open a new store, HD must spend cash to purchase the land and construct the building—these are the capital expenditures, and they lead to a cor- responding increase in the fi rm’s fi xed assets as shown on the balance sheet. But

288 Part 3 Financial Assets

HD also needs to increase its working capital, especially inventory. Putting everything together, HD generates positive free cash fl ow for its investors if and only if the money from its existing stores exceeds the money required to build and equip its new stores.

9-7a The Corporate Valuation Model In Chapter 3, we explained that a fi rm’s value is determined by its ability to gener- ate cash fl ow both now and in the future. Therefore, its market value can be expressed as follows:

Market Value of company

! VCompany ! PV of expected future free cash fl ows

9-7 ! FCF1 ___________ (1 " WACC)1 "

FCF2 ___________ (1 " WACC)2 " . . . "

FCF # ___________ (1 " WACC)#

Here FCFt is the free cash fl ow in Year t; and the discount rate, the WACC, is the weighted average cost of all the fi rm’s capital. When thinking about the WACC, note these two points: 1. The fi rm fi nances with debt, preferred stock, and common equity. The WACC

is the weighted average of these three types of capital, and we discuss it in detail in Chapter 10.

2. Free cash fl ow is the cash generated before any payments are made to any investors; so it must be used to compensate common stockholders, preferred stockholders, and bondholders. Moreover, each type of investor has a required rate of return; and the weighted average of those returns is the WACC, which is used to discount the free cash fl ows.

Free cash fl ows are generally forecasted for 5 to 10 years, after which it is assumed that the fi nal explicitly forecasted FCF will grow at some long-run constant rate. Once the company reaches its horizon date, when cash fl ows begin to grow at a constant rate, we can use the following formula to calculate the market value of the company as of that date:

9-8 Horizon value ! VCompany at t ! N ! FCFN " 1/(WACC $ gFCF)

The corporate model is applied internally by the fi rm’s fi nancial staff and by outside security analysts. For illustrative purposes, we discuss an analysis conducted by Susan Buskirk, senior food analyst for the investment banking fi rm Morton Staley and Company. Her analysis is summarized in Table 9-2, which was reproduced from the chapter Excel model. • Based on Allied’s history and Buskirk’s knowledge of the fi rm’s business plan,

she estimated sales, costs, and cash fl ows on an annual basis for 5 years. Growth will vary during those years, but she assumes that things will stabilize and growth will be constant after the fi fth year. She would have made explicit forecasts for more years if she thought it would take longer to reach a steady- state, constant growth situation.

• Buskirk next calculated the expected free cash fl ows (FCFs) for each of the 5 nonconstant growth years, and she found the PV of those cash fl ows dis- counted at the WACC.

• After Year 5, she assumed that FCF growth would be constant; hence, the con- stant growth model could be used to fi nd Allied’s total market value at Year 5. This “horizon, or terminal, value” is the sum of the PVs of the FCFs from Year 6 on out into the future, discounted back to Year 5 at the WACC. It follows that: Horizon Value at t " 5 " FCF 6/(WACC – gFCF), where gFCF represents the long-run growth rate of free cash fl ow.

289Chapter 9 Stocks and Their Valuation

• Next, she discounted the Year 5 terminal value back to the present to fi nd its PV at Year 0.

• She then summed all the PVs, the annual cash fl ows during the nonconstant period plus the PV of the horizon value, to fi nd the fi rm’s estimated total mar- ket value.

• Then she subtracted the value of the debt and preferred stock to fi nd the value of the common equity.

• Finally, she divided the equity value by the number of shares outstanding, and the result was her estimate of Allied’s intrinsic value per share. This value was quite close to the stock’s market price, so she concluded that Allied’s stock is priced at its equilibrium level. Consequently, she issued a “Hold” recommen- dation on the stock. If the estimated intrinsic value had been signifi cantly below the market price, she would have issued a “Sell” recommendation; if the estimated intrinsic value had been well above the market price, she would have called the stock a “Buy.”

A B C D E F G H 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172

Part 1. Key Inputs Forecasted Years 2010 2011 2012 20132009

2010 2011 2012 201320092008

Sales growth rate Operating costs as a % of sales Growth in operating capital Depr'n as a % of operating capital Tax rate WACC Long-run FCF growth, gLR

9.0% 87.0

8.0 8.0

9.0% 86.0

8.0 7.0

9.0% 85.0

8.0 7.0

8.0% 85.0

8.0 7.0

10.0% 87.0

8.0 6.0

40.0 10.0

6.0

Part 2. Forecast of Cash Flows During Period of Nonconstant Growth Historical Forecasted Years

$4,615.5 3,923.2

185.1 $507.2 $304.3

$2,644.8 195.9

$108.4 $67.3

Sales Operating costs Depreciation

EBIT EBIT " (1 - T)

Total operating capital Net new operating cap Free Cash Flow, FCF PV of FCFs

$3,000.0 2,616.2

100.0 $283.8 $170.3

$1,800.0 280

-$109.7 N.A.

$3,300.0 2,871.0

116.6 $312.4 $187.4

$1,944.0 144.0 $43.4 $39.5

$3,597.0 3,129.4

168.0 $299.6 $179.8

$2,099.5 155.5 $24.3 $20.1

$3,920.7 3,371.8

158.7 $390.2 $234.1

$2,267.5 168.0 $66.1 $49.7

$4,273.6 3,632.6

171.4 $469.6 $281.8

$2,448.9 181.4

$100.4 $68.6

Part 3. Terminal Value and Intrinsic Value Estimation Estimated Value at the Horizon, 2013 Free Cash Flow (2014) Terminal Value at 2013, TV PV of the 2013 TV

Calculation of Firm's Intrinsic Value Sum of PVs of FCFs, 2009-2013 PV of 2013 TV Total corporate value Less: market value of debt and pfd Intrinsic value of common equity Shares outstanding (millions)

$114.9 $2,872.7 $1,783.7

$245.1 1,783.7

$2,028.8 860.0

$1,168.8 50.0

Intrinsic Value Per Share $23.38

FCF2013(1 + gLR)

TV / (1 + WACC)N

FCF2014 WACC - g

TV2013 =

Allied Food Products: Free Cash Flow ValuationT a b l e 9 - 2

290 Part 3 Financial Assets

While the dividend growth and the corporate valuation models presented in this chapter are the most widely used methods for valuing common stocks, they are by no means the only approaches. Analysts often use a number of diff er- ent techniques to value stocks. Two of these alternative approaches are described here.

The P/E Multiple Approach Investors have long looked for simple rules of thumb to deter- mine whether a stock is fairly valued. One such approach is to look at the stock’s price-to-earnings (P/E) ratio. Recall from Chapter 4 that a company’s P/E ratio shows how much inves- tors are willing to pay for each dollar of reported earnings. As a starting point, you might conclude that stocks with low P/E ratios are undervalued since their price is “low” given current earnings, while stocks with high P/E ratios are overvalued. Unfortunately, however, valuing stocks is not that sim- ple. We should not expect all companies to have the same P/E ratio. P/E ratios are aff ected by risk—investors discount the earnings of riskier stocks at a higher rate. Thus, all else equal, riskier stocks should have lower P/E ratios. In addition, when you buy a stock, you have a claim not only on current earn- ings but also on all future earnings. All else equal, companies with stronger growth opportunities will generate larger future earnings and thus should trade at higher P/E ratios. Therefore, eBay is not necessarily overvalued just because its P/E ratio is 121.2 at a time when the median fi rm has a P/E of 19.7. Investors believe that eBay’s growth potential is well above average. Whether the stock’s future prospects justify its P/E ratio remains to be seen; but in and of itself, a high P/E ratio does not mean that a stock is overvalued. Nevertheless, P/E ratios can provide a useful starting point in stock valuation. If a stock’s P/E ratio is well above its industry average and if the stock’s growth potential and risk are similar to other fi rms in the industry, the stock’s price may be too high. Likewise, if a company’s P/E ratio falls well below its historical average, the stock may be undervalued—particularly if the company’s growth prospects and risk are unchanged and if the overall P/E for the market has remained constant or increased. One obvious drawback of the P/E approach is that it depends on reported accounting earnings. For this reason,

some analysts choose to rely on other multiples to value stocks. For example, some analysts look at a company’s price-to-cash-fl ow ratio, while others look at the price-to- sales ratio.

The EVA Approach In recent years, analysts have looked for more rigorous alter- natives to the discounted dividend model. More than a quar- ter of all stocks listed on the NYSE pay no dividends. This proportion is even higher on Nasdaq. While the discounted dividend model can still be used for these stocks (see “Evalu- ating Stocks That Don’t Pay Dividends”), this approach requires that analysts forecast when the stock will begin pay- ing dividends, what the dividend will be once it is estab- lished, and what the future dividend growth rate will be. In many cases, these forecasts contain considerable errors. An alternative approach is based on the concept of Eco- nomic Value Added (EVA), which we discussed in Chapter 4 in “Economic Value Added (EVA) versus Net Income,” that can be written as follows:

EVA ! (Equity capital)(ROE $ Cost of equity capital) This equation suggests that companies can increase their EVA by investing in projects that provide shareholders with returns that are above their cost of equity capital, which is the return they could expect to earn on alternative invest- ments with the same level of risk. When you purchase stock in a company, you receive more than just the book value of equity—you also receive a claim on all future value that is created by the fi rm’s managers (the present value of all future EVAs). It follows that a company’s market value of equity can be written as follows:

Market value of equity ! Book value " PV of all future EVAs

We can fi nd the “fundamental” value of the stock, P0, by simply dividing the preceding expression by the number of shares outstanding. As is the case with the discounted dividend model, we can simplify the expression by assuming that at some point in time, annual EVA becomes a perpetuity, or grows at some constant rate over time.a

aWhat we have presented here is a simplifi ed version of what is often referred to as the Edwards-Bell-Ohlson (EBO) model. For a more com- plete description of this technique and an excellent summary of how it can be used in practice, read the article “Measuring Wealth,” by Charles M. C. Lee, in CA Magazine, April 1996, pp. 32–37.

OTHER APPROACHES TO VALUING COMMON STOCKS

9-7b Comparing the Corporate Valuation and Discounted Dividend Models

Analysts use both the discounted dividend model and the corporate valuation model when valuing mature, dividend-paying fi rms; and they generally use the corporate model when valuing divisions and fi rms that do not pay dividends. In principle, we

291Chapter 9 Stocks and Their Valuation

should fi nd the same intrinsic value using either model, but differences are often observed. When a confl ict exists, the assumptions embedded in the corporate model can be reexamined; and once the analyst is convinced they are reasonable, the results of that model are used. In our Allied example, the estimates were extremely close— the discounted dividend model predicted a price of $23.06 per share versus $23.38 using the corporate model; both are essentially equal to Allied’s actual $23.06 price.

In practice, intrinsic value estimates based on the two models normally deviate from one another and from actual stock prices, leading different analysts to reach dif- ferent conclusions about the attractiveness of a given stock. The better the analyst, the more often his or her valuations turn out to be correct; but no one can make perfect predictions because too many things can change randomly and unpredictably in the future. Given all this, does it matter whether you use the corporate model or the dis- counted dividend model to value stocks? We would argue that it does. If we had to value, for example, 100 mature companies whose dividends were expected to grow steadily in the future, we would probably use the discounted dividend model. Here we would estimate only the growth rate in dividends, not the entire set of pro forma fi nancial statements; hence, it would be more feasible to use the dividend model.

However, if we were studying just one company or a few companies, espe- cially companies still in the high-growth stage of their life cycles, we would want to project future fi nancial statements before estimating future dividends. Because we would already have projected future fi nancial statements, we would go ahead and apply the corporate model. Intel, which pays a dividend of $0.56 versus earn- ings of about $1.17, is an example of a company where either model could be used; but we think the corporate model is better.

Now suppose you were trying to estimate the value of a company such as eBay that, to date (2008), has never paid a dividend or a new fi rm that is about to go pub- lic. In either situation, you would be better off using the corporate valuation model. Actually, even if a company is paying steady dividends, much can be learned from the corporate model; so analysts today use it for all types of valuations. The process of projecting future fi nancial statements can reveal a great deal about a company’s operations and fi nancing needs. Also, such an analysis can provide insights into ac- tions that might be taken to increase the company’s value; and for this reason, it is integral to the planning and forecasting process, as we discuss in a later chapter.

SEL F TEST Write out the equation for free cash fl ows and explain it.

Why might someone use the corporate valuation model for companies that have a history of paying dividends?

What steps are taken to fi nd a stock price using the corporate model?

Why might the calculated intrinsic value diff er from the stock’s current market price? Which would be “correct,” and what does “correct” mean?

9-8 PREFERRED STOCK12 Preferred stock is a hybrid—it is similar to a bond in some respects and to common stock in others. This hybrid nature becomes apparent when we try to classify pre- ferred stock in relation to bonds and common stock. Like bonds, preferred stock

12 Preferred stock is discussed in more detail in Chapter 20 of Fundamentals of Financial Management, 12th ed., (Mason, OH: Cengage Learning, 2010) and in Chapter 20 of Brigham & Daves, Intermediate Financial Management, 9th ed., (Mason, OH: Thomson/South-Western, 2007).

292 Part 3 Financial Assets

has a par value and a fi xed dividend that must be paid before dividends can be paid on the common stock. However, the directors can omit (or “pass”) the pre- ferred dividend without throwing the company into bankruptcy. So although pre- ferred stock calls for a fi xed payment like bonds, skipping the payment will not lead to bankruptcy.

As noted earlier, a preferred stock entitles its owners to regular, fi xed dividend payments. If the payments last forever, the issue is a perpetuity whose value, Vp, is found as follows:

9-9 VP ! DP ___ rP

Vp is the value of the preferred stock, Dp is the preferred dividend, and rp is the required rate of return on the preferred. Allied Food has no preferred outstanding, but discussions about such an issue suggested that its preferred should pay a divi- dend of $10 per year. If its required return was 10.3%, the preferred’s value would be $97.09, found as follows:

Vp ! $10.00 ______ 0.103 ! $97.09

In equilibrium, the expected return, r̂P , must be equal to the required return, rp. Thus, if we know the preferred’s current price and dividend, we can solve for the expected rate of return as follows:

9-9a r̂P ! DP ___ VP

Some preferreds have a stated maturity, often 50 years. Assume that our illustrative preferred matured in 50 years, paid a $10 annual dividend, and had a required return of 8%. We could then fi nd its price as follows: Enter N " 50, I/YR " 8, PMT " 10, and FV " 100. Then press PV to fi nd the price, Vp " $124.47. If rp rose to 10%, change I/YR to 10, in which case Vp " PV " $100. If you know the price of a share of preferred stock, you can solve for I/YR to fi nd the expected rate of return, r̂P .

SEL F TEST Explain the following statement: Preferred stock is a hybrid security.

Is the equation used to value preferred stock more like the one used to evalu- ate a bond or the one used to evaluate a “normal” constant growth common stock? Explain.

Corporate decisions should be analyzed in terms of how alternative courses of action are likely to aff ect a fi rm’s value. However, it is necessary to know how stock prices are established before attempting to measure how a given decision will aff ect a spe- cifi c fi rm’s value. This chapter discussed the rights and privileges of common stock- holders, showed how stock values are determined, and explained how investors estimate stocks’ intrinsic values and expected rates of return.

T YING I T ALL TO GETHER

293Chapter 9 Stocks and Their Valuation

KEY TERMS Define the following terms: a. Proxy; proxy fight; takeover b. Preemptive right c. Classified stock; founders’ shares d. Marginal investor; intrinsic value (P̂0); market price (P0) e. Required rate of return, rs; expected rate of return, r̂s ; actual (realized) rate

of return, r̄s f. Capital gains yield; dividend yield; expected total return; growth rate, g g. Zero growth stock h. Constant growth (Gordon) model; supernormal (nonconstant) growth i. Corporate valuation model j. Terminal (horizon) date; horizon (terminal) value k. Preferred stock

STOCK GROWTH RATES AND VALUATION You are considering buying the stocks of two companies that operate in the same industry. They have very similar characteristics except for their dividend payout policies. Both companies are expected to earn $3 per share this year; but Company D (for “dividend”) is expected to pay out all of its earnings as dividends, while Company G (for “growth”) is expected to pay out only one-third of its earnings, or $1 per share. D’s stock price is $25. G and D are equally risky. Which of the following statements is most likely to be true? a. Company G will have a faster growth rate than Company D. Therefore, G’s stock

price should be greater than $25. b. Although G’s growth rate should exceed D’s, D’s current dividend exceeds that of G,

which should cause D’s price to exceed G’s. c. A long-term investor in Stock D will get his or her money back faster because D pays

out more of its earnings as dividends. Thus, in a sense, D is like a short-term bond and G is like a long-term bond. Therefore, if economic shifts cause rd and rs to increase and if the expected dividend streams from D and G remain constant, both Stocks D and G will decline, but D’s price should decline further.

d. D’s expected and required rate of return is r̂s " rs " 12%. G’s expected return will be higher because of its higher expected growth rate.

e. If we observe that G’s price is also $25, the best estimate of G’s growth rate is 8%.

CONSTANT GROWTH STOCK VALUATION Fletcher Company’s current stock price is $36.00, its last dividend was $2.40, and its required rate of return is 12%. If dividends are expected to grow at a constant rate, g, in the future and if rs is expected to remain at 12%, what is Fletcher’s expected stock price 5 years from now?

NONCONSTANT GROWTH STOCK VALUATION Snyder Computers Inc. is experiencing rapid growth. Earnings and dividends are expected to grow at a rate of 15% during the

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

ST-3ST-3

ST-4ST-4

Two types of stock valuation models were discussed: the discounted dividend model and the corporate valuation model. The discounted dividend model is useful for mature, stable companies. It is easier to use, but the corporate valuation model is more fl exible and better for use with companies that do not pay dividends or whose dividends would be especially hard to predict.

We also discussed preferred stock, which is a hybrid security that has some char- acteristics of a common stock and some of a bond. Preferreds are valued using mod- els similar to those for perpetual and “regular” bonds.

294 Part 3 Financial Assets

next 2 years, at 13% the following year, and at a constant rate of 6% during Year 4 and thereafter. Its last dividend was $1.15, and its required rate of return is 12%. a. Calculate the value of the stock today. b. Calculate P̂1 and P̂2. c. Calculate the dividend and capital gains yields for Years 1, 2, and 3.

It is frequently stated that the one purpose of the preemptive right is to allow individuals to maintain their proportionate share of the ownership and control of a corporation. a. How important do you suppose control is for the average stockholder of a firm whose

shares are traded on the New York Stock Exchange? b. Is the control issue likely to be of more importance to stockholders of publicly owned

or closely held (private) firms? Explain.

Is the following equation correct for finding the value of a constant growth stock? Explain.

P̂0 ! D0 _____ rs " g

If you bought a share of common stock, you would probably expect to receive dividends plus an eventual capital gain. Would the distribution between the dividend yield and the capital gains yield be influenced by the firm’s decision to pay more dividends rather than to retain and reinvest more of its earnings? Explain.

Two investors are evaluating GE’s stock for possible purchase. They agree on the expected value of D1 and on the expected future dividend growth rate. Further, they agree on the riskiness of the stock. However, one investor normally holds stocks for 2 years, while the other holds stocks for 10 years. On the basis of the type of analysis done in this chapter, should they both be willing to pay the same price for GE’s stock? Explain.

A bond that pays interest forever and has no maturity is a perpetual bond. In what respect is a perpetual bond similar to a no-growth common stock? Are there preferred stocks that are evaluated similarly to perpetual bonds and other preferred stocks that are more like bonds with finite lives? Explain.

DPS CALCULATION Warr Corporation just paid a dividend of $1.50 a share (that is, D0 " $1.50). The dividend is expected to grow 7% a year for the next 3 years and then at 5% a year thereafter. What is the expected dividend per share for each of the next 5 years?

CONSTANT GROWTH VALUATION Thomas Brothers is expected to pay a $0.50 per share dividend at the end of the year (that is, D1 " $0.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, rs, is 15%. What is the stock’s current value per share?

CONSTANT GROWTH VALUATION Harrison Clothiers’ stock currently sells for $20.00 a share. It just paid a dividend of $1.00 a share (that is, D0 " $1.00). The dividend is expected to grow at a constant rate of 6% a year. What stock price is expected 1 year from now? What is the required rate of return?

NONCONSTANT GROWTH VALUATION Hart Enterprises recently paid a dividend, D0, of $1.25. It expects to have nonconstant growth of 20% for 2 years followed by a constant rate of 5% thereafter. The firm’s required return is 10%. a. How far away is the terminal, or horizon, date? b. What is the firm’s horizon, or terminal, value? c. What is the firm’s intrinsic value today, P̂0?

CORPORATE VALUATION Smith Technologies is expected to generate $150 million in free cash flow next year, and FCF is expected to grow at a constant rate of 5% per year

QUESTIONSQUESTIONS

9-19-1

9-29-2

9-39-3

9-49-4

9-59-5

PROBLEMSPROBLEMS

9-19-1Easy Problems 1–6 Easy Problems 1–6

9-29-2

9-39-3

9-49-4

9-59-5

295Chapter 9 Stocks and Their Valuation

indefinitely. Smith has no debt or preferred stock, and its WACC is 10%. If Smith has 50 million shares of stock outstanding, what is the stock’s value per share?

PREFERRED STOCK VALUATION Fee Founders has perpetual preferred stock outstanding that sells for $60 a share and pays a dividend of $5 at the end of each year. What is the required rate of return?

PREFERRED STOCK RATE OF RETURN What will be the nominal rate of return on a perpetual preferred stock with a $100 par value, a stated dividend of 8% of par, and a current market price of (a) $60, (b) $80, (c) $100, and (d) $140?

PREFERRED STOCK VALUATION Ezzell Corporation issued perpetual preferred stock with a 10% annual dividend. The stock currently yields 8%, and its par value is $100. a. What is the stock’s value? b. Suppose interest rates rise and pull the preferred stock’s yield up to 12%. What is its

new market value?

PREFERRED STOCK RETURNS Bruner Aeronautics has perpetual preferred stock outstanding with a par value of $100. The stock pays a quarterly dividend of $2, and its current price is $80. a. What is its nominal annual rate of return? b. What is its effective annual rate of return?

VALUATION OF A DECLINING GROWTH STOCK Martell Mining Company’s ore reserves are being depleted, so its sales are falling. Also, because its pit is getting deeper each year, its costs are rising. As a result, the company’s earnings and dividends are declining at the con- stant rate of 5% per year. If D0 " $5 and rs " 15%, what is the value of Martell Mining’s stock?

VALUATION OF A CONSTANT GROWTH STOCK A stock is expected to pay a dividend of $0.50 at the end of the year (that is, D1 " 0.50), and it should continue to grow at a con- stant rate of 7% a year. If its required return is 12%, what is the stock’s expected price 4 years from today?

VALUATION OF A CONSTANT GROWTH STOCK Investors require a 15% rate of return on Levine Company’s stock (that is, rs " 15%). a. What is its value if the previous dividend was D0 " $2 and investors expect dividends

to grow at a constant annual rate of (1) #5%, (2) 0%, (3) 5%, or (4) 10%? b. Using data from Part a, what would the Gordon (constant growth) model value be

if the required rate of return was 15% and the expected growth rate was (1) 15% or (2) 20%? Are these reasonable results? Explain.

c. Is it reasonable to think that a constant growth stock could have g > rs? Explain.

CONSTANT GROWTH You are considering an investment in Keller Corp’s stock, which is expected to pay a dividend of $2.00 a share at the end of the year (D1 " $2.00) and has a beta of 0.9. The risk-free rate is 5.6%, and the market risk premium is 6%. Keller currently sells for $25.00 a share, and its dividend is expected to grow at some constant rate g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is P̂3?)

NONCONSTANT GROWTH Microtech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Microtech to begin paying dividends, beginning with a dividend of $1.00 coming 3 years from today. The dividend should grow rapidly—at a rate of 50% per year—during Years 4 and 5; but after Year 5, growth should be a constant 8% per year. If the required return on Microtech is 15%, what is the value of the stock today?

CORPORATE VALUATION Dozier Corporation is a fast-growing supplier of office products. Analysts project the following free cash flows (FCFs) during the next 3 years, after which FCF is expected to grow at a constant 7% rate. Dozier’s WACC is 13%.

210Year

FCF ($ millions)

#$20NA $30 $40

a. What is Dozier’s terminal, or horizon, value? (Hint: Find the value of all free cash flows beyond Year 3 discounted back to Year 3.)

b. What is the firm’s value today?

9-69-6

9-79-7Intermediate Problems 7–15 Intermediate Problems 7–15

9-89-8

9-99-9

9-109-10

9-119-11

9-129-12

9-139-13

9-149-14

9-159-15

296 Part 3 Financial Assets

c. Suppose Dozier has $100 million of debt and 10 million shares of stock outstanding. What is your estimate of the current price per share?

NONCONSTANT GROWTH Mitts Cosmetics Co.’s stock price is $58.88, and it recently paid a $2.00 dividend. This dividend is expected to grow by 25% for the next 3 years, then grow forever at a constant rate, g; and rs " 12%. At what constant rate is the stock expected to grow after Year 3?

CONSTANT GROWTH Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $2.00 yesterday. Bahnsen’s dividend is expected to grow at 5% per year for the next 3 years. If you buy the stock, you plan to hold it for 3 years and then sell it. The appropriate discount rate is 12%. a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and

D3. Note that D0 " $2.00. b. Given that the first dividend payment will occur 1 year from now, find the present

value of the dividend stream; that is, calculate the PVs of D1, D2, and D3 and then sum these PVs.

c. You expect the price of the stock 3 years from now to be $34.73; that is, you expect P̂3 to equal $34.73. Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $34.73.

d. If you plan to buy the stock, hold it for 3 years, and then sell it for $34.73, what is the most you should pay for it today?

e. Use Equation 9-2 to calculate the present value of this stock. Assume that g " 5% and that it is constant.

f. Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period was 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P̂0? Explain.

NONCONSTANT GROWTH STOCK VALUATION Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This same growth rate is expected to last for another 2 years, then decline to gn " 6%. a. If D0 " $1.60 and rs " 10%, what is TTC’s stock worth today? What are its expected

dividend and capital gains yields at this time, that is, during Year 1? b. Now assume that TTC’s period of supernormal growth is to last for 5 years rather

than 2 years. How would this affect the price, dividend yield, and capital gains yield? Answer in words only.

c. What will TTC’s dividend and capital gains yields be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy.)

d. Of what interest to investors is the changing relationship between dividend and capital gains yields over time?

CORPORATE VALUATION Barrett Industries invests a large sum of money in R&D; as a result, it retains and reinvests all of its earnings. In other words, Barrett does not pay any dividends and it has no plans to pay dividends in the near future. A major pension fund is interested in purchasing Barrett’s stock. The pension fund manager has estimated Bar- rett’s free cash flows for the next 4 years as follows: $3 million, $6 million, $10 million, and $15 million. After the fourth year, free cash flow is projected to grow at a constant 7%. Barrett’s WACC is 12%, its debt and preferred stock total $60 million, and it has 10 million shares of common stock outstanding. a. What is the present value of the free cash flows projected during the next 4 years? b. What is the firm’s terminal value? c. What is the firm’s total value today? d. What is an estimate of Barrett’s price per share?

CORPORATE VALUE MODEL Assume that today is December 31, 2008, and that the following information applies to Vermeil Airlines: • After-tax operating income [EBIT(1 # T)] for 2009 is expected to be $500 million. • The depreciation expense for 2009 is expected to be $100 million. • The capital expenditures for 2009 are expected to be $200 million. • No change is expected in net working capital. • The free cash flow is expected to grow at a constant rate of 6% per year. • The required return on equity is 14%. • The WACC is 10%.

9-169-16Challenging Problems 16–21 Challenging Problems 16–21

9-179-17

9-189-18

9-199-19

9-209-20

297Chapter 9 Stocks and Their Valuation

• The market value of the company’s debt is $3 billion. • 200 million shares of stock are outstanding. Using the corporate valuation model approach, what should be the company’s stock

price today?

NONCONSTANT GROWTH Assume that it is now January 1, 2009. Wayne-Martin Electric Inc. (WME) has developed a solar panel capable of generating 200% more electricity than any other solar panel currently on the market. As a result, WME is expected to experience a 15% annual growth rate for the next 5 years. Other firms will have developed comparable technology at the end of 5 years, and WME’s growth rate will slow to 5% per year indefinitely. Stockholders require a return of 12% on WME’s stock. The most recent annual dividend (D0), which was paid yesterday, was $1.75 per share. a. Calculate WME’s expected dividends for 2009, 2010, 2011, 2012, and 2013. b. Calculate the value of the stock today, P̂0. Proceed by finding the present value of the

dividends expected at the end of 2009, 2010, 2011, 2012, and 2013 plus the present value of the stock price that should exist at the end of 2013. The year-end 2013 stock price can be found by using the constant growth equation. Notice that to find the December 31, 2013, price, you must use the dividend expected in 2014, which is 5% greater than the 2013 dividend.

c. Calculate the expected dividend yield (D1/P0), capital gains yield, and total return (dividend yield plus capital gains yield) expected for 2009. (Assume that P̂0 " P0 and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Then calculate these same three yields for 2014.

d. How might an investor’s tax situation affect his or her decision to purchase stocks of companies in the early stages of their lives, when they are growing rapidly, versus stocks of older, more mature firms? When does WME’s stock become “mature” for purposes of this question?

e. Suppose your boss tells you she believes that WME’s annual growth rate will be only 12% during the next 5 years and that the firm’s long-run growth rate will be only 4%. Without doing any calculations, what general effect would these growth rate changes have on the price of WME’s stock?

f. Suppose your boss also tells you that she regards WME as being quite risky and that she believes the required rate of return should be 14%, not 12%. Without doing any calculations, determine how the higher required rate of return would affect the price of the stock, the capital gains yield, and the dividend yield. Again, assume that the long-run growth rate is 4%.

NONCONSTANT GROWTH AND CORPORATE VALUATION Rework Problem 9-18, Parts a, b, and c, using a spreadsheet model. For Part b, calculate the price, dividend yield, and capital gains yield as called for in the problem. After completing Parts a through c, answer the following additional question using the spreadsheet model. d. TTC recently introduced a new line of products that has been wildly successful. On

the basis of this success and anticipated future success, the following free cash flows were projected:

5 6 7 8 9321Year

FCF

4 10

$5.5 $12.1 $69.0 $88.8 $107.5 $128.9 $147.1$44.1$23.8 $161.3

After the tenth year, TTC’s financial planners anticipate that its free cash flow will grow at a constant rate of 6%. Also, the firm concluded that the new product caused the WACC to fall to 9%. The market value of TTC’s debt is $1,200 million, it uses no preferred stock, and there are 20 million shares of common stock outstanding. Use the corporate valuation model approach to value the stock.

9-219-21

COMPREHENSIVE/SPREADSHEET PROBLEM COMPREHENSIVE/SPREADSHEET PROBLEM

9-229-22

298 Part 3 Financial Assets

STOCK VALUATION Robert Balik and Carol Kiefer are senior vice presidents of the Mutual of Chicago Insur- ance Company. They are codirectors of the company’s pension fund management division, with Balik having re- sponsibility for fixed-income securities (primarily bonds) and Kiefer being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities; and Balik and Kiefer, who will make the actual presentation, have asked you to help them.

To illustrate the common stock valuation process, Balik and Kiefer have asked you to analyze the Bon Temps Company, an employment agency that supplies word processor operators and computer programmers to busi- nesses with temporarily heavy workloads. You are to answer the following questions:

a. Describe briefly the legal rights and privileges of common stockholders. b. (1) Write a formula that can be used to value any stock, regardless of its dividend pattern. (2) What is a constant growth stock? How are constant growth stocks valued? (3) What are the implications if a company forecasts a constant g that exceeds its rs? Will many stocks have

expected g > rs in the short run (that is, for the next few years)? in the long run (that is, forever)? c. Assume that Bon Temps has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7%, and

that the required rate of return on the market is 12%. What is Bon Temps’s required rate of return? d. Assume that Bon Temps is a constant growth company whose last dividend (D0, which was paid yesterday)

was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate. (1) What is the firm’s expected dividend stream over the next 3 years? (2) What is its current stock price? (3) What is the stock’s expected value 1 year from now? (4) What are the expected dividend yield, capital gains yield, and total return during the first year? e. Now assume that the stock is currently selling at $30.29. What is its expected rate of return? f. What would the stock price be if its dividends were expected to have zero growth? g. Now assume that Bon Temps is expected to experience nonconstant growth of 30% for the next 3 years, then

return to its long-run constant growth rate of 6%. What is the stock’s value under these conditions? What are its expected dividend and capital gains yields in Year 1? Year 4?

h. Suppose Bon Temps is expected to experience zero growth during the first 3 years and then resume its steady- state growth of 6% in the fourth year. What would be its value then? What would be its expected dividend and capital gains yields in Year 1? in Year 4?

i. Finally, assume that Bon Temps’s earnings and dividends are expected to decline at a constant rate of 6% per year, that is, g " #6%. Why would anyone be willing to buy such a stock, and at what price should it sell? What would be its dividend and capital gains yields in each year?

j. Suppose Bon Temps embarked on an aggressive expansion that requires additional capital. Management decided to finance the expansion by borrowing $40 million and by halting dividend payments to increase retained earnings. Its WACC is now 10%, and the projected free cash flows for the next 3 years are #$5 mil- lion, $10 million, and $20 million. After Year 3, free cash flow is projected to grow at a constant 6%. What is Bon Temps’s total value? If it has 10 million shares of stock and $40 million of debt and preferred stock com- bined, what is the price per share?

k. Suppose Bon Temps decided to issue preferred stock that would pay an annual dividend of $5.00 and that the issue price was $50.00 per share. What would be the stock’s expected return? Would the expected rate of return be the same if the preferred was a perpetual issue or if it had a 20-year maturity?

9-239-23

IN TEGRATED C ASE MUTUAL OF CHICAGO INSURANCE COMPANY

299Chapter 9 Stocks and Their Valuation

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions.

Estimating ExxonMobil’s Intrinsic Stock Value In this chapter, we described the various factors that infl uence stock prices and the approaches that ana- lysts use to estimate a stock’s intrinsic value. By comparing these intrinsic value estimates to the current price, an investor can assess whether it makes sense to buy or sell a particular stock. Stocks trading at a price far below their estimated intrinsic values may be good candidates for purchase, whereas stocks trading at prices far in excess of their intrinsic value may be good stocks to avoid or sell.

While estimating a stock’s intrinsic value is a complex exercise that requires reliable data and good judgment, we can use the data available in Thomson ONE to arrive at a quick “back-of-the-envelope” calculation of intrinsic value.

Discussion Questions 1. For purposes of this exercise, let’s take a closer look at the stock of ExxonMobil Corporation (XOM). Looking at

the COMPANY ANALYSIS OVERVIEW, we can see the company’s current stock price and its performance relative to the overall market in recent months. What is ExxonMobil’s current stock price? How has the stock performed relative to the market over the past few months?

2. Click on “NEWS & EVENTS” on the left-hand side of your screen to see the company’s recent news stories for the company. Have there been any recent events impacting the company’s stock price, or have things been relatively quiet?

3. To provide a starting point for gauging a company’s relative valuation, analysts often look at a company’s price-to-earnings (P/E) ratio. Return to the COMPANY OVERVIEW page. Here you can see XOM’s forward P/E ratio, which uses XOM’s next 12-month estimate of earnings in the calculation. To see its current P/E ratio, click on “FINANCIALS” (on the left-hand side of your screen), scroll down to “WORLDSCOPE” (under Financial Ratios on the left-hand side of your screen), and click on “ANNUAL INCOME STATEMENT RATIOS.” The firm’s current P/E ratio is shown at the top right of your screen. What is the firm’s current P/E ratio?

4. To put XOM’s P/E ratio in perspective, it is useful to see how this ratio has varied over time. Scroll down to the Stock Performance section of this screen. The first two lines of this section show the firm’s P/E ratio using the end-of-year closing price and the 5-year average over time. Is XOM’s current P/E ratio well above or well below its latest 5-year average? Do you have any explanation for why the current P/E deviates from its historical trend? Explain. On the basis of this information, does XOM’s current P/E suggest that the stock is undervalued or overvalued? Explain.

5. To put the firm’s current P/E ratio in perspective, it is useful to compare this ratio with that of other companies in the same industry. To see how XOM’s P/E ratio stacks up to its peers, click on “COMPARABLES” (left-hand side of your screen). Select “KEY FINANCIAL RATIOS.” Toward the bottom of the table, you should see information on the P/E ratio in the section titled “Market Value Ratios.” For the most part, is XOM’s P/E ratio above or below that of its peers? In Chapter 4, we discussed the various factors that may influence P/E ratios. Can any of these factors explain why XOM’s P/E ratio differs from its peers? Explain. If you want to compare XOM to a different set of firms, click on “CLICK TO SELECT NEW PEER SET.” (This appears toward the top of the screen.)

6. In the text, we discussed using the discounted dividend model to estimate a stock’s intrinsic value. To keep things as simple as possible, let’s assume at first that XOM’s dividend is expected to grow at some constant rate over time. If so, the intrinsic value equals D1/(rs – g), where D1 is the expected annual dividend 1 year from now, rs is the stock’s required rate of return, and g is the dividend’s constant growth rate. To estimate the dividend growth rate, it’s helpful to look at XOM’s dividend history. Go back to the COMPANY OVERVIEW page. Select “FINANCIALS”; and under “FINANCIAL RATIOS,” select “WORLDSCOPE” and “ANNUAL INCOME STATEMENT RATIOS.” On your screen at the bottom of the Per Share Data section, you should see the firm’s annual dividend over the past several years. On the basis of this information, what has been the average annual

300 Part 3 Financial Assets

dividend growth rate? Another way to obtain estimates of dividend growth rates is to look at analysts’ forecasts for future dividends, which can be found under “ESTIMATES” (on the left-hand side of your screen). Near the top of your screen, you should see an area marked “Consensus Estimates.” Use the scroll bar to change from EPS estimates to DPS estimates. What is the median year-end dividend forecast? You can use this as an estimate of D1 in your measure of intrinsic value. Also notice that the last line of this area shows the long-term growth rate. What is the median forecast of the company’s long-term growth rate? You can use this as a forecast of the firm’s dividend growth rate, g.

7. The required return on equity, rs, is the final input needed to estimate intrinsic value. For our purposes, you can assume a number (say, 8% or 9%) or you can use the CAPM to calculate an estimate of the cost of equity using the data available in Thomson ONE. (For more details, look at the Thomson ONE exercise for Chapter 8.) Having decided on your best estimates for D1, rs, and g, you can calculate XOM’s intrinsic value. How does this estimate compare with the current stock price? Does your preliminary analysis suggest that XOM is undervalued or overvalued? Explain.

8. It is often useful to perform a sensitivity analysis, where you show how your estimate of intrinsic value varies according to different estimates of D1, rs, and g. To do so, recalculate your intrinsic value estimate for a range of different estimates for each of these key inputs. One convenient way to do this is to set up a simple data table in Excel. Refer to the Excel tutorial accessed through the CengageNOW™ web site for instructions on data tables. On the basis of this analysis, what inputs justify the current stock price?

9. On the basis of the dividend history you uncovered in Question 6 and your assessment of XOM’s future dividend payout policies, do you think it is reasonable to assume that the constant growth model is a good proxy for intrinsic value? If not, how would you use the available data in Thomson ONE to estimate intrinsic value using the nonconstant growth model?

10. Finally, you can also use the information in Thomson ONE to value the entire corporation. This approach requires that you estimate XOM’s annual free cash flows. Once you estimate the value of the entire corpora- tion, you subtract the value of debt and preferred stock to arrive at an estimate of the company’s equity value. By dividing this number by the number of shares of common stock outstanding, you calculate an alternative estimate of the stock’s intrinsic value. While this approach may take additional time and involves more judg- ment concerning forecasts of future free cash flows, you can use the financial statements and growth forecasts in Thomson ONE as useful starting points. Go to Worldscope’s Cash Flow Ratios Report (which you find by clicking on “FINANCIALS, WORLDSCOPE”—under “FINANCIAL RATIOS”—and “ANNUAL CASH FLOW RATIOS”). There you will find an estimate of free cash flow per share. While this number is useful, Worldscope’s definition of free cash flow subtracts out dividends per share; therefore, to make it comparable to the mea- sure in this text, you must add back dividends. To see Worldscope’s definition of free cash flow (or any term), go to the top of your screen and click on “GLOSSARY”. In the middle of your screen on the right-hand side, you will see a dialog box with terms. Use the down arrow to scroll through the terms, highlighting the term for which you would like to see a definition. Then click the SELECT button immediately below the dialog box.

301Chapter 9 Stocks and Their Valuation

APPENDIX 9A Stock Market Equilibrium Recall that rX, the required return on Stock X, can be found using the Security Market Line (SML) equation from the Capital Asset Pricing Model (CAPM) as discussed in Chapter 8:

rX ! rRF " (rM $ rRF)bX ! rRF " (RPM)bX

If the risk-free rate is 6%, the market risk premium is 5%, and Stock X has a beta of 2, the marginal investor will require a return of 16% on the stock:

rX ! 6% " (5%)2.0

! 16%

This 16% required return is shown as the point on the SML in Figure 9A-1 associ- ated with beta " 2.0.

A marginal investor will purchase Stock X if its expected return is more than 16%, will sell it if the expected return is less than 16%, and will be indifferent (will hold but not buy or sell) if the expected return is exactly 16%. Now suppose the investor’s portfolio contains Stock X; he or she analyzes its prospects and con- cludes that its earnings, dividends, and price can be expected to grow at a constant rate of 5% per year. The last dividend was D0 " $2.8571, so the next expected divi- dend is as follows:

D1 ! $2.8571(1.05) ! $3

The investor observes that the present price of the stock, P0, is $30. Should he or she buy more of Stock X, sell the stock, or maintain the present position?

The investor can calculate Stock X’s expected rate of return as follows:

r̂X ! D1 __ P0

" g ! $3 ____ $30 " 5% ! 15%

Expected and Required Returns on Stock XFIGURE 9A-1

Rate of Return (%)

rX = 16 rX = 15

rM = 11

rRF = 6

0 1.0 Risk, bi

SML: ri = rRF + (rM – rRF) bi

2.0

302 Part 3 Financial Assets

This value is plotted on Figure 9A-1 as Point X, which is below the SML. Because the expected rate of return is less than the required return, he or she (and many other investors) would want to sell the stock. However, few people would want to buy at the $30 price; so the present owners would be unable to fi nd buyers unless they cut the price of the stock. Thus, the price would decline, and the decline would continue until the price hit $27.27. At that point, the stock would be in equilibrium, defi ned as the price at which the expected rate of return, 16%, is equal to the required rate of return:

r̂X ! $3.00 ______ $27.27 " 5% ! 11% " 5% ! 16% ! rX

Had the stock initially sold for less than $27.27 (say, $25), events would have been reversed. Investors would have wanted to purchase the stock because its expected rate of return would have exceeded its required rate of return, buy orders would have come in, and the stock’s price would have been driven up to $27.27.

To summarize, in equilibrium, two related conditions must hold: 1. A stock’s expected rate of return as seen by the marginal investor must equal

its required rate of return: r̂i " ri. 2. The actual market price of the stock must equal its intrinsic value as estimated

by the marginal investor: P0 " P̂0.

Of course, some individual investors may believe that r̂i > ri and P̂0 > P0 (hence, they would invest most of their funds in the stock), while other investors might have an opposite view and sell all of their shares. However, investors at the margin establish the actual market price; and for these investors, we must have r̂i " ri and P̂0 " P0. If these conditions do not hold, trading will occur until they do.

9A-1 CHANGES IN EQUILIBRIUM STOCK PRICES Stock prices are not constant—they undergo violent changes at times. For example, on October 27, 1997, the Dow Jones Industrials fell 554 points, a 7.18% drop in value. Even worse, on October 19, 1987, the Dow lost 508 points, causing an average stock to lose 23% of its value on that one day, and some individual stocks lost more than 70%. To see what could cause such changes to occur, assume that Stock X is in equi- librium, selling at a price of $27.27 per share. If all expectations were met exactly, dur- ing the next year the price would gradually rise to $28.63, or by 5%. However, suppose conditions changed as indicated in the second column of the following table:

VARIABLE VALUE Original New

Risk-free rate, rRF 6% 5% Market risk premium, rM # rRF 5% 4% Stock X’s beta coefficient, bX 2.0 1.25 Stock X’s expected growth rate, gX 5% 6% D0 $2.8571 $2.8571 Price of Stock X $27.27 ?

Now give yourself a test: How would the change in each variable, by itself, affect the price; and what new price would result?

Every change, taken alone, would lead to an increase in the price. The fi rst three changes together lower rX, which declines from 16% to 10%:

Original rx ! 6% " 5%(2.0) ! 16%

New rx ! 5% " 4%(1.25) ! 10%

Equilibrium The condition under which the expected return on a security is just equal to its required return, r̂ " r. Also, P̂ " P0 , and the price is stable.

303Chapter 9 Stocks and Their Valuation

1 A price change of this magnitude is by no means rare. The prices of many stocks double or halve during a year. For example, during 2007, Amazon.com, a large online retailer of books, music, and videos, increased in value by 134.8%. On the other hand, E*Trade Financial, a discount brokerage fi rm, fell in value by 84.2%. 2 It should be obvious by now that actual realized rates of return are not necessarily equal to expected and required returns. Thus, an investor might have expected to receive a return of 15% if he or she had bought Amazon.com or E*Trade Financial stock in 2007; but after the fact, the realized return on Amazon.com was far above 15%, whereas the return on E*Trade Financial was far below.

Using these values, together with the new g, we fi nd that P̂0 rises from $27.27 to $75.71, or by 178%:1

Original P̂0 ! $2.8571(1.05) ____________ 0.16 $ 0.05 !

$3.00 _____ 0.11 ! $27.27

New P̂0 ! $2.8571(1.06) ____________ 0.10$0.06 !

$3.0285 _______ 0.04 ! $75.71

Note too that at the new price, the expected and required rates of return will be equal:2

r̂X ! $3.0285 _______ $75.71 " 6% ! 10% ! rX

Evidence suggests that stocks, especially those of large companies, adjust rapidly when their fundamental positions change. Such stocks are followed closely by a number of security analysts; so as soon as things change, so does the stock price. Consequently, equilibrium ordinarily exists for any given stock, and required and expected returns are generally close to equal. Stock prices certainly change, sometimes violently and rapidly; but this simply refl ects changing condi- tions and expectations. There are, of course, times when a stock will continue to react for several months to unfolding favorable or unfavorable developments. However, this does not signify a long adjustment period; rather, it simply indi- cates that as more new information about the situation becomes available, the market adjusts to it.

For a stock to be in equilibrium, what two conditions must hold? If a stock is not in equilibrium, explain how financial markets adjust to bring it into equilibrium.

RATES OF RETURN AND EQUILIBRIUM Stock C’s beta coefficient is bC " 0.4, while Stock D’s is bD " #0.5. (Stock D’s beta is negative, indicating that its return rises when returns on most other stocks fall. There are very few negative beta stocks, although collection agency stocks are sometimes cited as an example.) a. If the risk-free rate is 7% and the expected rate of return on an average stock is 11%,

what are the required rates of return on Stocks C and D? b. For Stock C, suppose the current price, P0, is $25.00; the next expected dividend, D1, is

$1.50; and the stock’s expected constant growth rate is 4%. Is the stock in equilibrium? Explain and describe what will happen if the stock is not in equilibrium.

QUESTIONS QUESTIONS

9A-19A-1 9A-29A-2

PROBLEMS PROBLEMS

9A-19A-1

304 Part 3 Financial Assets

EQUILIBRIUM STOCK PRICE The risk-free rate of return, rRF, is 6%; the required rate of return on the market, rM, is 10%; and Upton Company’s stock has a beta coefficient of 1.5. a. If the dividend expected during the coming year, D1, is $2.25 and if g " a constant 5%,

at what price should Upton’s stock sell? b. Now suppose the Federal Reserve Board increases the money supply, causing the

risk-free rate to drop to 5% and rM to fall to 9%. What would happen to Upton’s price? c. In addition to the change in Part b, suppose investors’ risk aversion declines and this,

combined with the decline in rRF, causes rM to fall to 8%. Now what is Upton’s price? d. Suppose Upton has a change in management. The new group institutes policies that

increase the expected constant growth rate from 5% to 6%. Also, the new management smoothes out fluctuations in sales and profits, causing beta to decline from 1.5 to 1.3. Assume that rRF and rM are equal to the values in Part c. After all these changes, what is its new equilibrium price? (Note: D1 is now $2.27.)

BETA COEFFICIENTS Suppose Chance Chemical Company’s management conducted a study and concluded that if it expands its consumer products division (which is less risky than its primary business, industrial chemicals), its beta will decline from 1.2 to 0.9. However, consumer products have a somewhat lower profit margin, and this would cause its constant growth rate in earnings and dividends to fall from 6% to 4%. The following also apply: rM " 9%, rRF " 6%, and D0 " $2.00. a. Should management expand the consumer products division? Explain. b. Assume all the facts given except the change in the beta coefficient. How low would

the beta have to fall to cause the expansion to be a good one? (Hint: Set P̂0 under the new policy equal to P̂0 under the old one and find the new beta that will produce this equality.)

9A-29A-2

9A-39A-3

INVESTING IN LONG -TERM ASSETS:

CAPITAL BUDGETING

10 The Cost of Capital

11 The Basics of Capital Budgeting

12 Cash Flow Estimation and Risk Analysis

PART 4

C H

A P

T E

C r e a t i n g Va l u e a t G E

The Cost of Capital10 CHAPTER

306

TA N

H O

N D

A/ AF

P/ G

ET TY

IM AG

General Electric (GE) is one of the world’s best- managed companies, and it has rewarded its shareholders with outstanding returns. GE cre- ates shareholder value by investing in assets that earn more than the cost of the capital used to acquire them. For example, if a project earns 20% but the capital invested in it costs only 10%, taking on the project will increase the firm’s value and thus its stock price.

Capital is obtained in three primary forms: debt, preferred stock, and common equity, with equity acquired by retaining earnings and by the issuance of new stock. The investors who pro- vide capital to GE expect to earn at least their required rate of return on that capital, and the required return represents the firm’s cost of capital.1 A variety of factors influence the cost of capital. Some—including interest rates, state

and federal tax policies, and general economic conditions—are outside the firm’s control. How- ever, the firm’s decisions regarding how it raises capital and how it invests those funds also have a profound effect on its cost of capital.

Estimating the cost of capital for a company such as GE is conceptually straightforward. GE’s capital comes largely from debt plus common equity obtained by retaining earnings, so its cost of capital depends largely on the level of interest rates in the economy and the marginal stock- holder’s required rate of return on equity. How- ever, GE operates many different divisions throughout the world; so the corporation is simi- lar to a portfolio that contains a number of differ- ent stocks, each with a different risk. Recall that portfolio risk is a weighted average of the rele- vant risks of the different stocks in the portfolio.

1 Recall from earlier chapters that expected and required returns as seen by the marginal investor must be equal; otherwise, the security will not be in equilibrium. Therefore, buying and selling will force this equality to hold, except for short periods immediately following the release of new information. Since expected and required returns are normally equal, we use the two terms interchangeably.

en er

a l

El ec

tr ic

In the last four chapters, we explained how risk infl uences prices and required rates of return on bonds and stocks. A fi rm’s primary objective is to maximize its share- holders’ value. The principal way value is increased is by investing in projects that earn more than their cost of capital. In the next two chapters, we will see that a proj- ect’s future cash fl ows can be forecasted and that those cash fl ows can be discounted to fi nd their present value. Then if the PV of the future cash fl ows exceeds the proj- ect’s cost, the fi rm’s value will increase if the project is accepted. However, we need a discount rate to fi nd the PV of the future cash fl ows, and that discount rate is the fi rm’s cost of capital. Finding the cost of the capital required to take on new projects is the primary focus of this chapter.2

Most formulas used in this chapter were developed earlier, when we examined the required rates of return on bonds and stocks. Indeed, the rates of return that inves- tors require on bonds and stocks represent the costs of those securities to the fi rm. As we shall see, companies estimate the required returns on their securities, calculate a weighted average of the costs of their diff erent types of capital, and use this average cost for capital budgeting purposes.

When you fi nish this chapter, you should be able to: • Explain why the weighted average cost of capital (WACC) is used in capital

budgeting. • Estimate the costs of diff erent capital components—debt, preferred stock,

retained earnings, and common stock. • Combine the diff erent component costs to determine the fi rm’s WACC. These concepts are necessary to understand the firm’s capital budgeting process.

10-1 AN OVERVIEW OF THE WEIGHTED AVERAGE COST OF CAPITAL (WACC)

Table 10-1 shows Allied Food Products’ balance sheet as presented in Chapter 3, with two additions: (1) the actual capital supplied by investors (banks, bondhold- ers, and stockholders) and (2) the capital structure that Allied plans to use in the future. Allied’s overall cost of capital is an average of the costs of the various types of capital it uses. Allied’s debt costs 10%, it currently uses no preferred stock but

Similarly, each of GE’s divisions has its own level of risk (hence, its own cost of capital). GE’s overall cost of capital is an average of its divisions’ costs. For example, GE’s NBC subsidiary probably has a different cost of capital than its aircraft engine division; and even within divisions, some projects are riskier than others. Moreover, overseas projects

may have different risks and thus different costs of capital than similar domestic projects.

As we will see in this chapter, the cost of capital is an essential element in the capital budgeting process. This process is the primary determinant of the firm’s long-run stock price.

PU T TING THINGS IN PER SPECTIVE

Chapter 10 The Cost of Capital 307

2 If projects diff er in risk, risk-adjusted costs of capital should be used, not one single corporate cost of capital. We discuss this point later in the chapter.

308 Part 4 Investing in Long-Term Assets: Capital Budgeting

plans to use a small amount of preferred in the future, and its common equity costs about 13.5%. (This is the return that stockholders require on the stock.)3 Now assume that Allied has made the decision to fi nance all of next year’s projects with debt. The argument is sometimes made that the cost of capital for next year’s proj- ects will be 10% because only debt will be used to fi nance them. However, this position is incorrect. If Allied fi nances this set of projects with debt, it will be using up some of its future borrowing capacity. As expansion occurs in subsequent years, the fi rm will at some point have to raise more equity to prevent the debt ratio from getting too high.

Our concern is with capital that must be provided by investors—interest- bearing debt, preferred stock, and common equity. Accounts payable and accruals increase automatically when capital budgeting projects are taken on, so increases in these items are deducted from projects’ costs. This point is discussed in detail in Chapter 12, but the result is that we are concerned only with investor-supplied capital when we calculate the cost of capital.

To illustrate, suppose Allied borrows heavily at 10% during 2009 and, in the process, uses up its capacity to borrow, to fi nance projects yielding 11%. In 2010, it has new projects available that yield 13% (well above the return on 2009 projects), but it could not accept them because they would have to be fi nanced with 13.5% equity. To avoid this problem, Allied and other fi rms take a long-run view; and the cost of capital is calculated as a weighted average, or composite, of the various types of funds used over time, regardless of the specifi c fi nancing used in a given year.

We explore the weights in more detail in the capital structure chapter, where we see how the optimal capital structure is estimated. As we will see, there is an optimal capital structure—one where the percentages of debt, preferred stock, and common equity maximize the fi rm’s value. As shown in the last column of Table 10-1, Allied Foods has concluded that it should use 45% debt, 2% preferred stock, and

3 We estimate this 13.5% later in the chapter. It diff ers slightly from the number we found in an earlier chapter. As you will see, there are several ways to estimate rs and those methods generally produce diff erent estimates. Allied concluded that its rs is somewhere in the range of 13% to 14%, and it compromised by using 13.5%. The costs of debt and preferred stock are set by contract, so they can be estimated with relatively little error; but the cost of equity cannot be measured precisely.

Allied Food Products: Capital Structure Used to Calculate the WACCT a b l e 1 0 - 1

REGULAR BALANCE SHEET: at 12/31/08 All Liabilities

& Equity

Actual Investor-Supplied

Capital

Target Capital

Structure Cash $ 10 Accounts payable $ 60 3.0% Receivables 375 Accruals 140 7.0 Inventories 615 Spontaneous debt $ 200 10.0% Total C.A. $1,000 Notes payable 110 5.5 $ 110

Total C.L. $ 310 15.5% Net fixed assets $1,000 Long-term debt 750 37.5 750

Total debt $1,060 53.0% $ 860 47.8% 45.0% Preferred stock 0 0.0 0 0.0 2.0 Common stock 130 6.5 130 Retained earnings 810 40.5 810 Total equity $ 940 47.0% $ 940 52.2 53.0

Total $2,000 Total $2,000 100.0% $1,800 100.0% 100.0%

309Chapter 10 The Cost of Capital

53% common equity; and it plans to raise capital in those proportions in the future. Therefore, we use those target weights when we calculate Allied’s weighted aver- age cost of capital.

SEL F TEST Why should the cost of capital be calculated as a weighted average of the

various types of funds that a fi rm generally uses, not as the cost of the specifi c type of capital used during a given year?

What is the riskiest and thus highest-cost type of capital? least-cost type?

Why can’t a fi rm fi nance with only the lowest-cost type of capital?

10-2 BASIC DEFINITIONS The investor-supplied items—debt, preferred stock, and common equity—are called capital components. Increases in assets must be fi nanced by increases in these capital components. The cost of each component is called its component cost; for example, Allied can borrow money at 10%, so its component cost of debt is 10%.4 These costs are then combined to form a weighted average cost of capital, which is used in the capital budgeting process. Throughout this chapter, we con- centrate on the three major capital components. The following symbols identify the cost and weight of each:

Capital Component One of the types of capital used by firms to raise funds.

4 We will see shortly that there is a before-tax and an after-tax cost of debt; for now, it is suffi cient to know that 10% is the before-tax component cost of debt. Also, for simplicity, we assume that long- and short-term debt have the same cost; hence, we deal with just one type of debt.

rd ! interest rate on the fi rm’s new debt ! before-tax component cost of debt. It can be found in several ways, including calculating the yield to maturity on the fi rm’s currently outstanding bonds.

rd(1 – T) ! after-tax component cost of debt, where T is the fi rm’s marginal tax rate. rd(1 " T) is the debt cost used to calculate the weighted aver- age cost of capital. As we shall see, the after-tax cost of debt is lower than its before-tax cost because interest is tax deductible.

rp ! component cost of preferred stock, found as the yield investors expect to earn on the preferred stock. Preferred dividends are not tax-deductible; hence, the before- and after-tax costs of pre- ferred are equal.

rs ! component cost of common equity raised by retaining earnings, or internal equity. It is the rs developed in Chapters 8 and 9 and defi ned there as the rate of return that investors require on a fi rm’s common stock. Most fi rms, once they have become well established, obtain all of their new equity as retained earnings; hence, rs is their cost of all new equity.

re ! component cost of external equity, or common equity raised by issuing new stock. As we will see, re is equal to rs plus a factor that refl ects the cost of issuing new stock. Note, though, that es- tablished fi rms such as Allied Foods rarely issue new stock; hence, re is rarely a relevant consideration except for very young, rapidly growing fi rms.

310 Part 4 Investing in Long-Term Assets: Capital Budgeting

The target proportions of debt (wd), preferred stock (wp), and common equity (wc), along with the costs of those components, are used to calculate the fi rm’s weighted average cost of capital, WACC. We assume at this point that all new common equity is raised as retained earnings, as is true for most companies; hence, the cost of common equity is rs.

WACC ! ( % of debt ) ( After-tax cost of debt ) " ( % of preferred stock ) ( Cost of preferred stock ) " ( % of common equity ) ( Cost of common equity ) 10-1 ! wdrd(1 # T) " wprp " wcrs

Note that only debt has a tax adjustment factor, (1 – T). As discussed in the next section, this is because interest on debt is tax-deductible but preferred dividends and the returns on common stock (dividends and capital gains) are not.

These defi nitions and concepts are discussed in the remainder of the chapter, using Allied Foods for illustrative purposes. Later in the capital structure chapter, we extend the discussion to show how the optimal mix of securities minimizes the fi rm’s cost of capital and maximizes its value.

Weighted Average Cost of Capital (WACC) A weighted average of the component costs of debt, preferred stock, and common equity.

wd, wp, ws, we ! target weights of debt, preferred stock, retained earnings (inter- nal equity), and new common stock (external equity). The weights are the percentages of the different types of capital the fi rm plans to use when it raises capital in the future. Target weights may differ from actual current weights.5

WACC ! the fi rm’s weighted average, or overall, cost of capital.

5 We should also note that the weights could be based on the book values of the capital components or on their market values. The market value of the equity is found by multiplying the stock’s price by the number of shares outstanding. Market value weights are theoretically superior; but accountants show assets on a book-value basis, bond rating agencies and security analysts generally focus on book values, and market value weights are quite unstable because stock prices fl uctuate widely. If a fi rm’s book and market values diff er widely, the fi rm may set its target weights as a blend of book and market weights. We will discuss this at greater length in the capital structure chapter; but for now, just take the target weights provided in this chapter as management determined.

SEL F TEST Identify the fi rm’s three major capital structure components and give their

respective component cost and weight symbols.

Why might there be two diff erent component costs for common equity? Which one is generally relevant, and for what type of fi rm is the second one likely to be relevant?

If a fi rm now has a debt ratio of 50% but plans to fi nance with only 40% debt in the future, what should it use as wd when it calculates its WACC?

10-3 COST OF DEBT, rd(1 – T) The interest rate a fi rm must pay on its new debt is defi ned as its before-tax cost of debt, rd. Firms can estimate rd by asking their bankers what it will cost to borrow or by fi nding the yield to maturity (or yield to call if the debt is likely

Before-Tax Cost of Debt, rd The interest rate the firm must pay on new debt.

311Chapter 10 The Cost of Capital

to be called) on their currently outstanding debt (see Chapter 7).6 However, the after-tax cost of debt, rd(1 – T), should be used to calculate the weighted average cost of capital. This is the interest rate on new debt, rd, less the tax savings that result because interest is tax deductible:7

After-tax cost of debt ! Interest rate on new debt # Tax savings ! rd # rdT ! rd(1 # T) 10-2

In effect, the government pays part of the cost of debt because interest is tax deductible. Therefore, if Allied can borrow at an interest rate of 10% and its mar- ginal federal-plus-state tax rate is 40%, its after-tax cost of debt will be 6%:8

After-tax cost of debt ! rd(1 # T) ! 10%(1.0 # 0.4) ! 10%(0.6) ! 6.0%

We use the after-tax cost of debt in calculating the WACC because we are inter- ested in maximizing the value of the fi rm’s stock, and the stock price depends on after-tax cash fl ows. Because we are concerned with after-tax cash fl ows and because cash fl ows and rates of return should be calculated on a comparable basis, we adjust the interest rate downward due to debt’s preferential tax treatment.

Note that the cost of debt is the interest rate on new debt, not on already out- standing debt. We are interested in the cost of new debt because our primary con- cern with the cost of capital is its use in capital budgeting decisions. For example, would a new machine earn a return greater than the cost of the capital needed to ac- quire the machine? The rate at which the fi rm has borrowed in the past is irrelevant when answering this question because we need to know the cost of new capital.9

After-Tax Cost of Debt, rd(1 – T) The relevant cost of new debt, taking into account the tax deductibility of interest; used to calculate the WACC.

6 If the yield curve is sharply upward- or downward-sloping, the costs of long- and short-term debt will diff er. In this case, the fi rm should calculate an average of its debt costs based on the proportions of long- and short-term debt that it plans to use. 7 If Allied borrowed $100,000 at 10%, it would have to write a check for $10,000 to pay interest charges for a year. However, that $10,000 would be a tax deduction, which at a 40% tax rate would save $4,000 in taxes. 8 Note that in 2008, the federal tax rate for most large corporations is 35%. However, most corporations are also subject to state income taxes; so for illustrative purposes, we assume that the eff ective federal-plus-state tax rate on marginal income is 40%. 9 Three additional points should also be noted: (1) The tax rate is zero for a fi rm with losses. Therefore, for a company that does not pay taxes, the cost of debt is not reduced. That is, in Equation 10-2, the tax rate equals zero; so the after-tax cost of debt is equal to the interest rate. (2) Strictly speaking, the after-tax cost of debt should refl ect the expected cost of debt, which is very slightly below the promised 10% yield. (3) Allied raises most of its debt from commercial banks and sells bonds directly to fi nancial institutions; but if it sold new bonds through investment bankers, a fl otation cost would be incurred. We can adjust for fl otation costs by deducting the dollar fl otation costs from the issue price (par value) of the bond and calculating an adjusted YTM. If the bonds had a fl otation cost of 0.5% (or $5 per $1,000 bond), an annual interest rate of 10%, and a 20-year maturity, the calculated YTM would be 10.06% versus 10.00% with no fl otation costs. Because the diff erence is so small, most fi rms ignore bond fl otation costs.

SEL F TEST Why is the after-tax cost of debt rather than the before-tax cost used to

calculate the WACC?

Why is the relevant cost of debt the interest rate on new debt, not that on already outstanding, or old, debt?

How can the yield to maturity on a fi rm’s outstanding debt be used to estimate its before-tax cost of debt?

312 Part 4 Investing in Long-Term Assets: Capital Budgeting

10-4 COST OF PREFERRED STOCK, rp The component cost of preferred stock used to calculate the weighted average cost of capital, rp, is the preferred dividend, Dp, divided by the current price of the preferred stock, Pp.

10-3 Component cost of preferred stock ! rp ! Dp ___ Pp

Allied does not have any preferred stock outstanding, but the company plans to issue some in the future and therefore has included it in its target capital structure. Allied would sell this stock to a few large hedge funds, the stock would have a $10.00 dividend per share, and it would be priced at $97.50 a share. Therefore, Allied’s cost of preferred stock would be 10.3%:10

rp ! $10.00/$97.50 ! 10.3%

As we can see from Equation 10-3, calculating the cost of preferred stock is easy. This is particularly true for traditional “plain vanilla” preferred that pays a fi xed dividend in perpetuity. However, in Chapter 9, we noted that some preferred issues have a specifi ed maturity date and we described how to calculate the expected re- turn on these issues. Also, preferred stock may include an option to convert to com- mon stock, which adds another layer of complexity. We leave these more compli- cated situations for advanced classes. Finally, note that no tax adjustments are made when calculating rp because preferred dividends, unlike interest on debt, are not tax deductible; so no tax savings are associated with preferred stock.

Cost of Preferred Stock, rp The rate of return investors require on the firm’s preferred stock. rp is calculated as the preferred dividend, Dp , divided by the current price, Pp.

SEL F TEST Is a tax adjustment made to the cost of preferred stock? Why or why not?

A company’s preferred stock currently trades at $80 per share and pays a $6 annual dividend per share. Ignoring fl otation costs, what is the fi rm’s cost of preferred stock? (7.50%)

10-5 THE COST OF RETAINED EARNINGS, rs The costs of debt and preferred stock are based on the returns that investors require on these securities. Similarly, the cost of common equity is based on the rate of return that investors require on the company’s common stock. Note, though, that new common equity is raised in two ways: (1) by retaining some of the

10 This preferred stock would be sold directly to a group of hedge funds, so no fl otation costs would be incurred. If signifi cant fl otation costs were involved, the cost of the preferred should be adjusted upward, as we explain in a later section.

A company has outstanding 20-year non-callable bonds with a face value of $1,000, an 11% annual coupon, and a market price of $1,294.54. If the company was to issue new debt, what would be a reasonable estimate of the interest rate on that debt? If the company’s tax rate is 40%, what is its after-tax cost of debt? (8.0%; 4.8%)

313Chapter 10 The Cost of Capital

current year’s earnings and (2) by issuing new common stock.11 We use the symbol rs to designate the cost of retained earnings and re to designate the cost of new common stock, or external equity. Equity raised by issuing stock has a higher cost than equity from retained earnings due to the fl otation costs required to sell new common stock. Therefore, once fi rms get beyond the startup stage, they normally obtain all of their new equity by retaining earnings.

Some have argued that retained earnings should be “free” because they represent money that is “left over” after dividends are paid. While it is true that no direct costs are associated with retained earnings, this capital still has a cost, an opportunity cost. The fi rm’s after-tax earnings belong to its stockholders. Bond- holders are compensated by interest payments; preferred stockholders, by pre- ferred dividends. But the net earnings remaining after interest and preferred dividends belong to the common stockholders, and these earnings serve to com- pensate them for the use of their capital. The managers, who work for the stock- holders, can either pay out earnings in the form of dividends or retain earnings for reinvestment in the business. When managers make this decision, they should recognize that there is an opportunity cost involved—stockholders could have received the earnings as dividends and invested this money in other stocks, in bonds, in real estate, or in anything else. Therefore, the fi rm needs to earn at least as much on any earnings retained as the stockholders could earn on alternative investments of comparable risk.

What rate of return can stockholders expect to earn on equivalent-risk invest- ments? First, recall from Chapter 9 that stocks are normally in equilibrium, with expected and required rates of return being equal: r̂s ! rs. Thus, Allied’s stockhold- ers expect to be able to earn rs on their money. Therefore, if the fi rm cannot invest re- tained earnings to earn at least rs , it should pay those funds to its stockholders and let them invest directly in stocks or other assets that will provide that return.

Whereas debt and preferred stocks are contractual obligations whose costs are clearly stated on the contracts, stocks have no comparable stated cost rate. That makes it diffi cult to measure rs. However, we can employ the techniques devel- oped in Chapters 8 and 9 to produce reasonably good estimates of the cost of eq- uity from retained earnings. To begin, recall that if a stock is in equilibrium, its required rate of return, rs , must be equal to its expected rate of return, r̂s. Further, its required return is equal to a risk-free rate, rRF , plus a risk premium, RP, whereas the expected return on the stock is its dividend yield, D1/P0 , plus its expected growth rate, g. Thus, we can write the following equation and estimate rs using the left term, the right term, or both terms:

Required rate of return ! Expected rate of return

rs ! rRF " RP ! D1/P0 " g ! r̂s 10-4

The left term is based on the Capital Asset Pricing Model (CAPM) as discussed in Chapter 8, and the right term is based on the discounted dividend model as devel- oped in Chapter 9. We discuss these two procedures, in addition to one based on the fi rm’s own cost of debt, in the following sections.

Cost of Retained Earnings, rs The rate of return required by stockholders on a firm’s common stock.

Cost of New Common Stock, re The cost of external equity based on the cost of retained earnings but increased for flotation costs.

11 The term retained earnings can be interpreted to mean the balance sheet item retained earnings, consisting of all the earnings retained in the business throughout its history or the income statement item addition to retained earnings. The income statement item is relevant in this chapter; for our purpose, retained earnings refers to that part of the current year’s earnings not paid as dividends (hence, available for reinvestment in the business this year). If this is not clear, look back at Allied’s balance sheet shown in Table 3-1 and note that at the end of 2007, Allied had $750 million of retained earnings; but that fi gure rose to $810 million by the end of 2008. Then look at the 2008 income statement, where you will see that Allied retained $60 million of its 2008 income. This $60 million was the new equity from retained earnings that was used, along with some additional debt, to fund the 2008 capital budgeting projects. Also, you can see from the 2007 and 2008 balance sheets that Allied had $130 million of common stock at the end of both years. This indicates that it did not sell any new common stock to raise capital during 2008.

314 Part 4 Investing in Long-Term Assets: Capital Budgeting

10-5a The CAPM Approach The most widely used method for estimating the cost of common equity is the Capital Asset Pricing Model (CAPM) as developed in Chapter 8.12 Here are the steps used to fi nd rs: Step 1: Estimate the risk-free rate, rRF . We generally use the 10-year Treasury bond

rate as the measure of the risk-free rate, but some analysts use the short- term Treasury bill rate.

Step 2: Estimate the stock’s beta coeffi cient, bi, and use it as an index of the stock’s risk. The i signifi es the ith company’s beta.

Step 3: Estimate the expected market risk premium. Recall that the market risk premium is the difference between the return that investors require on an average stock and the risk-free rate.13

Step 4: Substitute the preceding values in the CAPM equation to estimate the re- quired rate of return on the stock in question:

rs ! rRF " (RPM)bi 10-5 ! rRF " (rM # rRF)bi

Thus, the CAPM estimate of rs is equal to the risk-free rate, rRF , plus a risk pre- mium that is equal to the risk premium on an average stock, (rM – rRF), scaled up or down to refl ect the particular stock’s risk as measured by its beta coeffi cient.

Assume that in today’s market, rRF ! 5.6%, the market risk premium is RPM ! 5.0%, and Allied’s beta is 1.48. Using the CAPM approach, Allied’s cost of equity is estimated to be 13.0%:

rs ! 5.6% " (5.0%)(1.48)

! 13.0%

Although the CAPM appears to produce an accurate, precise estimate of rs, several potential problems exist. First, as we saw in Chapter 8, if a fi rm’s stock- holders are not well diversifi ed, they may be concerned with stand-alone risk rather than just market risk. In that case, the fi rm’s true investment risk would not be measured by its beta and the CAPM estimate would understate the correct value of rs. Further, even if the CAPM theory is valid, it is hard to obtain accurate esti- mates of the required inputs because (1) there is controversy about whether to use long-term or short-term Treasury yields for rRF , (2) it is hard to estimate the beta that investors expect the company to have in the future, and (3) it is diffi cult to estimate the proper market risk premium. As we indicated earlier, the CAPM approach is used most often; but because of the just-noted problems, analysts also estimate the cost of equity using the other approaches discussed in the following sections.

12 A recent survey by John Graham and Campbell Harvey indicates that the CAPM approach is most often used to estimate the cost of equity. More than 70% of the surveyed fi rms used the CAPM approach. In some cases, they used beta from the CAPM as one determinant of rs, but they also added other factors thought to improve the estimate. For more details, see John R. Graham and Campbell R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics, Vol. 60, nos. 2 and 3 (May–June 2001), pp. 187–243, for the survey and Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Return on Stocks and Bonds,” Journal of Financial Economics, 1993, pp. 3–56. 13 It is important to be consistent in the use of a long-term versus a short-term rate for rRF and for the market risk premium. The market risk premium (RPM ! rM " rRF) depends on the measure used for the risk-free rate. The yield curve is normally upward-sloping, so the 10-year Treasury bond rate normally exceeds the short-term Treasury bill rate. In this case, it follows that one will obtain a lower estimate of the market risk premium if the higher longer-term bond rate is used as the risk-free rate. At any rate, the rRF used to fi nd the market risk premium should be the same as the rRF used as the fi rst term in the CAPM equation.

315Chapter 10 The Cost of Capital

10-5b Bond-Yield-plus-Risk-Premium Approach In situations where reliable inputs for the CAPM approach are not available, as would be true for a closely held company, analysts often use a somewhat subjective procedure to estimate the cost of equity. Empirical studies suggest that the risk pre- mium on a fi rm’s stock over its own bonds generally ranges from 3 to 5 percentage points.14 Based on this evidence, one might simply add a judgmental risk premium of 3% to 5% to the interest rate on the fi rm’s own long-term debt to estimate its cost of equity. Firms with risky, low-rated, and consequently high-interest-rate debt also have risky, high-cost equity; and the procedure of basing the cost of equity on the fi rm’s own readily observable debt cost utilizes this logic. For example, given that Allied’s bonds yield 10%, its cost of equity might be estimated as follows:

rs ! Bond yield " Risk premium ! 10.0% " 4.0% ! 14.0%

The bonds of a riskier company might have a higher yield, 12%, in which case the estimated cost of equity would be 16%:

rs ! 12.0% " 4.0% ! 16.0%

Because the 4% risk premium is a judgmental estimate, the estimated value of rs is also judgmental. Therefore, one might use a range of 3% to 5% for the risk pre- mium and obtain a range of 13% to 15% for Allied. While this method does not produce a precise cost of equity, it should “get us in the right ballpark.”

10-5c Dividend-Yield-plus-Growth-Rate, or Discounted Cash Flow (DCF), Approach

In Chapter 9, we saw that both the price and the expected rate of return on a share of common stock depend, ultimately, on the stock’s expected cash fl ows. For com- panies that are expected to remain in business indefi nitely, the cash fl ows are the dividends; on the other hand, if investors expect the fi rm to be acquired by some other company or to be liquidated, the cash fl ows will be dividends for some num- ber of years plus a terminal price when the fi rm is expected to be acquired or liqui- dated. Like most fi rms, Allied is expected to continue indefi nitely, in which case the following equation applies:

P0 ! D1 _______ (1 " rs)

1 " D2 _______ (1 " rs)

2 " . . . " D

$ _______ (1 " rs) $

! ∑ t!1

Dt _______ (1 " rs)

t 10-6

Here P0 is the current stock price, Dt is the dividend expected to be paid at the end of Year t, and rs is the required rate of return. If dividends are expected to grow at a con- stant rate, as we saw in Chapter 9, Equation 10-6 reduces to this important formula:15

P0 ! D1 _____ rs # g

10-7

14 Ibbotson Associates, a well-known research fi rm, has calculated the historical returns on common stocks and on corporate bonds and used the diff erential as an estimate of the historical risk premium of stocks over corporate bonds. Historical risk premiums vary from year to year, but a range of 3% to 5% is common. Also, analysts have calculated the CAPM-required return on equity for publicly traded fi rms in a given industry, averaged them, subtracted those fi rms’ average bond yield, and used the diff erential as an expected risk premium. Again, these risk premium estimates are often generally in the 3% to 5% range. 15 If the growth rate is not expected to be constant, the DCF procedure can still be used to estimate rs; but in this case, it is necessary to calculate an average growth rate using the procedures described in this chapter’s Excel model.

316 Part 4 Investing in Long-Term Assets: Capital Budgeting

We can solve for rs to obtain the required rate of return on common equity, which for the marginal investor is also equal to the expected rate of return:

10-8 rs ! r̂s ! D1 __ P0

" Expected g

Thus, investors expect to receive a dividend yield, D1/P0, plus a capital gain, g, for a total expected return of r̂s; and in equilibrium, this expected return is also equal to the required return, rs. This method of estimating the cost of equity is called the discounted cash fl ow, or DCF, method. Henceforth, we will assume that equilibrium exists, which permits us to use the terms rs and r̂s interchangeably.

It is easy to calculate the dividend yield; but since stock prices fl uctuate, the yield varies from day to day, which leads to fl uctuations in the DCF cost of equity. Also, it is diffi cult to determine the proper growth rate. If past growth rates in earnings and dividends have been relatively stable and if investors expect a con- tinuation of past trends, g may be based on the fi rm’s historic growth rate. How- ever, if the company’s past growth has been abnormally high or low because of its own unique situation or because of general economic fl uctuations, investors will not project historical growth rates into the future. In this case, which applies to Allied, g must be obtained in some other manner.

Security analysts regularly forecast growth rates for earnings and dividends, looking at such factors as projected sales, net profi t margins, and competition. For example, Value Line, which is available in most libraries, provides growth rate fore- casts for 1,700 companies; and Merrill Lynch, Citi Smith Barney, and other organi- zations make similar forecasts. Averages of these forecasts are available on Yahoo Finance and other web sites. Therefore, someone estimating a fi rm’s cost of equity can obtain analysts’ forecasts and use them as a proxy for the growth expectations of investors in general. Then they can combine this g with the current dividend yield to estimate r̂s:

r̂s ! D1 __ P0

" Growth rate as projected by security analysts

Again, note that this estimate of r̂s is based on the assumption that g is expected to remain constant in the future. Otherwise, we must use an average of expected future rates.16

To illustrate the DCF approach, Allied’s stock sells for $23.06, its next expected dividend is $1.25, and analysts expect its growth rate to be 8.3%. Thus, Allied’s expected and required rates of return (hence, its cost of retained earnings) are esti- mated to be 13.7 %:

r̂s ! rs ! $1.25 ______ $23.06 " 8.3%

! 5.4% " 8.3%

! 13.7 %

Based on the DCF method, 13.7% is the minimum rate of return that should be earned on retained earnings to justify plowing earnings back into the business

16 Analysts’ growth rate forecasts are usually for 5 years into the future, and the rates provided represent the aver- age growth rate over that 5-year horizon. Studies have shown that analysts’ forecasts represent the best source of growth rate data for DCF cost of capital estimates. See Robert Harris, “Using Analysts’ Growth Rate Forecasts to Estimate Shareholder Required Rates of Return,” Financial Management, Spring 1986.

Two organizations—IBES and Zacks—collect the forecasts of leading analysts for most larger companies, average these forecasts, and publish the averages. The IBES and Zacks data are available through online computer data services.

317Chapter 10 The Cost of Capital

rather than paying them out as dividends. Put another way, since investors are thought to have an opportunity to earn 13.7 % if earnings are paid out as dividends, the opportunity cost of equity from retained earnings is 13.7%.

10-5d Averaging the Alternative Estimates In our examples, Allied’s estimated cost of equity was 13.0% by the CAPM, 14.0% by the bond-yield-plus-risk premium method, and 13.7% by the DCF method. Which method should the fi rm use? If management is highly confi dent of one method, it would probably use that method’s estimate. Otherwise, it might use an average of the three methods, which for Allied is 13.6%:

Average ! (13.0% " 13.7% " 14.0%)/3 ! 13.6%

One could, of course, give different weights to the different methods and thus cal- culate a weighted average.

As consultants, we have estimated companies’ costs of capital on numerous occasions. We generally use all three methods and average them, but we rely most heavily on the method that seems best under the circumstances. Judgment is important and comes into play here, as is true for most of fi nance. Also, we recognize that our fi nal estimate will almost certainly be incorrect to some ex- tent.17 Therefore, we always provide a range and state that in our judgment, the cost of equity is within that range. For Allied, we used a range of 13% to 14%; the company then used 13.5% as the cost of retained earnings when it calculated its WACC:

Final estimate of rs used to calculate the WACC: 13.5%.

17 Investment bankers are generally regarded as experts on concepts such as the cost of capital, and they are paid big salaries for their analysis. But those investment bankers aren’t always too accurate. To illustrate, the stock price of the fi fth-largest investment bank, Bear Stearns, closed on Friday, March 14, 2008, at $30. Its employees owned 33% of the stock. On Sunday, in a special meeting, its board of directors agreed to sell the company to JP Morgan for $2 per share. Even investment bankers don’t always get it right, so don’t expect too much precision unless you are given a set of numbers and told to do some relatively simple calculations. As of this writing, JP Morgan has since increased its off er for Bear Stearns to $10 per share.

SEL F TEST Why must a cost be assigned to retained earnings?

What three approaches are used to estimate the cost of common equity? Which approach is most commonly used in practice?

Identify some potential problems with the CAPM.

Which of the two components of the DCF formula, the dividend yield or the growth rate, do you think is more diffi cult to estimate? Why?

What’s the logic behind the bond-yield-plus-risk-premium approach?

Suppose you are an analyst with the following data: rRF ! 5.5%, rM " rRF ! 6%, b ! 0.8, D1 ! $1.00, P0 ! $25.00, g ! 6%, and rd ! fi rm’s bond yield ! 6.5%. What is this fi rm’s cost of equity using the CAPM, DCF, and bond-yield- plus-risk-premium approaches? Use the midrange of the judgmental risk premium for the bond-yield-plus-risk-premium approach. (CAPM ! 10.3%; DCF ! 10%; Bond yield " RP ! 10.5%)

318 Part 4 Investing in Long-Term Assets: Capital Budgeting

10-6 COST OF NEW COMMON STOCK, re Companies generally use an investment banker when they issue new common stock and sometimes when they issue preferred stock or bonds. In return for a fee, investment bankers help the company structure the terms, set a price for the issue, and sell the issue to investors. The bankers’ fees are called fl otation costs, and the total cost of the capital raised is the investors’ required return plus the fl otation cost.

For most fi rms at most times, equity fl otation costs are not an issue because most equity comes from retained earnings. Therefore, in our discussion to this point, we have ignored fl otation costs. However, as you can see in “How Much Does It Cost to Raise External Capital,” which follows, fl otation costs can be sub- stantial. So if a fi rm does plan to issue new stock, these costs should not be ignored. When fi rms use investment bankers to raise capital, two approaches can be used to account for fl otation costs.18 We describe them next.

10-6a Add Flotation Costs to a Project’s Cost In the next chapter, we show that capital budgeting projects typically involve an initial cash outlay followed by a series of cash infl ows. One approach to handling fl otation costs, found as the sum of the fl otation costs for the debt, preferred, and common stock used to fi nance the project, is to add this sum to the initial invest- ment cost. Because the investment cost is increased, the project’s expected rate of return is reduced. For example, consider a 1-year project with an initial cost (not including fl otation costs) of $100 million. After 1 year, the project is expected to produce an infl ow of $115 million. Therefore, its expected rate of return is $115/$100 " 1 ! 0.15 ! 15.0%. However, if the project requires the company to raise $100 million of new capital and incur $2 million of fl otation costs, the total up-front cost will rise to $102 million, which will lower the expected rate of return to $115/$102 " 1 ! 0.1275 ! 12.75%.

10-6b Increase the Cost of Capital The second approach involves adjusting the cost of capital rather than increasing the project’s investment cost. If the fi rm plans to continue using the capital in the future, as is generally true for equity, this second approach theoretically will be better. The adjustment process is based on the following logic. If there are fl otation costs, the issuing fi rm receives only a portion of the capital provided by investors, with the remainder going to the underwriter. To provide investors with their required rate of return on the capital they contributed, each dollar the fi rm actually receives must “work harder”; that is, each dollar must earn a higher rate of return than the investors’ required rate of return. For example, suppose investors require a 13.7% return on their investment, but fl otation costs represent 10% of the funds raised. Therefore, the fi rm actually keeps and invests only 90% of the amount that investors supplied. In that case, the fi rm must earn about 14.3% on the available funds in order to provide investors with a 13.7% return on their investment. This higher rate of return is the fl otation-adjusted cost of equity.

The DCF approach can be used to estimate the effects of fl otation costs. Here is the equation for the cost of new common stock, re:

10-9 Cost of equity from new stock ! re ! D1 ________ P0(1 # F)

" g

18 A more complete discussion of fl otation cost adjustments can be found in Brigham and Daves, Intermediate Financial Management, 9th edition (Mason, OH: Thomson/South-Western, 2007), and other advanced texts.

319Chapter 10 The Cost of Capital

Here F is the percentage fl otation cost required to sell the new stock, so P0(1 " F) is the net price per share received by the company.

Assuming that Allied has a fl otation cost of 10%, its cost of new common equity, re, would be computed as follows:

re ! $1.25 _______________ $23.06(1 # 0.10) " 8.3%

! $1.25 ______ $20.75 " 8.3%

! 6.0% " 8.3 % ! 14.3%

This is 0.6% higher than the previously estimated 13.7% DCF cost of equity, so the fl otation cost adjustment is 0.6%:

Flotation adjustment ! Adjusted DCF cost # Pure DCF cost ! 14.3% # 13.7% ! 0.6%

The 0.6% adjustment factor can be added to the previously estimated rs = 13.5% (Allied management’s estimate), resulting in a cost of equity from new com- mon stock, or external equity, of 14.1%:

Cost of external equity ! rS " Adjustment factor ! 13.5% " 0.6% ! 14.1%

If Allied earns 14.1% on funds obtained from selling new stock, the investors who purchased that stock will end up earning 13.5%, their required rate of return, on

Flotation Cost, F The percentage cost of issuing new common stock.

Flotation Cost Adjustment The amount that must be added to rs to account for flotation costs to find re.

Text not available due to copyright restrictions

320 Part 4 Investing in Long-Term Assets: Capital Budgeting

the money they invested. If Allied earns more than 14.1%, its stock price should rise; but the price should fall if Allied earns less than 14.1%.19

10-6c When Must External Equity Be Used? Because of fl otation costs, dollars raised by selling new stock must “work harder” than dollars raised by retaining earnings. Moreover, because no fl otation costs are involved, retained earnings cost less than new stock. Therefore, fi rms should uti- lize retained earnings to the greatest extent possible. However, if a fi rm has more good investment opportunities than can be fi nanced with retained earnings plus the debt and preferred stock supported by those retained earnings, it may need to issue new common stock. The total amount of capital that can be raised before new stock must be issued is defi ned as the retained earnings breakpoint, and it can be calculated as follows:

10-10 Retained earnings breakpoint

! Addition to retained earnings for the year

____________________________________ Equity fraction

Allied’s addition to retained earnings in 2009 is expected to be $66 million; and its target capital structure consists of 45% debt, 2% preferred, and 53% equity. Therefore, its retained earnings breakpoint for 2009 is as follows:

Retained earnings breakpoint ! $66/0.53 ! $124.5 million

To prove that this is correct, note that a capital budget of $124.5 million could be fi nanced as 0.45($124.5) ! $56 million of debt, 0.02($124.5) ! $2.5 million of pre- ferred stock, and 0.53($124.5) ! $66 million of equity raised from retained earn- ings. Up to a total of $124.5 million of new capital, equity would have a cost of rs ! 13.5%. However, if the capital budget exceeded $124.5 million, Allied would have to obtain equity by issuing new common stock at a cost of re ! 14.1%.

Retained Earnings Breakpoint The amount of capital raised beyond which new common stock must be issued.

SEL F TEST What are the two approaches that can be used to adjust for fl otation costs?

Would a fi rm that has many good investment opportunities be likely to have a higher or a lower dividend payout ratio than a fi rm with few good invest- ment opportunities? Explain.

A fi rm’s common stock has D1 ! $1.50, P0 ! $30.00, g ! 5%, and F ! 4%. If the fi rm must issue new stock, what is its cost of new external equity? (10.21%)

Suppose Firm A plans to retain $100 million of earnings for the year. It wants to fi nance using its current target capital structure of 46% debt, 3% preferred, and 51% common equity. How large could its capital budget be before it must issue new common stock? ($196.08 million)

19 Flotation costs for preferred stock and bonds are handled similarly to common stock. In both cases, the dollars of fl otation costs are deducted from the price of the security, Pp for preferred stock and $1,000 for bonds issued at par. Then for preferred, the cost is found using Equation 10-9 with g ! 0. For bonds, we fi nd the YTM based on $1,000 " Flotation costs (say, $970 if fl otation costs are 3% of the issue price). 20 This breakpoint is only suggestive—it is not written in stone. For example, rather than issuing new common stock, the company could use more debt (hence, increase its debt ratio) or it could increase its addition to retained earnings by reducing its dividend payout ratio. Both actions would change the retained earnings breakpoint. Also, breakpoints could occur due to increases in the costs of debt and preferred. Indeed, all manner of changes could occur; and the end result would be a large number of potential breakpoints. All of this is discussed in more detail in Brigham and Ehrhardt, Financial Management Theory and Practice, 12th edition (Mason, OH: Thomson/South-Western, 2008), Web Extension 11B.

321Chapter 10 The Cost of Capital

10-7 COMPOSITE, OR WEIGHTED AVERAGE, COST OF CAPITAL, WACC

Allied’s target capital structure calls for 45% debt, 2% preferred stock, and 53% common equity. Earlier we saw that its before-tax cost of debt is 10.0%, its after-tax cost of debt is rd(1 " T) ! 10%(0.6) ! 6.0%, its cost of preferred stock is 10.3%, its cost of common equity from retained earnings is 13.5%, and its marginal tax rate is 40%. Equation 10-1, presented earlier, can be used to calculate its WACC when all of the new common equity comes from retained earnings:

WACC ! wdrd(1 # T) " wprp " wcrs ! 0.45(10%)(0.6) " 0.02(10.3%) " 0.53(13.5%) ! 10.1% if equity comes from retained earnings

Under these conditions, every dollar of new capital that Allied raises would consist of 45 cents of debt with an after-tax cost of 6%, 2 cents of preferred stock with a cost of 10.3%, and 53 cents of common equity from additions to retained earnings with a cost of 13.5%. The average cost of each whole dollar, or the WACC, would be 10.1%.

This estimate of Allied’s WACC assumes that common equity comes exclu- sively from retained earnings. If, instead, Allied was to issue new common stock, its WACC would be slightly higher because of the additional fl otation costs.

WACC ! wdrd(1 # T) " wprp " wcre ! 0.45(10%)(0.6) " 0.02(10.3%) " 0.53(14.1%) ! 10.4% with equity raised by selling new stock

In the Web Appendix 10A, we discuss in more detail the connection between the WACC and the costs of issuing new common stock.

SEL F TEST Write the equation for the WACC.

Firm A has the following data: Target capital structure of 46% debt, 3% preferred, and 51% common equity; Tax rate ! 40%; rd ! 7%; rp ! 7.5%; rs ! 11.5%; and re ! 12.5%. What is the fi rm’s WACC if it does not issue any new stock? (8.02%)

What is Firm A’s WACC if it issues new common stock? (8.53%)

Firm A has 11 equally risky capital budgeting projects, each costing $19.608 million and each having an expected rate of return of 8.25%. Firm A’s retained earnings breakpoint is $196.08 million. How much capital should Firm A raise and invest? Why? ($196.08 million; the 11th project would have a higher WACC than its expected rate of return. This question anticipates some of the analysis in Chapter 11.)

10-8 FACTORS THAT AFFECT THE WACC The cost of capital is affected by a number of factors. Some are beyond the fi rm’s control, but others can be infl uenced by its fi nancing and investment decisions.

10-8a Factors the Firm Cannot Control The three most important factors that the fi rm cannot directly control are interest rates in the economy, the general level of stock prices, and tax rates. If interest rates in

322 Part 4 Investing in Long-Term Assets: Capital Budgeting

the economy rise, the cost of debt increases because the fi rm must pay bondhold- ers more when it borrows. Similarly, if stock prices in general decline, pulling the fi rm’s stock price down, its cost of equity will rise. Also, since tax rates are used in the calculation of the component cost of debt, they have an important effect on the fi rm’s cost of capital. Taxes also affect the cost of capital in other less apparent ways. For example, when tax rates on dividends and capital gains were lowered relative to rates on interest income, stocks became relatively more attractive than debt; consequently, the cost of equity and WACC declined.

10-8b Factors the Firm Can Control A fi rm can directly affect its cost of capital in three primary ways: (1) by changing its capital structure, (2) by changing its dividend payout ratio, and (3) by altering its capital budgeting decision rules to accept projects with more or less risk than projects previously undertaken.

Capital structure impacts a fi rm’s cost of capital. So far we have assumed that Allied has a given target capital structure, and we used the target weights to calcu- late its WACC. However, if the fi rm changes its target capital structure, the weights used to calculate the WACC will change. Other things held constant, an increase in the target debt ratio tends to lower the WACC (and vice versa if the debt ratio is lowered) because the after-tax cost of debt is lower than the cost of equity. How- ever, other things are not likely to remain constant. An increase in the use of debt will increase the riskiness of both the debt and the equity, and these increases in component costs might more than offset the effects of the changes in the weights and raise the WACC. In the capital structure chapter, we will discuss how a fi rm can try to balance these effects to reach its optimal capital structure.

Dividend policy affects the amount of retained earnings available to the fi rm and thus the need to sell new stock and incur fl otation costs. This suggests that the higher the dividend payout ratio, the smaller the addition to retained earnings and thus the higher the cost of equity and therefore the WACC. However, investors may prefer dividends to retained earnings, in which case reducing dividends might lead to an increase in both rs and re. As we will see in the dividend chapter, the optimal dividend policy is a complicated issue, but one that can have an im- portant effect on the cost of capital.

For U.S. fi rms to be competitive in world markets, they must have capital costs similar to those their international com- petitors face. In the past, many experts argued that U.S. fi rms were at a disadvantage. In particular, Japanese fi rms enjoyed lower costs of capital, which lowered their total costs and made it harder for U.S. fi rms to compete. Recent events, however, have considerably narrowed cost of capital diff er- ences between U.S. and Japanese fi rms. In particular, despite its recent decline, the U.S. stock market has outperformed the Japanese market over the past decade, which has made it relatively easy for U.S. fi rms to raise equity capital.

As capital markets become increasingly integrated, cross- country diff erences in the costs of capital are disappearing. Today most large corporations raise capital throughout the world; hence, we are moving toward one global capital market rather than distinct capital markets in each country. Although government policies and market conditions can aff ect the costs of capital within a given country, this aff ects primarily smaller fi rms that do not have access to global capital markets. However, even these diff erences are becoming less important as time goes by. What matters most to investors is the risk of the individual fi rm, not the market in which it raises capital.

GLOBAL VARIATIONS IN THE COST OF CAPITAL

323Chapter 10 The Cost of Capital

The fi rm’s capital budgeting decisions can also affect its cost of capital. When we estimate the fi rm’s cost of capital, we use as the starting point the required rates of return on its outstanding stock and bonds. These cost rates refl ect the riskiness of the fi rm’s existing assets. Therefore, we have been implicitly assuming that new capital will be invested in assets that have the same risk as existing assets. This assumption is generally correct, as most fi rms do invest in assets similar to ones they currently operate. However, if the fi rm decides to invest in an entirely new and risky line of business, its component costs of debt and equity (and thus its WACC) will increase. To illustrate, in 1996 when ITT Corporation sold off its fi nance com- pany and purchased Caesar’s World, which operates gambling casinos, its dramatic shift in corporate focus almost certainly affected ITT’s cost of capital. (Subsequently, ITT’s hospitality and entertainment division has become part of Starwood Hotels & Resorts.) The effects of such investment decisions are discussed in Chapter 12.

SEL F TEST Name three factors that aff ect the cost of capital and that are beyond the

fi rm’s control.

What are three factors under the fi rm’s control that can aff ect its cost of capital?

Suppose interest rates in the economy increase. How would such a change aff ect the costs of both debt and common equity based on the CAPM?

10-9 ADJUSTING THE COST OF CAPITAL FOR RISK As you will see in the chapters on capital budgeting that follow, the cost of capital is a key element in the capital budgeting process. Projects should be accepted if and only if their estimated returns exceed their costs of capital. Thus, the cost of capital is a “hurdle rate”—a project’s expected rate of return must “jump the hurdle” for it to be accepted. Moreover, investors require higher returns on riskier investments. Consequently, companies that are raising capital to take on risky projects will have higher costs of capital than companies that are investing in safer projects.

Figure 10-1 illustrates the trade-off between risk and the cost of capital. Firm L is in a low-risk business and has a WACC of 8%. Firm A is an average-risk business with a WACC of 10%, while Firm H’s business is exposed to greater risk and con- sequently has a WACC of 12%. Thus, Firm L will accept a typical project if its ex- pected return is above 8%. Firm A’s hurdle rate is 10%, while the corresponding hurdle rate for Firm H is 12%.

It’s important to remember that the costs of capital for Firms L, A, and H in Figure 10-1 represent the overall, or composite, WACCs for the three fi rms and thus apply only to “typical” projects for each fi rm. However, different projects often have different risks, even for a given fi rm. Therefore, each project’s hurdle rate should refl ect the risk of the project, not the risk associated with the fi rm’s average project as refl ected in its composite WACC. Empirical studies do indicate that fi rms consider the risks of individual projects, but the studies also indicate that most fi rms regard most projects as having about the same risk as the fi rm’s average existing assets. Therefore, the WACC is used to evaluate most projects; but if a project has an es- pecially high or low risk, the WACC will be adjusted up or down to account for the risk differential.

For example, assume that Firm A (the average-risk fi rm with a composite WACC of 10%) has two divisions, L and H. Division L has relatively little risk;

324 Part 4 Investing in Long-Term Assets: Capital Budgeting

and if it were operated as a separate fi rm, its WACC would be 7%. Division H has higher risk, and its divisional cost of capital is 13%. Since the two divisions are of equal size, Firm A’s composite WACC is calculated as 0.50(7%) + 0.50(13%) = 10%. However, it would be a mistake to use this 10% WACC for either division. To see this point, assume that Division L is considering a relatively low-risk project with an expected return of 9%, while Division H is considering a higher-risk project with an expected return of 11%. As shown in Figure 10-2, Division L’s project should be accepted because its return is above its risk-based cost of capital, whereas Division H’s project should be rejected. If the 10% corporate WACC was used by each division, the decision would be reversed: Division H would incor- rectly accept its project, and Division L would incorrectly reject its project. In gen- eral, failing to adjust for differences in risk would lead the fi rm to accept too many risky projects and reject too many safe ones. Over time, the fi rm would become riskier, its WACC would increase, and its shareholder value would suffer. We will return to these issues in Chapter 12, when we consider different approaches for measuring project risk.

Risk and the Cost of CapitalFIGURE 10-1

Risk L Risk A Risk H Risk

8.0

10.0

12.0

Firm L’s WACC

Firm A’s WACC

Firm H’s WACC

WACC

Acceptance Region

Rejection Region

Rate of Return (%)

SEL F TEST Why is the cost of capital sometimes referred to as a “hurdle rate”?

How should fi rms evaluate projects with diff erent risks?

Should all divisions within the same fi rm use the fi rm’s composite WACC for evaluating all capital budgeting projects? Explain.

325Chapter 10 The Cost of Capital

Risk L Risk HRisk A Risk

7.0

9.0

10.0

13.0 WACC

Rate of Return (%)

11.0

Project L

Division L’s WACC

Composite WACC

Division H’s WACC

Project H

Divisional Cost of CapitalFIGURE 10-2

10-10 SOME OTHER PROBLEMS WITH COST OF CAPITAL ESTIMATES

A number of issues related to the cost of capital have not been mentioned or were glossed over in this chapter. These topics are covered in advanced fi nance courses, but they deserve mention now to alert you to potential dangers and to provide a preview of some matters covered in advanced courses. 1. Depreciation-generated funds.21 The largest single source of capital for many

fi rms is depreciation, yet we have not discussed how the cost of this capital is determined. In brief, depreciation cash fl ows can either be reinvested or returned to investors (stockholders and creditors). The cost of depreciation- generated funds is thus an opportunity cost; and it is approximately equal to the WACC from retained earnings, preferred stock, and debt. Therefore, we can ignore it in our estimate of the WACC.

2. Privately owned fi rms. Our discussion of the cost of equity focused on pub- licly owned corporations, and we have concentrated on the rate of return required by public stockholders. However, there is a serious question about how to measure the cost of equity for a fi rm whose stock is not traded. Tax issues are also especially important in these cases. As a general rule, the same principles of cost of capital estimation apply to both privately held

21 See Table 3-3, the statement of cash fl ows, for an illustration of the cash fl ows provided from depreciation. Refer to advanced fi nance textbooks for a discussion on the treatment of depreciation-generated funds.

326 Part 4 Investing in Long-Term Assets: Capital Budgeting

and publicly owned fi rms, but the problems of obtaining input data are somewhat different.

3. Measurement problems. We cannot overemphasize the practical diffi culties encountered when estimating the cost of equity. It is very diffi cult to obtain good input data for the CAPM, for g in the formula r̂s ! D1/P0 # g, and for the risk premium in the formula rs ! Bond yield # Risk premium. As a result, we can never be sure of the accuracy of our estimated cost of capital.

4. Costs of capital for projects of differing risk. We touched briefl y on the fact that different projects can differ in risk and, thus, in their required rates of return. However, it is diffi cult to measure a project’s risk (hence, to adjust the cost of capital for capital budgeting projects with different risks).

5. Capital structure weights. In this chapter, we took as given the target capital structure and used it to calculate the WACC. As we shall see in the capital structure chapter, establishing the target capital structure is a major task in itself.

Although this list of problems appears formidable, the state of the art in cost of capital estimation is not in bad shape. The procedures outlined in this chapter can be used to obtain costs of capital estimates that are suffi ciently accurate for practi- cal purposes, so the problems listed previously merely indicate the desirability of refi nements. The refi nements are not unimportant, but the problems noted do not invalidate the usefulness of the procedures outlined in this chapter.

SEL F TEST Identify some problem areas in cost of capital analysis. Do these problems

invalidate the cost of capital procedures discussed in this chapter? Explain.

We began this chapter by discussing the concept of the weighted average cost of capital. We then discussed the four capital components (debt, preferred stock, re- tained earnings, and new common equity) and the procedures used to estimate each component’s cost. Next, we calculated the WACC, which is a key element in capital budgeting. A key issue here is the weights that should be used to fi nd the WACC. In general, companies consider a number of factors, then establish a target capital structure that is used to calculate the WACC. We discuss the target capital structure and its aff ect on the WACC in more detail in the capital structure chapter.

The cost of capital is a key element in capital budgeting decisions, our focus in the following chapters. Indeed, capital budgeting as it should be done is impossible without a good estimate of the cost of capital; so you need to have a good under- standing of cost of capital concepts before you move on.

T YING I T ALL TO GETHER

327Chapter 10 The Cost of Capital

KEY TERMS Define the following terms: a. Capital components b. Before-tax cost of debt, rd; after-tax cost of debt, rd(1 " T) c. Cost of preferred stock, rp d. Cost of retained earnings, rs; cost of new common stock, re e. Weighted average cost of capital, WACC f. Flotation cost, F; flotation cost adjustment; retained earnings breakpoint

WACC Lancaster Engineering Inc. (LEI) has the following capital structure, which it considers to be optimal:

Debt 25% Preferred stock 15 Common equity 60

100%

LEI’s expected net income this year is $34,285.72; its established dividend payout ratio is 30%; its federal-plus-state tax rate is 40%; and investors expect future earnings and divi- dends to grow at a constant rate of 9%. LEI paid a dividend of $3.60 per share last year, and its stock currently sells for $54.00 per share. LEI can obtain new capital in the following ways: • Preferred: New preferred stock with a dividend of $11.00 can be sold to the public at

a price of $95.00 per share. • Debt: Debt can be sold at an interest rate of 12%. a. Determine the cost of each capital component. b. Calculate the WACC. c. LEI has the following investment opportunities that are average-risk projects:

Project Cost at t ! 0 Rate of Return

A $10,000 17.4%

B 20,000 16.0

C 10,000 14.2

D 20,000 13.7

E 10,000 12.0

Which projects should LEI accept? Why?

How would each of the following scenarios affect a firm’s cost of debt, rd(1 " T); its cost of equity, rs; and its WACC? Indicate with a plus (#), a minus ("), or a zero (0) if the factor would raise, would lower, or would have an indeterminate effect on the item in question. Assume for each answer that other things are held constant even though in some instances this would probably not be true. Be prepared to justify your answer but recognize that several of the parts have no single correct answer. These questions are designed to stimu- late thought and discussion.

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

QUESTIONS QUESTIONS

10-110-1

328 Part 4 Investing in Long-Term Assets: Capital Budgeting

EFFECT ON

rd(1 # T) rs WACC

a. The corporate tax rate is lowered.

b. The Federal Reserve tightens credit.

c. The firm uses more debt; that is, it increases its debt/assets ratio.

d. The dividend payout ratio is increased.

e. The firm doubles the amount of capital it raises during the year.

f. The firm expands into a risky new area.

g. The firm merges with another firm whose earnings are countercyclical both to those of the first firm and to the stock market.

h. The stock market falls drastically, and the firm’s stock price falls along with the rest of the stocks.

i. Investors become more risk-averse.

j. The firm is an electric utility with a large investment in nuclear plants. Several states are considering a ban on nuclear power generation.

Assume that the risk-free rate increases. What impact would this have on the cost of debt? What impact would it have on the cost of equity?

How should the capital structure weights used to calculate the WACC be determined?

Suppose a firm estimates its WACC to be 10%. Should the WACC be used to evaluate all of its potential projects, even if they vary in risk? If not, what might be “reasonable” costs of capital for average-, high-, and low-risk projects?

The WACC is a weighted average of the costs of debt, preferred stock, and common equity. Would the WACC be different if the equity for the coming year came solely in the form of retained earnings versus some equity from the sale of new common stock? Would the calculated WACC depend in any way on the size of the capital budget? How might dividend policy affect the WACC?

AFTER-TAX COST OF DEBT The Heuser Company’s currently outstanding bonds have a 10% coupon and a 12% yield to maturity. Heuser believes it could issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 35%, what is Heuser’s after-tax cost of debt?

COST OF PREFERRED STOCK Tunney Industries can issue perpetual preferred stock at a price of $47.50 a share. The stock would pay a constant annual dividend of $3.80 a share. What is the company’s cost of preferred stock, rp?

COST OF COMMON EQUITY Percy Motors has a target capital structure of 40% debt and 60% common equity, with no preferred stock. The yield to maturity on the company’s outstanding bonds is 9%, and its tax rate is 40%. Percy’s CFO estimates that the company’s WACC is 9.96%. What is Percy’s cost of common equity?

10-210-2

10-310-3 10-410-4

10-510-5

PROBLEMSPROBLEMS

10-110-1Easy Problems 1–5 Easy Problems 1–5

10-210-2

10-310-3

329Chapter 10 The Cost of Capital

COST OF EQUITY WITH AND WITHOUT FLOTATION Javits & Sons’ common stock currently trades at $30.00 a share. It is expected to pay an annual dividend of $3.00 a share at the end of the year (D1 ! $3.00), and the constant growth rate is 5% a year. a. What is the company’s cost of common equity if all of its equity comes from retained

earnings? b. If the company issued new stock, it would incur a 10% flotation cost. What would be

the cost of equity from new stock?

PROJECT SELECTION Midwest Water Works estimates that its WACC is 10.5%. The company is considering the following capital budgeting projects:

Project Size Rate of Return A $1 million 12.0% B 2 million 11.5 C 2 million 11.2 D 2 million 11.0 E 1 million 10.7 F 1 million 10.3 G 1 million 10.2

Assume that each of these projects is just as risky as the firm’s existing assets and that the firm may accept all the projects or only some of them. Which set of projects should be accepted? Explain.

COST OF COMMON EQUITY The future earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow 7% per year. Carpetto’s common stock currently sells for $23.00 per share; its last dividend was $2.00; and it will pay a $2.14 dividend at the end of the current year. a. Using the DCF approach, what is its cost of common equity? b. If the firm’s beta is 1.6, the risk-free rate is 9%, and the average return on the market

is 13%, what will be the firm’s cost of common equity using the CAPM approach? c. If the firm’s bonds earn a return of 12%, based on the bond-yield-plus-risk-premium

approach, what will be rs? Use the midpoint of the risk premium range discussed in Section 10-5 in your calculations.

d. If you have equal confidence in the inputs used for the three approaches, what is your estimate of Carpetto’s cost of common equity?

COST OF COMMON EQUITY WITH AND WITHOUT FLOTATION The Evanec Company’s next expected dividend, D1, is $3.18; its growth rate is 6%; and its common stock now sells for $36.00. New stock (external equity) can be sold to net $32.40 per share. a. What is Evanec’s cost of retained earnings, rs? b. What is Evanec’s percentage flotation cost, F? c. What is Evanec’s cost of new common stock, re?

COST OF COMMON EQUITY AND WACC Patton Paints Corporation has a target capital structure of 40% debt and 60% common equity, with no preferred stock. Its before-tax cost of debt is 12%, and its marginal tax rate is 40%. The current stock price is P0 ! $22.50. The last dividend was D0 ! $2.00, and it is expected to grow at a 7% constant rate. What is its cost of common equity and its WACC?

WACC The Patrick Company’s cost of common equity is 16%, its before-tax cost of debt is 13%, and its marginal tax rate is 40%. The stock sells at book value. Using the following balance sheet, calculate Patrick’s WACC.

Assets Liabilities and Equity Cash $ 120 Accounts receivable 240 Inventories 360 Long-term debt $1,152 Plant and equipment, net 2,160 Common equity 1,728 Total assets $2,880 Total liabilities and equity $2,880

10-410-4

10-510-5

10-610-6Intermediate Problems 6–13

Intermediate Problems 6–13

10-710-7

10-810-8

10-910-9

330 Part 4 Investing in Long-Term Assets: Capital Budgeting

WACC Klose Outfitters Inc. believes that its optimal capital structure consists of 60% common equity and 40% debt, and its tax rate is 40%. Klose must raise additional capital to fund its upcoming expansion. The firm will have $2 million of new retained earnings with a cost of rs ! 12%. New common stock in an amount up to $6 million would have a cost of re ! 15%. Furthermore, Klose can raise up to $3 million of debt at an interest rate of rd ! 10% and an additional $4 million of debt at rd ! 12%. The CFO estimates that a proposed expansion would require an investment of $5.9 million. What is the WACC for the last dollar raised to complete the expansion?

WACC AND PERCENTAGE OF DEBT FINANCING Hook Industries’ capital structure consists solely of debt and common equity. It can issue debt at rd ! 11%, and its common stock currently pays a $2.00 dividend per share (D0 ! $2.00). The stock’s price is currently $24.75, its dividend is expected to grow at a constant rate of 7% per year, its tax rate is 35%, and its WACC is 13.95%. What percentage of the company’s capital structure consists of debt?

WACC Midwest Electric Company (MEC) uses only debt and common equity. It can borrow unlimited amounts at an interest rate of rd ! 10% as long as it finances at its target capital structure, which calls for 45% debt and 55% common equity. Its last dividend was $2, its expected constant growth rate is 4%, and its common stock sells for $20. MEC’s tax rate is 40%. Two projects are available: Project A has a rate of return of 13%, while Project B’s return is 10%. These two projects are equally risky and about as risky as the firm’s existing assets. a. What is its cost of common equity? b. What is the WACC? c. Which projects should Midwest accept?

COST OF COMMON EQUITY WITH FLOTATION Ballack Co.’s common stock currently sells for $46.75 per share. The growth rate is a constant 12%, and the company has an expected dividend yield of 5%. The expected long-run dividend payout ratio is 25%, and the expected return on equity (ROE) is 16%. New stock can be sold to the public at the current price, but a flotation cost of 5% would be incurred. What would be the cost of new equity?

COST OF PREFERRED STOCK INCLUDING FLOTATION Trivoli Industries plans to issue perpetual preferred stock with an $11.00 dividend. The stock is currently selling for $97.00; but flotation costs will be 5% of the market price, so the net price will be $92.15 per share. What is the cost of the preferred stock, including flotation?

WACC AND COST OF COMMON EQUITY Kahn Inc. has a target capital structure of 60% common equity and 40% debt to fund its $10 billion in operating assets. Furthermore, Kahn Inc. has a WACC of 13%, a before-tax cost of debt of 10%, and a tax rate of 40%. The company’s retained earnings are adequate to provide the common equity portion of its capital budget. Its expected dividend next year (D1) is $3, and the current stock price is $35. a. What is the company’s expected growth rate? b. If the firm’s net income is expected to be $1.1 billion, what portion of its net

income is the firm expected to pay out as dividends? (Hint: Refer to Equation 9-4 in Chapter 9.)

COST OF COMMON EQUITY The Bouchard Company’s EPS was $6.50 in 2008, up from $4.42 in 2003. The company pays out 40% of its earnings as dividends, and its common stock sells for $36.00. a. Calculate the past growth rate in earnings. (Hint: This is a 5-year growth period.) b. The last dividend was D0 ! 0.4($6.50) ! $2.60. Calculate the next expected dividend,

D1, assuming that the past growth rate continues. c. What is Bouchard’s cost of retained earnings, rs?

CALCULATION OF g AND EPS Sidman Products’ common stock currently sells for $60.00 a share. The firm is expected to earn $5.40 per share this year and to pay a year-end dividend of $3.60, and it finances only with common equity. a. If investors require a 9% return, what is the expected growth rate? b. If Sidman reinvests retained earnings in projects whose average return is equal to the

stock’s expected rate of return, what will be next years’ EPS? (Hint: Refer to Equation 9-4 in Chapter 9.)

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331Chapter 10 The Cost of Capital

WACC AND OPTIMAL CAPITAL BUDGET Adams Corporation is considering four average-risk projects with the following costs and rates of return:

Project Cost Expected Rate of Return 1 $2,000 16.00% 2 3,000 15.00 3 5,000 13.75 4 2,000 12.50

The company estimates that it can issue debt at a rate of rd = 10%, and its tax rate is 30%. It can issue preferred stock that pays a constant dividend of $5.00 per year at $49.00 per share. Also, its common stock currently sells for $36.00 per share; the next expected dividend, D1, is $3.50; and the dividend is expected to grow at a constant rate of 6% per year. The target capital structure consists of 75% common stock, 15% debt, and 10% preferred stock. a. What is the cost of each of the capital components? b. What is Adams’ WACC? c. Only projects with expected returns that exceed WACC will be accepted. Which

projects should Adams accept?

ADJUSTING COST OF CAPITAL FOR RISK Ziege Systems is considering the following independent projects for the coming year:

Project Required

Investment Rate of Return Risk

A $4 million 14.0% High B 5 million 11.5 High C 3 million 9.5 Low D 2 million 9.0 Average E 6 million 12.5 High F 5 million 12.5 Average G 6 million 7.0 Low H 3 million 11.5 Low

Ziege’s WACC is 10%, but it adjusts for risk by adding 2% to the WACC for high-risk projects and subtracting 2% for low-risk projects. a. Which projects should Ziege accept if it faces no capital constraints? b. If Ziege can only invest a total of $13 million, which projects should it accept and

what would be the dollar size of its capital budget? c. Suppose Ziege can raise additional funds beyond the $13 million, but each new

increment (or partial increment) of $5 million of new capital will cause the WACC to increase by 1%. Assuming that Ziege uses the same method of risk adjustment, which projects should it now accept and what would be the dollar size of its capital budget?

WACC The following table gives Foust Company’s earnings per share for the last 10 years. The common stock, 7.8 million shares outstanding, is now (1/1/09) selling for $65.00 per share. The expected dividend at the end of the current year (12/31/09) is 55% of the 2008 EPS. Because investors expect past trends to continue, g may be based on the historical earnings growth rate. (Note that 9 years of growth are reflected in the 10 years of data.)

Year EPS Year EPS 1999 $3.90 2004 $5.73 2000 4.21 2005 6.19 2001 4.55 2006 6.68 2002 4.91 2007 7.22 2003 5.31 2008 7.80

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332 Part 4 Investing in Long-Term Assets: Capital Budgeting

The current interest rate on new debt is 9%; Foust’s marginal tax rate is 40%; and its capi- tal structure, considered to be optimal, is as follows:

Debt $104,000,000 Common equity 156,000,000 Total liabilities and equity $260,000,000

a. Calculate Foust’s after-tax cost of debt and common equity. Calculate the cost of equity as rs ! D1/P0 # g.

b. Find Foust’s WACC.

CALCULATING THE WACC Here is the condensed 2008 balance sheet for Skye Computer Company (in thousands of dollars):

2008 Current assets $2,000 Net fixed assets 3,000 Total assets $5,000

Current liabilities $ 900 Long-term debt 1,200 Preferred stock 250 Common stock 1,300 Retained earnings 1,350 Total common equity $2,650 Total liabilities and equity $5,000

Skye’s earnings per share last year were $3.20, the common stock sells for $55.00, last year’s dividend was $2.10, and a flotation cost of 10% would be required to sell new com- mon stock. Security analysts are projecting that the common dividend will grow at a rate of 9% per year. Skye’s preferred stock pays a dividend of $3.30 per share, and new pre- ferred could be sold at a price to net the company $30.00 per share. The firm can issue long-term debt at an interest rate (or before-tax cost) of 10%, and its marginal tax rate is 35%. The market risk premium is 5%, the risk-free rate is 6%, and Skye’s beta is 1.516. In its cost of capital calculations, the company considers only long-term capital; hence, it dis- regards current liabilities. a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost

of preferred stock, the cost of equity from retained earnings, and the cost of newly is- sued common stock. Use the DCF method to find the cost of common equity.

b. Now calculate the cost of common equity from retained earnings using the CAPM method.

c. What is the cost of new common stock based on the CAPM? (Hint: Find the difference between re and rs as determined by the DCF method and add that differential to the CAPM value for rs.)

d. If Skye continues to use the same capital structure, what is the firm’s WACC assum- ing that (1) it uses only retained earnings for equity? (2) If it expands so rapidly that it must issue new common stock?

COMPREHENSIVE/SPREADSHEET PROBLEMCOMPREHENSIVE/SPREADSHEET PROBLEM

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333Chapter 10 The Cost of Capital

COST OF CAPITAL Coleman Technologies is considering a major expansion program that has been proposed by the company’s information technology group. Before proceeding with the expansion, the company must estimate its cost of capital. Assume that you are an assistant to Jerry Lehman, the financial vice president. Your first task is to estimate Coleman’s cost of capital. Lehman has provided you with the following data, which he believes may be relevant to your task.

(1) The firm’s tax rate is 40%. (2) The current price of Coleman’s 12% coupon, semiannual payment, noncallable bonds with 15 years remain-

ing to maturity is $1,153.72. Coleman does not use short-term interest-bearing debt on a permanent basis. New bonds would be privately placed with no flotation cost.

(3) The current price of the firm’s 10%, $100.00 par value, quarterly dividend, perpetual preferred stock is $111.10.

(4) Coleman’s common stock is currently selling for $50.00 per share. Its last dividend (D0) was $4.19, and divi- dends are expected to grow at a constant rate of 5% in the foreseeable future. Coleman’s beta is 1.2, the yield on T-bonds is 7%, and the market risk premium is estimated to be 6%. For the bond-yield-plus-risk-premium approach, the firm uses a risk premium of 4%.

(5) Coleman’s target capital structure is 30% debt, 10% preferred stock, and 60% common equity.

To structure the task somewhat, Lehman has asked you to answer the following questions. a. (1) What sources of capital should be included when you estimate Coleman’s WACC? (2) Should the component costs be figured on a before-tax or an after-tax basis? (3) Should the costs be historical (embedded) costs or new (marginal) costs? b. What is the market interest rate on Coleman’s debt and its component cost of debt? c. (1) What is the firm’s cost of preferred stock? (2) Coleman’s preferred stock is riskier to investors than its debt, yet the preferred’s yield to investors is

lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? (Hint: Think about taxes.)

d. (1) Why is there a cost associated with retained earnings? (2) What is Coleman’s estimated cost of common equity using the CAPM approach? e. What is the estimated cost of common equity using the DCF approach? f. What is the bond-yield-plus-risk-premium estimate for Coleman’s cost of common equity? g. What is your final estimate for rs? h. Explain in words why new common stock has a higher cost than retained earnings. i. (1) What are two approaches that can be used to adjust for flotation costs? (2) Coleman estimates that if it issues new common stock, the flotation cost will be 15%. Coleman incorpo-

rates the flotation costs into the DCF approach. What is the estimated cost of newly issued common stock, considering the flotation cost?

j. What is Coleman’s overall, or weighted average, cost of capital (WACC)? Ignore flotation costs. k. What factors influence Coleman’s composite WACC? l. Should the company use the composite WACC as the hurdle rate for each of its projects? Explain.

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334 Part 4 Investing in Long-Term Assets: Capital Budgeting

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions.

Calculating 3M’s Cost of Capital In this chapter, we described how to estimate a company’s WACC, which is the weighted average of its costs of debt, preferred stock, and common equity. Most of the data we need to do this can be found in Thomson ONE. Here we walk through the steps used to calculate Minnesota Mining & Manufacturing’s (MMM) WACC.

Discussion Questions 1. As a first step, we need to estimate what percentage of MMM’s capital comes from long-term debt, preferred

stock, and common equity. If we click on “FINANCIALS,” we can see from the balance sheet the amount of MMM’s long-term debt and common equity. (As of year-end 2007, MMM had no preferred stock.) Alterna- tively, under “Financial Ratios,” you can click on “WORLDSCOPE” and “ANNUAL BALANCE SHEET RA- TIOS.” Here you will find a recent measure of long-term debt as a percentage of total capital. Recall that the weights used in the WACC are based on the company’s target capital structure. If we assume that the company wants to maintain the same mix of capital that it currently has on its balance sheet, what weights should you use to estimate the WACC for MMM? (In the capital structure and leverage chapter, we might arrive at different estimates for these weights if we assume that MMM bases its target capital structure on the market values of debt and equity rather than on the book values.)

2. Once again we can use the CAPM to estimate MMM’s cost of equity. Thomson ONE provides various estimates of beta—select the measure that you believe is best and combine this with your estimates of the risk-free rate and the market risk premium to obtain an estimate of its cost of equity. (See the Thomson ONE exercise in Chapter 8 for more details.) What is your estimate for MMM’s cost of equity? Why might it not make much sense to use the DCF approach to estimate MMM’s cost of equity?

3. Next, we need to calculate MMM’s cost of debt. Unfortunately, Thomson ONE doesn’t provide a direct measure of the cost of debt. However, we can use different approaches to estimate it. One approach is to take the compa- ny’s long-term interest expense and divide it by the amount of long-term debt. This approach only works if the historical cost of debt equals the yield to maturity in today’s market (that is, if MMM’s outstanding bonds are trading at close to par). This approach may produce misleading estimates in years in which MMM issues a sig- nificant amount of new debt. For example, if a company issues a great deal of debt at the end of the year, the full amount of debt will appear on the year-end balance sheet, yet we still may not see a sharp increase in interest expense on the annual income statement because the debt was outstanding for only a small portion of the entire year. When this situation occurs, the estimated cost of debt will likely understate the true cost of debt. Another approach is to try to find this number in the notes to the company’s annual report by accessing the company’s home page and its Investor Relations section. Alternatively, you can go to other external sources, such as www. bondsonline.com, for corporate bond spreads, which can be used to find estimates of the cost of debt. Remem- ber that you need the after-tax cost of debt to calculate a firm’s WACC, so you will need MMM’s tax rate (which has averaged about 32% in recent years). What is your estimate of MMM’s after-tax cost of debt?

4. Putting all this information together, what is your estimate of MMM’s WACC? How confident are you in this estimate? Explain your answer.

www.bondsonline.com

C o m p e t i t i o n i n t h e A i r c r a f t I n d u s t r y : A i r b u s v s. B o e i n g

11 CHAPTER

335

In early 2008, Boeing was involved in a titanic struggle with European consortium Airbus SAS for dominance of the commercial aircraft indus- try.1 Several years ago Airbus committed to spend $16 billion to develop the A380, the larg- est plane ever built. Boeing countered by announcing that it would spend $6 billion on a superefficient new plane, the 7E7 Dreamliner. Airbus then announced plans to spend another $6 billion on the A350, a competitor to the 7E7. Many detailed calculations went into these multibillion-dollar investment decisions— development costs were estimated, the cost of each plane was forecasted, a sales price per plane was established, and the number of planes that would be sold through 2025 was predicted.

Both companies projected negative cash flows for 5 or 6 years, then positive cash flows

for the following 20 years. Given their fore- casted cash flows, both managements decided that taking on the projects would increase each company’s intrinsic value. Because the planes will compete with one another, either Boeing’s or Airbus’s forecast is probably incor- rect. One will probably be a winner and the other a loser, and one set of stockholders will likely be happy and the other unhappy. As of the winter of 2008, both companies received orders for their planes, but both have encoun- tered problems that have delayed the actual introduction of the aircraft. The winner is still undecided.

Projects such as the A350, A380, and 7E7 receive a great deal of attention; but Boeing, Airbus, and other companies make a great many routine investment decisions every year, ranging from buying new trucks or machinery

1 Airbus SAS is owned by European Aeronautics Defense & Space Company (EADS), which is owned by the French government and several large European companies. Airbus was formed because the Europeans wanted to create an organization large enough to compete with Boeing.

The Basics of Capital Budgeting

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336 Part 4 Investing in Long-Term Assets: Capital Budgeting

In the last chapter, we discussed the cost of capital. Now we turn to investment deci- sions involving fi xed assets, or capital budgeting. Here capital refers to long-term assets used in production, while a budget is a plan that outlines projected expendi- tures during some future period. Thus, the capital budget is a summary of planned investments in long-term assets, and capital budgeting is the whole process of ana- lyzing projects and deciding which ones to include in the capital budget. Boeing, Airbus, and other companies use the techniques in this chapter when deciding to accept or reject proposed capital expenditures.

When you fi nish this chapter, you should be able to:

• Discuss capital budgeting. • Calculate and use the major capital budgeting decision criteria, which are NPV,

IRR, MIRR, and payback. • Explain why NPV is the best criterion and how it overcomes problems inherent in

the other methods.

With an understanding of the theory of capital budgeting developed in this chapter, which uses simplifi ed examples, you will be ready for the next chapter, where we dis- cuss how cash fl ows are estimated, how risk is measured, and how capital budgeting decisions are made.

11-1 AN OVERVIEW OF CAPITAL BUDGETING The same concepts used in security valuation are also used in capital budgeting, but there are two major differences. First, stocks and bonds exist in the security markets, and investors select from the available set; fi rms, however, create capital budgeting projects. Second, for most securities, investors have no infl uence on the cash fl ows produced by their investments, whereas corporations have a major infl uence on projects’ results. Still, in both security valuation and capital budget- ing, we forecast a set of cash fl ows, fi nd the present value of those fl ows, and make the investment only if the PV of the infl ows exceeds the investment’s cost.

A fi rm’s growth, and even its ability to remain competitive and to survive, de- pends on a constant fl ow of ideas relating to new products, to improvements in existing products, and to ways of operating more effi ciently. Accordingly, well- managed fi rms go to great lengths to develop good capital budgeting proposals. For example, the executive vice president of one successful corporation said that his company takes the following steps to generate projects:

Our R&D department constantly searches for new products and ways to improve existing products. In addition, our Executive Committee, which consists of senior

Capital Budgeting The process of planning expenditures on assets with cash flows that are expected to extend beyond one year.

to purchasing computers and software to optimize inventory management. The techniques described in this

chapter are required to analyze projects of all types and sizes.

Sources: John Newhouse, Boeing Versus Airbus: The Inside Story of the Greatest International Competition in Business (New York: Random House, 2007).

PU T TING THINGS IN PER SPECTIVE

337Chapter 11 The Basics of Capital Budgeting

executives in marketing, production, and fi nance, identifi es the products and mar- kets in which our company should compete, and the Committee sets long-run targets for each division. These targets, which are spelled out in the corporation’s strategic business plan, provide a general guide to the operating executives who must meet them. The operating executives then seek new products, set expan- sion plans for existing products, and look for ways to reduce production and dis- tribution costs. Since bonuses and promotions are based on each unit’s ability to meet or exceed its targets, these economic incentives encourage our operating ex- ecutives to seek out profi table investment opportunities.

While our senior executives are judged and rewarded on the basis of how well their units perform, people further down the line are given bonuses and stock options for suggestions that lead to profi table investments. Additionally, a per- centage of our corporate profi t is set aside for distribution to nonexecutive employees, and we have an Employees’ Stock Ownership Plan (ESOP) to provide further incentives. Our objective is to encourage employees at all levels to keep an eye out for good ideas, especially those that lead to capital investments.

Analyzing capital expenditure proposals is not costless—benefi ts can be gained, but analysis does have a cost. For certain types of projects, an extremely detailed analysis may be warranted, while for other projects, simpler procedures are adequate. Accordingly, fi rms generally categorize projects and then analyze them in each category somewhat differently: 1. Replacement: needed to continue current operations. One category consists of

expenditures to replace worn-out or damaged equipment required in the production of profi table products. The only questions here are should the operation be continued and if so, should the fi rm continue to use the same production processes? If the answers are yes, the project will be approved without going through an elaborate decision process.

2. Replacement: cost reduction. This category includes expenditures to replace ser- viceable but obsolete equipment and thereby to lower costs. These decisions are discretionary, and a fairly detailed analysis is generally required.

3. Expansion of existing products or markets. These are expenditures to increase out- put of existing products or to expand retail outlets or distribution facilities in markets now being served. Expansion decisions are more complex because they require an explicit forecast of growth in demand, so a more detailed analy- sis is required. The go/no-go decision is generally made at a higher level within the fi rm.

4. Expansion into new products or markets. These investments relate to new prod- ucts or geographic areas, and they involve strategic decisions that could change the fundamental nature of the business. Invariably, a detailed analysis is required, and the fi nal decision is generally made at the top level of management.

5. Safety and/or environmental projects. Expenditures necessary to comply with government orders, labor agreements, or insurance policy terms fall into this category. How these projects are handled depends on their size, with small ones being treated much like the Category 1 projects.

6. Other projects. This catch-all includes items such as offi ce buildings, parking lots, and executive aircraft. How they are handled varies among companies.

7. Mergers. In a merger, one fi rm buys another one. Buying a whole fi rm is differ- ent from buying an asset such as a machine or investing in a new airplane, but the same principles are involved. The concepts of capital budgeting underlie merger analysis.

In general, relatively simple calculations, and only a few supporting documents, are required for replacement decisions, especially maintenance investments in

Strategic Business Plan A long-run plan that outlines in broad terms the firm’s basic strategy for the next 5 to 10 years.

338 Part 4 Investing in Long-Term Assets: Capital Budgeting

profi table plants. More detailed analyses are required for cost-reduction projects, for expansion of existing product lines, and especially for investments in new products or areas. Also, within each category, projects are grouped by their dollar costs: Larger investments require increasingly detailed analysis and approval at higher levels. Thus, a plant manager might be authorized to approve maintenance expenditures up to $10,000 using a relatively unsophisticated analysis, but the full board of directors might have to approve decisions that involve amounts greater than $1 million or expansions into new products or markets.

If a fi rm has capable and imaginative executives and employees and if its in- centive system is working properly, many ideas for capital investment will be ad- vanced. Some ideas will be good ones, but others will not. Therefore, procedures must be established for screening projects. Companies use, and we discuss, the following criteria for deciding to accept or reject projects:2

1. Net Present Value (NPV) 2. Internal Rate of Return (IRR) 3. Modifi ed Internal Rate of Return (MIRR) 4. Regular Payback 5. Discounted Payback

The NPV is the best method, primarily because it addresses directly the central goal of fi nancial management—maximizing shareholder wealth. However, all of the methods provide useful information, and all are used in practice at least to some extent.

11-2 NET PRESENT VALUE (NPV) The net present value (NPV) tells us how much a project contributes to share- holder wealth—the larger the NPV, the more value the project adds; and added value means a higher stock price.3 Thus, NPV is the best selection criterion. We use the data for Projects S and L shown in Table 11-1 to illustrate the calculation. The S stands for Short; the L, for Long. Project S is a short-term project in the sense that its cash infl ows come in relatively soon, while L has more total cash infl ows but they come in later in its life. The projects are equally risky, and they both have a 10%

Net Present Value (NPV) A method of ranking investment proposals using the NPV, which is equal to the present value of future net cash flows, discounted at the cost of capital.

SEL F TEST How is capital budgeting similar to security valuation? How is it diff erent?

What are some ways that fi rms generate ideas for capital projects?

Identify the major project classifi cation categories and explain how and why they are used.

What is the single best capital budgeting decision criterion?

2 Two other rarely used criteria, the Profi tability Index and the Accounting Rate of Return, are covered in Chapter 12 and its Web Extension of Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 9th ed. (Mason, OH: Thomson/South-Western, 2007). 3 We could divide the NPV by the number of shares outstanding to estimate a project’s eff ect on the stock price. However, given the lag between project acceptance and visible eff ects on earnings, this is rarely done for routine projects. However, for major projects, this procedure is useful.

339Chapter 11 The Basics of Capital Budgeting

cost of capital. Furthermore, the cash fl ows have been adjusted to refl ect deprecia- tion, taxes, and salvage values.4 The investment outlays shown as CF0 include fi xed assets and any necessary investments in working capital, and cash fl ows come in at the end of the year. Finally, we show the table with an “Excel look,” which simply means adding row and column headings to a “regular” table. All of the calculations can be done easily with a fi nancial calculator; but since some stu- dents may want to work with Excel, we show how problems would be set up in Excel. Do keep in mind, though, that Excel is not necessary.

We fi nd the NPVs as follows: 1. The present value of each cash fl ow is calculated, discounted at the project’s

risk-adjusted cost of capital, r ! 10% in our example. 2. The sum of the discounted cash fl ows is defi ned as the project’s NPV.

The equation for the NPV, set up with input data for Project S, is as follows:

NPV ! CF0 " CF1 _______ (1 " r)1 "

CF2 _______ (1 " r)2 " . . . "

CFN _______ (1 " r)N

! ∑ t!0

CFt ______ (1 " r)t 11-1

NPVS ! #$1,000 " $500 ______ (1.10)1 "

$400 ______ (1.10)2 " $300 ______ (1.10)3 "

$100 ______ (1.10)4

Here CFt is the expected net cash fl ow at Time t, r is the project’s risk-adjusted cost of capital (or WACC), and N is its life. Projects generally require an initial investment—for example, developing the product, buying the equipment needed to make it, building a factory, and stocking inventory. The initial investment is a negative cash fl ow. For Projects S and L, only CF0 is negative; but for a large project such as Boeing’s 7E7, outfl ows occur for several years before cash infl ows begin.

Figure 11-1 shows the cash fl ow time line for Project S; the PV of each cash fl ow; and the sum of the PVs, which is by defi nition the NPV.

The cost, at t ! 0, is "$1,000. The fi rst positive cash fl ow is $500; and with a regular calculator, you could fi nd its PV as $500/(1.10)1 ! $454.55. You could also fi nd the PV of the $500 with a fi nancial calculator. Other PVs could be found simi- larly, and the end result would be the numbers in the left column of the diagram. When we sum those numbers, the result is $78.82, which is NPVS. Note that the initial cost, the "$1,000, is not discounted because it occurs at Time 0. The NPV for Project L, $100.40, could be found similarly.

1 2 3 4 5 6 7 8

WACC for both projects: 10%

Initial Cost: Total Inflows

After-Tax, End of Year Net Cash Inflows, CFt: Years: Project S: Project L:

0 -$1,000 -$1,000

1 $500 $100

2 $400 $300

3 $300 $400

4 $100 $675

$1,300 $1,475

A B C D E F G

Data on Projects S and LT a b l e 1 1 - 1

4 The most diffi cult aspect of capital budgeting is estimating the relevant cash fl ows. For simplicity, the net cash fl ows are treated as a given in this chapter, which allows us to focus on the rules for making capital budgeting decisions. However, in Chapter 12, we discuss cash fl ow estimation in detail. Also note that net working capital is defi ned as the increase in current assets required for a project minus the associated increases in payables and accruals. Thus, in capital budgeting, investment in working capital means the net amount that must be fi nanced by investors.

340 Part 4 Investing in Long-Term Assets: Capital Budgeting

The step-by-step procedure shown in Figure 11-1 is useful for illustrating how the NPV is calculated; but in practice (and on exams), it is far more effi cient to use a fi nancial calculator or Excel. Different calculators are set up somewhat differently; but as we discussed in Chapter 5, they all have a “cash fl ow register” that can be used to evaluate uneven cash fl ows such as those for Projects S and L. Equation 11-1 is programmed into these calculators, and all you must do is enter the cash fl ows (with the correct signs) along with r ! I/YR ! 10. Once the data have been entered and you press the NPV key, the answer, 78.82, appears on the screen.5

If you are familiar with Excel, you can use it to fi nd the NPVs for S and L:

NPVS ! $78.82

NPVL ! $100.40

The model used to obtain these values is provided in the chapter’s Excel model. If you want to know something about Excel, you should look at the model, as this is the way most people in practice fi nd NPVs.

Before using these NPVs in the decision process, we need to know whether Projects S and L are independent or mutually exclusive. Independent projects are projects whose cash fl ows are not affected by one another. If Wal-Mart was considering a new store in Boise and another in Atlanta, the projects would be independent; and if both had positive NPVs, Wal-Mart should accept both. Mutu- ally exclusive projects, on the other hand, are projects where if one project is accepted, the other must be rejected. A conveyor belt system to move goods in a warehouse and a fl eet of forklifts used for the same purpose would be mutually exclusive—accepting one implies rejecting the other.

What should be the decision if Projects S and L are independent? In this case, both should be accepted because both have positive NPVs and thus add value to the fi rm. However, if they are mutually exclusive, Project L should be chosen be- cause it has the higher NPV and thus adds more value than S. Here is a summary of the NPV decision rules:

Independent projects: If NPV exceeds zero, accept the project.

Mutually exclusive projects: Accept the project with the highest positive NPV. If no project has a positive NPV, reject them all.

Independent Projects Projects with cash flows that are not affected by the acceptance or nonacceptance of other projects.

Mutually Exclusive Projects A set of projects where only one can be accepted.

11 12 13 14 15 16 17 18 19

A B C D E F G H 0

500-1,000.00 454.55 330.58 225.39

68.30

400 300 100

1r = 10% 2 43

78.82NPVS =

Project S

Sum = NPV for Project S

100.40NPVL = NPVL found with the cash flow register of a calculator or Excel

Finding the NPV for Projects S and LFIGURE 11-1

5 The keystrokes for fi nding the NPV are shown for several calculators in the calculator tutorials provided on the text’s web site.

341Chapter 11 The Basics of Capital Budgeting

11-3 INTERNAL RATE OF RETURN (IRR) In Chapter 7, we discussed the yield to maturity on a bond and we explained that if you hold it to maturity, you will earn the YTM on your investment. The YTM is found as the discount rate that forces the PV of the cash infl ows to equal the price of the bond. This same concept is involved in capital budgeting when we calculate a project’s internal rate of return (IRR):

A project’s IRR is the discount rate that forces the PV of the infl ows to equal the cost. This is equivalent to forcing the NPV to equal zero. The IRR is an estimate of the project’s rate of return, and it is comparable to the YTM on a bond.

To calculate the IRR, we begin with Equation 11-1 for the NPV, replace r in the denominator with the term IRR, and set the NPV equal to zero. This transforms Equation 11-1 into Equation 11-2, the one used to fi nd the IRR. The rate that forces NPV to equal zero is the IRR.6

NPV ! CF0 " CF1 _________ (1 " IRR)1 "

CF2 _________ (1 " IRR)2 " . . . "

CFN _________ (1 " IRR)N ! 0

0 ! ∑ t!0

CFt ________ (1 " IRR)t 11-2

NPVS ! 0 ! "$1,000 " $500 _________ (1 " IRR)1 "

$400 _________ (1 " IRR)2 " $300 _________ (1 " IRR)3 "

$100 _________ (1 " IRR)4

Figure 11-2 illustrates the process of fi nding the IRR for Project S. Three procedures can be used:

1. Trial and Error. We could use a trial-and-error procedure—try a discount rate; see if the equation solves to zero; and if it doesn’t, try a different rate. We could

Internal Rate of Return (IRR) The discount rate that forces a project’s NPV to equal zero.

SEL F TEST Why is the NPV the primary capital budgeting decision criterion?

What is the diff erence between independent and mutually exclusive projects?

Projects SS and LL have the following cash fl ows:

END-OF-YEAR CASH FLOWS 0 1 2 3 WACC ! r ! 10%

SS "$700 $500 $300 $100 LL "$700 $100 $300 $600

If a 10% cost of capital is appropriate for both projects, what are their NPVs? (NPVSS ! $77.61; NPVLL ! $89.63)

Which project(s) would you accept if SS and LL were (a) independent? (b) mutually exclusive?

6 For a large, complex project like Boeing’s 7E7 jetliner, costs are incurred for several years before cash infl ows begin. That means that we have a number of negative cash fl ows before the positive cash fl ows begin.

Since projects must be either independent or mutually exclusive, one or the other of these rules applies to every project.

342 Part 4 Investing in Long-Term Assets: Capital Budgeting

then continue until we found the rate that forces the NPV to zero; that rate would be the IRR. For Project S, the IRR is 14.489%. Note, though, that the trial-and-error procedure is so time-consuming that before computers and fi nancial calculators were available, the IRR was rarely used. It’s useful to think about the trial-and-error procedure, but it’s far better to use a calculator or Excel to do the actual calculations.

2. Calculator Solution. Enter the cash fl ows in the calculator’s cash fl ow register just as we did to fi nd the NPV; then press the button labeled “IRR.” Instantly, you get the IRR. Here are the values for Projects S and L:7

IRRS ! 14.489%

IRRL ! 13.549%

3. Excel Solution. It is even easier to fi nd IRRS using Excel, as we demonstrate in the chapter model.

Why is the discount rate that causes a project’s NPV to equal zero so special? The reason is that the IRR is an estimate of the project’s rate of return. If this return exceeds the cost of the funds used to fi nance the project, the difference will be a bonus that goes to the fi rm’s stockholders and causes the stock price to rise. Project S has an estimated return of 14.489% versus a 10% cost of capital, so its bonus is 4.489%. On the other hand, if the IRR is less than the cost of capital, stockholders must make up the shortfall, which will hurt the stock price.

Note again that the IRR formula, Equation 11-2, is simply the NPV formula, Equation 11-1, solved for the particular discount rate that forces the NPV to zero. Thus, the same basic equation is used for both methods. The only difference is that with the NPV method, the discount rate is given and we fi nd the NPV; with the IRR method, however, the NPV is set equal to zero and we fi nd the interest rate that produces this equality.

As we noted earlier, projects should be accepted or rejected depending on whether their NPVs are positive. However, the IRR is sometimes used (improperly

24 25 26 27 28 29 30 31 32

A B C D E F G H 0

500-1,000.00 436.72 305.16 199.91

58.20

400 300 100

1IRR = 14.489% 2 43

0.00 = NPV at a discount rate of 14.489%. Since the NPV is zero, 14.489% must be the IRR.

Project S

Finding the IRR for Project SFIGURE 11-2

7 See the calculator tutorials on the text’s web site. Note that once the cash fl ows have been entered in the cash fl ow register, you can fi nd the NPV and the IRR. To fi nd the NPV, enter the interest rate (I/YR) and then press the NPV key. Then with no further entries, press the IRR key to fi nd the IRR. Thus, once you set up the calculator to fi nd the NPV, it is trivially easy to fi nd the IRR. This is one reason most fi rms calculate the NPV and the IRR. If you calculate one, it is easy to calculate the other; and both provide information that decision makers fi nd useful. The same is true with Excel.

343Chapter 11 The Basics of Capital Budgeting

we believe) to rank projects and make capital budgeting decisions. When this is done, here are the decision rules:

Independent projects: If IRR exceeds the project’s WACC, accept the project. If IRR is less than the project’s WACC, reject it.

Mutually exclusive projects. Accept the project with the highest IRR, pro- vided that IRR is greater than WACC. Reject all projects if the best IRR does not exceed WACC.

The IRR is logically appealing—it is useful to know the rates of return on proposed investments. However, as we demonstrate in a later section, NPV and IRR can produce confl icting conclusions when a choice is being made between mutually exclusive projects; and when confl icts occur, the NPV is generally better.

Buff ett University recently hosted a seminar on business methods for managers. A fi nance professor covered capital budgeting, explaining how to calculate the NPV and stating that it should be used to screen potential projects. In the Q&A session, Ed Wilson, the treasurer of an electronics fi rm, said that his fi rm used the IRR primarily because the CFO and the directors understood the selection of projects based on their rates of return but didn’t understand the NPV. Ed had tried to explain why the NPV was better, but he simply con- fused everyone; so the company stuck with the IRR. Now a meeting on the fi rm’s capital budget is coming up, and Ed asked the professor for a simple, easy-to-understand expla- nation of why the NPV was better. The professor recommended the following extreme example. A fi rm with adequate access to capital and a 10% WACC is choosing between two equally risky, mutually exclu- sive projects. Project Large calls for investing $100,000 and then receiving $50,000 per year for 10 years, while Project Small calls for investing $1 and receiving $0.60 per year for 10 years. Here is each project’s NPV and IRR: Project Large (L) Project Small (S) NPVL : $207,228.36 NPVS : $2.69 IRRL: 49.1% IRRS: 59.4%

The IRR says choose S, but the NPV says take L. Intuitively, it’s obvious that the firm would be better off choosing the large project in spite of its lower IRR. With a cost of capital of only 10%, a 49% rate of return on a $100,000 invest- ment is more profitable than a 59% return on a $1 investment. When Ed gave this example in his fi rm’s executive meeting on the capital budget, the CFO argued that this example was extreme and unrealistic and that no one would choose S in spite of its higher IRR. Ed agreed, but he asked the CFO where the line should be drawn between realistic and unrealistic examples. When Ed received no answer, he went on to say that (1) it’s hard to draw this line and (2) the NPV is always better because it tells us how much value each project will add, which is what the fi rm should maxi- mize. The president was listening, and he declared Ed the winner. The company switched from IRR to NPV, and Ed is now the CFO.

WHY NPV IS BETTER THAN IRR SEL

F TEST In what sense is a project’s IRR similar to the YTM on a bond?

The cash fl ows for projects SS and LL are as follows:

END-OF-YEAR CASH FLOWS 0 1 2 3 WACC ! r ! 10%

SS "$700 $500 $300 $100 LL "$700 $100 $300 $600

344 Part 4 Investing in Long-Term Assets: Capital Budgeting

11-4 MULTIPLE INTERNAL RATES OF RETURN8 A problem with the IRR is that under certain conditions, a project may have more than one IRR. First, note that a project is said to have normal cash fl ows if it has one or more cash outfl ows (costs) followed by a series of cash infl ows. If, however, a cash outfl ow occurs sometime after the infl ows have commenced, meaning that the signs of the cash fl ows change more than once, the project is said to have nonnormal cash fl ows. Examples:

Normal: # " " " " " or # # # " " " " "

Nonnormal: # " " " " # or # " " " # " " "

An example of nonnormal fl ows would be a strip coal mine where the company spends money to buy the property and prepare the site for mining, has positive infl ows for several years, and spends more money to return the land to its original condition. In such a case, the project might have two IRRs, that is, multiple IRRs.9

To illustrate multiple IRRs, suppose a fi rm is considering a potential strip mine (Project M) that has a cost of $1.6 million and will produce a cash fl ow of $10 mil- lion at the end of Year 1. Then at the end of Year 2, the fi rm must spend $10 million to restore the land to its original condition. Therefore, the project’s expected net cash fl ows are as follows (in millions):

Cash flows Year 0 End of Year 1 End of Year 2 "$1.6 +$10 "$10

We can substitute these values into Equation 11-2 and solve for the IRR:

NPV ! #$1.6 millon ____________ (1 " IRR)0 " $10 millon __________ (1 " IRR)1 "

#$10 million ____________ (1 " IRR)2 ! 0

NPV equals 0 when IRR ! 25%, but it also equals 0 when IRR ! 400%.10 Therefore, Project M has an IRR of 25% and another of 400%, and we don’t know which one to use. This relationship is depicted graphically in Figure 11-3.11 The graph is con- structed by plotting the project’s NPV at different discount rates.

Multiple IRRs The situation where a project has two or more IRRs.

8 This section is relatively technical, but it can be omitted without loss of continuity. 9 Equation 11-2 is a polynomial of degree n; so it has n diff erent roots, or solutions. All except one of the roots is an imaginary number when investments have normal cash fl ows (one or more cash outfl ows followed by cash infl ows). So in the normal case, only one value of IRR appears. However, the possibility of multiple real roots (hence multiple IRRs) arises when negative net cash fl ows occur after the project has been placed in operation. 10 If you attempt to fi nd Project M’s IRR with an HP calculator, you will get an error message, while TI calculators give only the IRR that’s closest to zero. When you encounter either situation, you can fi nd the approximate IRRs by calculating NPVs using several diff erent values for r = I/YR, plotting NPV on the vertical axis with the corresponding discount rate on the horizontal axis of a graph, and seeing about where NPV = 0. The intersection with the x-axis provides a rough idea of the IRRs’ values. With some calculators and with Excel, you can fi nd both IRRs by entering guesses, as explained in the calculator and Excel tutorials. 11 Figure 11-3 is called an NPV profi le. Profi les are discussed in more detail in Section 11-7.

What are the projects’ IRRs, and which one would the IRR method select if the fi rm had a 10% cost of capital and the projects were (a) independent or (b) mutually exclusive? (IRRSS ! 18.0%; IRRLL ! 15.6%)

345Chapter 11 The Basics of Capital Budgeting

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

A B C D E

WACC = 10%

10% 25%

110% 400% 500%

-$0.7736 $0.0000 $0.8943 $0.0000

-$0.2111

= IRR #1

= IRR #2

-$0.30

$0.70

NPV (millions)

0% 100% 200% 300% 400% 500%

Cost of Capital (%)

NPV = -$1.6 + $10/(1 + r) +-$10/(1 + r)2

IRR = 25% IRR = 400%

Disc. Rate NPV (millions)

Graph for Multiple IRRs: Project MFIGURE 11-3

SEL F TEST What condition regarding cash fl ows would cause more than one IRR to exist?

Project MM has the following cash fl ows:

END-OF-YEAR CASH FLOWS 0 1 2 3

"$1,000 $2,000 $2,000 "$3,350

Calculate MM’s NPV at discount rates of 0%, 10%, 12.2258%, 25%, 122.1470%, and 150%. What are MM’s IRRs? If the cost of capital is 10%, should the project be accepted or rejected? (NPVs range from #$350 to "$164 and then back down to #$94; the IRRs are 12.23% and 122.15%.)

Note that no dilemma regarding Project M would arise if the NPV method was used; we would simply fi nd the NPV and use it to evaluate the project. We would see that if Project M’s cost of capital was 10%, its NPV would be "$0.7736 million and the project should be rejected. However, if r was between 25% and 400%, NPV would be positive, but those numbers would not be realistic or useful for anything.

346 Part 4 Investing in Long-Term Assets: Capital Budgeting

11-5 REINVESTMENT RATE ASSUMPTIONS12 The NPV calculation is based on the assumption that cash infl ows can be rein- vested at the project’s risk-adjusted WACC, whereas the IRR calculation is based on the assumption that cash fl ows can be reinvested at the IRR. To see why this is so, consider the following diagram, which was fi rst used in Chapter 5 to illustrate the future value of $100 when the interest rate was 5%.

Going from PV to FV: PV = $100.00

0 215% 5% 5% 3

$105.00 $110.25 $115.76 = FV

Observe that the FV calculation assumes that the interest earned during each year can be reinvested to earn the same 5% in each succeeding year.

Now recall that when we found the PV, we reversed the process, discounting rather than compounding at the 5% rate. This diagram was used to demonstrate this point:

Going from FV to PV: PV = $100.00

0 215% 5% 5% 3

$105.00 $110.25 $115.76 = FV

This led to the following conclusion: When we calculate a present value, we are implic- itly assuming that cash fl ows can be reinvested at a specifi ed interest rate, 5% in our exam- ple. This applies to Projects S and L: When we calculated their NPVs, we discounted at the WACC, 10%, which means that we were assuming that their cash fl ows could be reinvested at 10%.

Now consider the IRR. In Section 11-3 we presented a cash fl ow diagram set up to show the PVs of the cash fl ows when discounted at the IRR. We saw that the sum of the PVs is equal to the cost at a discount rate of 14.489%; so by defi nition, 14.489% is the IRR. Now we can ask this question: What reinvestment rate is built into the IRR?

Since discounting at a given rate assumes that cash fl ows can be reinvested at that same rate, the IRR assumes that cash fl ows are reinvested at the IRR.

The NPV assumes reinvestment at the WACC, while the IRR assumes reinvest- ment at the IRR. Which assumption is more reasonable? For most fi rms, assuming reinvestment at the WACC is more reasonable for the following reasons: • If a fi rm has reasonably good access to the capital markets, it can raise all the

capital it needs at the going rate, which in our example is 10%. • Since the fi rm can obtain capital at 10%, if it has investment opportunities with

positive NPVs, it should take them on and it can fi nance them at a 10% cost. • If the fi rm uses internally generated cash fl ows from past projects rather than

external capital, this will save it the 10% cost of capital. Thus, 10% is the opportunity cost of the cash fl ows, and that is the effective return on reinvested funds.

To illustrate all this, suppose a project’s IRR is 50%, the fi rm’s WACC is 10%, and the fi rm has adequate access to the capital markets. Thus, the fi rm can raise all the capital it needs at the 10% rate. Unless the fi rm is a monopoly, the 50% return would attract competition, which would make it hard to fi nd new projects with a

12 This section gives a theoretical explanation of the key diff erence between NPV and IRR. However, it is relatively technical; so if time is a constraint, professors may decide to have students skip it and just read the box titled, “Why NPV Is Better Than IRR,” which appears earlier in the chapter.

347Chapter 11 The Basics of Capital Budgeting

similar high return, which is what the IRR assumes. Moreover, even if the fi rm does fi nd such projects, it could take them on with external capital that costs 10%. The logical conclusion is that the original project’s cash fl ows will save the 10% cost of the external capital, and that is the effective return on those fl ows.

If a fi rm does not have good access to external capital and if it has many poten- tial projects with high IRRs, it might be reasonable to assume that a project’s cash fl ows could be reinvested at rates close to their IRRs. However, that situation rarely exists: Firms with good investment opportunities generally do have good access to debt and equity markets.

Our conclusion is that the assumption built into the IRR—that cash fl ows can be reinvested at the IRR—is fl awed, whereas the assumption built into the NPV— that cash fl ows can be reinvested at the WACC—is generally correct. Moreover, if the true reinvestment rate is less than the IRR, the true rate of return on the invest- ment must be less than the calculated IRR; thus, the IRR is misleading as a measure of projects’ profi tability. This point is discussed further in the next section.

SEL F TEST Why is it true that a reinvestment rate is implicitly assumed whenever we

fi nd the present value of a future cash fl ow? Would it be possible to fi nd the PV of a FV without specifying an implicit reinvestment rate? (PVs are the reverse of FVs. We need r to fi nd FV; hence, we need r to fi nd the PV.)

What reinvestment rate is built into the NPV calculation? the IRR calcula- tion? (WACC, IRR)

For a fi rm that has adequate access to capital markets, is it more reason- able to assume reinvestment at the WACC or the IRR? (WACC)

11-6 MODIFIED INTERNAL RATE OF RETURN (MIRR)13 It is logical for managers to want to know the expected rate of return on invest- ments, and this is what the IRR is supposed to tell them. However, the IRR is based on the assumption that projects’ cash fl ows can be reinvested at the IRR. This assumption is generally incorrect, and this causes the IRR to overstate the project’s true return.14 Given this fundamental fl aw, is there a percentage evaluator that is better than the regular IRR? The answer is yes—we can modify the IRR to make it a better measure of profi tability.

This new measure, the modifi ed IRR (MIRR), is illustrated for Project S in Figure 11-4. It is similar to the regular IRR except that it is based on the assumption that cash fl ows are reinvested at the WACC (or some other explicit rate if that is a more reasonable assumption). Refer to Figure 11-4 as you read about its construction. 1. Project S has just one outfl ow, the minus $1,000 at t ! 0. Since it occurs at

Time 0, it is not discounted and its PV is "$1,000. If the project had additional outfl ows, we would fi nd the PV at t ! 0 for each one and sum them for use in the MIRR calculation.

2. Next, we fi nd the future value of each infl ow compounded at the WACC out to the “terminal year,” which is the year the last infl ow is received. We assume

Modified IRR (MIRR) The discount rate at which the present value of a project’s cost is equal to the present value of its terminal value, where the terminal value is found as the sum of the future values of the cash inflows, compounded at the firm’s cost of capital.

13 Again, this section is relatively technical, but it too can be omitted without loss of continuity. 14 The IRR overstates the expected return for accepted projects because cash fl ows cannot generally be reinvested at the IRR. Therefore, the average IRR for accepted projects is greater than the true expected rate of return. This imparts an upward bias on corporate projections based on IRRs.

348 Part 4 Investing in Long-Term Assets: Capital Budgeting

that cash fl ows are reinvested at the WACC. For Project S, the fi rst cash fl ow, $500, is compounded at WACC ! 10% for 3 years and it grows to $665.50. The second infl ow, $400, grows to $484.00; the third, to $330.00. The last infl ow is received at the end, so it is not compounded at all. The sum of the future values, $1,579.50, is called the “terminal value,” or TV.

3. We now have the cost at t ! 0, "$1,000, and the TV at Year 4, $1,579.50. There is some discount rate that will cause the PV of the terminal value to equal the cost. That interest rate is defi ned as the MIRR. In a calculator, enter N ! 4, PV ! "1000, PMT ! 0, and FV ! 1579.50. Then when you press the I/YR key, you get the MIRR, 12.11%.

4. The MIRR can be found in a number of ways. Figure 11-4 illustrates how the MIRR is calculated: We compound each cash infl ow, sum them to determine the TV, and then fi nd the rate that causes the PV of the TV to equal the cost. That rate is 12.11%. However, some of the better calculators have a built-in MIRR function that streamlines the process, as does Excel. We explain how to use the calculator function in the calculator tutorials, and we explain how to fi nd MIRR with Excel in the chapter Excel model.15

The MIRR has two signifi cant advantages over the regular IRR. First, whereas the regular IRR assumes that the cash fl ows from each project are reinvested at

71 72 73 74 75 76 77 78 79

A B C D E F G H

$500!$1,000.00 $400 $300 $100.00 $330.00 $484.00 $665.50

1r = 10% 2 4 WACC = 10%

!$1,000.00 $1,579.50

$1,000 = TV/(1"MIRR)N = $1,579.50/(1"MIRR)4. Solve for MIRR with calculator or Excel. Calculator: N = 4, PV = !1000, PMT = 0, FV = 1579.5. Press I/YR to get:

Excel: = RATE(F70,0,B71,F75) Direct Excel calculation, MIRR function: =MIRR(B71:F71,F69,F69)

Rate = MIRR 12.11% 12.11% 12.11%

Project S

Terminal Value (TV) =

Finding the MIRR for Projects S and L, WACC ! 10%FIGURE 11-4

15 Equation 11-2a summarizes these steps.

∑ t!0

COFt ______ (1 " r)t !

∑ t!0

CIFt(1 " r) N#t

______________ (1 " MIRR)N

11-2a PV costs ! TV ___________ (1 " MIRR)N

COFt is the cash outfl ow at time t, and CIFt is the cash infl ow at time t. The left term is the PV of the investment outlays when discounted at the cost of capital; the numerator of the second term is the compounded value of the infl ows, assuming the infl ows are reinvested at the cost of capital. The MIRR is the discount rate that forces the PV of the TV to equal the PV of the costs.

Also note that there are alternative defi nitions for the MIRR. One diff erence relates to whether negative cash fl ows, after the positive cash fl ows begin, should be compounded and treated as part of the TV or discounted and treated as a cost. A related issue is whether negative and positive fl ows in a given year should be netted or treated separately. For a complete discussion, see William R. McDaniel, Daniel E. McCarty, and Kenneth A. Jessell, “Discounted Cash Flow with Explicit Reinvestment Rates: Tutorial and Extension,” The Financial Review, August 1988, pp. 369–385 and David M. Shull, “Interpreting Rates of Return: A Modifi ed Rate of Return Approach,” Financial Practice and Education, Fall 1993, pp. 67–71.

349Chapter 11 The Basics of Capital Budgeting

the IRR, the MIRR assumes that cash fl ows are reinvested at the cost of capital (or some other explicit rate). Since reinvestment at the IRR is generally not correct, the MIRR is generally a better indicator of a project’s true profi tability. Second, the MIRR eliminates the multiple IRR problem—there can never be more than one MIRR, and it can be compared with the cost of capital when deciding to accept or reject projects.

Our conclusion is that the MIRR is better than the regular IRR; however, this question remains: Is MIRR as good as the NPV? Here are our conclusions: • For independent projects, the NPV, IRR, and MIRR always reach the same

accept/reject conclusion; so the three criteria are equally good when evaluat- ing independent projects.

• However, if projects are mutually exclusive and they differ in size, confl icts can arise. In such cases, the NPV is best because it selects the project that maxi- mizes value.16

• Our overall conclusions are that (1) the MIRR is superior to the regular IRR as an indicator of a project’s “true” rate of return but that (2) NPV is better than IRR and MIRR when choosing among competing projects.

11-7 NPV PROFILES Figure 11-5 presents the net present value profi le for Project S. To make the profi le, we fi nd the project’s NPV at a number of different discount rates and then plot those values to create a graph. Note that at a zero cost of capital, the NPV is simply the net total of the undiscounted cash fl ows, $1,300 " $1,000 ! $300. This value is plotted as the vertical axis intercept. Also recall that the IRR is the discount rate that causes the NPV to equal zero, so the discount rate at which the profi le line crosses the horizontal axis is the project’s IRR. When we connect the data points, we have the NPV profi le.17

Net Present Value Profile A graph showing the relationship between a project’s NPV and the firm’s cost of capital.

16 See Brigham and Daves, Intermediate Financial Management, 9th ed. (Mason, OH: South-Western, 2007), pp. 412–413. 17 Notice that the NPV profi le is curved—it is not a straight line. NPV approaches CF0, which is the "$1,000 project cost, as the discount rate increases toward infi nity. The reason is that at an infi nitely high cost of capital, all the PVs of the infl ows would be zero; so NPV at r ! ∞ must be CF0. We should also note that under certain conditions, the NPV profi les can cross the horizontal axis several times or never cross it. This point was discussed in Section 11-4.

SEL F TEST What’s the primary diff erence between the MIRR and the regular IRR?

(reinvestment rate) Which provides a better estimate of a project’s “true” rate of return, the MIRR or the regular IRR? Explain.

Projects A and B have the following cash fl ows:

0 1 2 A – $1,150 $ 100 B – $ 100 $1,300

Their cost of capital is 10%. What are the projects’ IRRs, MIRRs, and NPVs? Which project would each method select? (IRRA ! 23.1%, IRRB ! 19.1%; MIRRA ! 16.8%, MIRRB !18.7%; NPVA ! $128.10, NPVB ! $165.29)

350 Part 4 Investing in Long-Term Assets: Capital Budgeting

Now consider Figure 11-6, which shows two NPV profi les—one for Project S and one for L—and note the following points: • The IRRs are fi xed, and S has the higher IRR regardless of the cost of capital. • However, the NPVs vary depending on the actual cost of capital. • The two NPV profi le lines cross at a cost of capital of 11.975%, which is called

the crossover rate. The crossover rate can be found by calculating the IRR of the differences in the projects’ cash fl ows, as demonstrated:

0 1 2 3 4 Project S "$1,000 $500 $400 $300 $100 " Project L "$1,000 $100 $300 $400 $675 # CFs " CFL $ 0 $400 $100 "$100 "$575 IRR # ! 11.975% ! Crossover Rate

• Project L has the higher NPV if the cost of capital is less than the crossover rate, but S has the higher NPV if the cost of capital is greater than that rate.

Notice that Project L has the steeper slope, indicating that a given increase in the cost of capital causes a larger decline in NPVL than in NPVS. To see why this is so, recall that L’s cash fl ows come in later than those of S. Therefore, L is a long- term project and S is a short-term project. Next, recall the equation for the NPV:

NPV ! CF0 " CF1 _______ (1 " r)1 "

CF2 _______ (1 " r)2 " . . . "

CFN _______ (1 " r)N

Crossover Rate The cost of capital at which the NPV profiles of two projects cross and, thus, at which the projects’ NPVs are equal.

NPV Profi le for Project SFIGURE 11-5

NPV ($)

5 10 15 20 0

300

200

100

–100

NPV = 0, so IRRs = 14.489% IRR > r = 10%, so accept

At r = 10%, NPV > 0, so accept

Cost of Capital (%)

Cost of Capital NPVs 0% $300.00

5 180.00 10 78.82

IRRs ! 14.489 0.00 15 "8.33 20 "83.72

351Chapter 11 The Basics of Capital Budgeting

Now recognize that the impact of an increase in the cost of capital is much greater on distant than near-term cash fl ows, as we demonstrate here:

Effect of doubling r on a Year 1 cash fl ow:

PV of $100 due in 1 year @ r ! 5%: $100 ______ (1.05)1 ! $95.24

PV of $100 due in 1 year @ r ! 10%: $100 ______ (1.10)1 ! $90.91

Percentage decline due to higher r ! $95.24 # $90.91 _______________ $95.24 ! 4.5%

Effect of doubling r on a Year 20 cash fl ow:

PV of $100 due in 20 years @ r ! 5%: $100 _______ (1.05)20 ! $37.69

PV of $100 due in 20 years @ r ! 10%: $100 _______ (1.10)20 ! $14.86

Percentage decline due to higher r ! $37.69 # $14.86 _______________ $37.69 ! 60.6%

NPV Profi les for Projects S and LFIGURE 11-6

NPV ($)

At r = 10%, NPVL > NPVs, but IRRs > IRRL, so there is a conflict

Cost of Capital (%)

5 10

IRRs

IRRL

20 0

500

400

300

200

100

–100

Crossover rate; conflict if r is to the left, no conflict if r is to the right

Cost of Capital NPVs NPVL 0% $300.00 $475.00

5 180.42 268.21 10 78.82 100.40

Crossover ! 11.975 42.84 42.84 IRRL ! 13.549 15.64 0.00 IRRS ! 14.489 0.00 "24.37

15 "8.33 "37.26 20 "83.72 "151.33

352 Part 4 Investing in Long-Term Assets: Capital Budgeting

Thus, a doubling of the discount rate results in only a 4.5% decline in the PV of a Year 1 cash fl ow, but the same discount rate increase causes the PV of a Year 20 cash fl ow to fall by more than 60%. Therefore, if a project has most of its cash fl ows com- ing in the later years, its NPV will decline sharply if the cost of capital increases; but a project whose cash fl ows come earlier will not be severely penalized by high capital costs. Most of Project L’s cash fl ows come in its later years; so if the cost of capital is high, L is hurt much worse than Project S. Therefore, Project L’s NPV profi le has the steeper slope.

Sometimes the NPV and IRR methods produce confl icting results. We can use NPV profi les to see when confl icts can and cannot arise.

Independent Projects. If an independent project with normal cash fl ows is being evaluated, the NPV and IRR criteria always lead to the same accept/reject decision: If NPV says accept, IRR also says accept, and vice versa. To see why this is so, look at Figure 11-5 and notice that (1) the IRR says accept if the project’s cost of capital is less than (or to the left of) the IRR and (2) if the cost of capital is less than the IRR, the NPV will be positive. Thus, at any cost of capital less than 14.489%, Project S will be recommended by both the NPV and IRR criteria; but both meth- ods reject the project if the cost of capital is greater than 14.489%. A similar graph could be used for Project L or any other normal project, and we would always reach the same conclusion: For normal, independent projects, if the IRR says accept, so will the NPV.

Mutually Exclusive Projects. Assume that Projects S and L are mutually exclusive rather than independent. Therefore, we can choose either S or L, or we can reject both; but we can’t accept both. Now look at Figure 11-6 and note these points: • As long as the cost of capital is greater than the crossover rate, 11.975%, both

methods agree that Project S is better: NPVS > NPVL and IRRS > IRRL. There- fore, if r is greater than the crossover rate, no confl ict occurs.

• However, if the cost of capital is less than the crossover rate, a confl ict arises: NPV ranks L higher, but IRR ranks S higher.

Two basic conditions cause NPV profi les to cross and thus lead to confl icts:18

1. Timing differences. If most of the cash fl ows from one project come in early while most of those from the other project come in later, as occurred with Projects S and L, the NPV profi les may cross and result in a confl ict.

2. Project size (or scale) differences. If the amount invested in one project is larger than the other, this too can lead to profi les crossing and a resulting confl ict.

When size or timing differences occur, the fi rm will have different amounts of funds to invest in the various years depending on which of the two mutually exclusive projects it chooses. If it chooses S, it will have more funds to invest in Year 1 because S has a higher infl ow that year. Similarly, if one project costs more than the other, the fi rm will have more money to invest at t ! 0 if it selects the smaller project.

Given this situation, the rate of return at which differential cash fl ows can be rein- vested is a critical issue. We saw earlier that the NPV assumes reinvestment at the cost of capital and that this is generally the best assumption. Therefore, when con- fl icts exist between mutually exclusive projects, use the NPV method.

18 Of course, mutually exclusive projects can diff er with respect to both scale and timing. Also, if mutually exclu- sive projects have diff erent lives (as opposed to diff erent cash fl ow patterns over a common life), this introduces further complications; and for meaningful comparisons, some mutually exclusive projects must be evaluated over a common life. This point is discussed later in the text and in an appendix on the text’s web site.

353Chapter 11 The Basics of Capital Budgeting

11-8 PAYBACK PERIOD NPV is the most commonly used method today; but historically, the fi rst selection criterion was the payback period, defi ned as the number of years required to recover the funds invested in a project from its operating cash fl ows. Equation 11-3 is used for the calculation, and the process is diagrammed in Figure 11-7. We start with the project’s cost, a negative, and then add the cash infl ow for each year until the cumulative cash fl ow turns positive. The payback year is the year prior to full recovery plus a fraction equal to the shortfall at the end of that year divided by the cash fl ow during the full recovery year:19

Payback ! Number of

years prior to full recovery

" Unrecovered cost

at start of year ________________ Cash fl ow during

full recovery year 11-3

The shorter the payback, the better the project. Therefore, if the fi rm requires a payback of three years or less, S would be accepted, but L would be rejected. If the projects were mutually exclusive, S would be ranked over L because of its shorter payback.

Payback Period The length of time required for an investment’s net revenues to cover its cost.

SEL F TEST Describe in words how an NPV profi le is constructed. How are the intercepts

of the x- and y-axes determined?

What is the crossover rate, and how does its value relative to the cost of capital determine whether a confl ict exists between NPV and IRR?

What two characteristics can lead to confl icts between the NPV and the IRR when evaluating mutually exclusive projects?

19 Equation 11-3 assumes that cash fl ows come in uniformly during the full recovery year.

Payback CalculationsFIGURE 11-7

YearsProject L

Cash flow Cumulative cash flow

Payback L = 3 + 200/675 =

675 475

400 !200

300 !600

100 !900

!1,000 !1,000

3.30

0 4321

0Years

Cash flow Cumulative cash flow

Payback S = 2 + 100/300 =

Project S 4

100 300

300 200

400 !100

500 !500

!1,000 !1,000

2.33

354 Part 4 Investing in Long-Term Assets: Capital Budgeting

The payback has three fl aws: (1) All dollars received in different years are given the same weight (i.e., the time value of money is ignored). (2) Cash fl ows be- yond the payback year are given no consideration regardless of how large they might be. (3) Unlike the NPV, which tells us how much wealth a project adds, and the IRR, which tells us how much a project yields over the cost of capital, the pay- back merely tells us when we recover our investment. There is no necessary rela- tionship between a given payback and investor wealth maximization, so we do not know what an acceptable payback is. The fi rm might use 2 years, 3 years, or any other number as the minimum acceptable payback; but the choice is purely arbitrary.

To counter the fi rst criticism, analysts developed the discounted payback. Here cash fl ows are discounted at the WACC; then those discounted cash fl ows are used to fi nd the payback. In Figure 11-8, we calculate the discounted paybacks for S and L assuming that both have a 10% cost of capital. Each infl ow is divided by (1 $ r)t ! (1.10)t, where t is the year in which the cash fl ow occurs and r is the project’s cost of capital; and those PVs are used to fi nd the payback. Project S’s discounted payback is 2.95, while L’s is 3.78.

Note that the payback is a “break-even” calculation in the sense that if cash fl ows come in at the expected rate, the project will break even. However, since the regular payback doesn’t consider the cost of capital, it doesn’t specify the true break-even year. The discounted payback does consider capital costs; but it still disregards cash fl ows beyond the payback year, which is a serious fl aw. Further, if mutually exclusive projects vary in size, both payback methods can confl ict with the NPV, which might lead to a poor choice. Finally, there is no way of telling how low the paybacks must be to justify project acceptance.

Although the payback methods have faults as ranking criteria, they do pro- vide information about liquidity and risk. The shorter the payback, other things held constant, the greater the project’s liquidity. This factor is often important for smaller fi rms that don’t have ready access to the capital markets. Also, cash fl ows expected in the distant future are generally riskier than near-term cash fl ows, so the payback is used as one risk indicator.

Discounted Payback The length of time required for an investment’s cash flows, discounted at the investment’s cost of capital, to cover its cost.

Discounted Payback Calculations at 10% Cost of CapitalFIGURE 11-8

YearsProject L

Cash flow Discounted cash flow

Cumulative discounted CF

Discounted payback L = 3 + 361/461 =

675 461 100

400 301

!361

300 248

!661

100 91

!909

!1,000 !1,000 !1,000

3.78

0 4321

0Years

Cash flow Discounted cash flow

Cumulative discounted CF

Discounted payback S = 2 + 215/225 =

Project S 4

100 68 79

300 225

400 331

!215

500 455

!545

!1,000 !1,000 !1,000

2.95

355Chapter 11 The Basics of Capital Budgeting

11-9 CONCLUSIONS ON CAPITAL BUDGETING METHODS We have discussed fi ve capital budgeting decision criteria—NPV, IRR, MIRR, pay- back, and discounted payback. We compared these methods with one another and highlighted their strengths and weaknesses. In the process, we may have created the impression that “sophisticated” fi rms should use only one method, the NPV. However, virtually all capital budgeting decisions are analyzed by computer, so it is easy to calculate all fi ve decision criteria. In making the accept/reject decision, large, sophisticated fi rms such as GE, Boeing, and Airbus generally calculate and consider all fi ve measures because each provides a somewhat different piece of information about the decision.

NPV is the single best criterion because it provides a direct measure of value the project adds to shareholder wealth. IRR and MIRR measure profi tability ex- pressed as a percentage rate of return, which is interesting to decision makers. Further, IRR and MIRR contain information concerning a project’s “safety mar- gin.” To illustrate, consider a fi rm whose WACC is 10% that must choose between these two mutually exclusive projects: SS (for small), which costs $10,000 and is expected to return $16,500 at the end of one year, and LL (for large), which costs $100,000 and has an expected payoff of $115,550 after one year. SS has a huge IRR, 65%, while LL’s IRR is a more modest 15.6%. The NPV paints a somewhat different picture—at the 10% cost of capital, SS’s NPV is $5,000 while LL’s is $5,045. By the NPV rule, we would choose LL. However, SS’s IRR indicates that it has a much larger margin for error: Even if its cash fl ow was 39% below the $16,500 forecast, the fi rm would still recover its $10,000 investment. On the other hand, if LL’s in- fl ows fell by only 13.5% from its forecasted $115,550, the fi rm would not recover its investment. Further, if neither project generated any cash fl ows, the fi rm would lose only $10,000 on SS but $100,000 if it accepted LL.

The modifi ed IRR has all the virtues of the IRR, but it incorporates a better re- investment rate assumption and avoids the multiple rate of return problem. So if decision makers want to know projects’ rates of return, the MIRR is a better indica- tor than the regular IRR.

Payback and discounted payback provide indications of a project’s liquidity and risk. A long payback means that investment dollars will be locked up for a long time; hence, the project is relatively illiquid. In addition, a long payback means that cash fl ows must be forecasted far out into the future, and that proba- bly makes the project riskier than one with a shorter payback. A good analogy for this is bond valuation. An investor should never compare the yields to maturity on two bonds without also considering their terms to maturity because a bond’s risk is signifi cantly infl uenced by its maturity. The same holds true for capital projects.

SEL F TEST What information does the payback convey that is absent from the other capi-

tal budgeting decision methods?

What three fl aws does the regular payback have? Does the discounted payback correct all of these fl aws? Explain.

Project P has a cost of $1,000 and cash fl ows of $300 per year for three years plus another $1,000 in Year 4. The project’s cost of capital is 15%. What are P’s regular and discounted paybacks? (3.10, 3.55) If the com- pany requires a payback of three years or less, would the project be accepted? Would this be a good accept/reject decision considering the NPV and/or the IRR? (NPV ! $256.72, IRR ! 24.78%)

356 Part 4 Investing in Long-Term Assets: Capital Budgeting

In summary, the different measures provide different types of information. Since it is easy to calculate all of them, all should be considered when capital budgeting de- cisions are being made. For most decisions, the greatest weight should be given to the NPV, but it would be foolish to ignore the information provided by the other criteria.

SEL F TEST Describe the advantages and disadvantages of the fi ve capital budgeting

methods discussed in this chapter.

Should capital budgeting decisions be made solely on the basis of a project’s NPV? Explain.

11-10 DECISION CRITERIA USED IN PRACTICE Surveys designed to fi nd out which of the criteria managers actually use have been taken over the years. Surveys prior to 1999 asked companies to indicate which method they gave the most weight, while the most recent survey, in 1999, asked what method(s) managers actually calculated and used. A summary of all these surveys is shown in Table 11-2, and it reveals some interesting trends.

First, the NPV criterion was not used signifi cantly before 1980; but by 1999, it was close to the top in usage. Moreover, informal discussions with companies sug- gest that if a survey were to be taken in 2008, NPV would be at the top of this list. Second, the IRR method is widely used, but its recent growth is less dramatic than that of NPV. Third, payback was the most important criterion years ago, but its use as the primary criterion had fallen drastically by 1980. Companies still use payback because it is easy to calculate and it does provide some information, but it is rarely used today as the primary criterion. Fourth, “other methods,” primarily the accounting rate of return and the profi tability index, have been fading due to the increased use of IRR and especially NPV.

These trends are consistent with our evaluation of the various methods. NPV is the best single criterion, but all of the methods provide useful information and all are easy to calculate; thus, all are used, along with judgment and common sense. We will have more to say about all this in the next chapter.

Capital Budgeting Methods Used in PracticeT a b l e 1 1 - 2

PRIMARY CRITERION CALCULATE AND USE 1960 1970 1980 1999

NPV 0% 0% 15% 75% IRR 20 60 65 76 Payback 35 15 5 57 Discounted Payback NA NA NA 29 Other 45 25 15 NA Totals 100% 100% 100%

Sources: The 1999 data are from John R. Graham and Campbell R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics, 2001, pp. 187–244. Data from prior years are our estimates based on averaging data from these studies: J. S. Moore and A. K. Reichert, “An Analysis of the Financial Management Techniques Currently Employed by Large U.S. Corporations,” Journal of Business Finance and Accounting, Winter 1983, pp. 623–645; and M. T. Stanley and S. R. Block, “A Survey of Multinational Capital Budgeting,” The Financial Review, March 1984, pp. 36–51.

357Chapter 11 The Basics of Capital Budgeting

SEL F TEST What trends in capital budgeting methodology can be seen from Table 11-2?

In this chapter, we described fi ve techniques—NPV, IRR, MIRR, payback, and dis- counted payback—that are used to evaluate proposed capital budgeting projects. NPV is the best single measure as it tells us how much value each project contributes to shareholder wealth. Therefore, NPV is the method that should be given the great- est weight in decisions. However, the other approaches provide useful information; and in this age of computers, it is easy to calculate all of them. Therefore, managers generally look at all fi ve criteria when deciding to accept or reject projects and when choosing among mutually exclusive projects.

In this chapter, we took the cash fl ows given and used them to illustrate the diff erent capital budgeting methods. As you will see in the next chapter, estimating cash fl ows is a major task. Still, the framework established in this chapter is critically important for sound capital budgeting analyses; and at this point, you should:

• Understand capital budgeting. • Know how to calculate and use the major capital budgeting decision criteria,

which are NPV, IRR, MIRR, and payback. • Understand why NPV is the best criterion and how it overcomes problems inher-

ent in the other methods. • Recognize that while NPV is the best method, the other methods do provide infor-

mation that decision makers fi nd useful.

T YING I T ALL TO GETHER

KEY TERMS Define the following terms: a. Capital budgeting; strategic business plan b. Net present value (NPV) c. Internal rate of return (IRR) d. NPV profile; crossover rate e. Mutually exclusive projects; independent projects f. Nonnormal cash flows; normal cash flows; multiple IRRs g. Modified internal rate of return (MIRR) h. Payback period; discounted payback

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

358 Part 4 Investing in Long-Term Assets: Capital Budgeting

CAPITAL BUDGETING CRITERIA You must analyze two projects, X and Y. Each project costs $10,000, and the firm’s WACC is 12%. The expected net cash flows are as follows:

0 2 3

$1,000 $3,500

$3,000 $3,500

$6,500 $3,500

!$10,000 !$10,000

Project X Project Y

a. Calculate each project’s NPV, IRR, MIRR, payback, and discounted payback. b. Which project(s) should be accepted if they are independent? c. Which project(s) should be accepted if they are mutually exclusive? d. How might a change in the WACC produce a conflict between the NPV and IRR

rankings of the two projects? Would there be a conflict if WACC were 5%? (Hint: Plot the NPV profiles. The crossover rate is 6.21875%.)

e. Why does the conflict exist?

How are project classifications used in the capital budgeting process?

What are three potential flaws with the regular payback method? Does the discounted payback method correct all three flaws? Explain.

Why is the NPV of a relatively long-term project (one for which a high percentage of its cash flows occurs in the distant future) more sensitive to changes in the WACC than that of a short-term project?

What is a mutually exclusive project? How should managers rank mutually exclusive projects?

If two mutually exclusive projects were being compared, would a high cost of capital favor the longer-term or the shorter-term project? Why? If the cost of capital declined, would that lead firms to invest more in longer-term projects or shorter-term projects? Would a decline (or an increase) in the WACC cause changes in the IRR ranking of mutually exclusive projects?

Discuss the following statement: If a firm has only independent projects, a constant WACC, and projects with normal cash flows, the NPV and IRR methods will always lead to identical capital budgeting decisions. What does this imply about the choice between IRR and NPV? If each of the assumptions were changed (one by one), how would your answer change?

Why might it be rational for a small firm that does not have access to the capital markets to use the payback method rather than the NPV method?

Project X is very risky and has an NPV of $3 million. Project Y is very safe and has an NPV of $2.5 million. They are mutually exclusive, and project risk has been properly considered in the NPV analyses. Which project should be chosen? Explain.

What reinvestment rate assumptions are built into the NPV, IRR, and MIRR methods? Give an explanation (other than “because the text says so”) for your answer.

A firm has a $100 million capital budget. It is considering two projects, each costing $100 million. Project A has an IRR of 20%; has an NPV of $9 million; and will be terminated after 1 year at a profit of $20 million, resulting in an immediate increase in EPS. Project B, which cannot be postponed, has an IRR of 30% and an NPV of $50 million. However, the firm’s short-run EPS will be reduced if it accepts Project B because no revenues will be generated for several years. a. Should the short-run effects on EPS influence the choice between the two projects? b. How might situations like this influence a firm’s decision to use payback?

ST-2ST-2

QUESTIONSQUESTIONS

11-111-1 11-211-2

11-311-3

11-411-4

11-511-5

11-611-6

11-711-7

11-811-8

11-911-9

11-1011-10

359Chapter 11 The Basics of Capital Budgeting

NPV Project K costs $52,125, its expected net cash inflows are $12,000 per year for 8 years, and its WACC is 12%. What is the project’s NPV?

IRR Refer to Problem 11-1. What is the project’s IRR?

MIRR Refer to Problem 11-1. What is the project’s MIRR?

PAYBACK PERIOD Refer to Problem 11-1. What is the project’s payback?

DISCOUNTED PAYBACK Refer to Problem 11-1. What is the project’s discounted payback?

NPV Your division is considering two projects with the following net cash flows (in millions):

0 2

$17 $6

$10 $9

$5 $10

!$25 !$20

Project A Project B

a. What are the projects’ NPVs assuming the WACC is 5%? 10%? 15%? b. What are the projects’ IRRs at each of these WACCs? c. If the WACC was 5% and A and B were mutually exclusive, which project would you

choose? What if the WACC was 10%? 15%? (Hint: The crossover rate is 7.81%.)

CAPITAL BUDGETING CRITERIA A firm with a 14% WACC is evaluating two projects for this year’s capital budget. After-tax cash flows, including depreciation, are as follows:

0 2 3

$2,000 $5,600

!$6,000 !$18,000

Project A Project B

4 51

a. Calculate NPV, IRR, MIRR, payback, and discounted payback for each project. b. Assuming the projects are independent, which one(s) would you recommend? c. If the projects are mutually exclusive, which would you recommend? d. Notice that the projects have the same cash flow timing pattern. Why is there a

conflict between NPV and IRR?

CAPITAL BUDGETING CRITERIA: ETHICAL CONSIDERATIONS A mining company is considering a new project. Because the mine has received a permit, the project would be legal; but it would cause significant harm to a nearby river. The firm could spend an additional $10 million at Year 0 to mitigate the environmental problem, but it would not be required to do so. Developing the mine (without mitigation) would cost $60 million, and the expected net cash inflows would be $20 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $21 million. The risk-adjusted WACC is 12%. a. Calculate the NPV and IRR with and without mitigation. b. How should the environmental effects be dealt with when this project is evaluated? c. Should this project be undertaken? If so, should the firm do the mitigation?

CAPITAL BUDGETING CRITERIA: ETHICAL CONSIDERATIONS An electric utility is considering a new power plant in northern Arizona. Power from the plant would be sold in the Phoenix area, where it is badly needed. Because the firm has received a permit, the plant would be legal; but it would cause some air pollution. The company could spend an additional $40 million at Year 0 to mitigate the environmental problem, but it would not be required to do so. The plant without mitigation would cost $240 million, and the ex- pected net cash inflows would be $80 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $84 million. Unemployment in the area where the plant would be built is high, and the plant would provide about 350 good jobs. The risk-adjusted WACC is 17%. a. Calculate the NPV and IRR with and without mitigation. b. How should the environmental effects be dealt with when evaluating this project? c. Should this project be undertaken? If so, should the firm do the mitigation?

PROBLEMS PROBLEMS

11-111-1Easy Problems 1–6 Easy Problems 1–6

11-211-2 11-311-3 11-411-4 11-511-5 11-611-6

11-711-7Intermediate Problems 7–13 Intermediate Problems 7–13

11-811-8

11-911-9

360 Part 4 Investing in Long-Term Assets: Capital Budgeting

CAPITAL BUDGETING CRITERIA: MUTUALLY EXCLUSIVE PROJECTS A firm with a WACC of 10% is considering the following mutually exclusive projects:

0 2 3

$225 $49

$225 $50

$55 $50

$55 $300

!$400 !$600

Project A Project B

4 51

Which project would you recommend? Explain.

CAPITAL BUDGETING CRITERIA: MUTUALLY EXCLUSIVE PROJECTS Project S costs $15,000, and its expected cash flows would be $4,500 per year for 5 years. Mutually exclusive Project L costs $37,500, and its expected cash flows would be $11,100 per year for 5 years. If both projects have a WACC of 14%, which project would you recommend? Explain.

IRR AND NPV A company is analyzing two mutually exclusive projects, S and L, with the following cash flows:

0 2

$10 $800

$250 $250

$900 $0

!$1,000 !$1,000

Project S Project L

$10 $400

The company’s WACC is 10%. What is the IRR of the better project? (Hint: The better proj- ect may or may not be the one with the higher IRR.)

MIRR A firm is considering two mutually exclusive projects, X and Y, with the following cash flows:

0 2

$700 $50

$300 $100

$100 $1,000

!$1,000 !$1,000

Project X Project Y

$400 $50

The projects are equally risky, and their WACC is 12%. What is the MIRR of the project that maximizes shareholder value?

CHOOSING MANDATORY PROJECTS ON THE BASIS OF LEAST COST K. Kim Inc. must install a new air conditioning unit in its main plant. Kim must install one or the other of the units; otherwise, the highly profitable plant would have to shut down. Two units are available, HCC and LCC (for high and low capital costs, respectively). HCC has a high capital cost but relatively low operating costs, while LCC has a low capital cost but higher operating costs because it uses more electricity. The costs of the units are shown here. Kim’s WACC is 7%.

0 2 3

!$50,000 !$175,000

!$600,000 !$100,000

HCC LCC

4 51

a. Which unit would you recommend? Explain. b. If Kim’s controller wanted to know the IRRs of the two projects, what would you

tell him? c. If the WACC rose to 15% would this affect your recommendation? Explain your an-

swer and the reason this result occurred.

NPV PROFILES: TIMING DIFFERENCES An oil drilling company must choose between two mutually exclusive extraction projects, and each costs $12 million. Under Plan A, all the oil would be extracted in 1 year, producing a cash flow at t ! 1 of $14.4 million. Under Plan B, cash flows would be $2.1 million per year for 20 years. The firm’s WACC is 12%. a. Construct NPV profiles for Plans A and B, identify each project’s IRR, and show the

approximate crossover rate. b. Is it logical to assume that the firm would take on all available independent, average-

risk projects with returns greater than 12%? If all available projects with returns

11-1011-10

11-1111-11

11-1211-12

11-1311-13

11-1411-14Challenging Problems 14–22

Challenging Problems 14–22

11-1511-15

361Chapter 11 The Basics of Capital Budgeting

greater than 12% have been undertaken, does this mean that cash flows from past in- vestments have an opportunity cost of only 12% because all the company can do with these cash flows is to replace money that has a cost of 12%? Does this imply that the WACC is the correct reinvestment rate assumption for a project’s cash flows?

NPV PROFILES: SCALE DIFFERENCES A company is considering two mutually exclusive expansion plans. Plan A requires a $40 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.4 million per year for 20 years. Plan B requires a $12 million expenditure to build a somewhat less efficient, more labor-intensive plant with expected cash flows of $2.72 million per year for 20 years. The firm’s WACC is 10%. a. Calculate each project’s NPV and IRR. b. Graph the NPV profiles for Plan A and Plan B and approximate the crossover rate. c. Why is NPV better than IRR for making capital budgeting decisions that add to share-

holder value?

CAPITAL BUDGETING CRITERIA A company has a 12% WACC and is considering two mu- tually exclusive investments (that cannot be repeated) with the following net cash flows:

0 2 3

!$180 $0

$850 $134

!$100 $134

!$193 $134

!$387 $134

!$300 !$405

Project A Project B

6 7

$600 $134

a. What is each project’s NPV? b. What is each project’s IRR? c. What is each project’s MIRR? (Hint: Consider Period 7 as the end of Project B’s life.) d. From your answers to Parts a, b, and c, which project would be selected? If the

WACC was 18%, which project would be selected? e. Construct NPV profiles for Projects A and B. f. What is each project’s MIRR at a WACC of 18%?

NPV AND IRR A store has 5 years remaining on its lease in a mall. Rent is $2,000 per month, 60 payments remain, and the next payment is due in 1 month. The mall’s owner plans to sell the property in a year and wants rent at that time to be high so that the property will appear more valuable. Therefore, the store has been offered a “great deal” (owner’s words) on a new 5-year lease. The new lease calls for no rent for 9 months, then payments of $2,600 per month for the next 51 months. The lease cannot be broken, and the store’s WACC is 12% (or 1% per month). a. Should the new lease be accepted? (Hint: Make sure you use 1% per month.) b. If the store owner decided to bargain with the mall’s owner over the new lease pay-

ment, what new lease payment would make the store owner indifferent between the new and old leases? (Hint: Find FV of the old lease’s original cost at t ! 9; then treat this as the PV of a 51-period annuity whose payments represent the rent during months 10 to 60.)

c. The store owner is not sure of the 12% WACC—it could be higher or lower. At what nominal WACC would the store owner be indifferent between the two leases? (Hint: Calculate the differences between the two payment streams; then find its IRR.)

MULTIPLE IRRS AND MIRR A mining company is deciding whether to open a strip mine, which costs $2 million. Net cash inflows of $13 million would occur at the end of Year 1. The land must be returned to its natural state at a cost of $12 million, payable at the end of Year 2. a. Plot the project’s NPV profile. b. Should the project be accepted if WACC ! 10%? if WACC ! 20%? Explain your

reasoning. c. Think of some other capital budgeting situations in which negative cash flows during

or at the end of the project’s life might lead to multiple IRRs. d. What is the project’s MIRR at WACC ! 10%? at WACC ! 20%? Does MIRR lead to

the same accept/reject decision for this project as the NPV method? Does the MIRR method always lead to the same accept/reject decision as NPV? (Hint: Consider mutually exclusive projects that differ in size.)

NPV A project has annual cash flows of $7,500 for the next 10 years and then $10,000 each year for the following 10 years. The IRR of this 20-year project is 10.98%. If the firm’s WACC is 9%, what is the project’s NPV?

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362 Part 4 Investing in Long-Term Assets: Capital Budgeting

MIRR Project X costs $1,000, and its cash flows are the same in Years 1 through 10. Its IRR is 12%, and its WACC is 10%. What is the project’s MIRR?

MIRR A project has the following cash flows:

0 2 3

$451$350$196!$X$202!$500

4 51

This project requires two outflows at Years 0 and 2, but the remaining cash flows are posi- tive. Its WACC is 10%, and its MIRR is 14.14%. What is the Year 2 cash outflow?

CAPITAL BUDGETING CRITERIA Your division is considering two projects. Its WACC is 10%, and the projects’ after-tax cash flows (in millions of dollars) would be as follows:

0 2

$20 $6

$10 $10

$5 $20

!$30 !$30

Project A Project B

$15 $8

a. Calculate the projects’ NPVs, IRRs, MIRRs, regular paybacks, and discounted paybacks. b. If the two projects are independent, which project(s) should be chosen? c. If the two projects are mutually exclusive and the WACC is 10%, which project(s)

should be chosen? d. Plot NPV profiles for the two projects. Identify the projects’ IRRs on the graph. e. If the WACC was 5%, would this change your recommendation if the projects were

mutually exclusive? If the WACC was 15%, would this change your recommenda- tion? Explain your answers.

f. The crossover rate is 13.5252%. Explain what this rate is and how it affects the choice between mutually exclusive projects.

g. Is it possible for conflicts to exist between the NPV and the IRR when independent projects are being evaluated? Explain your answer.

h. Now look at the regular and discounted paybacks. Which project looks better when judged by the paybacks?

i. If the payback was the only method a firm used to accept or reject projects, what pay- back should it choose as the cutoff point, that is, reject projects if their payouts are not below the chosen cutoff? Is your selected cutoff based on some economic criteria, or is it more or less arbitrary? Are the cutoff criteria equally arbitrary when firms use the NPV and/or the IRR as the criteria? Explain.

j. Define the MIRR. What’s the difference between the IRR and the MIRR, and which generally gives a better idea of the rate of return on the investment in a project?

k. Why do most academics and financial executives regard the NPV as being the single best criterion and better than the IRR? Why do companies still calculate IRRs?

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BASICS OF CAPITAL BUDGETING You recently went to work for Allied Components Company, a supplier of auto repair parts used in the after-market with products from Daimler, Chrysler, Ford, and other automakers. Your boss, the chief financial officer (CFO), has just handed you the estimated cash flows for two proposed proj- ects. Project L involves adding a new item to the firm’s ignition system line; it would take some time to build up the market for this product, so the cash inflows would increase over time. Project S involves an add-on to an existing line, and its cash flows would decrease over time. Both projects have 3-year lives because Allied is plan- ning to introduce entirely new models after 3 years.

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IN TEGRATED C ASE ALLIED COMPONENTS COMPANY

363Chapter 11 The Basics of Capital Budgeting

Here are the projects’ net cash flows (in thousands of dollars):

0 2

$80 $20

$60 $50

$10 $70

!$100 !$100

Project L Project S

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows.

The CFO also made subjective risk assessments of each project, and he concluded that both projects have risk characteristics that are similar to the firm’s average project. Allied’s WACC is 10%. You must determine whether one or both of the projects should be accepted.

a. What is capital budgeting? Are there any similarities between a firm’s capital budgeting decisions and an individual’s investment decisions?

b. What is the difference between independent and mutually exclusive projects? Between projects with normal and nonnormal cash flows?

c. (1) Define the term net present value (NPV). What is each project’s NPV? (2) What is the rationale behind the NPV method? According to NPV, which project(s) should be accepted

if they are independent? mutually exclusive? (3) Would the NPVs change if the WACC changed? Explain. d. (1) Define the term internal rate of return (IRR). What is each project’s IRR? (2) How is the IRR on a project related to the YTM on a bond? (3) What is the logic behind the IRR method? According to IRR, which project(s) should be accepted if they

are independent? mutually exclusive? (4) Would the projects’ IRRs change if the WACC changed? e. (1) Draw NPV profiles for Projects L and S. At what discount rate do the profiles cross? (2) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which project(s) should

be accepted if they are independent? mutually exclusive? Explain. Are your answers correct at any WACC less than 23.6%?

f. (1) What is the underlying cause of ranking conflicts between NPV and IRR? (2) What is the reinvestment rate assumption, and how does it affect the NPV versus IRR conflict? (3) Which method is best? Why? g. (1) Define the term modified IRR (MIRR). Find the MIRRs for Projects L and S. (2) What are the MIRR’s advantages and disadvantages vis-à-vis the NPV? h. (1) What is the payback period? Find the paybacks for Projects L and S. (2) What is the rationale for the payback method? According to the payback criterion, which project(s)

should be accepted if the firm’s maximum acceptable payback is 2 years, if Projects L and S are indepen- dent, if Projects L and S are mutually exclusive?

(3) What is the difference between the regular and discounted payback methods? (4) What are the two main disadvantages of discounted payback? Is the payback method of any real useful-

ness in capital budgeting decisions? Explain. i. As a separate project (Project P), the firm is considering sponsoring a pavilion at the upcoming World’s Fair.

The pavilion would cost $800,000, and it is expected to result in $5 million of incremental cash inflows dur- ing its 1 year of operation. However, it would then take another year, and $5 million of costs, to demolish the site and return it to its original condition. Thus, Project P’s expected net cash flows look like this (in millions of dollars):

0 2

!$5.0$5.0!$0.8

The project is estimated to be of average risk, so its WACC is 10%. (1) What is Project P’s NPV? What is its IRR? its MIRR? (2) Draw Project P’s NPV profile. Does Project P have normal or nonnormal cash flows? Should this project

be accepted? Explain.

H o m e D e p o t Ke e p s G r ow i n g

Cash Flow Estimation and Risk Analysis

LA N

S CH

EI N

/A LA

M Y

12 CHAPTER

364

Home Depot Inc. (HD) has grown phenomenally in recent years, and that growth continues. At the beginning of 1990, HD had 118 stores with annual sales of $2.8 billion. By early 2008, it had 2,234 stores and annual sales of $77 billion. Stockholders have benefited mightily from this growth as the stock’s price has increased from a split-adjusted $1.87 in 1990 to $40 in early 2007, or by 2,039%.

However, the more recent news has not been as good. In the face of a declining housing market, the company has struggled. In May 2008, it announced the closing of 12 underperforming stores. Still, despite the poor housing market, the company continues to open new stores in areas it thinks the stores will do well. It costs, on average, over $20 million to purchase land, construct a new store, and stock it with inventory. Therefore, it is critical that the company perform a financial analysis to determine whether a potential store’s expected cash flows will cover its costs.

Home Depot uses information from its exist- ing stores to forecast its new stores’ expected

cash flows. Thus far, its forecasts have been outstanding, but there are always risks. First, a store’s sales might be less than projected, espe- cially if the economy weakens. Second, some of HD’s customers might bypass the store alto- gether and buy directly from manufacturers through the Internet. Third, its new stores could “cannibalize,” or take sales away from, its exist- ing stores. To avoid cannibalization while still opening enough new stores to generate sub- stantial growth, HD has been developing com- plementary formats. For example, it recently rolled out its Expo Design Center chain, which offers one-stop sales and service for kitchen and bath and other remodeling and renovation work; and in 2007, it acquired a Chinese home improvement chain to jump-start its operations in that nation.

Rational expansion decisions require detailed assessments of the forecasted cash flows, along with a measure of the risk that forecasted sales might not be realized. That information can then be used to determine the risk-adjusted NPV

o m

e D

ep o

The basic principles of capital budgeting were covered in Chapter 11. Given a proj- ect’s expected cash fl ows, it is easy to calculate the primary decision criterion—the NPV—as well as the supplemental criteria, IRR, MIRR, payback, and discounted pay- back. However, in the real world, cash fl ows are not just handed to you—rather, they must be estimated based on information from various sources. Moreover, uncer- tainty surrounds the forecasted cash fl ows, and some projects are more uncertain and thus riskier than others. In this chapter, we review examples that illustrate how project cash fl ows are estimated, discuss techniques for measuring and then dealing with risk, and discuss how projects are evaluated once they go into operation.

When you fi nish this chapter, you should be able to: • Identify “relevant” cash fl ows that should and should not be included in a capital

budgeting analysis. • Estimate a project’s relevant cash fl ows and put them into a time line format that

can be used to calculate a project’s NPV, IRR, and other capital budgeting metrics. • Explain how risk is measured and use this measure to adjust the fi rm’s WACC to

account for diff erential project riskiness. • Discuss how some projects can be altered after they have been accepted and how

these alterations can change a project’s cash fl ows and thus its realized NPV. • Describe the post-audit, which is an important part of the capital budgeting

process, and discuss its relevance in capital budgeting decisions.

12-1 CONCEPTUAL ISSUES IN CASH FLOW ESTIMATION Before the cash fl ow estimation process is illustrated, we need to discuss several important conceptual issues. A failure to handle these issues properly can lead to incorrect NPVs and thus bad capital budgeting decisions.

12-1a Cash Flow versus Accounting Income We saw in Chapter 3 that there is a difference between cash fl ows and accounting income. We also saw that cash is what people and fi rms spend or reinvest; so the present value of cash fl ows, not accounting income, is the basis of a fi rm’s value. That’s why, in the last chapter, we discounted net cash fl ows, not net income, to fi nd projects’ NPVs.

Many things can lead to differences between net cash fl ows and net income. First, depreciation is not a cash outlay, but it is deducted when net income is calcu- lated. Second, net income is based on the depreciation rate the fi rm’s accountants decide to use, not necessarily the depreciation rate allowed by the IRS, and it is the IRS rate that determines cash fl ows. Moreover, if a project requires an addition to working capital, this directly affects cash fl ows but not net income. Other factors also differentiate net income from cash fl ow, but the important thing to keep in

associated with each potential project. In this chapter, we describe techniques for estimating projects’ cash flows, as well as projects’ risks. Companies such as Home Depot use

these techniques on a regular basis when making capital budgeting decisions.

PU T TING THINGS IN PER SPECTIVE

Chapter 12 Cash Flow Estimation and Risk Analysis 365

366 Part 4 Investing in Long-Term Assets: Capital Budgeting

mind is this: For capital budgeting purposes, the project’s cash fl ows, not its accounting income, is the key item.

12-1b Timing of Cash Flows In theory, capital budgeting analyses should deal with cash fl ows exactly when they occur; hence, daily cash fl ows theoretically would be better than annual fl ows. However, it would be costly to estimate and then analyze daily fl ows, and they would probably be no more accurate than annual estimates because we simply cannot forecast accurately at a daily level out 10 years or so into the future. There- fore, we generally assume that all cash fl ows occur at the end of the year. Note, though, for projects with highly predictable cash fl ows, it might be useful to assume that cash fl ows occur at midyear (or even quarterly or monthly); but for most purposes, we assume end-of-year fl ows.

12-1c Incremental Cash Flows Incremental cash fl ows are fl ows that will occur if and only if some specifi c event occurs. In capital budgeting, the event is the fi rm’s acceptance of a project and the project’s incremental cash fl ows are ones that occur as a result of this decision. Cash fl ows such as investments in buildings, equipment, and working capital needed for the project are obviously incremental, as are sales revenues and operating costs associated with the project. However, some items are not so obvi- ous, as we explain later in this section.

12-1d Replacement Projects Two types of projects can be distinguished: expansion projects, where the fi rm makes an investment, such as a new Home Depot store, and replacement projects, where the fi rm replaces existing assets, generally to reduce costs. For example, suppose Home Depot is considering replacing some of its delivery trucks. The benefi t would be lower fuel and maintenance expenses, and the shiny new trucks also might improve the company’s image and reduce pollution. Replacement analysis is complicated by the fact that almost all of the cash fl ows are incremental, found by subtracting the new cost numbers from the old numbers. Thus, the fuel bill for a more effi cient new truck might be $10,000 per year versus $15,000 for the old truck. The $5,000 savings is the incremental cash fl ow that would be used in the replacement analysis. Similarly, we would need to fi nd the difference in depreciation and other factors that affect cash fl ows. Once we have found the incremental cash fl ows, we use them in a “regular” NPV analysis to decide whether to replace the asset or to continue using it.

12-1e Sunk Costs A sunk cost is an outlay that was incurred in the past and cannot be recovered in the future regardless of whether the project under consideration is accepted. In capital budgeting, we are concerned with future incremental cash fl ows—we want to know if the new investment will produce enough incremental cash fl ow to justify the incremental investment. Because sunk costs were incurred in the past and cannot be recovered regardless of whether the project is accepted or rejected, they are not relevant in the capital budgeting analysis.

To illustrate this concept, suppose Home Depot spent $2 million to investigate a potential new store and obtain the permits required to build it. That $2 million would be a sunk cost—the money is gone, and it won’t come back regardless of whether or not the new store is built.

Not handling sunk costs properly can lead to incorrect decisions. For example, suppose Home Depot completed the analysis and found that it must spend an

Incremental Cash Flow A cash flow that will occur if and only if the firm takes on a project.

Sunk Cost A cash outlay that has already been incurred and that cannot be recovered regardless of whether the project is accepted or rejected.

367Chapter 12 Cash Flow Estimation and Risk Analysis

additional $17 million, on top of the $2 million site study, to open the store. Suppose it then used as the required investment $19 million and found a projected NPV of !$1 million. This would indicate that HD should reject the new store. However, that would be a bad decision. The real issue is whether the incremental $17 million would result in incremental cash infl ows suffi cient to produce a positive NPV. If the $2 million sunk cost is disregarded, as it should be, the true NPV will be a positive $1 million. Therefore, the failure to deal properly with the sunk cost would lead to turning down a project that would add $1 million to stockholders’ value.

12-1f Opportunity Costs Associated with Assets the Firm Owns

Another issue relates to opportunity costs associated with assets the fi rm already owns. For example, suppose Home Depot owns land with a market value of $2 million and that land will be used for the new store if HD decides to build it. If HD decides to go forward with the project, only another $15 million will be required, not the typical $17 million because HD would not need to buy the required land. Does this mean that HD should use $15 million as the cost of the new store? The answer is no. If the new store is not built, HD could sell the land and get a cash fl ow of $2 million. This $2 million is an opportunity cost—something that HD would not receive if the land was used for the new store. Therefore, the $2 million must be charged to the new project, and a failure to do so would artifi cially and incorrectly increase the new project’s NPV.

If this is not clear, consider the following example. Assume that a fi rm owns a building and equipment with a market (resale) value of $10 million. The property is not being used, and the fi rm is considering using it for a new project. The only required additional investment would be $100,000 for working capital, and the new project would produce a cash infl ow of $50,000 forever. If the fi rm has a WACC of 10% and evaluates the project using only the $100,000 of working capital as the required investment, it would fi nd an NPV of $50,000/0.10 " $500,000. Does this mean that the project is a good one? The answer is no. The fi rm can sell the prop- erty for $10 million, which is much better than $500,000.

12-1g Externalities Another potential problem involves externalities, which are defi ned as the effects of a project on other parts of the fi rm or the environment. The three types of exter- nalities are explained next.

Negative Within-Firm Externalities As noted earlier, retailers such as Home Depot opening new stores that are too close to their existing stores takes customers away from their existing stores. In this case, even though the new store has positive cash fl ows, its existence reduces some of the fi rm’s current cash fl ows. This type of externality is called cannibalization because the new business eats into the company’s existing business. Manufacturers also can experience cannibalization effects. Thus, if Cengage Learning, the publisher of this book, decides to publish another introductory fi nance text, that new book will pre- sumably reduce sales of this one. Those lost cash fl ows should be taken into account, and that means charging them as a cost when analyzing the proposed new book.

Dealing properly with negative externalities can be tricky. If Cengage decided not to publish the new book because of its cannibalization effect, might another publisher publish it, causing our book to lose sales regardless of what Cengage does? Logically, Cengage must look at the total situation, which is more than a simple mechanical analysis. Experience and knowledge of the industry is required to make good decisions.

Opportunity Cost The best return that can be earned on assets the firm already owns if those assets are not used for the new project.

Externality An effect on the firm or the environment that is not reflected in the project’s cash flows.

Cannibalization The situation when a new project reduces cash flows that the firm would otherwise have had.

368 Part 4 Investing in Long-Term Assets: Capital Budgeting

One of the best examples of a company fouling up as a result of not dealing correctly with a cannibalization situation was IBM’s response when transistors made personal computers possible in the 1970s. IBM’s mainframe computers were the biggest game in town, and they generated huge profi ts. But IBM had the tech- nology, got into PCs, and for a time was the leading PC company. However, top management decided to rein back the PC division because managers were afraid it would hurt the more profi table mainframe business. That decision opened the door for Microsoft, Intel, Dell, Hewlett-Packard and others; and IBM went from being the most profi table fi rm in the world to one whose very survival was threat- ened. This experience highlights the fact that while it is essential to understand the theory of fi nance, it is equally important to understand the business environment, including how competitors are likely to react to a fi rm’s actions. A great deal of judgment goes into making good fi nancial decisions.

Positive Within-Firm Externalities Cannibalization occurs when new products compete with old ones. However, a new project also can be complementary to an old one, in which case cash fl ows in the old operation will be increased when the new one is introduced. For example, Apple’s iPod was a profi table product; but when Apple made an investment in another proj- ect, its music store, that investment boosted sales of the iPod. So if an analysis of the proposed music store indicated a negative NPV, the analysis would not be complete unless the incremental cash fl ows that would occur in the iPod division were cred- ited to the music store. That might well change an NPV from negative to positive.

Environmental Externalities The most common type of negative externality has to do with the environment. Government rules and regulations constrain what companies can do, but fi rms have some fl exibility in dealing with the environment. For example, suppose a manufac- turer is studying a proposed new plant. The company could meet the environmental regulations at a cost of $1 million, but the plant would still emit fumes that might cause ill feelings in its neighborhood. Those ill feelings would not show up in the cash fl ow analysis, but they still should be considered. Perhaps a relatively small additional expenditure would reduce the emissions substantially, make the plant look good relative to other plants in the area, and provide goodwill that would help the fi rm’s sales and negotiations with governmental agencies in the future.

Of course, everyone’s profi ts depend on the earth remaining healthy, so com- panies have an incentive to do things to protect the environment even though those actions are not required. However, if one fi rm decides to take actions that are good for the environment but costly, its products must refl ect the higher costs. If its competitors decide to get by with less costly but less environmentally friendly processes, they can price their products lower and make more money. Of course, the more environmentally friendly companies can advertise their environmental efforts, and this might—or might not—offset the higher costs. All of this illustrates why government regulations are necessary, both nationally and internationally. Finance, politics, and the environment are all interconnected.

SEL F TEST Why should companies use a project’s cash fl ows rather than accounting in-

come when fi nding a project’s NPV?

Explain the following terms: incremental cash fl ow, sunk cost, opportunity cost, externality, and cannibalization.

Give an example of a “good” externality, that is, one that increases a project’s true NPV.

369Chapter 12 Cash Flow Estimation and Risk Analysis

12-2 ANALYSIS OF AN EXPANSION PROJECT In Chapter 11, we analyzed two projects, S and L. We were given the cash fl ows and used them to illustrate how the NPV, IRR, MIRR, and payback are calculated. Now we demonstrate how cash fl ows are actually estimated, using our old Project S to demonstrate the procedure. We explain the process in Table 12-1. Look at it as we discuss the analysis. Note that the dollars are in thousands; we omitted

Cash Flow Estimation and Analysis for Expansion Project ST a b l e 1 2 - 1

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22

23 24 25

26 27 28

29 30 31 32 33 34

A B C D E F G H I

Investment Outlays at Time = 0

Net Cash Flows Over the Project’s Life

Equipment Net WC

Unit sales Sales price Variable cost per unit Sales revenues = Units ! Price Variable costs = Units ! Cost/unit Fixed operating costs except depr’n Depreciation: Accelerated from table below Total operating costs EBIT (or operating income) Taxes on operating income 40% After-tax project operating income Add back depreciation Salvage value (taxed as ordinary income) Tax on salvage value (SV is taxed at 40%) Recovery of net working capital Project net cash flows (Time Line)

537 $10.00 $5.092 $5,370

2,735 2,000

297 $5,032

$338 135

$203 297

520 $10.00 $5.391 $5,200

2,803 2,000

405 $5,208

-$8 -3

-$5 405

505 $10.00 $5.228 $5,050

2,640 2,000

135 $4,775

$275 110

$165 135

490 $10.00 $6.106 $4,900

2,992 2,000

63 $5,055 -$155

-62 -$93

63 50

-20 100

$100

-$900 -100

-$1,000

0 1 2 3 4

$300$400$500

Depreciation

Alternative depreciation

Project Evaluation @ WACC = 10%

Accelerated Rate Depreciation

Straight line Rate Depreciation

1 33% $297

45% $405

15% $135

7% $63

Cost: $900

Accelerated NPV IRR MIRR Payback

$78.82 14.489% 12.106%

2.33

=NPV(D29,F22:I22)+E22 =IRR(E22:I22) =MIRR(E22:I22,D29,D29) =G2+(-E22-F22-G22)/H22

$64.44 13.437% 11.731%

2.60

Formulas Straight line

2 3 4

25% $225

2. If the firm owned assets that would be used for the project but would be sold if the project is not accepted, the after-tax value of those assets would be shown as an ”opportunity cost” in the ”Investment Outlays” section. 3. If this project would reduce sales and cash flows from one of the firm's other divisions, then the after-tax cannibalization effect, or ”externality,” would be deducted from the net cash flows shown on Row 22.

1. Accelerated depreciation rates are set by Congress. We show the approximate rates for a 4-year asset in 2008. Companies also have the option of using straight-line depreciation. Under IRS rules, salvage value is not deducted when establishing the depreciable basis. However, if a salvage payment is received, it is called a recapture of depreciation and is taxed at the 40% rate.

4. If the firm had previously incurred costs associated with this project, but those costs could not be recovered regardless of whether this project is accepted, then they are ”sunk costs” and should not enter the analysis.

370 Part 4 Investing in Long-Term Assets: Capital Budgeting

three zeros to streamline the presentation. Also note that we used Excel to make Table 12-1. We could have used a calculator and plain paper, but Excel is much better when dealing with arithmetic. You don’t need to know Excel to understand the discussion; but if you plan to work in fi nance—or in almost any business function—you should learn something about it.

The column headers in the table, the A through I, and the row headers, 1 through 38, designate cells, which contain the data. For example, the equip- ment needed for Project S will cost $900, and that number is shown in Cell E4 as a negative. The equipment is expected to have a salvage value of $50 at the end of the project’s 4-year life; this is shown in Cell I19.1 The new project will require $100 of working capital; this is shown in Cell E5 as a negative number because it is a cost and then as a positive number in Cell I21 because it is recov- ered at the end of Year 4. The total investment at Time 0 is $1,000, which is shown in Cell E22.

Unit sales of Project S are shown on Row 7; they are expected to decline somewhat over the project’s 4-year life. The sales price, a constant $10, is shown on Row 8. The projected variable cost per unit is given on Row 9; it generally increases over time due to expected increases in materials and labor. Sales rev- enue, which is calculated as units multiplied by price, is given on Row 10. Vari- able costs, equal to units multiplied by VC/unit, are given on Row 11; and fi xed costs excluding depreciation, which are a constant $2,000, are shown on Row 12.

Depreciation is found as the annual rate allowed by the IRS times the depre- ciable basis. As noted in Chapter 3, Congress sets the depreciation rates that can be used for tax purposes and these are the tax rates used in capital budgeting. Congress permits fi rms to depreciate assets by the straight-line method or by an accelerated method. As we will see, profi table fi rms are better off using accelerated depreciation. We discuss depreciation more fully in Appendix 12A; but to simplify things for this chapter, we assume that the applicable accelerated rates for a project with a 4-year life are as given on Row 24 of the depreciation section of the table and that straight-line rates are as given on Row 27. Thus, we assume that if the fi rm uses accelerated depreciation, it will write off 33% of the basis during Year 1, another 45% in Year 2, and so forth. These are the rates used to obtain the cash fl ows shown in the table.

The depreciable basis is the cost of the equipment including any shipping or installation costs, or $900 as shown in Cells E4, C24, and C27. The total deprecia- tion over the 4 years equals the cost of the equipment.

If for some reason the fi rm decided to use straight-line depreciation, it could write off a constant $225 per year. Its total cash fl ows over the entire 4 years would be the same as under accelerated depreciation; but under straight line, those cash fl ows would come in a bit slower because the fi rm would have higher tax pay- ments in the early years and lower tax payments later on.

We calculate the annual cash fl ows for Project S over the 4 years in Columns F, G, H, and I, ending with the net cash fl ows shown on Row 22. The numbers in Cells E22 through I22 amount to a cash fl ow time line, and they are the same num- bers used in Chapter 11 for Project S. Since the numbers are the same, the NPV, IRR, MIRR, and payback shown in Cells C31 through C34 are the same as those we calculated in Chapter 11.

The Excel model used to make Table 12-1 is part of the chapter Excel model available on the text’s web site. We recommend that anyone with a computer and

1 The equipment will be fully depreciated after 4 years. Therefore, the $50 estimated salvage value will exceed the book value, which will be zero. This $50 gain is classifi ed as a recapture of depreciation, and it is taxed at the same rate as ordinary income.

371Chapter 12 Cash Flow Estimation and Risk Analysis

some familiarity with Excel access the model and work through it to see how the table was generated. Anyone doing real-world capital budgeting today would use such a model; and our model provides a good template, or starting point, if and when you need to analyze an actual project.

12-2a Effect of Different Depreciation Rates If we replaced the accelerated depreciation numbers in Table 12-1 with the con- stant $225 values that would exist under straight line, the result would be a cash fl ow time line on Row 22 that has the same total fl ows. However, in the early years, the cash fl ows resulting from straight-line depreciation would be lower than those now in the table; and the later years’ cash fl ows would show higher numbers. You know that dollars received earlier have a higher present value than dollars received later. Therefore, Project S’s NPV is higher if the fi rm uses acceler- ated depreciation. The exact effect is shown in the Project Evaluation section of Table 12-1—the NPV is $78.82 under accelerated depreciation and $64.44, or 18% less, with straight line.

Now suppose Congress wants to encourage companies to increase their capital expenditures to boost economic growth and employment. What change in depre- ciation would have the desired effect? The answer is to make accelerated deprecia- tion even more accelerated. For example, if the fi rm could write off this 4-year equipment at rates of 50%, 35%, 10%, and 5%, its early tax payments would be lower, early cash fl ows would be higher, and the project’s NPV would be higher than that shown in Table 12-1.

12-2b Cannibalization Project S does not involve any cannibalization effects. Suppose, however, that Project S would reduce the net after-tax cash fl ows of another division by $50 per year. No other fi rm would take on this project if our fi rm turns it down. In this case, we would add a row at about Row 18 and deduct $50 for each year. If this were done, Project S would end up with a negative NPV; hence, it would be rejected. On the other hand, if Project S would cause additional fl ows in some other division (a positive externality), those after-tax infl ows should be attrib- uted to Project S.

12-2c Opportunity Costs Now suppose the $900 initial cost shown in Table 12-1 was based on the assump- tion that the project would save money by using some equipment the company now owns and that equipment would be sold for $100, after taxes, if the project is rejected. The $100 is an opportunity cost, and it should be refl ected in our calcula- tions. We would add $100 to the project’s cost. The result would be an NPV of $78.82 ! $100 " ! $21.18, so the project would be rejected.

12-2d Sunk Costs Now suppose the fi rm had spent $150 on a marketing study to estimate potential sales. This $150 could not be recovered regardless of whether the project is accepted or rejected. Should the $150 be charged to Project S when determining its NPV for capital budgeting purposes? The answer is no. We are interested only in incremen- tal costs. The $150 is not an incremental cost; it is a sunk cost. Therefore, it should not enter into the analysis.

One additional point should be made about sunk costs. If the $150 expendi- ture was actually made, in the fi nal analysis, Project S would turn out to be a loser: Its NPV would be $78.82 ! $150 " !$71.18. If we could somehow back up

372 Part 4 Investing in Long-Term Assets: Capital Budgeting

and reconsider the project before the $150 had been spent, we would see that the project should be rejected. However, we can’t back up—at this point, we can either abandon the project or spend $1,000 and go forward with it. If we go for- ward, we will receive an incremental NPV of $78.82, which would reduce the loss from !$150 to !$71.18.

12-2e Other Changes to the Inputs Variables other than depreciation also could be varied, and these changes would alter the calculated cash fl ows and thus NPV and IRR. For example, we could increase or decrease the projected unit sales, the sales price, the variable and/or the fi xed costs, the initial investment cost, the working capital requirements, the salvage value, and even the tax rate if we thought Congress was likely to raise or lower taxes. Such changes could be made easily in an Excel model, making it pos- sible to see the resulting changes in NPV and IRR immediately. This is called sensitivity analysis, and we discuss it later in the chapter when we take up proce- dures for measuring projects’ risks.

SEL F TEST In what ways is the setup for fi nding a project’s cash fl ows similar to the

projected income statements for a new single-product fi rm? In what ways would the two statements be diff erent? (One would fi nd cash fl ows; the other, net income.)

Would a project’s NPV for a typical fi rm be higher or lower if the fi rm used accelerated rather than straight-line depreciation? Why?

How could the analysis in Table 12-1 be modifi ed to consider cannibalization, opportunity costs, and sunk costs?

Why does working capital appear as both a negative and a positive number in Table 12-1?

12-3 REPLACEMENT ANALYSIS2 In the last section, we assumed that Project S was an entirely new project. So all of its cash fl ows were incremental—they occurred only if the fi rm accepted the project. This is true for expansion projects; but for replacement projects, we must fi nd cash fl ow differentials between the new and old projects and these differentials are the incremental fl ows that we analyze.

We evaluate a replacement decision in Table 12-2, which is set up much like Table 12-1, but with data on both a new highly effi cient machine (which will be depreciated on an accelerated basis) and the old machine (which is depreciated on a straight-line basis). Here we fi nd the fi rm’s cash fl ows when it continues using the old machine, then the cash fl ows when it decides to use the new one. Finally, we subtract the old fl ows from the new to arrive at the incremental cash fl ows. We used Excel to do the analysis; but again, we could have used a calculator or pencil and paper. Here are the key inputs used in the analysis. No additional working capital is needed.

2 This section is somewhat technical, but it can be omitted without loss of continuity.

373Chapter 12 Cash Flow Estimation and Risk Analysis

Data applicable to both machines: Sales revenues, which would remain constant $2,500 Expected life of the new and old machines 4 years WACC for the analysis 10% Tax rate 40%

Data for old machine: Market (salvage) value of the old machine today $400 Old labor, materials, and other costs per year $1,000 Old machine’s annual depreciation $100

Data for new machine: Cost of new machine $2,000 New labor, materials, and other costs per year $400

The key here is to fi nd the incremental cash fl ows. As noted previously, we fi nd the cash fl ows from the operation with the old machine, then fi nd the cash fl ows with the new machine, then fi nd the differences in the cash fl ows. This is what we do in Parts I, II, and III of Table 12-2. Since there will be an additional expenditure to buy the new machine, that cost is shown in Cell E13. However, we can sell the old machine for $400, so that is shown as an infl ow in Cell E14. The net cash outlay at Time 0 is $1,600, as shown in Cell E23.

The net cash fl ows based on the old machine are shown on Row 11 and those for the new machine are on Row 23. Then on Row 25, we show the differences in the cash fl ows with and without replacement—these are the incremental cash fl ows used to fi nd the NPV. When we evaluate the incremental cash fl ows, we see that the replacement has an NPV of $80.28, so the old machine should be replaced.3

In some instances, replacements add capacity as well as lower operating costs. When this is the case, sales revenues in Part II would be increased; and if that led to a need for more working capital, that number would be shown as a Time 0 expenditure along with a recovery at the end of the project’s life. These changes would, of course, be refl ected in the differential cash fl ows on Row 25.

3 We could have found the incremental cash fl ows by calculating the diff erences in the only factors that change, the net cost of the new machine, operating cost savings reduced for the taxes, and the diff erences in deprecia- tion, which save some taxes. This procedure is shown in the lower section of the table. The two procedures pro- duce the same incremental cash fl ows and NPV, as they must.

SEL F TEST What role do incremental cash fl ows play in a replacement analysis?

If you were analyzing a replacement project and you suddenly learned that the old equipment could be sold for $1,000 rather than $100, would this new information make the replacement look better or worse? (Better; the net initial investment would be lower.)

In Table 12-2, we assumed that output would not change if the old machine was replaced. Suppose output would actually double. How would this change be dealt with in the framework of Table 12-2?

374 Part 4 Investing in Long-Term Assets: Capital Budgeting

4 Some professors may choose to cover some of the risk sections (12-4 through 12-6) and skip others. We off er a range of choices, and we tried to make the exposition clear enough that interested and self-motivated students can read sections on their own even if the sections are not assigned.

1 2 3 4 5 6 7 8 9

10 11

12 13 14 15 16 17 18 19 20 21 22 23

24 25 26 27 28 29 30 31

32 33 34 35 36 37

38 39

A B C D E F G H I

Part I. Net Cash Flows Before Replacement

Part II. Net Cash Flows After Replacement

Part III. Incremental Cash Flows and Evaluation

Part IV. Alternative (Streamlined) Calculation for NCF

Incremental CFs = CF After - CF Before

Project Evaluation @ WACC =

Sales revenues Costs except depreciation Depreciation Total operating costs Operating income Taxes 40% After-tax operating income Add back depreciation Net cash flows before replacement

New machine cost After-tax salvage value, old machine Sales revenues Costs except depreciation Depreciation Total operating costs Operating income Taxes 40% After-tax operating income Add back depreciation Net cash flows after replacement

10% NPV = IRR =

MIRR = Payback =

$80.28 12.51% 11.35%

2.76

-$2,000 400

$600 360

560 224

800 320

200 80

40 16

-$1,600

-$1,600 $584 $680 $440 $376

-$2,000 $400

-$1,600

-$1,600 $584 $680 $440 $376

New machine cost Salvage value, old machine Net cost of new machine Cost savings = Old - New A-T savings = Cost savings ! (1 - Tax rate)

! Depreciation = (New - old) Depr’n tax savings = ! Depreciation ! Tax rate NCF = A-T cost savings + Depr’n tax savings

$2,500 1,000

100 $1,100 $1,400

560 $840

100 $940

$2,500 1,000

100 $1,100 $1,400

560 $840

100 $940

$2,500 1,000

100 $1,100 $1,400

560 $840

100 $940

$2,500 1,000

100 $1,100 $1,400

560 $840

100 $940

0 1 2 3 4

$2,500 400 660

$1,060 $1,440

576 $864

660 $1,524

$2,500 400 900

$1,300 $1,200

480 $720

900 $1,620

$2,500 400 300

$700 $1,800

720 $1,080

300 $1,380

$2,500 400 140

$540 $1,960

784 $1,176

140 $1,316

Replacement Project RT a b l e 1 2 - 2

12-4 RISK ANALYSIS IN CAPITAL BUDGETING4 Projects differ in risk, and risk should be refl ected in capital budgeting decisions. However, it is diffi cult to measure risk, especially for new projects where no his- tory exists. For this reason, managers deal with risk in many different ways, ranging from almost totally subjective adjustments to highly sophisticated analy- ses that involve computer simulation and high-powered statistics.

375Chapter 12 Cash Flow Estimation and Risk Analysis

Three separate and distinct types of risk are involved: 1. Stand-alone risk, which is a project’s risk assuming (a) that it is the only asset

the fi rm has and (b) that the fi rm is the only stock in each investor’s portfolio. Stand-alone risk is measured by the variability of the project’s expected returns. Diversifi cation is totally ignored.

2. Corporate, or within-fi rm, risk, which is a project’s risk to the corporation as opposed to its investors. Within-fi rm risk takes account of the fact that the project is only one asset in the fi rm’s portfolio of assets; hence, some of its risk will be eliminated by diversifi cation within the fi rm. This type of risk is measured by the project’s impact on uncertainty about the fi rm’s future returns.

3. Market, or beta, risk, which is the riskiness of the project as seen by a well- diversifi ed stockholder who recognizes (a) that the project is only one of the fi rm’s assets and (b) that the fi rm’s stock is but one part of his or her stock portfolio. The project’s market risk is measured by its effect on the fi rm’s beta coeffi cient.

Taking on a project with a great deal of stand-alone or corporate risk will not necessarily affect the fi rm’s beta. However, if the project has high stand-alone risk and if its returns are highly correlated with returns on the fi rm’s other assets and with returns on most other stocks in the economy, the project will have a high degree of all three types of risk. Market risk is theoretically the most relevant of the three because it is the one refl ected in stock prices. Unfor- tunately, market risk is also the most diffi cult to estimate, primarily because new projects don’t have “market prices” that can be related to stock market returns. Therefore, most decision makers do a quantitative analysis of stand- alone risk and then consider the other two risk measures in a qualitative manner.

Projects are generally classifi ed into several categories. Then with the fi rm’s overall WACC as a starting point, a risk-adjusted cost of capital is assigned to each category. For example, a fi rm might establish three risk classes, assign the corporate WACC to average-risk projects, add a 5% risk premium for higher-risk projects, and subtract 2% for low-risk projects. Under this setup, if the company’s overall WACC was 10%, 10% would be used to evaluate average-risk projects, 15% for high-risk projects, and 8% for low-risk projects. While this approach is prob- ably better than not making any risk adjustments, these adjustments are highly subjective and diffi cult to justify. Unfortunately, there’s no perfect way to specify how high or low the adjustments should be.5

Stand-Alone Risk The risk an asset would have if it were a firm’s only asset and if investors owned only one stock. It is measured by the variability of the asset’s expected returns.

Corporate (Within- Firm) Risk Risk considering the firm’s diversification but not stockholder diversification. It is measured by a project’s effect on uncertainty about the firm’s expected future returns.

Market (Beta) Risk Considers both firm and stockholder diversification. It is measured by the project’s beta coefficient.

Risk-Adjusted Cost of Capital The cost of capital appropriate for a given project, given the riskiness of that project. The greater the risk, the higher the cost of capital.

5 We should note that the CAPM approach can be used for projects provided there are specialized publicly traded fi rms in the same business as that of the project under consideration. For further information on estimating the risk-adjusted cost of capital, see Web Appendix 12C; and for more information on measuring market (or beta) risk, see Web Appendix 12D.

SEL F TEST What are the three types of project risk?

Which type is theoretically the most relevant? Why?

What is one classifi cation scheme that fi rms often use to obtain risk-adjusted costs of capital?

376 Part 4 Investing in Long-Term Assets: Capital Budgeting

12-5 MEASURING STAND-ALONE RISK A project’s stand-alone risk refl ects uncertainty about its cash fl ows. The required investment, unit sales, sales prices, and operating costs shown in Table 12-1 for Project S are subject to uncertainty. First-year sales were projected at 537 units (actually, 537,000; but we shortened it to 537 to streamline the analysis) to be sold at a price of $10 per unit. However, unit sales would almost certainly be somewhat higher or lower than 537, and the price would probably turn out to be different from the projected $10 per unit. Similarly, the other variables would probably dif- fer from their indicated values. Indeed, all the inputs are expected values, and actual values can vary from expected values.

Three techniques are used to assess stand-alone risk: (1) sensitivity analysis, (2) scenario analysis, and (3) Monte Carlo simulation. We discuss them in the fol- lowing sections.

12-5a Sensitivity Analysis Intuitively, we know that a change in a key input variable such as units sold or sales price will cause the NPV to change. Sensitivity analysis measures the percent- age change in NPV that results from a given percentage change in an input, other variables held at their expected values. This is by far the most commonly used type of risk analysis, and it is used by most fi rms. It begins with a base-case situation, where the project’s NPV is found using the base-case value for each input variable. Here’s a list of the key inputs for Project S: • Equipment cost • Required working capital • Unit sales • Sales price • Variable cost per unit • Fixed operating costs • Tax rate • WACC

The data we used in Table 12-1 were the most likely, or base-case, values; and the resulting NPV, $78.82, is the base-case NPV. It’s easy to imagine changes in the inputs, and those changes would result in different NPVs.

When senior managers review capital budgeting studies, they are interested in the base-case NPV, but they always go on to ask the fi nancial analyst a series of “what if” questions: What if unit sales turn out to be 25% below the base case level? What if market conditions force us to price the product at $9, not $10? What if variable costs are higher than we forecasted? Sensitivity analysis is designed to provide answers to such questions. Each variable is increased or decreased from its expected value, holding other variables constant at their base- case levels. Then the NPV is calculated using the changed input. Finally, the re- sulting set of NPVs is plotted to show how sensitive NPV is to changes in each variable.

Figure 12-1 shows Project S’s sensitivity graph for six key variables. The table below the graph gives the NPVs based on different values of the inputs, and those NPVs were then plotted to make the graph. Figure 12-1 shows that as unit sales and price increase, the project’s NPV increases, whereas the oppo- site is true for the other four input variables. An increase in variable costs, fi xed costs, equipment costs, and WACC lowers the project’s NPV. The ranges shown at the bottom of the table and the slopes of the lines in the graph indicate how sensitive NPV is to changes in each input. When the data are plotted in

Sensitivity Analysis Percentage change in NPV resulting from a given percentage change in an input variable, other things held constant.

Base-Case NPV The NPV when sales and other input variables are set equal to their most likely (or base-case) values.

Figure 12-1, the slopes of the lines in the graph indicate how sensitive NPV is to each input: The larger the range, the steeper the variable’s slope and the more sensi- tive the NPV is to this variable. We see that NPV is very sensitive to changes in the sales price, fairly sensitive to changes in variable costs, a bit less sensitive to units sold and fi xed costs, but not very sensitive to changes in the equipment cost or the WACC.

If we were comparing two projects, the one with the steeper sensitivity lines would be riskier, other things held constant, because relatively small changes in

Sensitivity Graph for Project SFIGURE 12-1

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

A B C D E F G H I

0% 25%-25%

$2,500 NPV

-$2,500

-$1,500

-$500

$500

$1,500

Price

Equipment

Fixed Costs

WACC

Units

Percentage Deviation from Base

1. When all of the inputs are set at their base-case levels, their deviations from base are all zero and the NPV is $78.82. So the vertical axis intercept is at $78.82.

2. If the sales price is set 25% above its expected $10 price and all other variables are set at their expected values, the NPV would be +$2,526.86. If the price is set 25% below its expected $10 price, the NPV would be -$2,369.22. All the other NPVs shown in the table were found similarly. Excel data tables were used to streamline the calculations. 3. Note that the best and worst case NPVs are different from those in the next section, for scenario analysis. In scenario analysis, all the variables are 25% above or below their expected levels; so the best and worst case NPVs are much higher or lower than those in the sensitivity analysis, where only one variable is set at its best or worst level.

Deviation from Base

Range

NPV with Variables at Different Deviations from Base VC/UnitSales Price

$2,526.86 78.82

-2,369.22 $4,896.07

-$1,245.67 78.82

1,403.31 $2,648.97

Fixed Costs -$872.14

78.82 1,029.78

$1,901.92

Units Sold $1,202.37

78.82 -1,044.73 $2,247.10

WACC $33.62

78.82 127.62 $93.99

Equipment -$71.26

78.82 228.90

$300.17

25% 0%

-25%

377Chapter 12 Cash Flow Estimation and Risk Analysis

378 Part 4 Investing in Long-Term Assets: Capital Budgeting

the input variables would produce large changes in the NPV. Thus, sensitivity analysis provides useful insights into a project’s risk.6

12-5b Scenario Analysis In sensitivity analysis, we change one variable at a time. However, it is useful to know what would happen to the project’s NPV if all of the inputs turned out to be better or worse than expected. Also, we can assign probabilities to the good, bad, and most likely (or base-case) scenarios, then fi nd the expected value and the stan- dard deviation of the NPV. Scenario analysis allows for these extensions—it allows us to change more than one variable at a time, and it incorporates the prob- abilities of changes in the key variables.

In a scenario analysis, we begin with the base-case scenario, which uses the most likely set of input values. We then ask marketing, engineering, and other operating managers to specify a worst-case scenario (low unit sales, low sales price, high variable costs, and so forth) and a best-case scenario. Often the best and worst cases are defi ned as having a 25% probability of conditions being that good or bad, with a 50% probability for the base-case conditions. Obviously, con- ditions can take on many more than three values, but such a scenario setup is use- ful to provide an idea about the project’s riskiness.

The best-case, base-case, and worst-case values for Project S are shown in Figure 12-2, along with plots of the data. If the project is highly successful, the com- bination of a high sales price, low production costs, and high unit sales will result in a very high NPV, $7,450.38. However, if things turn out badly, the NPV will be a negative $4,782.40. The graphs show the wide range of possibilities, suggesting that this is a risky project. If the bad conditions materialize, the company will not go bankrupt—this is just one project for a large company. Still, losing $4,782.40 (or $4,782,400 since we are working in thousands) would hurt the stock price.

If we multiply each scenario’s probability by the NPV under that scenario and then sum the products, we will have the project’s expected NPV, $706.40 as shown in Figure 12-2. Note that the expected NPV differs from the base-case NPV. This is not an error—mathematically, they are not equal. We also calculate the standard deviation of the expected NPV; it is $5,028.94. When we divide the standard devia- tion by the expected NPV, we get the coeffi cient of variation, 7.12, which is a mea- sure of stand-alone risk. The fi rm’s average project has a coeffi cient of variation of about 2.0, so the CV of 7.12 indicates that this project is much riskier than most of the fi rm’s other projects.

Our fi rm’s WACC is 10%, so that rate should be used to fi nd the NPV of an average-risk project. Project S is riskier than average, so a higher discount rate should be used to fi nd its NPV. There is no way to determine the “correct” dis- count rate—this is a judgment call. However, some fi rms increase the corporate WACC when they evaluate projects deemed to be relatively risky and reduce it for low-risk projects. When the NPV was recalculated using a 12.5% WACC, the base- case NPV fell from $78.82 to $33.62; so the project still passed the NPV test.

Note that the base-case results are the same in our sensitivity and scenario analyses; but in the scenario analysis, the worst case is much worse than in the sen- sitivity analysis and the best case is much better. This is because in scenario analysis, all of the variables are set at their best or worst levels, while in sensitivity analysis, only one variable is adjusted and all the others are left at their base-case levels.

Scenario Analysis A risk analysis technique in which “bad” and “good” sets of financial circumstances are compared with a most likely, or base-case, situation.

Base-Case Scenario An analysis in which all of the input variables are set at their most likely values.

Worst-Case Scenario An analysis in which all of the input variables are set at their worst reasonably forecasted values.

Best-Case Scenario An analysis in which all of the input variables are set at their best reasonably forecasted values.

6 Sensitivity analysis is tedious using a regular calculator but easy using a spreadsheet. We used the chapter’s Excel model to calculate the NPVs and to draw the graph in Figure 12-1. To conduct such an analysis by hand would be quite time-consuming, and if the basic data were changed even slightly—say the cost of the equipment was increased slightly—all of the calculations would have to be redone. With a spreadsheet, by simply typing over the old input with the new one, the analysis changes instantaneously.

379Chapter 12 Cash Flow Estimation and Risk Analysis

12-5c Monte Carlo Simulation Monte Carlo simulation, so named because this type of analysis grew out of work on the mathematics of casino gambling, is a sophisticated version of scenario analysis. Here the project is analyzed under a large number of scenarios, or “runs.” In the fi rst run, the computer randomly picks a value for each variable—units sold, sales price, variable costs per unit, and so forth. Those values are then used to cal- culate an NPV, and that NPV is stored in the computer’s memory. Next, a second set of input values is selected at random and a second NPV is calculated. This pro- cess is repeated perhaps 1,000 times, generating 1,000 NPVs. The mean of the 1,000 NPVs is determined and used as a measure of the project’s expected profi tability, and the standard deviation (or perhaps the coeffi cient of variation) of the NPVs is used as a measure of risk.

Monte Carlo Simulation A risk analysis technique in which probable future events are simulated on a computer, generating estimated rates of return and risk indexes.

Cash Flows Under Alternative Scenarios

Prob: Best Case Base Case

Worst Case

25% 50% 25%

-$750 -$1,000 -$1,250

$2,685 $500

-$1,077

$2,520 $400

-$1,119

$2,390 $300

-$1,213

$2,135 $100

-$1,343 Expected NPV

Standard Deviation (SD) Coefficient of Variation (CV) = Std Dev/Expected NPV

7.50% 10.00% 12.50%

$7,450.38 $78.82

-$4,782.40 $706.40

$5,028.94 7.12

0 1 2 3 4 WACC NPV Predicted Cash Flow for Each Year

85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

117 118 119 120

A B C D E F G H I

50%

25%25%

$7,450.38-$4,782.40 NPV

ProbabilityDiscrete Probabilities

0 $78.82 $7,450.38-$4,782.40 NPV

Probability DensityContinuous Probabilities

$78.82

Scenario Analysis for Project SFIGURE 12-2

380 Part 4 Investing in Long-Term Assets: Capital Budgeting

Monte Carlo simulation is technically more complex than scenario analysis, but simulation software makes the process manageable. Simulation is useful; but because of its complexity, a detailed discussion is best left for advanced fi nance courses.7

7 To use Monte Carlo simulation, one needs probability distributions for the inputs and correlation coeffi cients between each pair of inputs. It is often diffi cult to obtain “reasonable” values for the correlations, especially for new projects where no historical data are available. This limits the use of simulation analysis.

A recent survey of executives in Australia, Hong Kong, Indo- nesia, Malaysia, the Philippines, and Singapore asked several questions about companies’ capital budgeting practices. The study yielded the results summarized here.

Techniques for Evaluating Corporate Projects Consistent with U.S. companies, most companies in this region evaluate projects using IRR, NPV, and payback. IRR usage ranged from 96% (in Australia) to 86% (in Hong Kong). NPV usage ranged from 96% (in Australia) to 81% (in the Phil- ippines). Payback usage ranged from 100% (in Hong Kong and the Philippines) to 81% (in Indonesia).

Techniques for Estimating the Cost of Equity Capital Recall from Chapter 10 that three basic approaches can be used to estimate the cost of equity: CAPM, dividend

yield plus growth rate (DCF), and cost of debt plus a risk premium. The use of these methods varied considerably from country to country. (See Table A.) The CAPM is used most often by U.S. firms. This is also true for Australian firms, but not for the other Asian/Pacific firms, which instead are more likely to use the DCF and risk premium approaches.

Techniques for Assessing Risk Firms in the Asian/Pacifi c region rely heavily on scenario and sensitivity analyses. They also use decision trees and Monte Carlo simulation, but less frequently. (See Table B.)

Source: Adapted from George W. Kester et al., “Capital Budgeting Practices in the Asia-Pacifi c Region: Australia, Hong Kong, Indonesia, Malaysia, Philippines, and Singapore,” Financial Practice and Education, Vol. 9, no. 1 (Spring/Summer 1999), pp. 25–33.

CAPITAL BUDGETING PRACTICES IN THE ASIAN/PACIFIC REGION

Table A

Method Australia Hong Kong Indonesia Malaysia Philippines Singapore CAPM 72.7% 26.9% 0.0% 6.2% 24.1% 17.0% Dividend yield plus

growth rate 16.4 53.8 33.3 50.0 34.5 42.6 Cost of debt plus

risk premium 10.9 23.1 53.4 37.5 58.6 42.6

Table B

Risk Assessment Technique Australia Hong Kong Indonesia Malaysia Philippines Singapore Scenario analysis 96% 100% 94% 80% 97% 90% Sensitivity analysis 100 100 88 83 94 79 Decision tree

analysis 44 58 50 37 33 46 Monte Carlo

simulation 38 35 25 9 24 35

381Chapter 12 Cash Flow Estimation and Risk Analysis

12-6 WITHIN-FIRM AND BETA RISK8 Sensitivity analysis, scenario analysis, and Monte Carlo simulation as described in the preceding section dealt with stand-alone risk. They provide useful information about a project’s risk; but if the project is negatively correlated with the fi rm’s other projects, it might actually stabilize the fi rm’s total earnings and thus be rela- tively safe. Similarly, if a project is negatively correlated with returns on most stocks, it might reduce the fi rm’s beta and thus be correctly evaluated with a rela- tively low WACC. So in theory, we should be more concerned with within-fi rm and beta risk than with stand-alone risk.

Although managers recognize the importance of within-fi rm and beta risk, they generally end up dealing with these risks subjectively, or judgmentally, rather than quantitatively. The problem is that to measure diversifi cation’s ef- fects on risk, we need the correlation coeffi cient between a project’s returns and re- turns on the fi rm’s other assets, which requires historical data that obviously does not exist for new projects. Experienced managers generally have a “feel” for how a project’s returns will relate to returns on the fi rm’s other assets. Gener- ally, positive correlation is expected; and if the correlation is high, stand-alone risk will be a good proxy for within-fi rm risk. Similarly, managers can make judgmental estimates about whether a project’s returns will be high when the economy and the stock market are strong (hence, what the project’s beta should be). But for the most part, those estimates are subjective, not based on actual data.

However, projects occasionally involve an entirely new product line, such as a steel company going into iron ore mining. In such cases, the fi rm may be able to obtain betas for “pure-play” companies in the new area. For example, this steel company might get the average beta for a group of mining companies such as Rio Tinto and BHP, assume that its mining subsidiary has similar characteristics, and use the average beta of the “comparables” to calculate a WACC for the mining subsidiary. While the pure-play approach makes sense for some projects, it is actu- ally rare. Just think about it. How would you fi nd a pure-play proxy for a new in- ventory control system, machine tool, truck, or most other projects? The answer is, you couldn’t.

Our conclusions regarding risk analysis are as follows: • It is very diffi cult, if not impossible, to quantitatively measure projects’ within-

fi rm and beta risks. • Most projects’ returns are positively correlated with returns on the fi rm’s other

assets and with returns on the stock market. This being the case, stand-alone risk is correlated with within-fi rm and market risk; so not much is lost by focusing just on stand-alone risk.

8 This section is relatively technical, but it can be omitted without a loss of continuity.

SEL F TEST Explain briefl y how a sensitivity analysis is done and what the analysis is

designed to show.

What is a scenario analysis, what is it designed to show, and how does it dif- fer from a sensitivity analysis?

What is Monte Carlo simulation? How does a simulation analysis diff er from a regular scenario analysis?

382 Part 4 Investing in Long-Term Assets: Capital Budgeting

• Experienced managers make many judgmental assessments, including those related to risk; and they work them into the capital budgeting process. Introductory students like neat, precise answers; and they want to make decisions on the basis of calculated NPVs. Experienced managers consider quantitative NPVs, but they also bring subjective judgment into the deci- sion process.

• If a fi rm does not use the types of analyses covered in this book, it will have trouble. On the other hand, if a fi rm tries to quantify everything and let a com- puter make its decisions, it too will have trouble. Good managers understand and use the theory of fi nance, but they apply it with judgment.

9 This section is relatively technical, but it can be omitted without loss of continuity if there is insuffi cient time to cover it. 10 Large investors such as Warren Buff ett and some hedge fund operators can buy stock in companies and then infl uence the fi rms’ operations and cash fl ows. However, the average stockholder does not have such infl uence.

SEL F TEST Is it easier to measure the stand-alone, within-fi rm, or beta risk for projects

such as a new delivery truck or a Home Depot warehouse?

If a fi rm cannot measure a potential project’s risk with precision, should it abandon the project? Explain your answer.

12-7 REAL OPTIONS9 Traditional discounted cash fl ow (DCF) analysis—where cash fl ows are estimated and then discounted to obtain the expected NPV—has been the cornerstone of capital budgeting since the 1950s. However, in recent years, it has been shown that DCF techniques do not always lead to proper capital budgeting decisions.

DCF techniques were originally developed to value securities such as stocks and bonds. These are passive investments—once the investment has been made, most investors can take no actions that infl uence the cash fl ow the investment pro- duces.10 However, capital budgeting projects are not passive investments— managers can often take positive actions after the investment has been made that alter the cash fl ow stream. Opportunities for such actions are called real options— “real” to distinguish them from fi nancial options, such as an option to buy shares of GE stock, and “options” because they offer the right but not the obligation to take the future action to increase cash fl ows. Real options are valuable, but this value is not captured by conventional NPV analysis. Therefore, a project’s real op- tions must be considered separately.

12-7a Types of Real Options There are several types of real options, including (1) abandonment, where the proj- ect can be shut down if its cash fl ows are low; (2) timing, where a project can be delayed until more information about demand and/or costs can be obtained; (3) expansion, where the project can be expanded if demand turns out to be stron- ger than expected; (4) output fl exibility, where the output can be changed if market conditions change; and (5) input fl exibility, where the inputs used in the production

Real Option The right but not the obligation to take some action in the future.

383Chapter 12 Cash Flow Estimation and Risk Analysis

process (e.g., coal versus natural gas for generating electricity) can be changed if input prices and/or availability change. We illustrate abandonment options here in the text, and we cover other types of options in Web Appendix 12F.

12-7b Abandonment Options In capital budgeting, we generally assume that a project will be operated for its full physical life. However, this is not always the best course of action. If the fi rm’s project has an abandonment option that can be implemented if things don’t go well, this can lower its risk, increase its expected profi tability, and raise its calcu- lated NPV.

Table 12-3 gives a picture of the decision tree for Project S. In the scenario analysis in Section 12-5, we examined Project S under the best-case, base-case, and worst-case assumptions. In the worst-case situation, the project has negative cash fl ows for its full 4-year life. However, if the company can abandon the project after Year 1, when it sees that the project is not a success, its expected NPV can be im- proved. The earlier analysis is reproduced in the top section of Table 12-3, labeled “No Abandonment.” In Column C, which is Time 0, we see that the fi rm must in- vest between $750 and $1,250. Columns D through G show the annual cash fl ows under each scenario; and in Column H, we show the WACCs for each scenario. Then in Column I, we show the NPV under each scenario when the cash fl ows are discounted at their respective WACCs. The sum of the products obtained by mul- tiplying each probability times each branch NPV is the expected NPV, which is $706.40. The standard deviation and the coeffi cient of variation are also calculated to provide an idea of the project’s risk. This project has a positive expected NPV; hence, by the NPV criterion, it should be accepted.

Now suppose the company could make a second decision, at t " 1, to aban- don (or shut down) the project if things go badly during Year 1. To see what would happen, we add another branch to the tree, as shown in the Worst #2 row in Table 12-3 under the “Can Abandon” situation. Here we assume that the com- pany abandons the project at the end of Year 1, when information about the actual production costs and demand conditions become available. If things were going well, the project would be continued. However, if things were going badly, the fi rm would close the operation and not suffer the indicated losses during the next 3 years.11

Given the “Can Abandon” option, the fi rm would clearly prefer to abandon the project than to continue. Therefore, we assign a zero probability to continuing after a bad start. Therefore, the 25% probability associated with the worst case is used for “Worst #2,” and a 0% probability is assigned to “Worst #1.”

The option to abandon raises the expected NPV from $706.40 to $1,350.09, and it lowers the standard deviation. Those changes combine to lower the coeffi cient of variation. The coeffi cient of variation is 3.05, which is above the company’s aver- age of 2.0, which indicates that the project is still riskier than most, even after the abandonment option has been factored in. Therefore, the 12.50% WACC is still ap- propriate. Also note that the difference between the expected NPVs with and with- out abandonment represents the option value to abandon this project. As shown in the lower part of Table 12-3, this option is worth $643.68.

In this case, the ability to abandon makes the NPV look better; but it does not reverse the accept/reject decision. However, it often turns out that if we fail to consider abandonment, the bad case is so bad that the expected NPV is negative.

Abandonment Option The option to abandon a project if operating cash flows turn out to be lower than expected. This option can raise expected profitability and lower project risk.

Decision Tree A diagram that lays out different branches that are the result of different decisions made or the result of different economic situations.

Option Value The difference between the expected NPVs with and without the relevant option. It is the value that is not accounted for in a traditional NPV analysis. A positive option value expands the firm’s opportunities.11 If the assets devoted to the project could be sold, this would be a cash infl ow at the time of the sale, presum-

ably at the end of Year 1.

384 Part 4 Investing in Long-Term Assets: Capital Budgeting

SEL F TEST Why might DCF techniques not lead to proper capital budgeting decisions?

What is a real option?

What are some types of real options? Briefl y explain each one.

Would you expect an abandonment option to increase or decrease a project’s NPV and its risk as measured by the coeffi cient of variation? Why or why not?

How can the value of an option be estimated?

But when abandonment is considered, the expected NPV becomes positive. Clearly, abandonment must be considered to obtain valid assessments for differ- ent projects, and the opportunity to abandon is an important way to limit down- side losses.

Note too that it might be necessary for the fi rm to make arrangements so that it has the option of abandoning a project when it is making the initial decision. This might require contractual arrangements with suppliers, customers, and its union; and there might be some costs to obtaining the advance permissions. Any such costs could be compared with the value of the option as we calculated it, which would enter into the initial decision.

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

A B C D E F G H I J

Situation 1. No Abandonment

Prob: Best Case Base Case

Worst Case

25% 50% 25%

-$750 -$1,000 -$1,250

$2,685 $500

-$1,077

$2,520 $400

-$1,119

$2,390 $300

-$1,213

$2,135 $100

-$1,343 Expected NPV

Standard Deviation (SD) Coefficient of Variation (CV) = Std Dev/Expected NPV

7.50% 10.00% 12.50%

$7,450.38 $78.82

-$4,782.40 $706.40

$5,028.94 7.12

0 1 2 3 4 WACC NPV Predicted Cash Flow for Each Year

Situation 2. Can Abandon

Prob. Best Case Base Case

Worst #1 Worst #2

25% 50% 0%

25%

-$750 -$1,000 -$1,250 -$1,250

$2,685 $500

-$1,077 -$1,077

$2,520 $400

-$1,119 $0

$2,390 $300

-$1,213 $0

$2,135 $100

-$1,343 $0

Expected NPV (includes #2, excludes #1) Standard Deviation (SD)

Coefficient of Variation (CV) = Std Dev/Expected NPV

Value of the Real Option to Abandon Expected NPV with Abandonment Expected NPV without Abandonment Difference = Value of the Option

$1,350.09 $706.40 $643.68

Don’t use Use

7.50% 10.00% 12.50% 12.50%

$7,450.38 $78.82

-$4,782.40 -$2,207.67 $1,350.09 $4,121.03

3.05

0 1 2 3 4 WACC NPV Predicted Cash Flow for Each Year

Decision Tree for Abandonment Option (Dollars in Thousands)T a b l e 1 2 - 3

385Chapter 12 Cash Flow Estimation and Risk Analysis

12-8 THE OPTIMAL CAPITAL BUDGET Thus far, we have described various factors that managers consider when they evaluate individual projects. For planning purposes, managers must also fore- cast the total capital budget because the amount of capital raised affects the WACC and thus infl uences projects’ NPVs. We use Data Devices Inc. (DDI), a manufacturer and distributor of storage devices, to illustrate how this process works. Step 1. The treasurer obtains an estimate of the fi rm’s overall composite WACC.

As we discussed in Chapter 10, this composite WACC is based on market conditions, the fi rm’s capital structure, and the riskiness of its assets. DDI’s projects are roughly similar from year to year in terms of their risks.

Step 2. The corporate WACC is scaled up or down for each of the fi rm’s divi- sions to refl ect the division’s risk. DDI, for example, assigns a factor of 0.9 to its stable, low-risk replacement battery division, but a factor of 1.1 to its large disk drives (an extremely competitive business), which it sells to computer manufacturers. Therefore, if the corporate cost of capital is determined to be 10.50%, the cost of capital for the battery division is 0.9(10.50%) " 9.45%, while that for the disk-drive division is 1.1(10.50%) " 11.55%.

Step 3. Financial managers within each of the fi rm’s divisions estimate the rele- vant cash fl ows and risks of each of their potential projects. The estimated cash fl ows should consider any embedded real options. Then within each division, projects are classifi ed into one of three groups—high risk, aver- age risk, and low risk—and the same 0.9 and 1.1 factors are used to adjust the divisional cost of capital estimates. (A factor of 1.0 would be used for an average-risk project.) For example, a low-risk project in the battery division would be assigned a cost of capital of 0.9(9.45%) " 8.51%, while a high-risk project in the disk-drive division would have a cost of 1.1(11.55%) " 12.71%.

Step 4. Each project’s NPV is determined using its risk-adjusted cost of capital. The optimal capital budget consists of all independent projects with positive NPVs plus those mutually exclusive projects with the highest positive NPVs.

In estimating its optimal capital budget, we assumed that DDI will be able to obtain fi nancing for all of its profi table projects. This assumption is reasonable for large, mature fi rms with good track records. However, smaller fi rms, new fi rms, and fi rms with dubious track records may have diffi culties raising capital, even for projects that the fi rm concludes would have highly positive NPVs. In such circum- stances, the size of the capital budget may be constrained, a situation called capital rationing. When capital is limited, it should be used in the most effi cient way pos- sible. Procedures have been developed for allocating capital so as to maximize the aggregate NPV subject to the constraint that the capital rationing ceiling is not ex- ceeded. However, because these procedures are extremely complicated, they are best left for advanced fi nance courses.

The procedures discussed in this section cannot be implemented with precision. However, they do force the fi rm to think carefully about each division’s relative risk, about the risk of each project within the divisions, and about the relationship between the total amount of capital raised and the cost of that capital. Further, the process forces the fi rm to adjust its capital budget to refl ect capital market condi- tions. If the costs of debt and equity rise, this fact will be refl ected in the cost of capital used to evaluate projects. Thus, projects that would be marginally accept- able when capital costs were low would (correctly) be ruled unacceptable when capital costs become high.

Optimal Capital Budget The annual investment in long-term assets that maximizes the firm’s value.

Capital Rationing The situation in which a firm can raise only a specified, limited amount of capital regardless of how many good projects it has.

386 Part 4 Investing in Long-Term Assets: Capital Budgeting

12-9 THE POST-AUDIT A fi nal aspect of the capital budgeting process is the post-audit, which involves (1) comparing actual results with those predicted by the project’s sponsors and (2) explaining why any differences occurred. For example, many fi rms require that the operating divisions send a monthly report for the fi rst 6 months after a project goes into operation and a quarterly report thereafter until the project’s results meet expectations. From then on, reports on the operation are reviewed on a regular basis like those of other operations. The post-audit has two main purposes: 1. Improve forecasts. When decision makers are forced to compare their projec-

tions with actual outcomes, there is a tendency for estimates to improve. Con- scious or unconscious biases are observed and eliminated; new forecasting methods are sought as the need for them becomes apparent; and people sim- ply tend to do everything better, including forecasting, when they know that their actions are being monitored.

2. Improve operations. Businesses are run by people, and people can perform at higher or lower levels of effi ciency. When a divisional team has made a fore- cast about an investment, the team members are, in a sense, putting their repu- tations on the line. Accordingly, if costs are above and sales are below pre- dicted levels, executives in production, marketing, and other areas will strive to improve operations and to bring results in line with forecasts. In a discus- sion related to this point, one executive made this statement: “You academi- cians only worry about making good decisions. In business, we also worry about making decisions good.”

The post-audit is not a simple process. First, we must recognize that each element of the cash fl ow forecast is subject to uncertainty, so a percentage of all projects under- taken by any reasonably aggressive fi rm will necessarily go awry. This fact must be considered when appraising the performances of the operating executives who spon- sor projects. Second, projects sometimes fail to meet expectations for reasons beyond the control of their sponsors and for reasons that no one could be expected to antici- pate. For example, the unanticipated run-up in oil prices in 2007 adversely affected many projects. Third, it is often diffi cult to separate the operating results of one in- vestment from those of a larger system. Although some projects stand alone and per- mit ready identifi cation of costs and revenues, the cost savings that result from assets such as new computers may be very hard to measure. Fourth, it is often hard to hand out blame or praise because the executives who were responsible for launching a given investment have moved on by the time the results are known.

Because of these diffi culties, some fi rms tend to play down the importance of the post-audit. However, observations of both businesses and governmental units suggest that the best-run and most successful organizations put a great deal of emphasis on post-audits. Accordingly, we regard the post-audit as an important element in a good capital budgeting system.

Post-Audit A comparison of actual versus expected results for a given capital project.

SEL F TEST Explain how a fi nancial manager might estimate his or her fi rm’s optimal

capital budget.

What is capital rationing?

What factors must be considered when a fi rm is developing its optimal capi- tal budget?

How does a fi rm’s annual capital budget refl ect market conditions?

387Chapter 12 Cash Flow Estimation and Risk Analysis

SEL F TEST What is done in the post-audit?

Identify several benefi ts of the post-audit.

What are some factors that complicate the post-audit process?

This chapter focused on estimating the cash fl ows that are used in a capital budget- ing analysis, appraising the riskiness of those fl ows, fi nding NPVs when risk is pres- ent, and determining the values of real options, which can raise expected returns and lower risks. Here is a summary of our primary conclusions:

• Some cash fl ows are relevant (hence, should be included in a capital budgeting analysis), while others should not be included. The key question is this: Is the cash fl ow incremental in the sense that it will occur if and only if the project is accepted?

• Sunk costs are not incremental costs—they are not aff ected by accepting or rejecting the project. Cannibalization and other externalities, on the other hand, are incremental—they will occur if and only if the project is accepted.

• The cash fl ows used to analyze a project are diff erent from a project’s net income. One important factor is that depreciation is deducted when accountants calcu- late net income; but because it is a noncash charge, it must be added back to fi nd cash fl ows.

• Many projects require additional net working capital. Net working capital is a nega tive fl ow when the project is started but a positive fl ow at the end of the project’s life, when the capital is recovered.

• We considered two types of projects—expansion and replacement. For a replace- ment project, we fi nd the diff erence in the cash fl ows when the fi rm continues to use the old asset versus the new asset. If the NPV of the diff erential fl ows is posi- tive, the replacement should be made.

• The forecasted cash fl ows (and hence NPV and other outputs) are only estimates— they may turn out to be incorrect, and this means risk.

• There are three types of risk: stand-alone, within-firm, and market (or beta) risk. In theory, market risk is most relevant; but since it cannot be measured for most projects, stand-alone risk is the one on which we generally focus. How- ever, firms subjectively consider within-firm and market risk, which they defi- nitely should not ignore. Note, though, that since the three types of risk are generally positively correlated, stand-alone risk is often a good proxy for the other risks.

• Stand-alone risk can be analyzed using sensitivity analysis, scenario analysis, and/ or Monte Carlo simulation.

• Once a decision has been made about a project’s relative risk, we determine a risk- adjusted WACC for evaluating it.

T YING I T ALL TO GETHER

388 Part 4 Investing in Long-Term Assets: Capital Budgeting

• Real options enable fi rms to take actions to alter the originally forecasted cash fl ows after a project is in operation. These options can increase NPVs.

• The post-audit, which compares the project’s actual performance to its expected results, is an important part of the capital budgeting process.

KEY TERMS Define the following terms: a. Incremental cash flow; sunk cost; opportunity cost; externality; cannibalization b. Stand-alone risk; corporate (within-firm) risk; market (beta) risk c. Risk-adjusted cost of capital d. Sensitivity analysis; base-case NPV e. Scenario analysis; base-case scenario; worst-case scenario; best-case scenario f. Monte Carlo simulation g. Real option; abandonment option; decision tree h. Option value i. Optimal capital budget; capital rationing j. Post-audit

PROJECT AND RISK ANALYSIS As a financial analyst, you must evaluate a proposed project to produce printer cartridges. The equipment would cost $55,000, plus $10,000 for installation. Annual sales would be 4,000 units at a price of $50 per cartridge, and the project’s life would be 3 years. Current assets would increase by $5,000 and payables by $3,000. At the end of 3 years, the equipment could be sold for $10,000. Depreciation would be based on the MACRS 3-year class; so the applicable rates would be 33%, 45%, 15%, and 7%. Variable costs would be 70% of sales revenues, fixed costs excluding depreciation would be $30,000 per year, the marginal tax rate is 40%, and the corporate WACC is 11%. a. What is the required investment, that is, the Year 0 project cash flow? b. What are the annual depreciation charges? c. What are the project’s annual net cash flows? d. If the project is of average risk, what is its NPV? Should it be accepted? e. Suppose management is uncertain about the exact unit sales. What would the

project’s NPV be if unit sales turned out to be 20% below forecast but other inputs were as forecasted? Would this change the decision? Explain.

f. The CFO asks you to do a scenario analysis using these inputs:

Probability Unit Sales VC% Best case 25% 4,800 65% Base case 50 4,000 70 Worst case 25 3,200 75

Other variables are unchanged. What are the expected NPV, its standard deviation, and the coefficient of variation? [Hint: To do the scenario analysis, you must change unit sales and VC% to the values specified for each scenario, get the scenario cash flows, and then find each scenario’s NPV. Then you must calculate the project’s expected NPV, standard deviation (SD), and coefficient of variation (CV). This is not difficult, but it requires many calculations. You might want to look at the answer, but make sure you understand how it was computed.]

g. The firm’s project CVs generally range from 1.0 to 1.5. A 3% risk premium is added to the WACC if the initial CV exceeds 1.5, and the WACC is reduced by 0.5% if the CV

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

389Chapter 12 Cash Flow Estimation and Risk Analysis

is 0.75 or less. Then a revised NPV is calculated. What WACC should be used for this project? What are the revised values for the expected NPV, standard deviation, and coefficient of variation? Would you recommend that the project be accepted? Why or why not?

Operating cash flows rather than accounting income are listed in Table 12-1. Why do we focus on cash flows as opposed to net income in capital budgeting?

Explain why sunk costs should not be included in a capital budgeting analysis but opportunity costs and externalities should be included. Give an example of each.

Explain why working capital is included in a capital budgeting analysis and how it is recovered at the end of a project’s life.

Why are interest charges not deducted when a project’s cash flows for use in a capital budgeting analysis are calculated?

Most firms generate cash inflows every day, not just once at the end of the year. In capital budgeting, should we recognize this fact by estimating daily project cash flows and then using them in the analysis? If we do not, are our results biased? If so, would the NPV be biased up or down? Explain.

What are some differences in the analysis for a replacement project versus that for a new expansion project?

Distinguish among beta (or market) risk, within-firm (or corporate) risk, and stand-alone risk for a project being considered for inclusion in the capital budget.

In theory, market risk should be the only “relevant” risk. However, companies focus as much on stand-alone risk as on market risk. What are the reasons for the focus on stand- alone risk?

Define (a) sensitivity analysis, (b) scenario analysis, and (c) simulation analysis. If GE was considering two projects (one for $500 million to develop a satellite communications system and the other for $30,000 for a new truck), on which project would the company be more likely to use a simulation analysis?

If you were the CFO of a company that had to decide on hundreds of potential projects every year, would you want to use sensitivity analysis and scenario analysis as described in the chapter or would the amount of arithmetic required take too much time and thus not be cost-effective? What involvement would nonfinancial people such as those in marketing, accounting, and production have in the analysis?

REQUIRED INVESTMENT Truman Industries is considering an expansion. The necessary equipment would be purchased for $9 million, and the expansion would require an addi- tional $3 million investment in working capital. The tax rate is 40%. a. What is the initial investment outlay? b. The company spent and expensed $50,000 on research related to the project last year.

Would this change your answer? Explain. c. The company plans to use another building that it owns to house the project. The

building could be sold for $1 million after taxes and real estate commissions. How would that fact affect your answer?

PROJECT CASH FLOW Eisenhower Communications is trying to estimate the first-year net cash flow (at Year 1) for a proposed project. The financial staff has collected the following information on the project:

QUESTIONS QUESTIONS

12-112-1

12-212-2

12-312-3

12-412-4

12-512-5

12-612-6

12-712-7

12-812-8

12-912-9

12-1012-10

PROBLEMS PROBLEMS

12-112-1Easy Problems 1–4 Easy Problems 1–4

12-212-2

390 Part 4 Investing in Long-Term Assets: Capital Budgeting

Sales revenues $10 million Operating costs (excluding depreciation) 7 million Depreciation 2 million Interest expense 2 million

The company has a 40% tax rate, and its WACC is 10%. a. What is the project’s net cash flow for the first year (t " 1)? b. If this project would cannibalize other projects by $1 million of cash flow before taxes

per year, how would this change your answer to Part a? c. Ignore Part b. If the tax rate dropped to 30%, how would that change your answer to

Part a?

NET SALVAGE VALUE Kennedy Air Services is now in the final year of a project. The equipment originally cost $20 million, of which 80% has been depreciated. Kennedy can sell the used equipment today for $5 million, and its tax rate is 40%. What is the equipment’s after-tax net salvage value?

REPLACEMENT ANALYSIS The Chang Company is considering the purchase of a new machine to replace an obsolete one. The machine being used for the operation has a book value and a market value of zero. However, the machine is in good working order and will last at least another 10 years. The proposed replacement machine will perform the operation so much more efficiently that Chang’s engineers estimate that it will produce after-tax cash flows (labor savings and depreciation) of $9,000 per year. The new machine will cost $40,000 delivered and installed, and its economic life is estimated to be 10 years. It has zero salvage value. The firm’s WACC is 10%, and its marginal tax rate is 35%. Should Chang buy the new machine?

DEPRECIATION METHODS Kristin is evaluating a capital budgeting project that should last 4 years. The project requires $800,000 of equipment. She is unsure what depreciation method to use in her analysis, straight-line or the 3-year MACRS accelerated method. Under straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life. (Ignore the half-year convention for the straight-line method.) The applicable MACRS depreciation rates are 33%, 45%, 15%, and 7% as discussed in Appen- dix 12A. The company’s WACC is 10%, and its tax rate is 40%. a. What would the depreciation expense be each year under each method? b. Which depreciation method would produce the higher NPV, and how much higher

would it be?

SCENARIO ANALYSIS Huang Industries is considering a proposed project whose estimated NPV is $12 million. This estimate assumes that economic conditions will be “average.” However, the CFO realizes that conditions could be better or worse, so she performed a scenario analysis and obtained these results:

Economic Scenario Probability of Outcome NPV Recession 0.05 ($70 million) Below average 0.20 (25 million) Average 0.50 12 million Above average 0.20 20 million Boom 0.05 30 million

Calculate the project’s expected NPV, standard deviation, and coefficient of variation.

NEW PROJECT ANALYSIS You must evaluate a proposed spectrometer for the R&D Department. The base price is $140,000, and it would cost another $30,000 to modify the equipment for special use by the firm. The equipment falls into the MACRS 3-year class and would be sold after 3 years for $60,000. The applicable depreciation rates are 33%, 45%, 15%, and 7% as discussed in Appendix 12A. The equipment would require an $8,000 increase in working capital (spare parts inventory). The project would have no effect on revenues, but it should save the firm $50,000 per year in before-tax labor costs. The firm’s marginal federal-plus-state tax rate is 40%. a. What is the net cost of the spectrometer; that is, what is the Year 0 project cash flow? b. What are the project’s annual net cash flows in Years 1, 2, and 3? c. If the WACC is 12%, should the spectrometer be purchased? Explain.

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391Chapter 12 Cash Flow Estimation and Risk Analysis

NEW PROJECT ANALYSIS You must evaluate a proposal to buy a new milling machine. The base price is $108,000, and shipping and installation costs would add another $12,500. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $65,000. The applicable depreciation rates are 33%, 45%, 15%, and 7% as discussed in Appendix 12A. The machine would require a $5,500 increase in working capital (increased inventory less increased accounts payable). There would be no effect on revenues, but pretax labor costs would decline by $44,000 per year. The marginal tax rate is 35%, and the WACC is 12%. Also, the firm spent $5,000 last year investigating the feasibility of using the machine. a. How should the $5,000 spent last year be handled? b. What is the net cost of the machine for capital budgeting purposes, that is, the Year 0

project cash flow? c. What are the project’s annual net cash flows during Years 1, 2, and 3? d. Should the machine be purchased? Explain your answer.

REPLACEMENT ANALYSIS The Dauten Toy Corporation uses an injection molding machine that was purchased 2 years ago. This machine is being depreciated on a straight-line basis, and it has 6 years of remaining life. Its current book value is $2,100, and it can be sold for $2,500 at this time. Thus, the annual depreciation expense is $2,100/6 " $350 per year. If the old machine is not replaced, it can be sold for $500 at the end of its useful life.

Dauten is offered a replacement machine that has a cost of $8,000, an estimated useful life of 6 years, and an estimated salvage value of $800. This machine falls into the MACRS 5-year class; so the applicable depreciation rates are 20%, 32%, 19%, 12%, 11%, and 6%. The replacement machine would permit an output expansion, so sales would rise by $1,000 per year. Even so, the new machine’s greater efficiency would cause operating expenses to decline by $1,500 per year. The new machine would require that inventories be increased by $2,000, but accounts payable would simultaneously increase by $500. Dauten’s marginal federal-plus-state tax rate is 40%, and its WACC is 15%. Should the company replace the old machine?

REPLACEMENT ANALYSIS Mississippi River Shipyards is considering replacing an 8-year-old riveting machine with a new one that will increase earnings before depreciation from $27,000 to $54,000 per year. The new machine will cost $82,500, and it will have an estimated life of 8 years and no salvage value. The new machine will be depreciated over its 5-year MACRS recovery period; so the applicable depreciation rates are 20%, 32%, 19%, 12%, 11%, and 6%. The applicable corporate tax rate is 40%, and the firm’s WACC is 12%. The old machine has been fully depreciated and has no salvage value. Should the old riveting machine be replaced by the new one? Explain your answer.

PROJECT RISK ANALYSIS The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $6,750 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

PROJECT A PROJECT B Probability Cash Flows Probability Cash Flows

0.2 $6,000 0.2 $ 0 0.6 6,750 0.6 6,750 0.2 7,500 0.2 18,000

BPC has decided to evaluate the riskier project at 12% and the less risky project at 10%. a. What is each project’s expected annual cash flow? Project B’s standard deviation

(σB) is $5,798, and its coefficient of variation (CVB) is 0.76. What are the values of σA and CVA?

b. Based on the risk-adjusted NPVs, which project should BPC choose? c. If you knew that Project B’s cash flows were negatively correlated with the firm’s

other cash flows whereas Project A’s flows were positively correlated, how might this affect the decision? If Project B’s cash flows were negatively correlated with gross domestic product (GDP) while A’s flows were positively correlated, would that influence your risk assessment? Explain.

SCENARIO ANALYSIS Your firm, Agrico Products, is considering a tractor that would have a net cost of $36,000, would increase pretax operating cash flows before taking account of depreciation by $12,000 per year, and would be depreciated on a straight-line

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12-1212-12Challenging Problems 12–15

Challenging Problems 12–15

392 Part 4 Investing in Long-Term Assets: Capital Budgeting

basis to zero over 5 years at the rate of $7,200 per year beginning the first year. (Thus, annual cash flows would be $12,000 before taxes plus the tax savings that result from $7,200 of depreciation.) The managers are having a heated debate about whether the tractor would last 5 years. The controller insists that she knows of tractors that have lasted only 4 years. The treasurer agrees with the controller, but he argues that most tractors do give 5 years of service. The service manager then states that some last as long as 8 years.

Given this discussion, the CFO asks you to prepare a scenario analysis to determine the importance of the tractor’s life on the NPV. Use a 40% marginal federal-plus-state tax rate, a zero salvage value, and a 10% WACC. Assuming each of the indicated lives has the same probability of occurring (probability " 1/3), what is the tractor’s expected NPV? (Hint: Use the 5-year straight-line depreciation for all analyses and ignore the MACRS half-year convention for this problem.)

NEW PROJECT ANALYSIS Holmes Manufacturing is considering a new machine that costs $250,000 and would reduce pretax manufacturing costs by $90,000 annually. Holmes would use the 3-year MACRS method to depreciate the machine, and management thinks the machine would have a value of $23,000 at the end of its 5-year operating life. The applicable depreciation rates are 33%, 45%, 15%, and 7% as discussed in Appendix 12A. Working capital would increase by $25,000 initially, but it would be recovered at the end of the project’s 5-year life. Holmes’s marginal tax rate is 40%, and a 10% WACC is appropriate for the project. a. Calculate the project’s NPV, IRR, MIRR, and payback. b. Assume that management is unsure about the $90,000 cost savings—this figure could

deviate by as much as plus or minus 20%. What would the NPV be under each of these situations?

c. Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine’s salvage value, and the working capital (WC) r equirement. She asks you to use the following probabilities and values in the scenario analysis:

Scenario Probability Cost Savings Salvage Value WC Worst case 0.35 $ 72,000 $18,000 $30,000 Base case 0.35 90,000 23,000 25,000 Best case 0.30 108,000 28,000 20,000

Calculate the project’s expected NPV, its standard deviation, and its coefficient of variation. Would you recommend that the project be accepted? Why or why not?

REPLACEMENT ANALYSIS The Erley Equipment Company purchased a machine 5 years ago at a cost of $90,000. The machine had an expected life of 10 years at the time of purchase, and it is being depreciated by the straight-line method by $9,000 per year. If the machine is not replaced, it can be sold for $10,000 at the end of its useful life.

A new machine can be purchased for $150,000, including installation costs. During its 5-year life, it will reduce cash operating expenses by $50,000 per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless. MACRS depreciation will be used. The machine will be depreciated over its 3-year class life rather than its 5-year economic life; so the applicable depreciation rates are 33%, 45%, 15%, and 7%.

The old machine can be sold today for $55,000. The firm’s tax rate is 35%. The appro- priate WACC is 16%. a. If the new machine is purchased, what is the amount of the initial cash flow at Year 0? b. What are the incremental net cash flows that will occur at the end of Years 1 through 5? c. What is the NPV of this project? Should Erley replace the old machine? Explain.

REPLACEMENT ANALYSIS The Bigbee Bottling Company is contemplating the replacement of one of its bottling machines with a newer and more efficient one. The old machine has a book value of $600,000 and a remaining useful life of 5 years. The firm does not expect to realize any return from scrapping the old machine in 5 years, but it can sell it now to another firm in the industry for $265,000. The old machine is being depreciated by $120,000 per year using the straight-line method.

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393Chapter 12 Cash Flow Estimation and Risk Analysis

The new machine has a purchase price of $1,175,000, an estimated useful life and MACRS class life of 5 years, and an estimated salvage value of $145,000. The applicable depreciation rates are 20%, 32%, 19%, 12%, 11%, and 6%. The machine is expected to economize on electric power usage, labor, and repair costs as well as to reduce the number of defective bottles. In total, an annual savings of $255,000 will be realized if the new machine is installed. The company’s marginal tax rate is 35%, and it has a 12% WACC. a. What initial cash outlay is required for the new machine? b. Calculate the annual depreciation allowances for both machines and compute the

change in the annual depreciation expense if the replacement is made. c. What are the incremental net cash flows in Years 1 through 5? d. Should the firm purchase the new machine? Support your answer. e. In general, how would each of the following factors affect the investment decision,

and how should each be treated? (1) The expected life of the existing machine decreases. (2) The WACC is not constant but is increasing as Bigbee adds more projects to its

capital budget for the year.

NEW PROJECT ANALYSIS You must analyze a potential new product—a caulking compound that Cory Materials’ R&D people developed for use in the residential construction industry. Cory’s marketing manager thinks the company can sell 115,000 tubes per year at a price of $3.25 each for 3 years, after which the product will be obsolete. The required equipment would cost $150,000, plus another $25,000 for shipping and installation. Current assets (receivables and inventories) would increase by $35,000, while current liabilities (accounts payable and accruals) would rise by $15,000. Variable costs would be 60% of sales revenues, fixed costs (exclusive of depreciation) would be $70,000 per year, and fixed assets would be depreciated under MACRS with a 3-year life. (Refer to Appendix 12A for MACRS depreciation rates.) When production ceases after 3 years, the equipment should have a market value of $15,000. Cory’s tax rate is 40%, and it uses a 10% WACC for average-risk projects. a. Find the required Year 0 investment and the project’s annual net cash flows. Then

calculate the project’s NPV, IRR, MIRR, and payback. Assume at this point that the project is of average risk.

b. Suppose you now learn that R&D costs for the new product were $30,000 and that those costs were incurred and expensed for tax purposes last year. How would this affect your estimate of NPV and the other profitability measures?

c. If the new project would reduce cash flows from Cory’s other projects and if the new project would be housed in an empty building that Cory owns and could sell, how would those factors affect the project’s NPV?

d. Are this project’s cash flows likely to be positively or negatively correlated with returns on Cory’s other projects and with the economy, and should this matter in your analysis? Explain.

e. Spreadsheet assignment: at instructor’s option Construct a spreadsheet that calculates the cash flows, NPV, IRR, payback, and MIRR.

f. The CEO expressed concern that some of the base-case inputs might be too optimistic or too pessimistic. He wants to know how the NPV would be affected if these six variables were 20% better or 20% worse than the base-case level: unit sales, sales price, variable costs, fixed costs, WACC, and equipment cost. Hold other things constant when you consider each variable and construct a sensitivity graph to illustrate your results.

g. Do a scenario analysis based on the assumption that there is a 25% probability that each of the six variables itemized in Part f will turn out to have their best-case values as calculated in Part f, a 50% probability that all will have their base-case values, and a 25% probability that all will have their worst-case values. The other variables re- main at base-case levels. Calculate the expected NPV, the standard deviation of NPV, and the coefficient of variation.

h. Does Cory’s management use the risk-adjusted discount rate to adjust for project risk? Explain.

COMPREHENSIVE/SPREADSHEET PROBLEM COMPREHENSIVE/SPREADSHEET PROBLEM

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394 Part 4 Investing in Long-Term Assets: Capital Budgeting

CAPITAL BUDGETING AND CASH FLOW ESTIMATION Allied Food Products is considering expanding into the fruit juice business with a new fresh lemon juice product. Assume that you were recently hired as assistant to the director of capital budgeting and you must evaluate the new project.

The lemon juice would be produced in an unused building adjacent to Allied’s Fort Myers plant; Allied owns the building, which is fully depreciated. The required equipment would cost $200,000, plus an additional $40,000 for shipping and installation. In addition, inventories would rise by $25,000, while accounts payable would increase by $5,000. All of these costs would be incurred at t " 0. By a special ruling, the machinery could be depreciated under the MACRS system as 3-year property. The applicable depreciation rates are 33%, 45%, 15%, and 7%.

The project is expected to operate for 4 years, at which time it will be terminated. The cash inflows are assumed to begin 1 year after the project is undertaken, or at t " 1, and to continue out to t " 4. At the end of the project’s life (t " 4), the equipment is expected to have a salvage value of $25,000.

Unit sales are expected to total 100,000 units per year, and the expected sales price is $2.00 per unit. Cash operating costs for the project (total operating costs less depreciation) are expected to total 60% of dollar sales. Allied’s tax rate is 40%, and its WACC is 10%. Tentatively, the lemon juice project is assumed to be of equal risk to Allied’s other assets.

You have been asked to evaluate the project and to make a recommendation as to whether it should be accepted or rejected. To guide you in your analysis, your boss gave you the following set of tasks/questions:

a. Allied has a standard form that is used in the capital budgeting process. (See Table IC12-1.) Part of the table has been completed, but you must replace the blanks with the missing numbers. Complete the table using the following steps:

(1) Fill in the blanks under Year 0 for the initial investment outlay. (2) Complete the table for unit sales, sales price, total revenues, and operating costs excluding depreciation. (3) Complete the depreciation data. (4) Complete the table down to after-tax operating income and then down to the project’s operating cash

flows. (5) Fill in the blanks under Year 4 for the terminal cash flows and complete the project cash flow line. Discuss

working capital. What would have happened if the machinery were sold for less than its book value? b. (1) Allied uses debt in its capital structure, so some of the money used to finance the project will be debt.

Given this fact, should the projected cash flows be revised to show projected interest charges? Explain. (2) Suppose you learned that Allied had spent $50,000 to renovate the building last year, expensing these

costs. Should this cost be reflected in the analysis? Explain. (3) Suppose you learned that Allied could lease its building to another party and earn $25,000 per year.

Should that fact be reflected in the analysis? If so, how? (4) Assume that the lemon juice project would take profitable sales away from Allied’s fresh orange juice

business. Should that fact be reflected in your analysis? If so, how? c. Disregard all the assumptions from Part b and assume there is no alternative use for the building over the

next 4 years. Now calculate the project’s NPV, IRR, MIRR, and payback. Do these indicators suggest that the project should be accepted? Explain.

d. If this project had been a replacement rather than an expansion project, how would the analysis have changed? Think about the changes that would have to occur in the cash flow table.

e. (1) What three levels, or types, of project risk are normally considered? (2) Which type is most relevant? (3) Which type is easiest to measure? (4) Are the three types of risk generally highly correlated? f. (1) What is sensitivity analysis? (2) How would you perform a sensitivity analysis on the unit sales, salvage value, and WACC for the

project? Assume that each of these variables deviates from its base-case, or expected, value by plus or minus 10%, 20%, and 30%. Explain how you would calculate the NPV, IRR, MIRR, and payback for each case; but don’t do the analysis unless your instructor asks you to.

(3) What is the primary weakness of sensitivity analysis? What are its primary advantages? Work out quantitative answers to the remaining questions only if your instructor asks you to. Also note that it will take a long time to do the calculations unless you are using an Excel model. g. Assume that inflation is expected to average 5% over the next 4 years and that this expectation is reflected in

the WACC. Moreover, inflation is expected to increase revenues and variable costs by this same 5%. Does it appear that inflation has been dealt with properly in the initial analysis to this point? If not, what should be done and how would the required adjustment affect the decision?

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395Chapter 12 Cash Flow Estimation and Risk Analysis

h. The expected cash flows, considering inflation (in thousands of dollars), are given in Table IC12-2. Allied’s WACC is 10%. Assume that you are confident about the estimates of all the variables that affect the cash flows except unit sales. If product acceptance is poor, sales would be only 75,000 units a year, while a strong consumer response would produce sales of 125,000 units. In either case, cash costs would still amount to 60% of revenues. You believe that there is a 25% chance of poor acceptance, a 25% chance of excellent ac- ceptance, and a 50% chance of average acceptance (the base case). Provide numbers only if you are using a computer model.

(1) What is the worst-case NPV? the best-case NPV? (2) Use the worst-case, most likely case (or base-case), and best-case NPVs with their probabilities of occur-

rence to find the project’s expected NPV, standard deviation, and coefficient of variation. i. Assume that Allied’s average project has a coefficient of variation (CV) in the range of 1.25 to 1.75. Would

the lemon juice project be classified as high risk, average risk, or low risk? What type of risk is being mea- sured here?

j. Based on common sense, how highly correlated do you think the project would be with the firm’s other as- sets? (Give a correlation coefficient or range of coefficients based on your judgment.)

k. How would the correlation coefficient and the previously calculated # combine to affect the project’s contri- bution to corporate, or within-firm, risk? Explain.

l. Based on your judgment, what do you think the project’s correlation coefficient would be with respect to the general economy and thus with returns on “the market”? How would correlation with the economy affect the project’s market risk?

m. Allied typically adds or subtracts 3% to its WACC to adjust for risk. After adjusting for risk, should the lemon juice project be accepted? Should any subjective risk factors be considered before the final decision is made? Explain.

Allied’s Lemon Juice Project (Total Cost in Thousands)T a b l e I C 1 2 - 1

End of Year: 0 1 2 3 4 I. Investment Outlay Equipment cost Installation Increase in inventory Increase in accounts payable Total net investment

II. Project Operating Cash Flows Unit sales (thousands) 100 Price/unit $ 2.00 $ 2.00 Total revenues $200.0 Operating costs excluding depreciation $ 120.0 Depreciation 36.0 16.8 Total costs $199.2 $ 228.0 Operating income before taxes (EBIT) $44.0 Taxes on operating income 0.3 25.3 After-tax operating income $26.4 Depreciation 79.2 36.0 Project operating cash flows $ 0.0 $ 79.7 $ 54.7

III. Project Termination Cash Flows Return of net working capital Salvage value Tax on salvage value Total project termination cash flows

IV. Project Net Cash Flows Project net cash flows ($260.0) $ 89.7

V. Results NPV = IRR = MIRR = Payback =

396 Part 4 Investing in Long-Term Assets: Capital Budgeting

Allied’s Lemon Juice Project Considering 5% Inflation (in Thousands)T a b l e I C 1 2 - 2

YEAR 0 1 2 3 4

Investment in: Fixed assets ($240) Net working capital (20) Unit sales (thousands) 100 100 100 100 Sales price (dollars) $ 2.100 $ 2.205 $ 2.315 $ 2.431 Total revenues $210.0 $220.5 $231.5 $243.1 Cash operating costs (60%) 126.0 132.3 138.9 145.9 Depreciation 79.2 108.0 36.0 16.8 Operating income before taxes (EBIT) $ 4.8 ($ 19.8) $ 56.6 $ 80.4 Taxes on operating income (40%) 1.9 (7.9) 22.6 32.1 After-tax operating income $ 2.9 ($ 11.9) $ 34.0 $ 48.3 Plus depreciation 79.2 108.0 36.0 16.8 Project operating cash flows $ 82.1 $ 96.1 $ 70.0 $ 65.1 Salvage value 25.0 Tax on SV (40%) (10.0) Recovery of NWC 20.0 Project net cash flows ($260) $ 82.1 $ 96.1 $ 70.0 $100.1 Cumulative cash flows for payback: (260.0) (177.9) (81.8) (11.8) 88.3 Compounded inflows for MIRR: 109.2 116.3 77.0 100.1 Sum of compounded inflows: 402.6 NPV " $15.0 IRR " 12.6% MIRR " 11.6%

397Chapter 12 Cash Flow Estimation and Risk Analysis

APPENDIX 12A Tax Depreciation Because depreciation is covered in detail in accounting courses, here we provide only some basic information that is needed for capital budgeting. First, note that accountants generally calculate each asset’s depreciation in two ways—they use straight line to fi gure the depreciation used for reporting profi ts to investors; but they use depreciation rates provided by the Internal Revenue Service (IRS), called MACRS (Modifi ed Accelerated Cost Recovery System) rates, when they calculate depreciation for tax purposes. In capital budgeting, we are concerned with tax depreciation; so the relevant rates are the MACRS rates.

Under MACRS, each type of fi xed asset is assigned to a “class” and is then de- preciated over the asset’s class life. Table 12A-1 provides class lives for different types of assets as they existed in 2008. Next, as shown in Table 12A-2, MACRS specifi es annual depreciation rates for assets in each class life. Real properties (buildings) are depreciated on a straight-line basis over 27.5 or 39 years; but all other assets are depreciated over shorter periods and on an accelerated basis, with high depreciation charges in the early years and less depreciation in the later years. The IRS tables are based on the half-year convention, where it is assumed that the asset is placed in service halfway through the fi rst year and is taken out of service halfway through the year after its class life.

In the following example, we calculate depreciation on equipment that would be classifi ed as a 5-year asset with a cost of $8 million. In developing the tables, the IRS assumes that the machinery would be used for only 6 months of the year in which it is acquired, for 12 months in each of the next 4 years, and then for 6 months of the sixth year. Here are the depreciation charges, in thousands, that could be deducted for tax purposes based on MACRS:

Year 1 2 3 4 5 6 Rate 20% 32% 19% 12% 11% 6% Depreciation $1,600 $2,560 $1,520 $960 $880 $480

The total of the annual depreciation charges equals the $8 million cost of the asset, but it would be taken over 6 years and thus would affect cash fl ows over those 6 years.

Class Life The specified life of assets under the MACRS system.

Annual Depreciation Rates The annual expense accountants charge against income for “wear and tear” of an asset. For tax purposes, the IRS provides that appropriate MACRS rates be used that are dependent on an asset’s class life.

Half-Year Convention Assumes assets are used for half the first year and half the last year.

Class Type of Property 3-year Certain special manufacturing tools 5-year Automobiles, light-duty trucks, computers, and certain special

manufacturing equipment 7-year Most industrial equipment, office furniture, and fixtures 10-year Certain longer-lived types of equipment 27.5-year Residential rental real property such as apartment buildings 39-year All nonresidential real property, including commercial and industrial

buildings

Major Classes and Asset Lives for MACRST a b l e 1 2 A - 1

398 Part 4 Investing in Long-Term Assets: Capital Budgeting

Recovery Allowance Percentage for Personal PropertyT a b l e 1 2 A - 2

CLASS OF INVESTMENT

Ownership Year 3-Year 5-Year 7-Year 10-Year 1 33% 20% 14% 10% 2 45 32 25 18 3 15 19 17 14 4 7 12 13 12 5 11 9 9 6 6 9 7 7 9 7 8 4 7 9 7

10 6 11 3

100% 100% 100% 100%

Notes: a. We developed these recovery allowance percentages based on the 200% declining balance method

prescribed by MACRS, with a switch to straight-line depreciation at some point in the asset’s life. For example, consider the 5-year recovery allowance percentages. The straight-line percentage would be 20% per year, so the 200% declining balance multiplier is 2.0(20%) " 40% " 0.4. However, because the half-year convention applies, the MACRS percentage for Year 1 is 20%. For Year 2, 80% of the depreciable basis remains to be depreciated; so the recovery allowance percentage is 0.40(80%) " 32%. In Year 3, 20% $ 32% " 52% of the depreciation has been taken, leaving 48%; so the percentage is 0.4(48%) " 19%. In Year 4, the percentage is 0.4(29%) " 12%. After 4 years, straight-line depreciation exceeds the declining balance depreciation; so a switch is made to straight-line. (This is permitted under the law.) However, the half-year convention must also be applied at the end of the class life, and the remaining 17% of depreciation must be taken (amortized) over 1.5 years. Thus, the percentage in Year 5 is 17%/1.5 ≈ 11% and in Year 6 is 17% ! 11% " 6%. Although the tax tables carry out the allowance percentages to two decimal places, we have rounded to the nearest whole number for ease of illustration.

b. Residential rental property (apartments) is depreciated over a 27.5-year life, whereas commercial and industrial structures are depreciated over 39 years. In both cases, straight-line depreciation must be used. The depreciation allowance for the first year is based, pro rata, on the month the asset was placed in service, with the remainder of the first year’s depreciation being taken in the 28th or 40th year.

CAPITAL STRUCTURE AND DIVIDEND POLICY

13 Capital Structure and Leverage

14 Distributions to Shareholders: Dividends and Share Repurchases

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If it is to grow, a firm needs capital; and capital comes primarily in the form of debt or equity. Debt financing has two important advantages: (1) The interest paid is tax deductible whereas dividends paid on stock are not deductible, which lowers debt’s relative cost. (2) The return on debt is fixed, so stockholders do not have to share the firm’s profits if the firm turns out to be extremely successful.

However, debt also has disadvantages: (1) Using more debt increases the firm’s risk, and that raises the costs of debt and equity. (2) If the company falls on hard times and its operating income is not sufficient to cover interest charges, the firm may go bankrupt. Good times may be just around the corner, but too much debt can bank- rupt the company before it reaches that corner.

Because of the risk of using debt, companies with volatile earnings and operating cash flows tend to limit its use. On the other hand, compa- nies with relatively little business risk and stable operating cash flows can benefit from taking on more debt. Kellogg Co., the world’s largest cereal

manufacturer, is a good example of such a com- pany. Indeed, just after its 2001 acquisition of Keebler Foods Co., Kellogg’s book value capital structure consisted of 86% debt and 14% equity. An 86% debt ratio is quite high, and Kellogg’s management was well aware that excessive debt can push an otherwise well-regarded com- pany into bankruptcy. Accordingly, Kellogg’s management began to pay down its debt and restore its balance sheet to a more “reasonable” debt level so that by early 2008, its debt ratio had fallen to around 70%.

For many companies, a 70% debt ratio would still be too high. However, because Kellogg’s busi- ness is so stable, this ratio is not too bad. After all, the consumption of Frosted Flakes, Froot Loops, and Pop Tarts has remained stable even during economic downturns. Moreover, if we examine Kellogg’s capital structure in more detail, it soon becomes apparent that there is more than meets the eye. According to its balance sheet, Kellogg has about $5.86 billion of total debt versus stock- holders’ equity of about $2.23 billion. But in

el lo

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When we calculated the weighted average cost of capital (WACC) in Chapter 10, we assumed that the fi rm had a specifi c target capital structure. However, target capital structures often change over time, such changes aff ect the risk and cost of each type of capital, and all this can change the WACC. Moreover, a change in the WACC will aff ect capital budgeting decisions and, ultimately, the stock price.

Many factors infl uence capital structure decisions; and as we will see, determin- ing the optimal capital structure is not an exact science. Therefore, even fi rms in the same industry often have dramatically diff erent capital structures. In this chapter, we consider the eff ects of debt on risk and on the optimal capital structure.

When you fi nish this chapter, you should be able to: • Identify the trade-off s that fi rms must consider when they determine their target

capital structure. • Distinguish between business risk and fi nancial risk and explain the eff ects that

debt fi nancing has on the fi rm’s expected return and risk. • Discuss the analytical framework used when determining the optimal capital

structure. • Discuss capital structure theory and use it to explain why fi rms in diff erent indus-

tries tend to have diff erent capital structures.

13-1 THE TARGET CAPITAL STRUCTURE A fi rm’s optimal capital structure is defi ned as the structure that would maximize its stock price. It is useful to analyze the situation and attempt to determine the optimal structure; but in practice, it is diffi cult to do this with much confi dence. As a result, in practice, many managers think of the optimal capital structure more as a range (e.g., from 40% to 50% debt) rather than as a precise number (e.g., 45%). Other fi rms study the situation; reach a conclusion as to the optimal structure; and then set a target capital structure, such as 45% debt.1 If the actual debt ratio is sig- nifi cantly below the target level, management will raise capital by issuing debt,

Optimal Capital Structure The capital structure that maximizes a firm’s stock price.

Target Capital Structure The mix of debt, preferred stock, and common equity the firm wants to have.

May 2008, the market capitalization of Kellogg’s equity (which is the stock price times the number of shares outstanding) was approximately $19.30 billion. From a market value per- spective, Kellogg’s debt ratio is only $5.86/($5.86 ! $19.30) " 23.3%, which is actually conservative and helps explain why the company has a relatively strong BBB! bond rating.

Kellogg and other companies can finance with debt or equity. Is one better than the other? If so, should firms finance with all debt or with all equity? Or if the best solu- tion is some mix of debt and equity, what is the optimal mix? As you read this chapter, think about those questions and consider how you would answer them.

PU T TING THINGS IN PER SPECTIVE

Chapter 13 Capital Structure and Leverage 401

1 A recent study by Graham and Harvey surveyed corporate managers and asked whether their fi rms established a target capital structure. Only 19% of the respondents indicated that their fi rm did not have a target capital structure. Ten percent of the respondents said that they had a strict target debt ratio, 34% indicated that they had a somewhat tight range for their target debt ratio, and 37% of the respondents indicated that they had a fl exible target. Refer to John R. Graham and Campbell R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics, Volume 60 (May 2001), pp. 187–243.

Two video clips of Steve Walsh, Assistant Treasurer at JCPenney, talking about capital structure are available at http://fisher.osu.edu/fin/ clips.htm. The first clip on capital structure discusses the cost of capital and debt, while the second clip discusses the optimal capital structure as seen by JCPenney relative to capital structure theory as seen by Modigliani/Miller.

http://fisher.osu.edu/fin/clips.htm

402 Part 5 Capital Structure and Dividend Policy

whereas if the debt ratio is above the target, equity will be used. The target may change over time as conditions change; but at any given moment, management generally has a specifi c debt ratio in mind.

Setting the capital structure involves a trade-off between risk and return: • Using more debt will raise the risk borne by stockholders. • However, using more debt generally increases the expected return on equity. The higher risk associated with using more debt tends to lower the stock price, but the higher debt-induced expected rate of return raises it. Therefore, we seek to fi nd the capital structure that strikes a balance between risk and return so as to maximize the stock price.

Four primary factors infl uence capital structure decisions: 1. Business risk, or the riskiness inherent in the fi rm’s operations if it used no

debt. The greater the fi rm’s business risk, the lower its optimal debt ratio. 2. The fi rm’s tax position. A major reason for using debt is that interest is tax

deductible, which lowers the effective cost of debt. However, if most of a fi rm’s income is already sheltered from taxes by depreciation tax shields or interest on currently outstanding debt or tax loss carry-forwards, its tax rate will be low. In this case, additional debt would not be as advantageous as it would be to a fi rm with a higher effective tax rate.

3. Financial fl exibility, or the ability to raise capital on reasonable terms even under adverse market conditions. Corporate treasurers know that a steady supply of capital is necessary for stable operations, which is vital for long-run success. They also know that when money is tight in the economy or when a fi rm is experiencing operating diffi culties, it is easier to raise debt than equity capital and lenders are more willing to accommodate companies with strong balance sheets. Therefore, the fi rm’s potential future need for funds and the consequences of a funds shortage combine to infl uence its target capital structure—the greater the probability that capital will be needed and the worse the consequences of not being able to obtain it, the less debt the fi rm should have on its balance sheet.

4. Managerial conservatism or aggressiveness. Some managers are more aggressive than others; hence, they are more willing to use debt in an effort to boost prof- its. This factor does not affect the true optimal, or value-maximizing, capital structure; but it does infl uence the fi rm’s target capital structure.

Those four points largely determine a fi rm’s target capital structure, but operating conditions can cause its actual capital structure to vary from the target. For exam- ple, a company’s actual stock price might for some reason be well below the intrin- sic value as seen by management. In this case, management would be reluctant to issue new stock to raise capital; so it might use debt fi nancing even though this would cause the debt ratio to rise above the target level. However, the company would probably take steps to return the capital structure to its target level as soon as the stock price approached its intrinsic value.

SEL F TEST Defi ne the optimal capital structure and diff erentiate it from the target capi-

tal structure.

Name four factors that infl uence a fi rm’s target capital structure.

In what sense does setting the target capital structure involve a trade-off between risk and return?

Why might market conditions cause a fi rm’s actual capital structure to vary from its target level?

403Chapter 13 Capital Structure and Leverage

13-2 BUSINESS AND FINANCIAL RISK In Chapter 8, we examined risk from the viewpoint of an individual investor and we distinguished between risk on a stand-alone basis, where an asset’s cash fl ows are ana- lyzed by themselves, and risk in a portfolio context, where cash fl ows from a number of assets are combined and consolidated cash fl ows are analyzed. In a portfolio con- text, we saw that an asset’s risk can be divided into two components: diversifi able risk, which can be diversifi ed away and hence is of little concern to most investors, and market risk, which is measured by the beta coeffi cient and refl ects broad market move- ments that cannot be eliminated by diversifi cation and therefore is of concern to investors. Then in Chapter 12, we examined risk from the viewpoint of the corpora- tion and we considered how capital budgeting decisions affect the fi rm’s riskiness.

Now we introduce two new dimensions of risk: 1. Business risk, which is the riskiness of the fi rm’s assets if no debt is used. 2. Financial risk, which is the additional risk placed on the common stockholders

as a result of using debt.

13-2a Business Risk Business risk is the single most important determinant of capital structure, and it represents the amount of risk that is inherent in the fi rm’s operations even if it uses no debt fi nancing. Consider Bigbee Electronics Company, a debt-free (unlevered) fi rm. Because the company has no debt, its ROE is equal to its ROA and either can be used to estimate business risk. Figure 13-1 gives some clues about the company’s business risk. The top graph shows the trend in ROE from 1998 through 2008; this graph gives both security analysts and Bigbee’s management an idea of the degree to which ROE has varied in the past and might vary in the future. The lower graph shows the beginning-of-year subjectively estimated probability distribution of Bigbee’s ROE for 2008 based on the trend line in the top section of Figure 13-1. As the graphs indicate, Bigbee’s actual ROE in 2008 (8%) fell below the expected value (12%); so the forecast had been too optimistic.

Bigbee’s past fl uctuations in ROE were caused by many factors—booms and recessions in the national economy, successful new product introductions by Big- bee and by its competitors, labor strikes, and a fi re in Bigbee’s main plant. Similar events will doubtless occur in the future; and when they do, the realized ROE will be higher or lower than the projected level. Further, there is always the possibility that a long-term disaster will strike, permanently depressing the company’s earn- ing power. For example, a competitor might introduce a new product that makes Bigbee’s products obsolete and puts the company out of business. Automobiles did this to buggy manufacturers about a century ago. The more uncertainty there is about future ROEs, the greater the company’s business risk. Bigbee uses no debt, so this is the risk its stockholders face. As we shall see, the stockholders face more risk if the company chooses to fi nance with both debt and equity.

Business risk varies from industry to industry and among fi rms in a given in- dustry. Further, business risk can change over time. For example, for many years, the electric utilities were regarded as having little business risk; but a combination of events in recent years altered the utilities’ situation, producing sharp declines in their ROEs and greatly increasing the industry’s risk. Today food processors and health care fi rms are examples of industries with low business risk, while cyclical manufacturing industries such as autos and steel, as well as many small start-up companies, are regarded as having especially high business risks.2

Business Risk The riskiness inherent in the firm’s operations if it uses no debt.

2 We have avoided any discussion of market versus company-specifi c risk in this section. We note now (1) that any action that increases business risk in the sense of stand-alone risk will generally increase a fi rm’s beta coeffi - cient and (2) that a part of business risk as we defi ne it will generally be company-specifi c and hence subject to elimination as a result of diversifi cation by the fi rm’s stockholders.

404 Part 5 Capital Structure and Dividend Policy

Business risk depends on a number of factors, the more important of which are listed here: 1. Demand variability. The more stable the demand for a fi rm’s products, other

things held constant, the lower its business risk. 2. Sales price variability. Firms whose products are sold in highly volatile markets

are exposed to more business risk than similar fi rms whose output prices are more stable.

3. Input cost variability. Firms whose input costs are highly uncertain are exposed to a high degree of business risk.

4. Ability to adjust output prices for changes in input costs. Some fi rms are better able than others to raise their own output prices when input costs rise. The greater the ability to adjust output prices to refl ect cost conditions, the lower the degree of business risk.

5. Ability to develop new products in a timely, cost-effective manner. Firms in high- tech industries such as drugs and computers depend on a constant stream of new products. The faster a fi rm’s products become obsolete, the greater the fi rm’s business risk.

6. Foreign risk exposure. Firms that generate a high percentage of their earnings overseas are subject to earnings declines due to exchange rate fl uctuations.

Bigbee Electronics: Trend in ROE, 1998–2008, and Estimated Probability Distribution of ROE, 2008FIGURE 13-1

– 10

2000 2002 2004 2006 2008

Actual 2008 ROE

2008 ROE as Projected at Beginning of Year = 12%

ROE (%)

a. Trend in Return on Equity (ROE)

Expected ROE

b. Subjective Probability Distribution of ROE for 2008

Probability Density

0 8 12 ROE (%)

Actual ROE

405Chapter 13 Capital Structure and Leverage

Also, if a fi rm operates in a politically unstable area, it may be subject to politi- cal risk.

7. The extent to which costs are fi xed: operating leverage. If a high percentage of its costs are fi xed (and hence do not decline when demand falls), the fi rm will be exposed to a relatively high degree of business risk. This factor is called operat- ing leverage, and it is discussed at length in the next section.

Each of those factors is determined partly by the fi rm’s industry characteristics, but each factor also is controllable to some extent by management. For example, most fi rms can, through their marketing policies, take actions to stabilize both unit sales and sales prices. However, this stabilization may require spending a great deal on advertising and/or making price concessions to obtain commitments from customers to purchase fi xed quantities at fi xed prices in the future. Similarly, fi rms such as Bigbee Electronics can reduce the volatility of future input costs by negoti- ating long-term labor and materials supply contracts, but they may have to pay prices above the current spot price to obtain those contracts. Many fi rms are also using hedging techniques to reduce business risk.

13-2b Operating Leverage As noted earlier, business risk depends in part on the extent to which a fi rm builds fi xed costs into its operations—if fi xed costs are high, even a small decline in sales can lead to a large decline in ROE. So other things held constant, the higher a fi rm’s fi xed costs, the greater its business risk. Higher fi xed costs are generally associated with more highly automated, capital-intensive fi rms and industries. However, businesses that employ highly skilled workers who must be retained and paid even during recessions also have relatively high fi xed costs, as do fi rms with high product development costs, because the amortization of development costs is a fi xed cost.

When a high percentage of total costs are fi xed, the fi rm is said to have a high degree of operating leverage. In physics, leverage implies the use of a lever to raise a heavy object with a small force. In politics, if people have leverage, their smallest word or action can accomplish a great deal. In business terminology, a high degree of operating leverage, other factors held constant, implies that a relatively small change in sales results in a large change in ROE.

Figure 13-2 illustrates the concept of operating leverage by comparing the results that Bigbee could expect if it used different degrees of operating lever- age. Plan A calls for a relatively small amount of fi xed costs, $20,000. Here the fi rm would not have much automated equipment; so its depreciation, mainte- nance, property taxes, and so forth, would be low. However, the total operating costs line has a relatively steep slope, indicating that variable costs per unit are higher than they would be if the fi rm used more operating leverage. Plan B calls for a higher level of fi xed costs, $60,000. Here the fi rm uses automated equipment (with which one operator can turn out a few or many units at the same labor cost) to a much larger extent. The break-even point is higher under Plan B—breakeven occurs at 60,000 units under Plan B versus only 40,000 units under Plan A.

We can calculate the break-even quantity by recognizing that operating breakeven occurs when earnings before interest and taxes (EBIT) " 0:3

EBIT ! PQ " VQ " F ! 0 13-1

Operating Leverage The extent to which fixed costs are used in a firm’s operations.

Operating Breakeven The output quantity at which EBIT " 0.

3 This defi nition of breakeven does not include any fi xed fi nancial costs. If there were fi xed fi nancial costs, the fi rm would suff er an accounting loss at the operating break-even point. We will introduce fi nancial costs shortly.

406 Part 5 Capital Structure and Dividend Policy

Here P is average sales price per unit of output, Q is units of output, V is variable cost per unit, and F is fi xed operating costs. If we solve for the break-even quantity, QBE, we get this expression:

13-1a QBE ! F _____ P " V

0 20 40 60 80 100 120

120

160

200

240

Sales (Thousands of Units)

Revenues and Costs (Thousands of Dollars)

Sales Revenues

0 20 40 60 80 100 120

120

160

200

240

Sales (Thousands of Units)

Revenues and Costs (Thousands of Dollars)

Total Operating Costs

Break-Even Point (EBIT = 0)

Fixed Costs

Plan A Plan B

Operating Profit (EBIT)

Operating Loss Break-Even Point (EBIT = 0)

Operating Profit (EBIT)

Sales Revenues

Operating Loss

Total Operating Costs

Illustration of Operating LeverageFIGURE 13-2

PLAN A PLAN B

Demand Proba- bility

Units Sold

Dollar Sales

Oper- ating Costs

Operating Profits (EBIT)

Net Income ROE

Oper- ating Costs

Operating Profits (EBIT)

Net Income ROE

Terrible 0.05 0 $ 0 $ 20,000 ($20,000) ($12,000) (6.00)% $ 60,000 ($ 60,000) ($36,000) (18.00)% Poor 0.20 40,000 80,000 80,000 0 0 0.00 100,000 (20,000) (12,000) (6.00) Normal 0.50 100,000 200,000 170,000 30,000 18,000 9.00 160,000 40,000 24,000 12.00 Good 0.20 160,000 320,000 260,000 60,000 36,000 18.00 220,000 100,000 60,000 30.00 Wonderful 0.05 200,000 400,000 320,000 80,000 48,000 24.00 260,000 140,000 84,000 42.00 Expected value 100,000 $200,000 $170,000 $30,000 $18,000 9.00% $160,000 $ 40,000 $24,000 12.00% Standard deviation $24,698 7.41% $ 49,396 14.82% Coefficient of variation 0.82 0.82 1.23 1.23

Notes: a. Operating costs " Variable costs ! Fixed costs. b. The federal-plus-state tax rate is 40%, so NI " EBIT(1 # Tax rate) " EBIT(0.6). c. ROE " NI/Equity. The firm has no debt, so Assets " Equity " $200,000. d. The break-even sales level for Plan B is not shown in the table, but it is 60,000 units or $120,000. e. The expected values, standard deviations, and coefficients of variation were found using procedures discussed in Chapter 8.

Plan A Plan B Price $ 2.00 $ 2.00 Variable costs $ 1.50 $ 1.00 Fixed costs $ 20,000 $ 60,000 Assets $200,000 $200,000 Tax rate 40% 40%

407Chapter 13 Capital Structure and Leverage

Thus, for Plan A,

QBE ! $20,000 _____________ $2.00 " $1.50 ! 40,000 units

And for Plan B,

QBE ! $60,000 _____________ $2.00 " $1.00 ! 60,000 units

How does operating leverage affect business risk? Other things held constant, the higher a fi rm’s operating leverage, the higher its business risk. This point is demon- strated in Figure 13-3, where we develop probability distributions for ROE under Plans A and B.

The top section of Figure 13-3 graphs the probability distribution of sales that was presented in tabular form in Figure 13-2. The sales probability distribution depends on how demand for the product varies, not on whether the product is manufactured by Plan A or by Plan B. Therefore, the same sales probability distri- bution applies to both production plans. This distribution has expected sales of $200,000; and it ranges from zero to about $400,000, with a standard deviation of $Sales " $98,793.

Note: We are using continuous distributions to approximate the discrete distributions contained in Figure 13-2.

Analysis of Business RiskFIGURE 13-3

Probability Density

0 $200,000 (Expected Sales)

Sales ($)

a. Sales Probability Distribution Under Either Plan A or B

0 9 12 ROE (%) (Expected

ROEA) (Expected

ROEB)

Probability Density

Plan B

Plans A and B

Plan A

b. ROE Probability Distribution

408 Part 5 Capital Structure and Dividend Policy

We use the sales probability distribution, together with the operating costs at each sales level, to develop graphs of the ROE probability distributions under Plans A and B. These are shown in the lower section of Figure 13-3. Plan B has a higher expected ROE, but this plan also entails a much higher probability of losses. Plan B, the one with more fi xed costs and a higher degree of operating leverage, is clearly riskier. In general, holding other factors constant, the higher the degree of operating leverage, the greater the fi rm’s business risk. In the discussion that follows, we assume that Bigbee has decided to go ahead with Plan B because its management believes that the higher expected return is suffi cient to compensate for the higher risk.

To what extent can fi rms control their operating leverage? To a large extent, operating leverage is determined by technology. Electric utilities, telephone companies, airlines, steel mills, and chemical companies must have large investments in fi xed assets; and this results in high fi xed costs and operating leverage. Similarly, pharmaceutical, auto, computer, and other companies must spend heavily to develop new products; and product-development costs increase operating leverage. Grocery stores and service businesses such as accounting and consulting fi rms, on the other hand, generally have signifi cantly lower fi xed costs and hence lower operating leverage. Still, although industry factors do exert a major infl uence, all fi rms have some control over their operat- ing leverage. For example, an electric utility can expand its generating capacity by building either gas-fi red or nuclear plants. Nuclear plants would require a larger investment and would have higher fi xed costs, but their variable operat- ing costs would be relatively low. Gas-fi red plants, on the other hand, would require a smaller investment and would have lower fi xed costs; but the variable costs (for gas) would be high. Thus, by its capital budgeting decisions, a utility (or any other company) can infl uence its operating leverage and hence its busi- ness risk.

The concept of operating leverage was originally developed for use in capital budgeting. Mutually exclusive projects that involve alternative production meth- ods for a given product often have different degrees of operating leverage and hence different break-even points and different degrees of risk. Bigbee Electronics and many other companies regularly undertake a type of break-even analysis (the sensitivity analysis discussed in Chapter 12) for each proposed project as a part of their regular capital budgeting process. Still, once a corporation’s operating lever- age has been established, this factor exerts a major infl uence on its capital structure decision.

13-2c Financial Risk Financial risk is the additional risk placed on the common stockholders as a result of the decision to fi nance with debt. Conceptually, stockholders face a cer- tain amount of risk that is inherent in the fi rm’s operations—this is its business risk, defi ned as the uncertainty inherent in projections of future operating income. If a fi rm uses debt (fi nancial leverage), this concentrates the business risk on com- mon stockholders. To illustrate, suppose 10 people decide to form a corporation to own and operate a large apartment complex. There is a certain amount of busi- ness risk in the operation. If the fi rm is capitalized only with common equity and if each person buys 10% of the stock, each investor will share equally in the busi- ness risk. However, suppose the fi rm is capitalized with 50% debt and 50% equity, with fi ve of the investors putting up their capital as debt and the other fi ve put- ting up their money as equity. The debtholders will receive a fi xed payment, and it will come before the stockholders receive anything. Also, if the fi rm goes bank- rupt, the debtholders must be paid off before the stockholders get anything. In this case, the fi ve investors who put up the equity will have to bear all of the

Financial Risk An increase in stockholders’ risk, over and above the firm’s basic business risk, resulting from the use of financial leverage.

409Chapter 13 Capital Structure and Leverage

business risk; so the common stock will be twice as risky as it would have been had the fi rm been fi nanced only with equity. Thus, the use of debt, or fi nancial leverage, concentrates the fi rm’s business risk on the stockholders. (In Web Appendix 13A, we describe in more detail the interaction between operating leverage and fi nancial leverage.)

To illustrate the business risk concentration, we can extend the Bigbee Elec- tronics example. To date, the company has never used debt, but the treasurer is now considering a possible change in its capital structure. Changes in the use of debt would cause changes in earnings per share (EPS) as well as changes in risk— both would affect the stock price. To understand the relationship between fi nan- cial leverage and EPS, fi rst consider Table 13-1, which shows how Bigbee’s cost of debt would vary if it used different amounts of debt to fi nance a fi xed amount of assets. The higher the percentage of debt in the capital structure, the riskier the debt and hence the higher the interest rate lenders would charge.

For now, assume that only two fi nancing choices are being considered— remain at 100% equity or shift to 50% debt and 50% equity. We also assume that with no debt, Bigbee has 10,000 shares of common stock outstanding and if it de- cides to change its capital structure, common stock would be repurchased at the $20 current stock price. Now consider Table 13-2, which shows how the fi nancing choice would affect Bigbee’s profi tability and risk.

First, focus on Section I, which assumes that Bigbee uses no debt. Because debt is zero, interest is also zero; hence, pretax income is equal to EBIT. Taxes at 40% are deducted to obtain net income, which is then divided by the $200,000 of equity to calculate ROE. Note that Bigbee will receive a tax credit if net income is negative (when demand is terrible or poor). Here we assume that Bigbee’s losses can be car- ried back to offset income earned in the prior year, thus resulting in a tax credit. The ROE at each sales level is then multiplied by the probability of that sales level to calculate the 12% expected ROE. Note that this 12% is the same as that found in Figure 13-2 for Plan B.

Section I of the table also calculates Bigbee’s earnings per share (EPS) for each scenario under the assumption that the company continues to use no debt. Net income is divided by the 10,000 common shares outstanding to obtain EPS. If demand is terrible, the EPS will be #$3.60; but if demand is wonderful, the EPS will rise to $8.40. The EPS at each sales level is then multiplied by the proba- bility of that level to calculate the expected EPS, which is $2.40 if Bigbee uses no debt. We also calculate the standard deviation of EPS and the coeffi cient of variation as indicators of the fi rm’s risk at a zero debt ratio: $EPS " $2.96, and CVEPS " 1.23.

Now look at Section II, the situation if Bigbee decides to use 50% debt with an interest rate of 12%. Neither sales nor operating costs will be affected; hence, the EBIT column is the same for zero debt and 50% debt. However, the company will

Financial Leverage The extent to which fixed- income securities (debt and preferred stock) are used in a firm’s capital structure.

Amount Borroweda Debt/Assets Ratio Interest Rate, rd, on All Debt $ 20,000 10% 8.0%

40,000 20 8.3 60,000 30 9.0 80,000 40 10.0

100,000 50 12.0 120,000 60 15.0

a We assume that the firm must borrow in increments of $20,000. We also assume that Bigbee is unable to borrow more than $120,000, which is 60% of its $200,000 of assets, due to restrictions in its corporate charter.

Interest Rates for Bigbee with Different Debt/Assets RatiosT a b l e 1 3 - 1

410 Part 5 Capital Structure and Dividend Policy

Section I. Zero Debt Debt ratio 0% Assets $200,000 Debt $ 0 Equity $200,000 Shares outstanding 10,000

Effects of Financial Leverage: Bigbee Electronics Financed with Zero Debt or 50% Debt

T a b l e 1 3 - 2

Demand For Product

(1) Probability

(2) EBIT (3)

Interest (4)

Pretax Income

(5)

Taxes (40%)

(6)

Net Income

(7) ROE (8)

EPSa (9)

Terrible 0.05 ($ 60,000) $0 ($ 60,000) ($24,000) ($36,000) (18.00)% ($3.60) Poor 0.20 (20,000) 0 (20,000) (8,000) (12,000) (6.00) (1.20) Normal 0.50 40,000 0 40,000 16,000 24,000 12.00 2.40 Good 0.20 100,000 0 100,000 40,000 60,000 30.00 6.00 Wonderful 0.05 140,000 0 140,000 56,000 84,000 42.00 8.40 Expected value $ 40,000 $0 $ 40,000 $16,000 $24,000 12.00% $2.40 Standard deviation 14.82% $2.96 Coefficient of variation 1.23 1.23

Section II. 50% Debt Debt ratio 50.00% Assets $200,000 Debt $100,000 Interest rate 12.00% Equity $100,000 Shares outstanding 5,000

Demand For Product

(1) Probability

(2) EBIT (3)

Interest (4)

Pretax Income

(5)

Taxes (40%)

(6)

Net Income

(7) ROE (8)

EPSa (9)

Terrible 0.05 ($ 60,000) $12,000 ($ 72,000) ($28,800) ($43,200) (43.20)% ($8.64) Poor 0.20 (20,000) 12,000 (32,000) (12,800) (19,200) (19.20) (3.84) Normal 0.50 40,000 12,000 28,000 11,200 16,800 16.80 3.36 Good 0.20 100,000 12,000 88,000 35,200 52,800 52.80 10.56 Wonderful 0.05 140,000 12,000 128,000 51,200 76,800 76.80 15.36 Expected value $ 40,000 $12,000 $ 28,000 $11,200 $16,800 16.80% $3.36 Standard deviation 29.64% 5.93 Coefficient of variation 1.76 1.76

Assumptions: 1. In terms of its operating leverage, Bigbee has chosen Plan B. The probability distribution and EBIT are obtained from Figure 13-2. 2. Sales and operating costs (and hence EBIT) are not affected by the financing decision. Therefore, EBIT under both financing

plans is identical and is taken from the EBIT column for Plan B in Figure 13-2. 3. All losses can be carried back to offset income in the prior year. a The EPS figures can also be obtained using the following formula in which the numerator amounts to an income statement at a given sales level

displayed horizontally:

EPS ! (Sales " Fixed costs " Variable costs " Interest)(1 " Tax rate) ______________________________________________________ Shares outstanding ! (EBIT " I) (1 " T) _________________ Shares outstanding

For example, with zero debt and sales " $200,000, EPS is $2.40:

EPSD/A ! 0 ! ($200,000 " $60,000 " $100,000 " 0)(0.6) _____________________________________ 10,000 ! $2.40

With 50% debt and sales ! $200,000, EPS is $3.36:

EPSD/A ! 0.5 ! ($200,000 " $60,000 " $100,000 " $12,000)(0.6) ___________________________________________ 5,000 ! $3.36

Refer to the tabular data given in Figure 13-2 to arrive at sales, fixed costs, and variable costs that are used in the preceding equations.

Note: Because the demand for the product has a normal distribution, the probability distribution is symmetrical. Consequently, the expected values equal the values under normal demand. This would not occur under an asymmetrical probability distribution.

411Chapter 13 Capital Structure and Leverage

now have $100,000 of debt with a cost of 12%; hence, its interest expense will be $12,000. This interest must be paid regardless of the state of the economy—if it is not paid, the company will be forced into bankruptcy and stockholders will be wiped out. Therefore, we show a $12,000 cost in Column 4 as a fi xed number for all sales levels. Column 5 shows pretax income; Column 6, the applicable taxes; and Column 7, the resulting net income. When net income is divided by the equity investment—which now will be only $100,000 because $100,000 of the $200,000 total assets were fi nanced with debt—we fi nd the ROE under each demand state. If demand is terrible and sales are zero, a very large loss will be incurred and the ROE will be –43.2%. However, if demand is wonderful, ROE will be 76.8%. The expected ROE is the probability-weighted average, which is 16.8% if the company uses 50% debt.

Typically, using debt increases the expected rate of return for an investment. However, debt also increases risk to the common stockholders. This situation holds with our example—fi nancial leverage raises the expected ROE from 12% to 16.8%, but it also increases the risk of the investment as measured by the coeffi - cient of variation, which rises from 1.23 to 1.76.

Figure 13-4 graphs the data in Table 13-2. It demonstrates that using fi nancial leverage increases the expected ROE but that leverage also fl attens out the proba- bility distribution, increases the probability of a large loss, and thus increases the risk borne by stockholders.

We can also calculate Bigbee’s EPS if it uses 50% debt. With Debt " $0, 10,000 shares would be outstanding; but if half the equity were replaced by debt (Debt " $100,000), only 5,000 shares would be outstanding. We can determine the EPS that would result at each of the possible demand levels under the dif- ferent capital structures.4 With no debt, EPS would be –$3.60 if demand were terrible, $2.40 if demand were normal, and $8.40 if demand were wonderful. With 50% debt, EPS would be –$8.64 if demand were terrible; $3.36 if demand were normal; and $15.36 if demand were wonderful. Expected EPS would be $2.40 with no debt but $3.36 with 50% fi nancial leverage.

The EPS distributions under the two fi nancial structures are graphed in Figure 13-5, where we use continuous distributions rather than the discrete

4 We assume in this example that the fi rm could change its capital structure by repurchasing common stock at its book value of $100,000/5,000 shares " $20 per share. However, the fi rm may have to pay a higher price to repurchase its stock on the open market. If Bigbee had to pay $22 per share, it could repurchase only $100,000/$22 " 4,545 shares; and in this case, expected EPS would be only $16,800/(10,000 # 4,545) " $16,800/5,455 " $3.08 rather than $3.36.

ROE Probability Distributions for Bigbee Electronics, With and Without LeverageFIGURE 13-4

0 ROE (%)

Probability Density

50% Debt

0% Debt

12 16.8

412 Part 5 Capital Structure and Dividend Policy

distributions contained in Table 13-2. Although expected EPS would be much higher if fi nancial leverage were employed, the graph makes it clear that the risk of low, or even negative, EPS would also be higher if debt were used.

Another view of the relationships among expected EPS, risk, and fi nancial le- verage is presented in Figure 13-6. The tabular data in the lower section were cal- culated in the manner set forth in Table 13-2, and the graphs plot these data. Here we see that expected EPS rises until the fi rm is fi nanced with 50% debt. Interest charges rise, but this effect is more than offset by the declining number of shares outstanding as debt is substituted for equity. However, EPS peaks at a debt ratio of 50%, beyond which interest rates rise so rapidly that EPS falls in spite of the falling number of shares outstanding.

The right panel of Figure 13-6 shows that risk, as measured by the coeffi cient of variation of EPS, rises continuously and at an increasing rate as debt is substi- tuted for equity.

These examples make it clear that using leverage has both positive and nega- tive effects: Higher leverage increases expected EPS (in this example, until the debt ratio equals 50%), but it also increases risk. When determining its optimal capital structure, Bigbee needs to balance these positive and negative effects of leverage. This issue is discussed in the following sections.

0 $2.40 $3.36 EPS ($)

Zero Debt Financing

50% Debt Financing

Probability Density

EPS Probability Distributions for Bigbee Electronics, With and Without LeverageFIGURE 13-5

SEL F TEST What is business risk, and how can it be measured?

What are some determinants of business risk?

Why does business risk vary from industry to industry?

What is operating leverage?

How does operating leverage aff ect business risk?

What is fi nancial risk, and how does it arise?

Explain this statement: Using leverage has both good and bad eff ects.

413Chapter 13 Capital Structure and Leverage

13-3 DETERMINING THE OPTIMAL CAPITAL STRUCTURE As we saw in Figure 13-6, Bigbee’s expected EPS is maximized at a debt ratio of 50%. Does that mean that Bigbee’s optimal capital structure calls for 50% debt? The answer is a resounding “No!” The optimal capital structure is the one that maxi- mizes the price of the fi rm’s stock, and this generally calls for a debt ratio that is lower than the one that maximizes expected EPS.

We know that stock prices are positively related to expected earnings but negatively related to higher risk. Therefore, to the extent that higher debt levels raise expected EPS, leverage works to increase the stock price. However, higher debt levels also increase the fi rm’s risk, which raises the cost of equity and works

3.50

3.00

2.50

2.00

Expected EPS ($)

Peak EPS = $3.36

0 10 20 30 40 50 60

Debt Ratio (%)

2.00

1.23

Risk (CV )

0 10 20 30 40 50 60

Debt Ratio (%)

Additional Risk to Stockholders from Use of Financial Leverage: Financial Risk

Basic Business Risk

EPS

Relationships among Expected EPS, Risk, and Financial LeverageFIGURE 13-6

Debt Ratio Expected

EPS Standard Deviation

of EPS Coefficient

of Variation 0%a $2.40a $2.96a 1.23a

10 2.56 3.29 1.29 20 2.75 3.70 1.35 30 2.97 4.23 1.43 40 3.20 4.94 1.54 50a 3.36a 5.93a 1.76a

60 3.30 7.41 2.25

a Values for debt ratios " 0% and 50% are taken from Table 13-2. Values at other debt ratios are calculated similarly.

414 Part 5 Capital Structure and Dividend Policy

to reduce the stock price. So even though increasing the debt ratio from 40% to 50% raises EPS, in our example, the higher EPS is more than offset by the corre- sponding increase in risk.

13-3a WACC and Capital Structure Changes Managers should set as the target capital structure the debt-equity mix that maxi- mizes the fi rm’s stock price. However, it is diffi cult to estimate how a given change in the capital structure will affect the stock price. As it turns out, the capital struc- ture that maximizes the stock price also minimizes the WACC; and at times, it is easier to predict how a capital structure change will affect the WACC than the stock price. Therefore, many managers use the estimated relationship between capital structure and the WACC to guide their capital structure decisions.

Recall from Chapter 10 that when a fi rm uses no preferred stock, the WACC is found as follows:

WACC ! wd(rd)(1 " T) # wc(rs)

! (D/A)(rd)(1 " T) # (E/A)(rs)

In this expression, D/A and E/A represent the debt-to-assets and equity-to- assets ratios, respectively, and they must sum to 1.0.

Note that in Table 13-3, an increase in the debt ratio increases the costs of both debt and equity. [The cost of debt, rd, is taken from Table 13-1 but multiplied by (1 # T) to put it on an after-tax basis.] Bondholders recognize that if a fi rm has a higher debt ratio, this increases the risk of fi nancial distress, which leads to higher interest rates.

Bigbee’s Stock Price and WACC Estimates with Different Debt/Assets Ratios

T a b l e 1 3 - 3

Debt/ Assets

(1)

Debt/ Equitya

(2) A-T rd

(3)

Expected EPS (and DPS)b

(4)

Estimated Betac

(5)

rs ! [rRF # (RPM)b]

d (6)

Estimated Pricee

(7)

Resulting P/E Ratio

(8) WACCf

(9) 0% 0.00% 4.8% $2.40 1.50 12.0% $20.00 8.33% 12.00%

10 11.11 4.8 2.56 1.60 12.4 20.65 8.06 11.64 20 25.00 5.0 2.75 1.73 12.9 21.33 7.75 11.32 30 42.86 5.4 2.97 1.89 13.5 21.90 7.38 11.10 40 66.67 6.0 3.20 2.10 14.4 22.22 6.94 11.04 50 100.00 7.2 3.36 2.40 15.6 21.54 6.41 11.40 60 150.00 9.0 3.30 2.85 17.4 18.97 5.75 12.36

a D/E ! D/A _______ 1 " D/A

b Bigbee pays all of its earnings as dividends, so EPS " DPS. c The firm’s unlevered beta, bU, is 1.5. The remaining betas were calculated using the Hamada equation, given the unlevered beta, tax rate, and

D/E ratio as inputs. d We assume that rRF " 6% and RPM " 4%. Therefore, at D/A " 0, rs " 6% ! (4%)1.5 " 12%. Other values of rs are calculated similarly. e Since all earnings are paid out as dividends, no retained earnings will be plowed back into the business and growth in EPS and DPS will be zero.

Hence, the zero growth stock price model developed in Chapter 9 can be used to estimate the price of Bigbee’s stock. For example, at D/A " 0,

P0 ! DPS ____ rS

! $2.40 _____ 0.12 ! $20

Other prices were calculated similarly. f Column 9 values are found with the weighted average cost of capital (WACC) equation developed in Chapter 10:

WACC ! wdrd(1 " T) # wcrs ! (D/A)(rd)(1 " T) # (1 " D/A)rs

For example, at D/A " 40%, WACC ! 0.4(10%)(0.6) # 0.6(14.4%) ! 11.04%

We use book weights here, but market value weights theoretically would be better. See Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 9th ed. (Mason, OH: Thomson/South-Western, 2007), Chapter 10, for a discussion of this point.

415Chapter 13 Capital Structure and Leverage

In practice, fi nancial managers use fi nancial statement forecasting models to determine how changes in the debt ratio will affect the current ratio, times- interest-earned ratio, and EBITDA coverage ratio.5 They then discuss their pro- jected ratios with bankers and bond rating agencies, who ask probing questions and may make their own adjustments to the fi rm’s forecasts. The bankers and rat- ing agencies compare the fi rm’s ratios with those of other fi rms in its industry and arrive at a “what if” rating and corresponding interest rate. Moreover, if the com- pany plans to issue bonds to the public, the SEC requires that it inform investors what the coverages will be after the new bonds have been sold. Recognizing all this, sophisticated fi nancial managers use their forecasted ratios to predict how bankers and other lenders will judge their fi rms’ risks and thus their costs of debt. Experienced fi nancial managers and investment bankers can judge quite accu- rately the effects of capital structure on the cost of debt.

13-3b The Hamada Equation Increasing the debt ratio increases the risks that bondholders face and thus the cost of debt. More debt also raises the risk borne by stockholders, which raises the cost of equity, rs. It is harder to quantify leverage’s effects on the cost of equity, but a theoretical formula can help measure the effect.

To begin, recall from Chapter 8 that a stock’s beta is the relevant measure of risk for a diversifi ed investor. Moreover, beta increases with fi nancial leverage, and Robert Hamada formulated the following equation to quantify this effect.6

bL ! bU[1 # (1 " T)(D/E)] 13-2

Here bL is the fi rm’s current beta, which we now assume is based on the existence of some fi nancial leverage, and bU is the fi rm’s beta if the fi rm was debt-free, or unlevered.7 If the fi rm was debt-free, its beta would depend entirely on its busi- ness risk and thus would be a measure of the fi rm’s “basic business risk.” D/E is the measure of fi nancial leverage as used in the Hamada equation, and T is the corporate tax rate.8

Now recall the CAPM version of the cost of equity:

rs ! rRF # (RPM)bi

5 We discuss fi nancial statement forecasts in Chapter 16. 6 See Robert S. Hamada, “Portfolio Analysis, Market Equilibrium, and Corporation Finance,” Journal of Finance, March 1969, pp. 13–31. 7 Note that Equation 13-2 is the original equation that Hamada put forward, and it was based on a set of assumptions. The most notable were (a) that the beta of the company’s debt is zero, (b) that the level of debt is constant, and (c) that the values of the company’s interest tax shields are discounted at the before-tax cost of debt. Other researchers have derived alternative equations that are based on diff erent assumptions. For example, one commonly used alternative assumes that the company’s debt ratio remains constant and that the interest tax shields are discounted at the unlevered cost of equity. In this case, the resulting equation is as follows:

bL " bU[1 ! D/E]

See Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 9th ed. (Mason, OH: Thomson/ South-Western, 2007), Chapter 15, for further discussion of the Hamada equation and the diff erent approaches for levering and unlevering betas. 8 Recall from Chapter 4 that the debt/equity ratio, D/E, is directly related to the D/A ratio:

D __ E " D/A ________ 1 # D/A

For example, if the fi rm has $40 of debt and $60 of equity, D/A = 0.4, E/A = 0.6, and

D __ E " 0.4 ______ 1 # 0.4 " 0.4/0.6 " 0.6667

Thus, any D/A ratio can be directly translated into a D/E ratio. Note also that Hamada’s equation assumes that assets are reported at market values rather than accounting book values. This point is discussed at length in Brigham and Daves, op cit., where feedbacks among capital structure, stock prices, and capital costs are examined.

416 Part 5 Capital Structure and Dividend Policy

Note that beta is the only variable in the equity cost equation that is under man- agement’s control. The other two variables, rRF and RPM, are determined by market forces that are beyond the fi rm’s control; but bL is determined by the fi rm’s operat- ing decisions, which, as we saw earlier, affect its basic business risk, and by its capital structure decisions as refl ected in its D/A (or D/E) ratio.

We can solve Equation 13-2 to fi nd the unlevered beta, bU, obtaining Equation 13-2a:

13-2a bU ! bL/[1 # (1 " T)(D/E)]

Since the current (levered) beta is known, as are the tax rate and the debt/equity ratio, we can insert values for these known variables and fi nd the unlevered beta. The unlevered beta can then be used in Equation 13-2 with different debt levels to fi nd the levered betas that would exist at those different debt levels. The resulting betas can be used to fi nd the cost of equity at different debt levels.

We can illustrate all this with Bigbee Electronics. First, assume that the risk- free rate of return, rRF , is 6% and that the market risk premium, RPM, is 4%. Next, we need the unlevered beta, bU. Because Bigbee has no debt, its D/E " 0. There- fore, its current 1.5 beta is also its unlevered beta; hence, bU " 1.5. With bU, rRF, and RPM specifi ed, we can use Equation 13-2 to estimate Bigbee’s betas at differ- ent degrees of fi nancial leverage and its resulting cost of equity at each debt ratio.

Bigbee’s betas at different debt/equity ratios are shown in Column 5 of Table 13-3. The current cost of equity is 12% as shown at the top of Column 6:

rs ! rRF # Risk premium ! 6% # (4%)(1.5) ! 6% # 6% ! 12%

The fi rst 6% is the risk-free rate; the second is the fi rm’s risk premium. Because Bigbee currently uses no debt, it has no fi nancial risk. Therefore, the 6% risk pre- mium is attributable entirely to business risk.

If Bigbee changes its capital structure by adding debt, this would increase the risk stockholders would have to bear. That, in turn, would result in a higher risk premium. Conceptually, a fi rm’s cost of equity consists of the following components:

rs ! rRF # Premium for business risk # Premium for fi nancial risk

Figure 13-7, which is based on data shown in Column 6 of Table 13-3, graphs Big- bee’s cost of equity at different debt ratios. As the fi gure shows, rs consists of the 6% risk-free rate, a constant 6% premium for business risk, and a premium for fi nancial risk that starts at zero but rises at an increasing rate as the fi rm’s debt ratio increases.

13-3c The Optimal Capital Structure Column 9 of Table 13-3 also shows Bigbee’s WACC at different capital structures. Currently, it has no debt; so its debt ratio is zero and its WACC is rs = 12%. As Big- bee begins to substitute lower-cost debt for higher-cost equity, its WACC declines. However, as the debt ratio rises, the costs of both debt and equity rise, at fi rst slowly but then at a faster and faster rate. Eventually, the increasing costs of the two components offset the fact that more low-cost debt is being used. Indeed, at 40% debt, the WACC hits a minimum of 11.04%; after that, it rises with further increases in the debt ratio.

Another way of looking at this is to note that even though the component cost of equity is higher than that of debt, using only lower-cost debt would not maximize

Unlevered Beta, bU The firm’s beta coefficient if it has no debt.

417Chapter 13 Capital Structure and Leverage

value because of the feedback effects of debt on the costs of debt and equity. For example, if Bigbee used more than 40% debt (say, 50%), it would have more of the cheaper capital; but this benefi t would be more than offset by the fact that the ad- ditional debt raises the costs of debt and equity.

These thoughts were echoed in a statement made by the Georgia-Pacifi c Corporation:

On a market-value basis, our debt-to-capital ratio is 47%. By employing this capi- tal structure, we believe that our weighted average cost of capital is minimized, at approximately 10%. Although reducing debt would reduce our marginal cost of debt, this action would likely increase our weighted average cost of capital because we would then have to use more higher-cost equity.

Finally, and very importantly, recall that the capital structure that minimizes the WACC is also the capital structure that maximizes the fi rm’s stock price. Bigbee pays out all of its earnings as dividends, so it plows zero earnings back into the business, which leads to an expected growth rate in earnings and dividends of zero. Thus, in Bigbee’s case, we can use the zero growth stock price model developed in Chapter 9 to estimate the stock price at each different capital structure. These esti- mates are shown in Column 7 of Table 13-3. Here we see that the stock price fi rst

10 20 60

Required Return on

Equity (%)

30 40 50

rRF = rRF

Debt Ratio (%)

Risk-Free Rate: Time Value of Money Plus Expected Inflation

Premium for Business Risk

Premium for Financial Risk

Bigbee’s Required Rate of Return on Equity at Diff erent Debt LevelsFIGURE 13-7

418 Part 5 Capital Structure and Dividend Policy

rises with fi nancial leverage, hits a peak of $22.22 at a debt ratio of 40%, and then begins to decline. Thus, Bigbee’s optimal capital structure occurs at a debt ratio of 40%, and that debt ratio both maximizes its stock price and minimizes its WACC.9

The EPS, cost of capital, and stock price data shown in Table 13-3 are plotted in Figure 13-8. As the graph shows, the debt ratio that maximizes Bigbee’s ex- pected EPS is 50%. However, the expected stock price is maximized, and the WACC

9 We could also estimate the stock price if some earnings were retained and the expected growth rate was positive. However, this would complicate the analysis, and it is another reason we generally analyze the optimal capital structure decision using the WACC rather than the stock price.

Eff ects of Capital Structure on EPS, Cost of Capital, and Stock PriceFIGURE 13-8

Expected EPS ($)

Maximum EPS = $3.36

0 10 20 30 40 50 60

3.50

3.00

2.50

Debt Ratio (%)

Cost of Capital (%)

Cost of Equity, rs

10 20 30 40 50 60

Debt Ratio (%)

Weighted Average Cost of Capital, WACC

After-Tax Cost of Debt, rd (1 – T)

Min. = 11.04%

Stock Price ($) Maximum = $22.22

0 10 20 30 40 50 60

Debt Ratio (%)

23 22 21 20 19

419Chapter 13 Capital Structure and Leverage

13-4 CAPITAL STRUCTURE THEORY Business risk is an important determinant of the optimal capital structure. More- over, fi rms in different industries have different business risks. So we would expect capital structures to vary considerably across industries, and this is the case. For example, pharmaceutical companies generally have very different capital struc- tures than airlines. In addition, capital structures vary among fi rms within a given industry, which is a bit harder to explain. What factors can explain these differ- ences? In an attempt to answer that question, academics and practitioners have developed a number of theories.

Modern capital structure theory began in 1958 when Professors Franco Modi- gliani and Merton Miller (hereafter, MM) published what has been called the most infl uential fi nance article ever written.10 MM proved, under a restrictive set of assumptions, that a fi rm’s value should be unaffected by its capital structure. Put another way, MM’s results suggest that it does not matter how a fi rm fi nances its operations—hence, that capital structure is irrelevant. However, the assumptions upon which MM’s study was based are not realistic, so their results are question- able. Here is a partial listing of their assumptions: 1. There are no brokerage costs. 2. There are no taxes. 3. There are no bankruptcy costs. 4. Investors can borrow at the same rate as corporations. 5. All investors have the same information as management about the fi rm’s

future investment opportunities. 6. EBIT is not affected by the use of debt.

10 Franco Modigliani and Merton H. Miller, “The Cost of Capital, Corporation Finance, and the Theory of Investment,” American Economic Review, June 1958. Both Modigliani and Miller won Nobel Prizes for their work.

is minimized at a 40% debt ratio. Thus, Bigbee’s optimal capital structure calls for 40% debt and 60% equity. Management should set its target capital structure at these ratios; and if the existing ratios are off target, it should move toward that tar- get when new securities are issued.

SEL F TEST What happens to the component costs of debt and equity when the debt

ratio is increased? Why does this occur?

Using the Hamada equation, explain the eff ects of fi nancial leverage on beta.

What is the equation for calculating a fi rm’s unlevered beta?

Use the Hamada equation to calculate the unlevered beta for Firm X with the following data: bL " 1.25, T " 40%, Debt/Assets " 0.42, and Equity/Assets " 0.58. (bU ! 0.8714)

What would be the cost of equity for Firm X at Equity/Assets ratios of 1.0 (no debt) and 0.58 assuming that rRF " 5% and RPM " 4%? (8.49%, 10%)

Using a graph and illustrative data, discuss the premiums for fi nancial risk and business risk at diff erent debt levels. Do these premiums vary depend- ing on the debt level? Explain.

Is expected EPS generally maximized at the optimal capital structure? Explain.

420 Part 5 Capital Structure and Dividend Policy

Despite the fact that some of these assumptions are unrealistic, MM’s irrele- vance result is extremely important. By indicating the conditions under which capital structure is irrelevant, MM provided clues about what is required to make capital structure relevant and hence to affect a fi rm’s value. MM’s work marked the beginning of modern capital structure research, and subsequent research has focused on relaxing the MM assumptions to develop a more robust and realistic theory. Research in this area is quite extensive, but the highlights are summarized in the following sections.

13-4a The Effect of Taxes11

MM’s original 1958 paper was criticized harshly, and they published a follow-up in 1963 that relaxed the assumption of no corporate taxes.12 They recognized that the Tax Code allows corporations to deduct interest payments as an expense, but dividend payments to stockholders are not deductible. This differential treatment encourages corporations to use debt in their capital structures. Indeed, MM dem- onstrated that if all their other assumptions hold, this differential treatment leads to an optimal capital structure of 100% debt.

MM’s 1963 work was modifi ed several years later by Merton Miller (this time without Modigliani), when he brought in the effects of personal taxes.13 Miller noted that bonds pay interest, which is taxed as personal income at rates going up to 35%, while income from stocks comes partly from dividends and partly from capital gains. Further, most long-term capital gains are taxed at a maximum rate of 15%, and this tax can be deferred until the stock is sold and the gain realized. If a stock is held until the owner dies, no capital gains tax must be paid. So on balance, returns on common stocks are taxed at lower effective rates than returns on debt.14

11 This section is relatively technical, and it can be omitted without loss of continuity. 12 Franco Modigliani and Merton H. Miller, “Corporate Income Taxes and the Cost of Capital: A Correction,” American Economic Review, Vol. 53 (June 1963), pp. 433–443. 13 Merton H. Miller, “Debt and Taxes,” Journal of Finance, Vol. 32 (May 1977), pp. 261–275. 14 When Miller wrote his article, dividends were taxed at a maximum rate of 70% and capital gains at a much lower rate. Today (2008) dividends and most capital gains are taxed at a maximum rate of 15%, but interest is taxed at a maximum rate of 35%. [Capital gains can be caught by the Alternative Minimum Tax (AMT), in which case they are taxed at either 26% or 28% depending on one’s income bracket.] These tax law changes would not aff ect Miller’s fi nal conclusion.

When a waitress asked Yogi Berra (Baseball Hall of Fame catcher for the New York Yankees) whether he wanted his pizza cut into four pieces or eight, Yogi replied: “Better make it four. I don’t think I can eat eight.”a

Yogi’s quip helps convey Modigliani and Miller’s basic insight. The fi rm’s choice of leverage divides future cash fl ows in a way that’s like slicing a pizza. MM recognized that if a company’s future investments are fi xed, it’s like fi xing the size of the pizza: No information costs means that everyone sees the same pizza, no taxes means that the IRS gets none of

the pie, and no “contracting” costs means that nothing sticks to the knife.

So just as the substance of Yogi’s meal is unaff ected by whether the pizza is sliced into four pieces or eight, the eco- nomic substance of the fi rm is unaff ected by whether the lia- bility side of the balance sheet is sliced to include more or less debt under the MM assumptions. Note, though, that whereas the IRS may get none of Yogi’s pizza, it is very likely to get some of the fi rm’s income. Yogi’s assumptions are more realistic than MM’s.

a Lee Green, Sportswit (New York: Fawcett Crest, 1984), p. 228. Source: Michael J. Barclay, Cliff ord W. Smith, and Ross L. Watts, “The Determinants of Corporate Leverage and Dividend Policies,” Journal of Applied Corporate Finance, Vol. 7, no. 4 (Winter 1995), pp. 4–19. Used by permission.

YOGI BERRA ON THE M&M PROPOSITION

421Chapter 13 Capital Structure and Leverage

15 The situation here is similar to that involving tax-exempt municipal bonds versus taxable bonds. 16 John R. Graham, “How Big Are the Tax Benefi ts of Debt?” Journal of Finance, Vol. 55 (2000), pp. 1901–1941 and “Estimating the Tax Benefi ts of Debt,” Journal of Applied Corporate Finance, Vol. 14, no. 1 (Spring 2001), pp. 42–54.

Because of the tax situation, Miller argued that investors are willing to accept relatively low before-tax returns on stocks as compared to the before-tax returns on bonds. For example, an investor in the 35% tax bracket might require a 10% pretax return on Bigbee’s bonds, which would result in a 10%(1 # T) " 10%(0.65) " 6.5% after-tax return. Bigbee’s stock is riskier than its bonds, so the investor would require a higher after-tax return (say, 8.5%) on the stock. Because the stock’s re- turns (either dividends or capital gains) would be taxed at only 15%, a pretax return of 8.5%/(1 # T) " 8.5%/0.85 " 10.0% would provide the required 8.5% after-tax return. In this example, the interest rate on the bonds would be 10%, the same as the required return on the stock, rs. Thus, the more favorable treatment of income on the stock would cause investors to accept the same before-tax returns on the stock and on the bond.15

As Miller pointed out, (1) the deductibility of interest favors the use of debt fi nancing, but (2) the more favorable tax treatment of income from stocks lowers the required rates of return on stocks and thus favors the use of equity. It is diffi cult to specify the net effect of these two factors. However, most observers believe that interest deductibility has a stronger effect and hence that our tax system favors the corporate use of debt. Still, that effect is certainly reduced by the lower taxes on stock income. Indeed, Duke University professor John Graham estimated the overall tax benefi ts of debt fi nancing.16 He concluded that the tax benefi ts associ- ated with debt fi nancing represent about 7% of the average fi rm’s value; so if a leverage-free fi rm decided to use an average amount of debt, its value would rise by 7%.

We can observe changes in corporate fi nancing patterns following major changes in tax rates. For example, in 1993, the top personal tax rate on interest and dividends was raised sharply, but the capital gains tax rate was not increased. This resulted in a greater use of equity, especially retained earnings. Subsequent reduc- tions in tax rates on both dividends and capital gains have continued the benefi ts of equity fi nancing over debt fi nancing, which has continued the trend toward a greater reliance on equity fi nancing.

13-4b The Effect of Potential Bankruptcy MM’s irrelevance results also depend on the assumption that fi rms don’t go bankrupt and hence that bankruptcy costs are irrelevant. However, in practice, bankruptcy exists and it can be quite costly. Firms in bankruptcy have high legal and accounting expenses; and they have a hard time retaining customers, sup- pliers, and employees. Moreover, bankruptcy often forces a fi rm to liquidate assets for less than they would be worth if the fi rm continued to operate. Assets such as plant and equipment are often illiquid because they are confi gured to a company’s individual needs and because they are diffi cult to disassemble and move.

Note too that the threat of bankruptcy, not just bankruptcy per se, brings about these problems. If they become concerned about the fi rm’s future, key employees start “jumping ship,” suppliers start refusing to grant credit, customers begin seek- ing more stable suppliers, and lenders start demanding higher interest rates and imposing stricter loan covenants.

Bankruptcy-related problems are likely to increase the more debt a fi rm has in its capital structure. Therefore, bankruptcy costs discourage fi rms from pushing their use of debt to excessive levels. Note too that bankruptcy-related costs have two components: (1) the probability of their occurrence and (2) the costs that will be incurred if fi nancial distress arises. A fi rm whose earnings are relatively volatile,

422 Part 5 Capital Structure and Dividend Policy

all else equal, faces a greater chance of bankruptcy and thus should use less debt than a more stable fi rm. This is consistent with our earlier point that fi rms with high operating leverage (and thus greater business risk) should limit their use of fi nancial leverage. Likewise, fi rms whose assets are illiquid and would have to be sold at “fi re sale” prices should limit their use of debt fi nancing.

13-4c Trade-Off Theory The preceding arguments led to the development of what is called “the trade-off theory of leverage.” This theory states that fi rms trade off the tax benefi ts of debt fi nancing against problems caused by potential bankruptcy. A summary of the trade-off theory is expressed graphically in Figure 13-9. Here are some observa- tions about the fi gure: 1. The fact that interest paid is a deductible expense makes debt less expensive

than common or preferred stock. In effect, the government pays part of the cost of debt—or to put it another way, debt provides tax shelter benefi ts. As a result, using more debt reduces taxes and thus allows more of the fi rm’s oper- ating income (EBIT) to fl ow through to investors. This factor, which MM focused on, tends to raise the stock’s price. Indeed, under the assumptions of MM’s original paper, the stock price would be maximized at 100% debt. The line labeled “MM Result Incorporating the Effects of Corporate Taxation” in Figure 13-9 expresses the relationship between stock prices and debt under their assumptions.

2. In the real world, fi rms have target debt ratios that call for less than 100% debt. The reason is to hold down the adverse effects of potential bankruptcy.

3. There is some threshold level of debt, labeled D1 in Figure 13-9, below which the probability of bankruptcy is so low as to be immaterial. Beyond D1, however,

Trade-Off Theory The capital structure theory that states that firms trade off the tax benefits of debt financing against problems caused by potential bankruptcy.

Eff ect of Leverage on the Value of Bigbee’s StockFIGURE 13-9

Value of Bigbee’s Stock

Value Added by Debt Tax Shelter Benefits

MM Result Incorporating the Effects of Corporate Taxation: Price of the Stock If There Were No Bankruptcy-Related Costs

Value Reduced by Bankruptcy-Related Costs

Actual Price of Stock

Value of Stock If the Firm Used No Financial Leverage

Leverage, D/A0 D D1 2

Value of the Stock with Zero Debt = $20

Threshold Debt Level Where Bankruptcy Costs Become Material

Optimal Capital Structure: Marginal Tax Shelter Benefits = Marginal Bankruptcy-Related Costs

423Chapter 13 Capital Structure and Leverage

bankruptcy-related costs become increasingly important; and they begin to off- set the tax benefi ts of debt. In the range from D1 to D2, bankruptcy-related costs reduce but do not completely offset the tax benefi ts of debt; so the fi rm’s stock price continues to rise (but at a decreasing rate) as its debt ratio increases. How- ever, beyond D2, bankruptcy-related costs exceed the tax benefi ts; so from this point on, increasing the debt ratio lowers the stock price. Therefore, D2 is the optimal capital structure, the one where the stock price is maximized. Of course, D1 and D2 vary from fi rm to fi rm depending on business risk and bankruptcy costs, and they can change for a given fi rm over time.

4. While theoretical and empirical work supports the general shape of the curves in Figures 13-8 and 13-9, these graphs must be taken as approximations, not as precisely defi ned functions. The numbers in Figure 13-8 are rounded to two decimal places, but that is merely for illustrative purposes—the numbers are not nearly that accurate since the graph is based on judgmental estimates.

5. Another disturbing aspect of capital structure theory expressed in Figure 13-9 is the fact that many large, successful fi rms such as Intel and Microsoft use far less debt than the theory suggests. This point led to the development of signal- ing theory, which is discussed in the next section.

13-4d Signaling Theory MM assumed that everyone—investors and managers alike—has the same infor- mation about a fi rm’s prospects. This is called symmetric information. However, in fact, managers often have better information than outside investors. This is called asymmetric information, and it has an important effect on the optimal capi- tal structure. To see why, consider two situations, one where the company’s man- agers know that its prospects are extremely favorable (Firm F) and one where the managers know that the future looks unfavorable (Firm U).

Now suppose Firm F’s R&D labs have just discovered a nonpatentable cure for the common cold. They want to keep the new product a secret as long as possi- ble to delay competitors’ entry into the market. New plants must be built to make the new product, so capital must be raised. But how should Firm F raise the needed capital? If it sells stock, when profi ts from the new product start fl owing in, the price of the stock will rise sharply and purchasers of the new stock will make a bo- nanza. The current stockholders (including the managers) also will do well, but not as well as they would have done if the company had not sold stock before the price increased. In that case, they would not have had to share the benefi ts of the new product with the new stockholders. Therefore, we would expect a fi rm with very favorable prospects to avoid selling stock and instead raise any required new capital by using new debt even if this moved its debt ratio beyond the target level.17

Now consider Firm U. Suppose its managers have information that new orders are off sharply because a competitor has installed new technology that improved the quality of its products. Firm U must upgrade its own facilities at a high cost just to maintain current sales. As a result, its return on investment will fall (but not by as much as if it took no action, which would lead to a 100% loss through bankruptcy). How should Firm U raise the needed capital? Here the situation is just the reverse of that facing Firm F—Firm U will want to sell stock so that some of the adverse conse- quences will be borne by new investors. Therefore, a fi rm with unfavorable prospects would want to fi nance with stock, which would mean bringing in new investors to share the losses.18

Symmetric Information The situation where investors and managers have identical information about firms’ prospects.

Asymmetric Information The situation where managers have different (better) information about firms’ prospects than investors.

17 It would be illegal for Firm F’s managers to personally purchase more shares on the basis of their inside knowl- edge of the new product. They could be sent to jail if they did. 18 Of course, Firm U would have to make certain disclosures when it off ered new shares to the public, but it might be able to meet the legal requirements without fully disclosing management’s worst fears.

424 Part 5 Capital Structure and Dividend Policy

19 Stock issues are more of a negative signal for mature companies than for new, rapidly growing fi rms, where in- vestors expect rapid growth to require additional equity. 20 See Paul Asquith and David W. Mullins, Jr., “The Impact of Initiating Dividend Payments on Shareholders’ Wealth,” Journal of Business, January 1983, pp. 77–96. 21 If you don’t believe that corporate managers can waste money, read Bryan Burrough, Barbarians at the Gate (New York: Harper & Row, 1990), the story of the takeover of RJR Nabisco. 22 Ben Bernanke, “Is There Too Much Corporate Debt?” Federal Reserve Bank of Philadelphia Business Review, September/October 1989, pp. 3–13.

The conclusion from all this is that fi rms with extremely bright prospects pre- fer not to fi nance through new stock offerings, whereas fi rms with poor prospects do like to fi nance with outside equity. How should you, as an investor, react to this conclusion? You ought to say, “If I see that a company plans to issue new stock, I should worry because I know that management would not want to issue stock if future prospects looked good. However, management would want to issue stock if things looked bad. Therefore, I should lower my estimate of the fi rm’s value, other things held constant, if it plans to issue new stock.”

If you gave that answer, your views are consistent with those of sophisticated portfolio managers. In a nutshell, the announcement of a stock offering is generally taken as a signal that the fi rm’s prospects as seen by its management are not bright. This, in turn, suggests that when a fi rm announces a new stock offering, more often than not, the price of its stock will decline.19 Empirical studies have shown that this situ- ation does exist.20

What are the implications of all this for capital structure decisions? Issuing stock emits a negative signal and thus tends to depress the stock price; so even if the company’s prospects are bright, a fi rm should, in normal times, maintain a reserve borrowing capacity that can be used in the event that some especially good investment opportunity comes along. This means that fi rms should, in normal times, use more equity and less debt than is suggested by the tax benefi t/bankruptcy cost trade-off model illustrated in Figure 13-9.

13-4e Using Debt Financing to Constrain Managers In Chapter 1, we stated that confl icts of interest may arise if managers and share- holders have different objectives. Such confl icts are particularly likely when the fi rm has more cash than is needed to support its core operations. Managers often use excess cash to fi nance their pet projects or for perquisites such as plush offi ces, corporate jets, and skyboxes at sports arenas, all of which may do little to benefi t stock prices.21 By contrast, managers with more limited free cash fl ow are less able to make wasteful expenditures.

Firms can reduce excess cash fl ow in a variety of ways. One way is to funnel some of it back to shareholders through higher dividends or stock repurchases. An- other alternative is to tilt the target capital structure toward more debt in the hope that higher debt service requirements will force managers to become more disci- plined. If debt is not serviced as required, the fi rm will be forced into bankruptcy, in which case its managers would lose their jobs. Therefore, a manager is less likely to buy an expensive corporate jet if the fi rm has large debt service requirements.

A leveraged buyout (LBO) is a good way to reduce excess cash fl ow. In an LBO, debt is used to fi nance the purchase of a high percentage of the company’s shares. Indeed, the projected savings from reducing frivolous waste has motivated quite a few leveraged buyouts. As noted, high debt payments after the LBO force managers to conserve cash by eliminating unnecessary expenditures.

Of course, increasing debt and reducing free cash fl ow has its downside: It increases the risk of bankruptcy. A former professor (who is currently the Federal Reserve chairman) has argued that adding debt to a fi rm’s capital structure is like putting a dagger into the steering wheel of a car.22 The dagger—which points

Signal An action taken by a firm’s management that provides clues to investors about how management views the firm’s prospects.

Reserve Borrowing Capacity The ability to borrow money at a reasonable cost when good investment opportunities arise. Firms often use less debt than specified by the MM optimal capital structure in “normal” times to ensure that they can obtain debt capital later if necessary.

425Chapter 13 Capital Structure and Leverage

toward your chest—motivates you to drive more carefully; but you may get stabbed if someone runs into you, even if you are being careful. The analogy applies to cor- porations in the following sense: Higher debt forces managers to be more careful with shareholders’ money; but even well-run fi rms can face bankruptcy (get stabbed) if some event beyond their control, such as a war, an earthquake, a strike, or a reces- sion, occurs. To complete the analogy, the capital structure decision comes down to deciding how big a dagger stockholders should use to keep managers in line.

If you fi nd the discussion of capital structure theory imprecise and somewhat confusing, you’re not alone. In truth, not even the chairman of the Federal Reserve Board knows how to identify a fi rm’s precise optimal capital structure or how to measure the effects of capital structure changes on stock prices and the cost of capi- tal. In practice, capital structure decisions must be made using a combination of judgment and numerical analysis. Still, an understanding of the theoretical issues presented here can help you make better judgments about capital structure issues.

SEL F TEST Why does MM’s theory with taxes lead to 100% debt?

How would an increase in corporate taxes tend to aff ect an average fi rm’s capital structure? What about an increase in the personal tax rate?

Explain what asymmetric information means and how signals aff ect capital structure decisions.

What is meant by reserve borrowing capacity, and why is it important to fi rms?

How can the use of debt serve to discipline managers?

13-5 CHECKLIST FOR CAPITAL STRUCTURE DECISIONS In addition to the types of analysis discussed previously, fi rms generally consider the following factors when making capital structure decisions: 1. Sales stability. A fi rm whose sales are relatively stable can safely take on more

debt and incur higher fi xed charges than a company with unstable sales. Util- ity companies, because of their stable demand, have historically been able to use more fi nancial leverage than industrial fi rms.

2. Asset structure. Firms whose assets are suitable as security for loans tend to use debt relatively heavily. General-purpose assets that can be used by many busi- nesses make good collateral, whereas special-purpose assets do not. Thus, real estate companies are usually highly leveraged, whereas companies involved in technological research are not.

3. Operating leverage. Other things the same, a fi rm with less operating leverage is better able to employ fi nancial leverage because it will have less business risk.

4. Growth rate. Other things the same, faster growing fi rms must rely more heav- ily on external capital. Further, the fl otation cost involved in selling common stock exceeds that incurred when selling debt, which encourages rapidly growing fi rms to rely more heavily on debt. At the same time, however, those fi rms often face higher uncertainty, which tends to reduce their willingness to use debt.

5. Profi tability. It is often observed that fi rms with very high rates of return on investment use relatively little debt. Although there is no theoretical justifi cation for this fact, one practical explanation is that very profi table fi rms such as Intel,

426 Part 5 Capital Structure and Dividend Policy

Microsoft, and Google do not need to do much debt fi nancing. Their high rates of return enable them to do most of their fi nancing with internally generated funds.

6. Taxes. Interest is a deductible expense, and deductions are most valuable to fi rms with high tax rates. Therefore, the higher a fi rm’s tax rate, the greater the advantage of debt.

7. Control. The effect of debt versus stock on a management’s control position can infl uence capital structure. If management currently has voting control (more than 50% of the stock) but is not in a position to buy any more stock, it may choose debt for new fi nancings. On the other hand, management may decide to use equity if the fi rm’s fi nancial situation is so weak that the use of debt might subject it to serious risk of default. The reason? If the fi rm goes into default, managers will probably lose their jobs. However, if too little debt is used, management runs the risk of a takeover. Thus, control considerations can lead to the use of debt or equity because the type of capital that best protects management varies from situation to situation. In any event, if man- agement is at all insecure, it will consider the control situation.

8. Management attitudes. No one can prove that one capital structure will lead to higher stock prices than another. Management, then, can exercise its own judg- ment about the proper capital structure. Some managers tend to be relatively conservative and thus use less debt than an average fi rm in the industry, whereas aggressive managers use a relatively high percentage of debt in their quest for higher profi ts.

9. Lender and rating agency attitudes. Regardless of a manager’s analysis of the proper leverage factors for his or her fi rm, the attitudes of lenders and rating agencies frequently infl uence fi nancial structure decisions. Corporations often discuss their capital structures with lenders and rating agencies and give much weight to their advice. For example, Moody’s and Standard & Poor’s recently told one large utility that its bonds would be downgraded if it issued more bonds. This infl uenced its decision, and its next fi nancing was with common equity.

10. Market conditions. Conditions in the stock and bond markets undergo long- and short-run changes that can have an important bearing on a fi rm’s optimal capital structure. For example, during a recent credit crunch, the junk bond market dried up and there simply was no market at a “reasonable” interest rate for any new long-term bonds rated below BBB. Therefore, low-rated companies in need of capital were forced to go to the stock market or to the short-term debt market, regardless of their target capital structures. When conditions eased, however, these companies sold long-term bonds to get their capital structures back on target.

11. The fi rm’s internal condition. A fi rm’s own internal condition can also have a bearing on its target capital structure. For example, suppose a fi rm just suc- cessfully completed an R&D program, and it forecasts higher earnings in the immediate future. However, the new earnings are not yet anticipated by inves- tors and hence are not refl ected in the stock price. This company would not want to issue stock—it would prefer to fi nance with debt until the higher earn- ings materialize and are refl ected in the stock price. Then it could sell an issue of common stock, use the proceeds to retire the debt, and return to its target capital structure. This point was discussed earlier in connection with asym- metric information and signaling.

12. Financial fl exibility. An astute corporate treasurer made this statement to the authors:

Our company can earn a lot more money from good capital budgeting and operat- ing decisions than from good fi nancing decisions. Indeed, we are not sure exactly how fi nancing decisions affect our stock price, but we know for sure that having

427Chapter 13 Capital Structure and Leverage

to turn down promising ventures because funds are not available will reduce our long-run profi tability. For this reason, my primary goal as treasurer is to always be in a position to raise the capital needed to support operations.

We also know that when times are good, we can raise capital with either stocks or bonds, but when times are bad, suppliers of capital are much more willing to make funds available if we give them a stronger position, and this means debt. Further, when we sell a new issue of stock, this sends a negative “signal” to investors, so stock sales by a mature company such as ours are not desirable.

Putting all these thoughts together gives rise to the goal of maintaining fi nan- cial fl exibility, which from an operational viewpoint means maintaining adequate “reserve borrowing capacity.” Determining the “adequate” reserve is judgmental; but it clearly depends on the fi rm’s forecasted need for funds, predicted capital market conditions, management’s confi dence in its forecasts, and the consequences of a capital shortage.

SEL F TEST How does sales stability aff ect the target capital structure?

How do the types of assets used aff ect a fi rm’s capital structure?

How do taxes aff ect the target capital structure?

How do the attitudes of lenders and rating agencies aff ect capital structure?

How does the fi rm’s internal condition aff ect its actual capital structure?

What is fi nancial fl exibility, and is it increased or decreased by a high debt ratio?

13-6 VARIATIONS IN CAPITAL STRUCTURES As might be expected, wide variations in the use of fi nancial leverage occur across industries and among individual fi rms in each industry. Table 13-4 illustrates dif- ferences for selected industries; the ranking is in descending order of the common equity ratio, as shown in Column 1.23

Pharmaceutical and aerospace/defense companies use relatively little debt because their industries tend to be cyclical, oriented toward research, or subject to huge product liability suits. Utility companies, on the other hand, use debt relatively heavily because their fi xed assets make good security for mortgage bonds and because their relatively stable sales make it safe to carry more than average debt.

The times-interest-earned (TIE) ratio gives an indication of how vulnerable the company is to fi nancial distress. This ratio depends on three factors: (1) the per- centage of debt, (2) the interest rate on the debt, and (3) the company’s profi tability. Generally, low-leveraged industries such as pharmaceuticals and aerospace/de- fense have high coverage ratios, whereas industries such as utilities, which fi nance heavily with debt, have low coverages.

23 Information on capital structures and fi nancial strength is available from a multitude of sources. We used the MSN Money web site to develop Table 13-4; but published sources include The Value Line Investment Survey, Robert Morris Association Annual Studies, and Dun & Bradstreet Key Business Ratios.

428 Part 5 Capital Structure and Dividend Policy

Wide variations also exist among fi rms within given industries. For example, although the average ratio of common equity to total capital in 2008 for the phar- maceutical industry was 70.4%, GlaxoSmithKline had a ratio of only 47.4%. Thus, factors unique to individual fi rms, including managerial attitudes, play an impor- tant role in setting target capital structures.

Capital Structure Percentages, 2008: Six Industries Ranked by Common Equity Ratiosa

T a b l e 1 3 - 4

Industry

Common Equity Ratiob

(1)

Long-Term Debt Ratio

(2)

Times-Interest- Earned Ratio

(3)

Return on Equity

(4) Pharmaceuticals 70.42% 29.58% 16.6 23.70% Aerospace/Defense 62.11 37.89 33.7 24.00 Railroads 59.17 40.83 7.7 15.90 Computers 55.56 44.44 18.8 30.30 Steel 52.63 47.37 15.2 32.80 Utilities 46.30 53.70 5.9 14.40

a Capital structure ratios are calculated as a percentage of total capital, where total capital is defined as long-term debt plus equity, with both measured at book value.

b These ratios are based on accounting (or book) values. Stated on a market-value basis, the equity percentages would rise because most stocks sell at prices that are much higher than their book values.

Source: MSN Money; http://moneycentral.msn.com; May 15, 2008.

To what extent does capital structure vary among diff erent countries? The following table, which is taken from a study by Raghuram Rajan and Luigi Zingales, both of the University of Chicago, shows the median debt ratios of fi rms in the larg- est industrial countries. Rajan and Zingales show that there is considerable variation in capital structure among firms within each of

the seven countries. They also show that capital structures for the firms in each country are generally determined by a similar set of factors: firm size, profitability, market-to- book ratio, and the ratio of fixed assets to total assets. All in all, the Rajan-Zingales study suggests that the points developed in this chapter apply to firms all around the world.

Source: Raghuram G. Rajan and Luigi Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data,” Journal of Finance, Vol. 50, no. 5 (December 1995), pp. 1421–1460. Used with permission.

TAKING A LOOK AT GLOBAL CAPITAL STRUCTURES

Median Percentage of Debt to Total Assets in Diff erent Countries

Country Book Value Debt Ratio United Kingdom 10% Germany 11 France 18 Italy 21 Japan 21 United States 25 Canada 32

http://moneycentral.msn.com

429Chapter 13 Capital Structure and Leverage

SEL F TEST Why do wide variations in the use of fi nancial leverage occur across indus-

tries and among individual fi rms in each industry?

When we studied the cost of capital in Chapter 10, we took the fi rm’s capital structure as given and calculated the cost of capital based on that structure. Then in Chapters 11 and 12, we described capital budgeting techniques, which use the cost of capital as input. Capital budgeting decisions determine the types of projects that a fi rm ac- cepts, which aff ect the nature of the fi rm’s assets and its business risk. In this chapter, we reverse the process, taking the fi rm’s assets and business risk as given and then seeking to determine the best way to fi nance those assets. More specifi cally, in this chapter, we examined the eff ects of fi nancial leverage on earnings per share, stock prices, and the cost of capital and we discussed various capital structure theories.

The diff erent theories lead to diff erent conclusions about the optimal capital structure, and no one has been able to prove that one theory is better than the oth- ers. Therefore, we cannot estimate the optimal capital structure with much precision. Accordingly, fi nancial executives generally treat the optimal capital structure as a range—for example, 40% to 50% debt—rather than as a precise point, such as 45%. The concepts discussed in this chapter are used as a guide, and they help managers understand the factors to consider when they are setting their target capital structures.

T YING I T ALL TO GETHER

KEY TERMS Define each of the following terms: a. Optimal capital structure; target capital structure b. Business risk; financial risk c. Financial leverage; operating leverage; operating breakeven d. Hamada equation; unlevered beta e. Symmetric information; asymmetric information f. Modigliani-Miller theories g. Trade-off theory; signaling theory h. Reserve borrowing capacity

OPERATING LEVERAGE AND BREAK-EVEN ANALYSIS Olinde Electronics Inc. produces stereo components that sell at P " $100 per unit. Olinde’s fixed costs are $200,000, variable costs are $50 per unit, 5,000 components are produced and sold each year, EBIT is currently $50,000, and Olinde’s assets (all equity financed) are $500,000. Olinde can change its production process by adding $400,000 to assets and $50,000 to fixed operating costs. This change would (1) reduce variable costs per unit by $10 and (2) increase output by 2,000 units,

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

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430 Part 5 Capital Structure and Dividend Policy

but (3) the sales price on all units would have to be lowered to $95 to permit sales of the additional output. Olinde has tax loss carry-forwards that cause its tax rate to be zero, it uses no debt, and its average cost of capital is 10%. a. Should Olinde make the change? Why or why not? b. Would Olinde’s break-even point increase or decrease if it made the change? c. Suppose Olinde were unable to raise additional equity financing and had to borrow

the $400,000 at an interest rate of 10% to make the investment. Use the DuPont equa- tion to find the expected ROA of the investment. Should Olinde make the change if debt financing must be used? Explain.

FINANCIAL LEVERAGE Gentry Motors Inc., a producer of turbine generators, is in this situation: EBIT " $4 million, tax rate " T " 35%, debt outstanding " D " $2 million, rd " 10%, rs " 15%, shares of stock outstanding " N0 " 600,000, and book value per share " $10. Because Gentry’s product market is stable and the company expects no growth, all earnings are paid out as dividends. The debt consists of perpetual bonds. a. What are Gentry’s earnings per share (EPS) and its price per share (P0)? b. What is Gentry’s weighted average cost of capital (WACC)? c. Gentry can increase its debt by $8 million to a total of $10 million, using the new debt

to buy back and retire some of its shares at the current price. Its interest rate on debt will be 12% (it will have to call and refund the old debt), and its cost of equity will rise from 15% to 17%. EBIT will remain constant. Should Gentry change its capital structure? Why or why not?

d. If Gentry did not have to refund the $2 million of old debt, how would this affect the situation? Assume that the new and the still outstanding debt are equally risky, with rd " 12%, but that the coupon rate on the old debt is 10%.

e. What is Gentry’s TIE coverage ratio under the original situation and under the condi- tions in Part c of this question?

Changes in sales cause changes in profits. Would the profit change associated with sales changes be larger or smaller if a firm increased its operating leverage? Explain your answer.

Would each of the following increase, decrease, or have an indeterminant effect on a firm’s break-even point (unit sales)? a. The sales price increases with no change in unit costs. b. An increase in fixed costs is accompanied by a decrease in variable costs. c. A new firm decides to use MACRS depreciation for both book and tax purposes

rather than the straight-line depreciation method. d. Variable labor costs decline; other things are held constant.

Discuss the following statement: All else equal, firms with relatively stable sales are able to carry relatively high debt ratios. Is the statement true or false? Why?

If Congress increased the personal tax rate on interest, dividends, and capital gains but simultaneously reduced the rate on corporate income, what effect would this have on the average company’s capital structure?

Which of the following would likely encourage a firm to increase the debt in its capital structure? a. The corporate tax rate increases. b. The personal tax rate increases. c. Due to market changes, the firm’s assets become less liquid. d. Changes in the bankruptcy code make bankruptcy less costly to the firm. e. The firm’s sales and earnings become more volatile.

Why do public utilities generally use different capital structures than pharmaceutical companies?

Why is EBIT generally considered independent of financial leverage? Why might EBIT actually be affected by financial leverage at high debt levels?

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QUESTIONSQUESTIONS

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431Chapter 13 Capital Structure and Leverage

Is the debt level that maximizes a firm’s expected EPS the same as the debt level that maximizes its stock price? Explain.

If a firm goes from zero debt to successively higher levels of debt, why would you expect its stock price to rise first, hit a peak, and then begin to decline?

When the Bell System was broken up, the old AT&T was split into a new AT&T in addi- tion to seven regional telephone companies. The specific reason for forcing the breakup was to increase the degree of competition in the telephone industry. AT&T had a monop- oly on local service, long distance, and the manufacture of all equipment used by tele- phone companies; and the breakup was expected to open most of those markets to compe- tition. In the court order that set the terms of the breakup, the capital structures of the surviving companies were specified and much attention was given to the increased com- petition telephone companies could expect in the future. Do you think the optimal capital structure after the breakup was the same as the pre-breakup optimal capital structure? Explain your position.

A firm is about to double its assets to serve its rapidly growing market. It must choose between a highly automated production process and a less automated one. It also must choose a capital structure for financing the expansion. Should the asset investment and financing decisions be jointly determined, or should each decision be made separately? How would these decisions affect one another? How could the leverage concept be used to help management analyze the situation?

BREAK-EVEN ANALYSIS A company’s fixed operating costs are $500,000, its variable costs are $3.00 per unit, and the product’s sales price is $4.00. What is the company’s break-even point; that is, at what unit sales volume will its income equal its costs?

OPTIMAL CAPITAL STRUCTURE Jackson Trucking Company is in the process of setting its target capital structure. The CFO believes the optimal debt ratio is somewhere between 20% and 50%, and her staff has compiled the following projections for EPS and the stock price at various debt levels:

Debt Ratio Projected EPS Projected Stock Price 20% $ 3.20 $35.00 30 3.45 36.50 40 3.75 36.25 50 3.50 35.50

Assuming that the firm uses only debt and common equity, what is Jackson’s optimal capital structure? At what debt ratio is the company’s WACC minimized?

RISK ANALYSIS a. Given the following information, calculate the expected value for Firm C’s EPS. Data

for Firms A and B are as follows: E(EPSA) " $5.10, and $A " $3.61; E(EPSB) " $4.20, and $B " $2.96.

PROBABILITY 0.1 0.2 0.4 0.2 0.1

Firm A: EPSA (1.50) $1.80 $5.10 $8.40 $11.70 Firm B: EPSB (1.20) 1.50 4.20 6.90 9.60 Firm C: EPSC (2.40) 1.35 5.10 8.85 12.60

b. You are given that $C " $4.11. Discuss the relative riskiness of the three firms’ earnings.

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PROBLEMS PROBLEMS

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432 Part 5 Capital Structure and Dividend Policy

UNLEVERED BETA Harley Motors has $10 million in assets, which were financed with $2 million of debt and $8 million in equity. Harley’s beta is currently 1.2, and its tax rate is 40%. Use the Hamada equation to find Harley’s unlevered beta, bU.

FINANCIAL LEVERAGE EFFECTS Firms HL and LL are identical except for their leverage ratios and the interest rates they pay on debt. Each has $20 million in assets, has $4 million of EBIT, and is in the 40% federal-plus-state tax bracket. Firm HL, however, has a debt ratio (D/A) of 50% and pays 12% interest on its debt, whereas LL has a 30% debt ratio and pays only 10% interest on its debt. a. Calculate the rate of return on equity (ROE) for each firm. b. Observing that HL has a higher ROE, LL’s treasurer is thinking of raising the debt

ratio from 30% to 60% even though that would increase LL’s interest rate on all debt to 15%. Calculate the new ROE for LL.

BREAK-EVEN ANALYSIS The Weaver Watch Company sells watches for $25, the fixed costs are $140,000, and variable costs are $15 per watch. a. What is the firm’s gain or loss at sales of 8,000 watches? at 18,000 watches? b. What is the break-even point? Illustrate by means of a chart. c. What would happen to the break-even point if the selling price was raised to $31?

What is the significance of this analysis? d. What would happen to the break-even point if the selling price was raised to $31 but

variable costs rose to $23 a unit?

FINANCIAL LEVERAGE EFFECTS The Neal Company wants to estimate next year’s return on equity (ROE) under different leverage ratios. Neal’s total assets are $14 million, it currently uses only common equity, and its federal-plus-state tax rate is 40%. The CFO has estimated next year’s EBIT for three possible states of the world: $4.2 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $700,000 with a 0.3 probability. Calculate Neal’s expected ROE, standard deviation, and coefficient of variation for each of the following debt ratios; then evaluate the results:

Debt Ratio Interest Rate 0% —

10 9% 50 11 60 14

HAMADA EQUATION Cyclone Software Co. is trying to establish its optimal capital structure. Its current capital structure consists of 25% debt and 75% equity; however, the CEO believes that the firm should use more debt. The risk-free rate, rRF, is 5%; the market risk premium, RPM, is 6%; and the firm’s tax rate is 40%. Currently, Cyclone’s cost of equity is 14%, which is determined by the CAPM. What would be Cyclone’s estimated cost of equity if it changed its capital structure to 50% debt and 50% equity?

RECAPITALIZATION Tapley Inc. currently has assets of $5 million, has zero debt, is in the 40% federal-plus-state tax bracket, has a net income of $1 million, and pays out 40% of its earnings as dividends. Net income is expected to grow at a constant rate of 5% per year, 200,000 shares of stock are outstanding, and the current WACC is 13.40%.

The company is considering a recapitalization where it will issue $1 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 11% and its cost of equity will rise to 14.5%. a. What is the stock’s current price per share (before the recapitalization)? b. Assuming that the company maintains the same payout ratio, what will be its stock

price following the recapitalization?

BREAKEVEN AND OPERATING LEVERAGE a. Given the following graphs, calculate the total fixed costs, variable costs per unit, and

sales price for Firm A. Firm B’s fixed costs are $120,000, its variable costs per unit are $4, and its sales price is $8 per unit.

b. Which firm has the higher operating leverage at any given level of sales? Explain. c. At what sales level, in units, do both firms earn the same operating profit?

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13-513-5

13-613-6Intermediate Problems 6–9 Intermediate Problems 6–9

13-713-7

13-813-8

13-913-9

13-1013-10Challenging Problems 10–13 Challenging Problems 10–13

433Chapter 13 Capital Structure and Leverage

RECAPITALIZATION Currently, Bloom Flowers Inc. has a capital structure consisting of 20% debt and 80% equity. Bloom’s debt currently has an 8% yield to maturity. The risk-free rate (rRF) is 5%, and the market risk premium (rM # rRF) is 6%. Using the CAPM, Bloom estimates that its cost of equity is currently 12.5%. The company has a 40% tax rate. a. What is Bloom’s current WACC? b. What is the current beta on Bloom’s common stock? c. What would Bloom’s beta be if the company had no debt in its capital structure?

(That is, what is Bloom’s unlevered beta, bU?) Bloom’s financial staff is considering changing its capital structure to 40% debt and 60% equity. If the company went ahead with the proposed change, the yield to maturity on the company’s bonds would rise to 9.5%. The proposed change will have no effect on the company’s tax rate. d. What would be the company’s new cost of equity if it adopted the proposed change

in capital structure? e. What would be the company’s new WACC if it adopted the proposed change in

capital structure? f. Based on your answer to Part e, would you advise Bloom to adopt the proposed

change in capital structure? Explain.

BREAKEVEN AND LEVERAGE Wingler Communications Corporation (WCC) produces premium stereo headphones that sell for $28.80 per set, and this year’s sales are expected to be 450,000 units. Variable production costs for the expected sales under present production methods are estimated at $10,200,000, and fixed production (operating) costs at present are $1,560,000. WCC has $4,800,000 of debt outstanding at an interest rate of 8%. There are 240,000 shares of common stock outstanding, and there is no preferred stock. The dividend payout ratio is 70%, and WCC is in the 40% federal-plus-state tax bracket.

The company is considering investing $7,200,000 in new equipment. Sales would not increase, but variable costs per unit would decline by 20%. Also, fixed operating costs would increase from $1,560,000 to $1,800,000. WCC could raise the required capital by borrowing $7,200,000 at 10% or by selling 240,000 additional shares at $30 per share. a. What would be WCC’s EPS (1) under the old production process, (2) under the new

process if it uses debt, and (3) under the new process if it uses common stock?

13-1113-11

13-1213-12

120

160

200

240

280

10 20 30 40 50 6025

Revenues and Costs (Thousands of Dollars)

Fixed Costs

Break-Even Point

Units (Thousands)

Total CostsTotal Revenues

Firm A

120

160

200

240

280

10 20 30 40 50 60

Revenues and Costs (Thousands of Dollars)

Fixed Costs

Break-Even Point

Units (Thousands)

Total CostsTotal Revenues

Firm B

0 0

Break-Even Charts for Problem 13-10

434 Part 5 Capital Structure and Dividend Policy

b. At what unit sales level would WCC have the same EPS assuming it undertakes the investment and finances it with debt and with stock? {Hint: V " variable cost per unit " $8,160,000/450,000, and EPS " [(PQ # VQ # F # I)(1 # T)]/N. Set EPSStock " EPSDebt and solve for Q.}

c. At what unit sales level would EPS " 0 under the three production/financing setups—that is, under the old plan, the new plan with debt financing, and the new plan with stock financing? (Hint: Note that VOld " $10,200,000/450,000 and use the hints for Part b, setting the EPS equation equal to zero.)

d. On the basis of the analysis in Parts a through c and given that operating leverage is lower under the new setup, which plan is the riskiest, which has the highest expected EPS, and which would you recommend? Assume that there is a fairly high probability of sales falling as low as 250,000 units and determine EPSDebt and EPSStock at that sales level to help assess the riskiness of the two financing plans.

FINANCING ALTERNATIVES The Severn Company plans to raise a net amount of $270 million to finance new equipment and working capital in early 2009. Two alternatives are being considered: Common stock may be sold to net $60 per share, or bonds yielding 12% may be issued. The balance sheet and income statement of the Severn Company prior to financing are as follows:

The Severn Company: Balance Sheet as of December 31, 2008 (Millions of Dollars) Current assets $ 900.00 Accounts payable $ 172.50

Notes payable to bank 255.00 Other current liabilities 225.00 Total current liabilities $ 652.50

Net fixed assets 450.00 Long-term debt (10%) 300.00 Common stock, $3 par 60.00

Retained earnings 337.50 Total assets $1,350.00 Total liabilities and equity $1,350.00

The Severn Company: Income Statement for Year Ended December 31, 2008 (Millions of Dollars)

Sales $2,475.00 Operating costs 2,227.50 Earnings before interest and taxes (10%) $ 247.50 Interest on short-term debt 15.00 Interest on long-term debt 30.00 Earnings before taxes $ 202.50 Federal-plus-state taxes (40%) 81.00 Net income $ 121.50

The probability distribution for annual sales is as follows:

Probability Annual Sales (Millions of Dollars) 0.30 $2,250 0.40 2,700 0.30 3,150

Assuming that EBIT equals 10% of sales, calculate earnings per share (EPS) under the debt financing and the stock financing alternatives at each possible level of sales. Then calculate expected EPS and $EPS under both debt and stock financing alternatives. Also calculate the debt ratio and the times-interest-earned (TIE) ratio at the expected sales level under each alter- native. The old debt will remain outstanding. Which financing method do you recommend?

WACC AND OPTIMAL CAPITAL STRUCTURE Elliott Athletics is trying to determine its optimal capital structure, which now consists of only debt and common equity. The firm does not currently use preferred stock in its capital structure, and it does not plan to do so in the future. Its treasury staff has consulted with investment bankers. On the basis of

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COMPREHENSIVE/SPREADSHEET PROBLEMCOMPREHENSIVE/SPREADSHEET PROBLEM

13-1413-14

435Chapter 13 Capital Structure and Leverage

those discussions, the staff has created the following table showing the firm’s debt cost at different levels:

Debt-to- Assets Ratio

(wd)

Equity-to- Assets Ratio

(wc) Debt-to-Equity

Ratio (D/E) Bond

Rating

Before-Tax Cost of

Debt (rd) 0.0 1.0 0.00 A 7.0% 0.2 0.8 0.25 BBB 8.0 0.4 0.6 0.67 BB 10.0 0.6 0.4 1.50 C 12.0 0.8 0.2 4.00 D 15.0

Elliott uses the CAPM to estimate its cost of common equity, rs, and estimates that the risk-free rate is 5%, the market risk premium is 6%, and its tax rate is 40%. Elliott estimates that if it had no debt, its “unlevered” beta, bU, would be 1.2. a. What is the firm’s optimal capital structure, and what would be its WACC at the opti-

mal capital structure? b. If Elliott’s managers anticipate that the company’s business risk will increase in the

future, what effect would this likely have on the firm’s target capital structure? c. If Congress were to dramatically increase the corporate tax rate, what effect would

this likely have on Elliott’s target capital structure? d. Plot a graph of the after-tax cost of debt, the cost of equity, and the WACC versus (1)

the debt/assets ratio and (2) the debt/equity ratio.

OPTIMAL CAPITAL STRUCTURE Assume that you have just been hired as business manager of Campus Deli (CD), which is located adjacent to the campus. Sales were $1,100,000 last year, variable costs were 60% of sales, and fixed costs were $40,000. Therefore, EBIT totaled $400,000. Because the university’s enrollment is capped, EBIT is expected to be constant over time. Because no expansion capital is required, CD pays out all earnings as dividends. Assets are $2 million, and 80,000 shares are outstanding. The management group owns about 50% of the stock, which is traded in the over-the-counter market.

CD currently has no debt—it is an all-equity firm—and its 80,000 shares outstanding sell at a price of $25 per share, which is also the book value. The firm’s federal-plus-state tax rate is 40%. On the basis of statements made in your finance text, you believe that CD’s shareholders would be better off if some debt financing were used. When you suggested this to your new boss, she encouraged you to pursue the idea but to provide support for the suggestion.

In today’s market, the risk-free rate, rRF, is 6% and the market risk premium, RPM, is 6%. CD’s unlevered beta, bU, is 1.0. CD currently has no debt, so its cost of equity (and WACC) is 12%.

If the firm was recapitalized, debt would be issued and the borrowed funds would be used to repurchase stock. Stockholders, in turn, would use funds provided by the repurchase to buy equities in other fast-food com- panies similar to CD. You plan to complete your report by asking and then answering the following questions.

a. (1) What is business risk? What factors influence a firm’s business risk? (2) What is operating leverage, and how does it affect a firm’s business risk? b. (1) What do the terms financial leverage and financial risk mean? (2) How does financial risk differ from business risk? c. To develop an example that can be presented to CD’s management as an illustration, consider two hypo-

thetical firms: Firm U with zero debt financing and Firm L with $10,000 of 12% debt. Both firms have $20,000 in total assets and a 40% federal-plus-state tax rate, and they have the following EBIT probability distribu- tion for next year:

Probability EBIT 0.25 $2,000 0.50 3,000 0.25 4,000

(1) Complete the partial income statements and the firms’ ratios in Table IC13-1. (2) Be prepared to discuss each entry in the table and to explain how this example illustrates the effect

of financial leverage on expected rate of return and risk.

13-1513-15

IN TEGRATED C ASE CAMPUS DELI INC.

436 Part 5 Capital Structure and Dividend Policy

d. After speaking with a local investment banker, you obtain the following estimates of the cost of debt at dif- ferent debt levels (in thousands of dollars):

Amount Borrowed

D/A Ratio

D/E Ratio

Bond Rating rd

$ 0 0 0 — — 250 0.125 0.1429 AA 8.0% 500 0.250 0.3333 A 9.0 750 0.375 0.6000 BBB 11.5

1,000 0.500 1.0000 BB 14.0

Now consider the optimal capital structure for CD. (1) To begin, define the terms optimal capital structure and target capital structure. (2) Why does CD’s bond rating and cost of debt depend on the amount of money borrowed? (3) Assume that shares could be repurchased at the current market price of $25 per share. Calculate CD’s

expected EPS and TIE at debt levels of $0, $250,000, $500,000, $750,000, and $1,000,000. How many shares would remain after recapitalization under each scenario?

(4) Using the Hamada equation, what is the cost of equity if CD recapitalizes with $250,000 of debt? $500,000? $750,000? $1,000,000?

(5) Considering only the levels of debt discussed, what is the capital structure that minimizes CD’s WACC? (6) What would be the new stock price if CD recapitalizes with $250,000 of debt? $500,000? $750,000?

$1,000,000? Recall that the payout ratio is 100%, so g " 0. (7) Is EPS maximized at the debt level that maximizes share price? Why or why not? (8) Considering only the levels of debt discussed, what is CD’s optimal capital structure? (9) What is the WACC at the optimal capital structure? e. Suppose you discovered that CD had more business risk than you originally estimated. Describe how this

would affect the analysis. How would the analysis be affected if the firm had less business risk than origi- nally estimated?

f. What are some factors a manager should consider when establishing his or her firm’s target capital structure? g. Put labels on Figure IC13-1 and then discuss the graph as you might use it to explain to your boss why CD

might want to use some debt. h. How does the existence of asymmetric information and signaling affect capital structure?

Firm U Firm L Assets $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 Equity $20,000 $20,000 $20,000 $10,000 $10,000 $10,000 Probability 0.25 0.50 0.25 0.25 0.50 0.25 Sales $ 6,000 $ 9,000 $12,000 $ 6,000 $ 9,000 $12,000 Operating costs 4,000 6,000 8,000 4,000 6,000 8,000 Earnings before interest and taxes $ 2,000 $ 3,000 $ 4,000 $ 2,000 $ 3,000 $ 4,000 Interest (12%) 0 0 0 1,200 1,200 Earnings before taxes $ 2,000 $ 3,000 $ 4,000 $ 800 $ $ 2,800 Taxes (40%) 800 1,200 1,600 320 1,120 Net income $ 1,200 $ 1,800 $ 2,400 $ 480 $ $ 1,680 Basic earning power (BEP = EBIT/Assets) 10.0% 15.0% 20.0% 10.0% % 20.0% ROE 6.0% 9.0% 12.0% 4.8% % 16.8% TIE & & & 1.7% % 3.3% Expected basic earning power 15.0% % Expected ROE 9.0% 10.8% Expected TIE & 2.5% $BEP 3.5% % $ROE 2.1% 4.2% $TIE 0 0.6%

Income Statements and RatiosT a b l e I C 1 3 - 1

437Chapter 13 Capital Structure and Leverage

Value of Firm’s Stock

0 D1 D2 Leverage, D/A

Relationship between Capital Structure and Stock PriceFIGURE IC13-1

438 Part 5 Capital Structure and Dividend Policy

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions.

Exploring the Capital Structures for Four of the World’s Leading Auto Companies This chapter provides an overview of the effects of leverage and describes the process that fi rms use to determine their optimal capital structure. The chapter also indicates that capital structures tend to vary across industries and across countries. If you are interested in exploring these differences in more detail, Thomson ONE provides information about the capital structures of each of the companies it follows.

The following discussion questions demonstrate how we can use this information to evaluate the capital structures for four of the world’s leading automobile companies: General Motors (GM-N), Ford (F-N), BMW (BMW-FF), and Toyota (7203-TO). (The combination of letters and numbers in parentheses are the Thomson ONE quote symbols.) As you gather information about these companies, be mindful of the currencies in which these companies’ fi nancial data are reported.

Discussion Questions 1. To get an overall picture of each company’s capital structure, it is helpful to look at a chart that summarizes the

company’s capital structure over the past decade. To obtain this chart, choose a company to start with and select FINANCIALS. Next, select MORE>THOMSON REPORTS & CHARTS>CAPITAL STRUCTURE. This should generate a chart that plots the company’s long-term debt, common equity, and total current liabilities over the past decade. What, if any, are the major trends that emerge from your looking at these charts? Do these companies tend to have relatively high or relatively low levels of debt? Do these companies have significant levels of current liabilities? Have their capital structures changed over time?

2. To get more details about the companies’ capital structures over the past 5 years, select FINANCIALS> FINANCIAL RATIOS>THOMSON RATIOS. From here, you can select ANNUAL RATIOS and/or 5 YEAR AVERAGE RATIOS REPORT. In each case, you can scroll down and look for “Leverage Ratios.” Here you will find a variety of leverage ratios for the past 5 years. (Notice that these two pages offer different information. The ANNUAL RATIOS page offers year-end leverage ratios, while the 5 YEAR AVERAGE RATIOS REPORT offers the average ratio over the previous 5 years for each calendar date. In other words, the 5 YEAR AVERAGE RATIOS REPORT smoothes the changes in capital structure over the reporting period.) Do these ratios suggest that the company has significantly changed its capital structure over the past 5 years? If so, what factors could possibly explain this shift? (Financial statements might be useful to detect any shifts that may have led to the company’s changing capital structure. You may also consult the company’s annual report to see if there is any discussion and/or explanation for these changes. Both the historical financial statements and annual report information can be found via Thomson ONE.)

3. Repeat this procedure for the other three auto companies. Do you find similar capital structures for each of the four companies? Do you find that the capital structures have moved in the same direction over the past 5 years, or have the different companies changed their capital structures in different ways over the past 5 years?

4. The financial ratios investigated thus far are based on book values of debt and equity. Determine whether using the market value of equity (market capitalization found on the OVERVIEW page) makes a significant difference in the most recent year’s “LT Debt Pct Common Equity” and “Total Debt Pct Total Assets.” (Note: “LT Debt” is defined by Thomson ONE as the “Long Term Debt” listed on the balance sheet, while “Total Debt” is defined as “Long Term Debt” plus “ST Debt & Current Portion Due LT Debt.”) Are there big differences between the capital structures measured on a book or market basis?

5. You can also use Thomson ONE to search for companies with very large or very small debt ratios. For example, if you want to find the top 50 companies with the highest debt ratio, select “SCREENING & TARGETING”. Now select ADVANCED SEARCH, ALL COMPANIES, THOMSON FINANCIAL, RATIOS, and LEVERAGE. From here, select “LT Debt Pct Total Cap 5 Yr. Avg.” (This will focus in on the average capital structure over the past 5 years, which should give us a better indication of the company’s long-run target capital structure.)

Discussion Questions 1. To get an overall picture of each company’s capital structure, it is helpful to look at a chart that summarizes the

439Chapter 13 Capital Structure and Leverage

Once you click on SELECT, you should see the “Search Expression Builder” screen. From here, click on “Rank” and select the top 50 by typing 50 in the box below rank; then click on ADD. You can easily change this to select the bottom 50 (or perhaps the bottom 5% or 10%). Take a close look at the resulting firms by clicking on SEARCH. Do you observe any differences between the types of firms that have high debt levels and the types of firms that have low debt levels? Are these patterns similar to what you expect after reading the chapter? (As a quick re- view, you may want to look at the average capital structures for different industries, which is summarized in the text.) Note: The searches are cumulative. So if you ask for the top 10% of the database and follow that by asking for the bottom 5%, you will be shown the bottom 5% of the top 10%. In other words, you will see only a small subset of the firms you are asking for. Hence, before beginning a new search, clear all existing searches.

6. From the submenu just above the list of firms, you may choose a number of options. “Companies” displays a list of the firms and allows you to access a firm report. “Profiles” provides key information about the firms, such as ticker, country, exchange, and industry code. “Financials” gives a couple of key financial figures (expressed in US dollars) from the firms’ balance sheets and income statements. “Market Data” includes the firms’ market capitalization, current price, P/E ratio, EPS, and so forth. Finally, “Report Writer” allows you to create customized company reports.

M i c r o s o f t S h i f t s G e a r s a n d B e g i n s t o U n l o a d Pa r t o f I t s Va s t Ca s h H o a r d

Distributions to Shareholders: Dividends and Share Repurchases

IG EL

T RE

BL IN

/A FP

/G ET

TY IM

AG ES

14 CHAPTER

440

Profitable companies regularly face three impor- tant questions: (1) How much of our free cash flow should we pass on to shareholders? (2) Should we provide this cash to stockholders by raising the dividend or by repurchasing stock? (3) Should we maintain a stable, consistent payment policy; or should we let the payments vary as conditions change?

In this chapter, we discuss many of the issues that affect firms’ cash distribution policies. As we will see, mature companies with stable cash flows and limited growth opportunities tend to return a significant amount of their cash to shareholders either by paying dividends or by using the cash to repurchase common stock. By contrast, rapidly growing companies with good investment opportunities are prone to invest most of their available cash in new projects rather than paying dividends or repurchasing stock. Microsoft, which has long been regarded as the epitome of a growth company, illustrates this tendency. Its sales grew from $786 million in 1989 to a projected $60.3 billion in 2008, which

translates to an annual growth rate of nearly 26%. Much of this growth came from large, long- term investments in new products and technol- ogy; and, given the firm’s emphasis on growth, it paid no dividends over most of its life.

However, over time, this quintessential growth company began to evolve into a mature “cash cow.” Its Windows® and Office products have saturated the market, and they help the company produce large amounts of free cash flow each month. Moreover, until 2003, the com- pany did not pay any dividends to its sharehold- ers because management wanted to keep the cash available for acquisitions and other invest- ments. As a result, the company reported a stag- gering $49 billion in cash on its balance sheet as of June 30, 2003.

Since then, Microsoft has shifted gears; and it now pays a significant portion of its cash to shareholders. First, in 2003, it initiated a regular quarterly dividend of 8 cents a share. That regu- lar dividend was doubled in 2004. However, the cash kept pouring in; and by mid-2004, Microsoft’s

ic ro

so ft

Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

Successful companies earn income. That income can be reinvested in operating assets, used to retire debt, or distributed to stockholders. If the decision is made to distribute income to stockholders, three key issues arise: (1) How much should be distributed? (2) Should the distribution be in the form of dividends, or should the cash be passed on to shareholders by buying back stock? (3) How stable should the distribution be? That is, should the funds paid out from year to year be stable and dependable, which stockholders like; or should they be varied depending on the fi rms’ cash fl ows and investment requirements, which managers tend to like? Those three issues are the primary focus of this chapter; and by the time you complete it, you should be able to: • Explain why some investors like the fi rm to pay more dividends while other inves-

tors prefer reinvestment and the resulting capital gains. • Discuss the various trade-off s that companies face when trying to establish their

optimal dividend policy. • Diff erentiate between stock splits and stock dividends. • List the advantages and disadvantages of stock repurchases vis-à-vis dividends

from both investors’ and companies’ perspectives.

14-1 DIVIDENDS VERSUS CAPITAL GAINS: WHAT DO INVESTORS PREFER?

When deciding how much cash to distribute, fi nancial managers must keep in mind that the fi rm’s objective is to maximize shareholder value. Consequently, the target payout ratio—defi ned as the percentage of net income to be paid out as cash dividends—should be based in large part on investors’ preferences for dividends versus capital gains: Do investors prefer to receive dividends; or would they rather have the fi rm plow the cash back into the business, which presumably will pro- duce capital gains? This preference can be considered in terms of the constant growth stock valuation model.

P̂0 ! D1 _____ rs " g

Target Payout Ratio The target percentage of net income paid out as cash dividends.

cash hoard had grown to more than $60 billion. At that point, the company took some larger steps to return cash to its shareholders. Once again, the regular quarterly dividend was doubled to 32 cents a share. More dramatically, Micro- soft announced plans to pay a one-time special dividend of $3 a share. In addition, it announced plans to repurchase up to $30 billion worth of stock in the open market. All told, this meant that $62.62 billion would be provided to its shareholders.

Microsoft continued to generate a great deal of cash, and its reported cash holdings in March 2008 were around $25 billion. But the company’s aggressive use of dividends

and share repurchases to return cash to shareholders in recent years represents an important shift in policy. When managers decide how and when to distribute cash to share- holders, they face a fundamental question: Could we earn more on the available cash if we kept it in the firm and used it to invest in new projects, or would shareholders earn more if they received the cash and invested it in alternative investments with the same risk? If the company could earn more, it would make sense to retain the cash. However, if investors could earn more, the company would increase shareholder value paying out more dividends and/or repur- chasing more shares.

PU T TING THINGS IN PER SPECTIVE

441

442 Part 5 Capital Structure and Dividend Policy

If the company increases the payout ratio, this will raise D1, which, taken alone, will cause the stock price to rise. However, if D1 is raised, less money will be available for reinvestment, which will cause the expected growth rate to decline; and that will tend to lower the stock’s price. Therefore, any change in the payout policy will have two opposing effects. As a result, the optimal dividend policy must strike the bal- ance between current dividends and future growth that maximizes the stock price. In the following sections, we discuss the major theories that have been advanced to explain how investors regard current dividends versus future growth.

14-1a Dividend Irrelevance Theory Professors Merton Miller and Franco Modigliani (MM) advanced the dividend irrelevance theory, which stated that dividend policy has no effect on either the price of a fi rm’s stock or its cost of capital.1 MM developed their theory under a stringent set of assumptions; and under those assumptions, they proved that a fi rm’s value is determined only by its basic earning power and its business risk. In other words, the value of the fi rm depends only on the income produced by its assets, not on how that income is split between dividends and retained earnings. Note, though, that MM assumed, among other things, that no taxes are paid on dividends, that stocks can be bought and sold with no transactions costs, and that everyone—investors and managers alike—has the same information regarding fi rms’ future earnings.

Given their assumptions, MM argued that each shareholder can construct his or her own dividend policy. For example, if a fi rm does not pay dividends, a share- holder who wants a 5% dividend can “create” it by selling 5% of his or her stock. Conversely, if a company pays a higher dividend than an investor wants, the inves- tor can use the unwanted dividends to buy additional shares of the company’s stock. Note, though, that in the real world, individual investors who want additional divi- dends would have to incur transactions costs to sell shares, and investors who do not want dividends would have to pay taxes on the unwanted dividends and then incur transactions costs to purchase shares with the after-tax dividends. Because taxes and transactions costs do exist, dividend policy may well be relevant and in- vestors may prefer policies that help them reduce taxes and transactions costs.

In defense of their theory, MM noted that many stocks are owned by institu- tional investors who pay no taxes and who can buy and sell stocks with very low transactions costs. For such investors, dividend policy might well be irrelevant; and if these investors dominate the market and represent the “marginal investor,” MM’s theory could be valid in spite of its unrealistic assumptions. Note too that for tax- paying investors, the taxes and transactions costs depend on the individual inves- tor’s income and how long he or she plans to hold the stock. As a result, when it comes to investors’ preferences for dividends, one size does not fi t all. Next, we discuss why some investors prefer dividends whereas others prefer capital gains.

14-1b Reasons Some Investors Prefer Dividends The principal conclusion of MM’s dividend irrelevance theory is that dividend policy does not affect either stock prices or the required rate of return on equity, rs. Early critics of MM’s theory suggested that investors preferred a sure dividend today to an uncertain future capital gain. In particular, Myron Gordon and John Lintner argued that rs declines as the dividend payout is increased because

Optimal Dividend Policy The dividend policy that strikes a balance between current dividends and future growth and maximizes the firm’s stock price.

Dividend Irrelevance Theory The theory that a firm’s dividend policy has no effect on either its value or its cost of capital.

1 Merton H. Miller and Franco Modigliani, “Dividend Policy, Growth, and the Valuation of Shares,” Journal of Business, October 1961, pp. 411–433.

443Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

investors are less certain of receiving the capital gains that should result from retaining earnings than they are of receiving dividend payments.2

MM disagreed. They argued that rs is independent of dividend policy, which implies that investors are indifferent between dividends and capital gains, that is, between D1/P0 and g. MM called the Gordon-Lintner argument the bird-in-the- hand fallacy because in MM’s view, most investors plan to reinvest their divi- dends in the stock of the same or similar fi rms and, in any event, the riskiness of the fi rm’s cash fl ows to investors in the long run is determined by the riskiness of operating cash fl ows, not by dividend payout policy.

Keep in mind, however, that MM’s theory relied on the assumption that there are no taxes or transactions costs, which means that investors who prefer divi- dends could simply create their own dividend policy by selling a percentage of their stock each year. In reality, most investors face transactions costs when they sell stock; so investors who are looking for a steady stream of income would logi- cally prefer that companies pay regular dividends. For example, retirees who have accumulated wealth over time and now want annual income from their invest- ments probably prefer dividend-paying stocks.

14-1c Reasons Some Investors Prefer Capital Gains While dividends reduce transactions costs for investors who are looking for steady income from their investments, dividends increase transactions costs for other investors who are less interested in income and more interested in saving money for the long-term future. These long-term investors want to reinvest their dividends, and that creates transactions costs. Given this concern, a number of companies have established dividend reinvestment plans that help investors automatically reinvest their dividends. (We discuss dividend reinvestment plans in Section 14-4 of this chapter.)

In addition (and perhaps more importantly), the Tax Code encourages many individual investors to prefer capital gains to dividends. Prior to 2003, dividends were taxed at the ordinary income tax rate, which went up to 38% versus a rate of 20% on capital gains. Since 2003, the maximum tax rate on dividends and long- term capital gains has been set at 15%.3 This change lowered the tax disadvantage of dividends, but reinvestment and the accompanying capital gains still have two tax advantages over dividends. First, taxes must be paid on dividends the year they are received, whereas taxes on capital gains are not paid until the stock is sold. Due to time value effects, a dollar of taxes paid in the future has a lower effective cost than a dollar of taxes paid today. Moreover, if a stock is held by some- one until he or she dies, there is no capital gains tax at all—the benefi ciaries who receive the stock can use the stock’s value on the death day as their cost basis, which permits them to escape the capital gains tax completely.

Because of these tax advantages, some investors prefer to have companies retain most of their earnings. Those investors might be willing to pay more for low-payout companies than for otherwise similar high-payout companies.

Finally, the provision in the 2003 Tax Act that lowered the maximum tax rate on dividends is set to expire in 2010 unless Congress votes to extend it or to make it permanent. Now in the middle of the 2008 election cycle, it is not clear what will

Bird-in-the-Hand Fallacy MM’s name for Gordon- Lintner’s theory that a firm’s value will be maximized by setting a high dividend payout ratio.

2 Myron J. Gordon, “Optimal Investment and Financing Policy,” Journal of Finance, May 1963, pp. 264–272; John Lintner, “Dividends, Earnings, Leverage, Stock Prices, and the Supply of Capital to Corporations,” Review of Economics and Statistics, August 1962, pp. 243–269. 3 However, long-term capital gains are classifi ed as income subject to the Alternative Minimum Tax (AMT), and the AMT rate in 2008 was 26% or 28% depending on your income bracket. The AMT was supposed to hit only the very wealthy, but it was not indexed for infl ation. However, by 2008, many not-so-wealthy individuals are being hit. Given the AMT situation, many investors would prefer dividends to capital gains from a tax standpoint.

444 Part 5 Capital Structure and Dividend Policy

happen, particularly after a new Congress and a new president are elected. If Con- gress chooses to let this provision expire and dividends are once again treated as ordinary income, even more investors will prefer capital gains over dividends. At this point, only time will tell.

SEL F TEST Explain briefl y the ideas behind the dividend irrelevance theory.

What did Modigliani and Miller assume about taxes and brokerage costs when they developed their dividend irrelevance theory?

Why did MM refer to the Gordon-Lintner dividend argument as the bird-in- the-hand fallacy?

Why do some investors prefer high-dividend-paying stocks?

Why might other investors prefer low-dividend-paying stocks?

14-2 OTHER DIVIDEND POLICY ISSUES Before we discuss how dividend policy is set in practice, we need to examine two other issues that affect dividend policy: (1) the information content, or signaling, hypothesis and (2) the clientele effect.

14-2a Information Content, or Signaling, Hypothesis An increase in the dividend is often accompanied by an increase in the stock price, while a dividend cut generally leads to a stock price decline. This observation was used to refute MM’s irrelevance theory—their opponents argued that stock price actions after changes in dividend payouts demonstrate that investors prefer dividends to capital gains. However, MM argued differently. They noted that cor- porations are reluctant to cut dividends and hence that corporations do not raise dividends unless they anticipate higher earnings in the future to support the higher dividends. Thus, MM argued that a higher-than-expected dividend increase is a signal to investors that management forecasts good future earnings.4 Conversely, a dividend reduction, or a smaller-than-expected increase, is a signal that management forecasts poor future earnings. If the MM position is correct, stock price changes after dividend increases or decreases do not demonstrate a preference for dividends over retained earnings. Rather, such price changes simply indicate that dividend announcements have information content, or signaling, about future earnings.

Managers often have better information about future prospects for dividends than public stockholders, so there is clearly some information content in dividend announcements. However, it is diffi cult to tell whether the stock price changes that follow dividend increases or decreases refl ect only signaling effects (as MM argue)

Signal An action taken by management that provides clues to investors about how management views the firm’s prospects.

Information Content (Signaling) The theory that investors regard dividend changes as signals of management’s earnings forecasts.

4 Stephen Ross has suggested that managers can use capital structure as well as dividends to give signals concerning a fi rm’s future prospects. For example, a fi rm with good earnings prospects can carry more debt than a similar fi rm with poor earnings prospects. This theory, called incentive signaling, rests on the premise that signals with cash-based variables (either debt interest or dividends) cannot be mimicked by unsuccessful fi rms because those fi rms do not have the future cash-generating power to maintain the announced interest or dividend payment. Thus, investors are more likely to believe a glowing verbal report when it is accompanied by a dividend increase or a debt-fi nanced expansion program. See Stephen A. Ross, “The Determination of Financial Structure: The Incentive-Signaling Approach,” The Bell Journal of Economics, Spring 1977, pp. 23–40.

445Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

or both signaling and dividend preference. Still, a fi rm should consider signaling effects when it is contemplating a change in dividend policy. For example, if a fi rm has good long-term prospects but also has a need for cash to fund current invest- ments, it might be tempted to cut the dividend to increase funds available for in- vestment. However, this action might cause the stock price to decline because the dividend reduction is taken as a signal that future earnings are likely to decline, when just the reverse is actually true. So managers should consider signaling ef- fects when they set dividend policy.

14-2b Clientele Effect As we indicated earlier, different groups, or clienteles, of stockholders prefer different dividend payout policies. For example, retired individuals, pension funds, and university endowment funds generally prefer cash income; so they often want the fi rm to pay out a high percentage of its earnings. Such investors are frequently in low or even zero tax brackets, so taxes are of little concern. On the other hand, stockholders in their peak-earning years might prefer reinvestment because they have less need for current investment income and simply reinvest dividends received after incurring income taxes and brokerage costs.

If a fi rm retains and reinvests income rather than paying dividends, those stockholders who need current income will be disadvantaged. The value of their stock might increase, but they will be forced to go to the trouble and ex- pense of selling off some of their shares to obtain cash. Also, some institutional investors (or trustees for individuals) might be legally precluded from selling stock and then “spending capital.” On the other hand, stockholders who are saving rather than spending dividends favor the low-dividend policy: The less the fi rm pays out in dividends, the less these stockholders have to pay in cur- rent taxes and the less trouble and expense they must go through to reinvest their after-tax dividends. Therefore, investors who want current investment in- come should own shares in high-dividend-payout fi rms, while investors with no need for current investment income should own shares in low-dividend-payout fi rms. For example, investors seeking high cash income might invest in electric utilities, which had an average payout of 60% in 2008, while investors favoring growth could invest in the software industry, which paid out only 18% that same year.

All of this suggests that a clientele effect exists, which means that fi rms have different clienteles and that the clienteles have different preferences—hence, that a change in dividend policy might upset the majority clientele and have a negative effect on the stock’s price.5 This suggests that a company should follow a stable, dependable dividend policy so as to avoid upsetting its clientele.

Clienteles Different groups of stockholders that prefer different dividend payout policies.

Clientele Effect The tendency of a firm to attract a set of investors that like its dividend policy.

5 For example, see R. Richardson Pettit, “Taxes, Transactions Costs and the Clientele Eff ect of Dividends,” The Journal of Financial Economics, December 1977, pp. 419–436.

SEL F TEST Defi ne (1) information content and (2) the clientele eff ect and explain how

they aff ect dividend policy.

446 Part 5 Capital Structure and Dividend Policy

14-3 ESTABLISHING THE DIVIDEND POLICY IN PRACTICE Investors may or may not prefer dividends to capital gains; however, because of the clientele effect, they almost certainly prefer predictable dividends. Given this situation, how should fi rms set their basic dividend policies? In particular, how should a company establish the specifi c percentage of earnings it will distribute, the form of that distribution, and the stability of its distributions over time? In this section, we describe how most fi rms answer those questions.

14-3a Setting the Target Payout Ratio: The Residual Dividend Model6

When a fi rm is deciding how much cash to distribute to stockholders, it should consider two points: (1) The overriding objective is to maximize shareholder value; and (2) the fi rm’s cash fl ows really belong to its shareholders, so management should not retain income unless they can reinvest those earnings at higher rates of return than shareholders can earn themselves. On the other hand, recall from Chapter 10 that internal equity (retained earnings) is cheaper than external equity (new common stock); so if good investments are available, it is better to fi nance them with retained earnings than with new stock.

When a dividend policy is established, one size does not fi t all. Some fi rms produce a large amount of cash but have limited investment opportunities—this is true for fi rms in profi table but mature industries where few growth opportunities exist. Such fi rms typically distribute a large percentage of their cash to sharehold- ers, thereby attracting investor clienteles who prefer high dividends. Other fi rms have many good investment opportunities but currently generate little or no ex- cess cash. Such fi rms generally distribute little or no cash but enjoy rising earnings and stock prices, thereby attracting investors who prefer capital gains.

The past few decades have seen increasing numbers of young, high-growth fi rms trading on the stock exchanges. A study by Eugene Fama and Kenneth French showed that the proportion of fi rms paying dividends has fallen sharply over time. In 1978, 66.5% of fi rms on the major stock exchanges paid dividends. By 1999, that proportion had fallen to 20.8%. Fama and French’s analysis suggested that part of this decline was due to the changing composition of fi rms on the ex- changes. However, their analysis also indicated that all fi rms, new and old, have become less likely to pay dividends.7

As a result of the 2003 tax changes, which lowered the tax rate on dividends, many companies initiated dividends or increased their payouts. For example, in 2002, only 113 companies raised or initiated dividends; however, in 2003 that num- ber doubled to 229. Previously, those companies would have been more inclined to buy back shares. As of 2007, 389 companies in the S&P 500 paid dividends; this is a historic high.

As Table 14-1 suggests, dividend payouts and dividend yields for large corpo- rations vary considerably. Generally, fi rms in stable, cash-producing industries

6 The term payout ratio can be interpreted two ways: (1) in the conventional way—the payout ratio means the percentage of net income paid out as cash dividends, or (2) as the percentage of net income distributed to stock- holders through dividends and share repurchases. In this section, we assume that no repurchases occur. Increasingly, though, fi rms are using the residual model to determine “distributions to shareholders” and then making a separate decision as to the form of those distributions. Further, over time, an increasing percentage of the total distribution has been in the form of share repurchases. 7 Eugene F. Fama and Kenneth R. French, “Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?” Journal of Applied Corporate Finance, Vol. 14, no. 1 (Spring 2001), pp. 67–79; “Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?” Journal of Financial Economics, Vol. 60 (April 2001), pp. 3–43. The last citation is a longer and more technical version of the fi rst paper cited.

447Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

such as utilities, food, and tobacco pay relatively high dividends, whereas compa- nies in rapidly growing industries such as computer software and biotechnology tend to pay lower dividends. Average dividends also differ signifi cantly across countries. Higher payout ratios in some countries can be partially explained by lower tax rates on earnings distributed as cash dividends relative to applicable rates on reinvested income. This biases the dividend policy toward higher payouts.

For a given fi rm, the optimal payout ratio is a function of four factors: (1) management’s opinion about its investors’ preferences for dividends versus capital gains, (2) the fi rm’s investment opportunities, (3) the fi rm’s target capital structure, and (4) the availability and cost of external capital. These factors are combined in what we call the residual dividend model. First, under this model, we assume that investors are indifferent between dividends and capital gains. Then the fi rm follows these four steps to establish its target payout ratio: (1) It determines the optimal capital budget; (2) given its target capital structure, it determines the amount of equity needed to fi nance that budget; (3) it uses retained earnings to meet equity requirements to the extent possible; and (4) it pays divi- dends only if more earnings are available than are needed to support the optimal capital budget. The word residual implies “leftover,” and the residual policy implies that dividends are paid out of “leftover” earnings.

If a fi rm rigidly follows the residual dividend policy, dividends paid in any given year can be expressed in the following equation:

Dividends ! Net income " Retained earnings required to help fi nance new investments

Dividends ! Net income " [(Target equity ratio)(Total capital budget)]

For example, suppose the company has $100 million of earnings, it has a target equity ratio of 60%, and it plans to spend $50 million on capital projects. In that case, it would need $50(0.6) ! $30 million of common equity plus $20 million of new debt to fi nance the capital budget. That would leave $100 " $30 ! $70 million available for dividends, which would result in a 70% payout ratio.

Note that the amount of equity needed to fi nance the capital budget might exceed the net income; in the preceding example, if the capital budget was $100/Equity percentage ! $100/0.6 ! $166.67 million, no dividends would be

Residual Dividend Model A model in which the dividend paid is set equal to net income minus the amount of retained earnings necessary to finance the firm’s optimal capital budget.

Company Industry Dividend

Payout Dividend

Yield I. COMPANIES THAT PAY HIGH DIVIDENDS Verizon Communications Telecommunications 83.63% 4.50% Bank of America Corporation Banking 72.61 6.86 Southern Copper Mining 71.02 5.85 Pfizer, Inc. Pharmaceuticals 52.24 6.41 AT&T Inc. Telecommunications 51.31 4.12

II. COMPANIES THAT PAY NO DIVIDENDS Amazon.com Online retail 0.00% 0.00% Cisco Systems Computer hardware/software " " Dell Inc. Personal computers " " eBay Inc. Internet software and services " " Genentech Inc. Biotechnology " "

Source: Value Line Investment Survey, May 15, 2008.

Dividend Payouts in 2008T a b l e 1 4 - 1

448 Part 5 Capital Structure and Dividend Policy

paid. If the capital budget exceeded $166.67, the company would have to issue new common stock in order to maintain its target capital structure.

Most fi rms have a target capital structure that calls for at least some debt, so new fi nancing is done partly with debt and partly with equity. As long as a fi rm fi nances with the optimal mix of debt and equity and uses only internally gener- ated equity (retained earnings), the marginal cost of each new dollar of capital will be minimized. So internally generated equity is available for fi nancing a certain amount of new investment; but beyond that amount, the fi rm must turn to more expensive new common stock. At the point where new stock must be sold, the cost of equity (and consequently the marginal cost of capital) rises.

To illustrate these points, consider the case of Texas and Western (T&W) Transport Company. T&W’s overall composite cost of capital is 10%. However, this cost assumes that all new equity comes from retained earnings. If the com- pany must issue new stock, its cost of capital will be higher. T&W has $60 million of net income and a target capital structure with 60% equity and 40% debt. Pro- vided it does not pay any cash dividends, T&W could make net investments ( investments in addition to asset replacements from depreciation) of $100 million, consisting of $60 million from retained earnings plus $40 million of new debt sup- ported by the retained earnings, at a 10% marginal cost of capital. If the capital budget exceeded $100 million, the required equity component would exceed net income, which is, of course, the maximum possible amount of retained earnings. In this case, T&W would have to issue new common stock, thereby pushing its cost of capital above 10%.8

At the beginning of its planning period, T&W’s fi nancial staff considers all proposed projects for the upcoming period. All independent projects are accepted if their estimated IRRs exceed their risk-adjusted costs of capital. In choosing among mutually exclusive projects, the project with the highest positive NPV is accepted. The capital budget represents the amount of capital that is required to fi nance all accepted projects. If T&W follows a strict residual dividend policy, we can see from Table 14-2 that the estimated capital budget will have a profound ef- fect on its dividend payout ratio. If investment opportunities are poor, the capital budget will be only $40 million. To maintain the target capital structure, 0.6($40) ! $24 million must be equity, with the remaining $16 million coming as debt. If T&W

8 If T&W does not retain all of its earnings, its cost of capital will rise above 10% before its capital budget reaches $100 million. For example, if T&W chose to retain $36 million, its cost of capital would increase once the capital budget exceeded $36/0.6 ! $60 million. To understand this point, note that a capital budget of $60 million would require $36 million of equity. If the capital budget rose above $60 million, the company’s required equity capital would exceed its retained earnings, thereby requiring it to issue new common stock.

T&W’s Dividend Payout Ratio with $60 Million of Net Income When Faced with Different Investment Opportunities (Dollars in Millions)

T a b l e 1 4 - 2

INVESTMENT OPPORTUNITIES

Poor Average Good Capital budget $40 $70 $150 Net income (NI) $60 $60 $ 60 Required equity (0.6 # Capital budget) 24 42 90 Dividends paid (NI " Required equity) $36 $18 ($ 30)a

Dividend payout ratio (Dividends/NI) 60% 30% 0% a With a $150 million capital budget, T&W would retain all of its earnings and issue $30 million of new stock.

449Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

followed a strict residual policy, it would pay out $60 " $24 ! $36 million as divi- dends; hence, its payout ratio would be $36/$60 ! 0.6 ! 60%.

If the company’s investment opportunities were average, its capital budget would be $70 million. This would require $42 million of equity; so dividends would be $60 " $42 ! $18 million, for a payout of $18/$60 ! 30%. Finally, if

Average dividend yields have varied over time, and they vary considerably in diff erent countries around the world. The accompanying graph, obtained from a recent study by Elroy Dimson, Paul Marsh, and Mike Staunton of the London Busi- ness School, shows how the average dividend yield for 16 diff erent countries has changed over the past century. In both 1900 and 1950, dividend yields varied from nation to

nation, but the average around the world was about 5%. However, by 2004, the yield in most countries had declined signifi cantly and the average had fallen to about 3%. For the United States, the average dividend yield was 4.3% in 1900, 7.2% in 1950, and 1.7% in 2004. Thus, U.S. stocks went from having one of the highest yields in 1900 to the second lowest in 2004.

Source: Elroy Dimson, Paul Marsh, and Mike Staunton, “Forecasting the Market,” London Business School, Working Paper Draft 1, March 10, 2004.

DIVIDEND YIELDS AROUND THE WORLD

1900 1950 2004

Japan

United States Germ

any Switzerland Canada

Denm ark

Sweden

Ireland

Italy

France

Belgium

United Kingdom South Africa Netherlands Austria

Spain

Dividend Yield (%)

Dividend Yields around the World: 1900, 1950, and 2004

450 Part 5 Capital Structure and Dividend Policy

investment opportunities were good, the capital budget would be $150 million and 0.6($150) ! $90 million of equity would be required. Therefore, all of the net income would be retained, dividends would be zero, and the company would have to issue some new common stock to maintain the target capital structure.

We see then that under the residual model, dividends and the payout ratio would vary with investment opportunities. Dividend variations would also occur if earnings fl uctuated. Because investment opportunities and earnings vary from year to year, strict adherence to the residual dividend policy would result in un- stable dividends. One year the fi rm might pay zero dividends because it needed the money to fi nance good investment opportunities, but the next year it might pay high dividends because investment opportunities were poor and it didn’t need to retain much. Similarly, fl uctuating earnings would also lead to variable dividends, even if investment opportunities were stable. Therefore, following the residual dividend policy would almost certainly lead to fl uctuating, unstable dividends. This would not be bad if investors were not bothered by fl uctuating dividends; but since investors do prefer stable, dependable dividends, it would not be opti- mal to follow the residual model in a strict sense. Therefore, fi rms should operate as follows: 1. Estimate earnings and investment opportunities, on average, over the next 5

or so years. 2. Use this forecasted information to fi nd the average residual model amount of

dividends (and the payout ratio) during the planning period. 3. Set a target payout policy based on the projected data.

Thus, fi rms should use the residual policy to help set their long-run target payout ratios, but not as a guide to the payout in any one year.

Most large companies use the residual dividend model in a conceptual sense, then implement it with a computerized fi nancial forecasting model. Information on projected capital expenditures and working capital requirements is entered into the model, along with sales forecasts, profi t margins, depreciation, and the other elements required to forecast cash fl ows. The target capital structure is also specifi ed; the model then generates the amount of debt and equity that will be re- quired to meet the capital budgeting requirements while maintaining the target capital structure.

Dividend payments are introduced; and the higher the payout ratio, the greater the required external equity. Most companies use the model to fi nd a dividend payout over the forecast period (generally 5 years) that will provide suffi cient equity to support the capital budget without having to sell new common stock or take the capital structure ratios outside the optimal range. This chapter’s Excel model includes an illustration of this process. In addition, Web Appendix 14A dis- cusses this approach in more detail. The end result might be a memo such as the following from the CFO to the chairperson of the board:

We forecasted the total market demand for our products, what our share of the market is likely to be, and our required investments in capital assets and working capital. Using this information, we developed projected balance sheets and income statements for the period 2009–2013.

Our 2008 dividends totaled $50 million, or $2.00 per share. On the basis of projected earnings, cash fl ows, and capital requirements, we can increase the divi- dend by 6% per year. This would be consistent with a payout ratio of 42%, on average, over the forecast period. Any faster dividend growth rate would require us to sell common stock, cut the capital budget, or raise the debt ratio. Any slower growth rate would lead to increases in the common equity ratio. Therefore, I recommend that the Board increase the dividend for 2009 by 6%, to $2.12, and that it plan for similar increases in the future.

451Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

Events over the next 5 years will undoubtedly lead to differences between our forecasts and actual results. If and when such events occur, we should reexamine our position. However, I am confi dent that we can meet random cash shortfalls by increasing our borrowings—we have unused debt capacity that gives us fl exibil- ity in this regard.

We ran the corporate model under several scenarios. If the economy totally collapses, our earnings will not cover the dividend. However, in all likely scenar- ios our cash fl ows would cover the recommended dividend. I know the Board does not want to push the dividend up to a level where we would have to cut it under bad conditions. Our model runs indicate, though, that the $2.12 dividend could be maintained under any reasonable set of forecasts. Only if we increased the dividend to over $3.00 would we be seriously exposed to the danger of having to reduce it.

I might also note that most analysts’ reports are forecasting that our divi- dends will grow in the 5% to 6% range. Thus, if we go to $2.12, we will be at the high end of the range, which should give our stock a boost. With takeover rumors so widespread, getting the stock up a bit would make us all breathe a lit- tle easier.

Finally, we considered distributing cash to shareholders through a stock repurchase program. Here we would reduce the dividend payout ratio and use the funds generated to buy our stock on the open market. Such a program has several advantages, but it would also have drawbacks. I do not recommend that we insti- tute a stock repurchase program at this time. However, if our free cash fl ows ex- ceed our forecasts, I would recommend that we use these surpluses to buy back stock. Also, I plan to continue looking into a regular repurchase program, and I may recommend such a program in the future.

This company has very stable operations, so it can plan its dividends with a fairly high degree of confi dence. Other companies, especially those in cyclical industries, have diffi culty maintaining a dividend in bad times that would be too low in good times. Such companies often set a very low “regular” dividend and then supplement it with an “extra” dividend when times are good. General Motors, Ford, and other auto companies have followed such low-regular- dividend-plus-extras policies in the past. Each company announced a low regu- lar dividend that it was confi dent it could maintain “through hell or high water,” one that stockholders could count on under all conditions. Then when times were good and profi ts and cash fl ows were high, the company would pay a clearly designated extra dividend. Because investors recognized that the extras might not be maintained in the future, they did not interpret them as a signal that the companies’ earnings were permanently higher nor did they take the elimination of the extra as a negative signal.

14-3b Earnings, Cash Flows, and Dividends We normally think of earnings as being the primary determinant of dividends, but cash fl ows are actually more important. This is demonstrated in Figure 14-1, which plots data for Chevron Corporation from 1985 through 2007. Panel A shows that Chevron’s dividends per share (DPS) rose slowly but steadily from 1985 to 2007. Earnings per share (EPS) also grew slowly; but they were more vol- atile, rising and falling with the price of oil. The earnings payout ratio (defi ned as DPS/EPS) averaged 70% over the entire 23 years, but it exceeded 100% on several occasions.

Cash fl ow per share (CFPS) tracked EPS very closely—the two were corre- lated at 0.99. However, CFPS was always higher than EPS, and it always exceeded the dividend by a substantial margin. Moreover, cash dividends are paid in cash;

Low-Regular-Dividend- Plus-Extras The policy of announcing a low regular dividend that can be maintained no matter what and then when times are good, paying a designated “extra” dividend.

452 Part 5 Capital Structure and Dividend Policy

so even when earnings were insuffi cient to cover the dividend, cash fl ows took up the slack and enabled the company to maintain a stable dividend policy.

Now look at Panel B. Here we see that the earnings payout is extremely vola- tile, but the cash fl ow payout (defi ned as DPS/CFPS) is relatively stable and always well below 100%. Those stable (and high) cash fl ows indicate that Chevron’s divi- dend is relatively safe, and investors can count on receiving it going forward. Indeed, given the very high cash fl ows per share, continued substantial dividend increases (or large share repurchases) are likely—provided something bad doesn’t happen in the oil market.

Chevron is typical of most large, strong companies. Its dividend is depend- able, and it grows at a steady rate. Earnings are relatively volatile; but cash fl ows are more stable, and those stable cash fl ows are responsible for the steady divi- dends. When earnings change dramatically, either up or down, dividends are likely to follow with a lag while management determines whether the earnings

Panel A

$0 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Above 100%, paying out more than earned: Bad, the higher the payout the riskier the dividend.

DPS

EPS

CFPS

$10

$12

$14

Panel B

Payout

Earnings Payout versus Cash Flow Payout

Below 100%, earning enough to pay the dividend: Good, the lower the payout the safer the dividend.

100%

200%

Oil Prices Rose

Oil Prices Fell

Earnings Payout

Cash Flow Payout

Note: For consistency, data have been adjusted for two-for-one splits in 1994 and 2004. Source: Adapted from Value Line Investment Survey, various issues.

Chevron: Cash Flows, Earnings, and Dividends, 1985–2007FIGURE 14-1

453Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

change is likely to continue. Thus, the dip in Chevron’s earnings in 2001 and 2002 turned out to be temporary, so the dividend was maintained and even increased during those years. The huge earnings and cash fl ow gains after 2002—which have continued into 2008—suggest that dividends, repurchases, and profi table new in- vestments will continue into the future. But Chevron does deal with oil; and with that commodity, strange things can happen.

14-3c Payment Procedures Companies normally pay dividends quarterly; and if conditions permit, the divi- dend is increased once each year. For example, Katz Corporation paid $0.50 per quarter in 2008, or at an annual rate of $2.00. In common fi nancial parlance, we say that Katz’s 2008 regular quarterly dividend was $0.50 and its annual dividend was $2.00. In late 2008, Katz’s board of directors met, reviewed projections for 2009, and decided to keep the 2009 dividend at $2.00. The directors announced the $2.00 rate, so stockholders could count on receiving it unless the company experienced unanticipated operating problems.

The actual payment procedure is as follows: 1. Declaration date. On the declaration date—say, November 7—the directors

meet and declare the regular dividend, issuing a statement similar to the following: “On November 7, 2008, the directors of Katz Corporation met and declared the regular quarterly dividend of 50 cents per share, payable to holders of record at the close of business on December 5, payment to be made on January 2, 2009.” For accounting purposes, the declared dividend becomes an actual liability on the declaration date. If a balance sheet was constructed, the amount ($0.50) # (Number of shares outstanding) would appear as a current liability and retained earnings would be reduced by a like amount.

2. Holder-of-record date. At the close of business on the holder-of-record date, December 5, the company closes its stock transfer books and makes up a list of shareholders as of that date. If Katz Corporation is notifi ed of the sale before 5 p.m. on December 5, the new owner will receive the dividend. However, if notifi cation is received on or after December 6, the previous owner receives the dividend check.

3. Ex-dividend date. Suppose Jean Buyer buys 100 shares of stock from John Seller on December 2. Will the company be notifi ed of the transfer in time to list Buyer as the new owner and thus pay the dividend to her? To avoid confl ict, the securities industry has set up a convention under which the right to the dividend remains with the stock until two business days prior to the holder-of-record date; on the second business day before that date, the right to the dividend no longer goes with the shares. The date when the right to the dividend leaves the stock is called the ex-dividend date. In this case, the ex- dividend date is two business days prior to December 5, or December 3:

Dividend goes with stock if it is bought on or before this date December 2 Ex-dividend date: Buyer does not receive the dividend December 3 Buyer does not receive the dividend December 4 Holder-of-record date; not normally of concern to stockholder December 5

Therefore, if Buyer is to receive the dividend, Buyer must buy the stock on or before December 2. If Buyer buys it on December 3 or later, Seller will receive the dividend because he or she will be the offi cial holder of record.

Katz’s dividend amounts to $0.50, so the ex-dividend date is important. Barring fl uctuations in the stock market, we would normally expect the price

Declaration Date The date on which a firm’s directors issue a statement declaring a dividend.

Holder-of-Record Date If the company lists the stockholder as an owner on this date, the stockholder will receive the dividend.

Ex-Dividend Date The date on which the right to the current dividend no longer accompanies a stock; it is usually two business days prior to the holder- of-record date.

454 Part 5 Capital Structure and Dividend Policy

of a stock to drop by approximately the amount of the dividend on the ex- dividend date. Thus, if Katz closed at $30.50 on December 2, it would probably open at about $30 on December 3.9

4. Payment date. The company actually mails the checks to the holders of record on January 2, the payment date.Payment Date

The date on which a firm actually mails dividend checks.

Payment Date The date on which a firm actually mails dividend checks.

9 Tax eff ects cause the price decline, on average, to be less than the full amount of the dividend. If you bought Katz’s stock on December 2, you would receive the dividend, but you would almost immediately pay 15% of it in taxes. Thus, you would want to wait until December 3 to buy the stock if you thought you could get it for $0.50 less per share. Your reaction (and that of others) would infl uence stock prices around dividend payment dates. Here is what would happen:

1. Other things held constant, a stock’s price should rise during the quarter, with the daily price increase (for Katz) equal to $0.50/90 ! $0.005556. Therefore, if the price started at $30 just after its last ex-dividend date, it would rise to $30.50 on December 2.

2. In the absence of taxes, the stock’s price would fall to $30 on December 3 and then start up as the next dividend accrual period began. Thus, over time, if everything else was held constant, the stock’s price would follow a sawtooth pattern if it was plotted on a graph.

3. Because of taxes, the stock’s price would neither rise by the full amount of the dividend nor fall by the full dividend amount when it goes ex-dividend.

4. The amount of the rise and subsequent fall would be the Dividend # (1 " T), where generally T ! 15%, the tax rate on individual dividends.

See Edwin J. Elton and Martin J. Gruber, “Marginal Stockholder Tax Rates and the Clientele Eff ect,” Review of Economics and Statistics, February 1970, pp. 68–74, for an interesting discussion of the subject. 10See Richard H. Pettway and R. Phil Malone, “Automatic Dividend Reinvestment Plans,” Financial Management, Winter 1973, pp. 11–18, for an old but still excellent discussion of the subject.

SEL F TEST Explain the logic of the residual dividend model, the steps a fi rm would take

to implement it, and why it is more likely to be used to establish a long-run payout target than to set the actual year-by-year payout ratio.

How do fi rms use long-run planning models to help set dividend policy?

Which are more critical to the dividend decision, earnings or cash fl ow? Explain.

Explain the procedures used to actually pay the dividend.

What is the ex-dividend date and why is it important to investors?

A fi rm has a capital budget of $30 million, net income of $35 million, and a target capital structure of 45% debt and 55% equity. If the residual dividend policy is used, what is the fi rm’s dividend payout ratio? (52.86%)

14-4 DIVIDEND REINVESTMENT PLANS During the 1970s, most large companies instituted dividend reinvestment plans (DRIPs), under which stockholders can automatically reinvest their dividends in the stock of the paying corporation.10 Today most large companies offer DRIPs, but participation rates vary considerably. There are two types of DRIPs: (1) plans that involve only old, already-outstanding stock and (2) plans that involve newly issued stock. In either case, the stockholder must pay taxes on the amount of the dividends even though stock rather than cash is received.

Under both types of DRIPs, stockholders choose between continuing to receive dividend checks versus having the company use the dividends to buy more stock in the corporation for the investor. Under an “old stock” plan, the company gives

Dividend Reinvestment Plan (DRIP) A plan that enables a stockholder to automatically reinvest dividends received back into the stock of the paying firm.

455Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

the money that stockholders who elect to use the DRIP would have received to a bank, which acts as a trustee. The bank then uses the money to purchase the cor- poration’s stock on the open market and allocates the shares purchased to the par- ticipating stockholders’ accounts on a pro rata basis. The transactions costs of buy- ing shares (brokerage costs) are low because of volume purchases, so these plans benefi t small stockholders who do not need current cash dividends.

A “new stock” DRIP invests the dividends in newly issued stock; hence, these plans raise new capital for the fi rm. AT&T, Xerox, and many other companies have used new stock plans to raise substantial amounts of equity. No fees are charged to stockholders, and some companies have offered stock at discounts of 2% to 5% below the actual market price. The companies offer discounts because they would have incurred fl otation costs if the new stock had been raised through investment bankers.

One interesting aspect of DRIPs is that they are forcing corporations to reexam- ine their basic dividend policies. A high participation rate in a DRIP suggests that stockholders might be better served if the fi rm simply reduced cash dividends, which would save stockholders some personal income taxes. Quite a few fi rms have surveyed their stockholders to learn more about their preferences and to fi nd out how they would react to a change in dividend policy. A more rational approach to basic dividend policy decisions may emerge from this research. Companies switch from old stock to new stock DRIPs depending on their need for equity capital.

Many companies offering DRIPs have expanded their programs by moving to “open enrollment,” whereby anyone can purchase the fi rm’s stock directly and thus bypass brokers’ commissions. ExxonMobil not only allows investors to buy their initial shares at no fee but also lets them pick up additional shares through automatic bank account withdrawals. Several plans, including ExxonMobil’s, offer dividend reinvestment for individual retirement accounts; and some allow partici- pants to invest weekly or monthly rather than on the quarterly dividend schedule. With all of these plans (and many others), stockholders can invest more than the dividends they are forgoing—they simply send a check to the company and buy shares without a brokerage commission.

SEL F TEST What are dividend reinvestment plans?

What are their advantages and disadvantages from both stockholders’ and fi rms’ perspectives?

14-5 SUMMARY OF FACTORS INFLUENCING DIVIDEND POLICY

In earlier sections, we described the theories of investor preference for dividends and the potential effects of dividend policy on the value of a fi rm. We also dis- cussed the residual dividend model for setting a fi rm’s long-run target payout ratio. In this section, we discuss several other factors that affect the dividend deci- sion. These factors may be grouped into four broad categories: (1) constraints on dividend payments, (2) investment opportunities, (3) availability and cost of alter- native sources of capital, and (4) effects of dividend policy on rs. We discuss these factors next.

456 Part 5 Capital Structure and Dividend Policy

14-5a Constraints 1. Bond indentures. Debt contracts often limit dividend payments to earnings gen-

erated after the loan was granted. Also, debt contracts often stipulate that no dividends can be paid unless the current ratio, times-interest-earned ratio, and other safety ratios exceed stated minimums.

2. Preferred stock restrictions. Typically, common dividends cannot be paid if the company has omitted its preferred dividend. The preferred arrearages must be satisfi ed before common dividends can be resumed.

3. Impairment of capital rule. Dividend payments cannot exceed the balance sheet item “retained earnings.” This legal restriction, known as the impairment of capital rule, is designed to protect creditors. Without the rule, a company that is in trouble might distribute most of its assets to stockholders and leave its debtholders out in the cold. (Liquidating dividends can be paid out of capital; but they must be indicated as such, and they must not reduce capital below the limits stated in debt contracts.)

4. Availability of cash. Cash dividends can be paid only with cash. Thus, a short- age of cash in the bank can restrict dividend payments. However, the ability to borrow can offset this factor.

5. Penalty tax on improperly accumulated earnings. To prevent wealthy individuals from using corporations to avoid personal taxes, the Tax Code provides for a special surtax on improperly accumulated income. Thus, if the IRS can dem- onstrate that a fi rm’s dividend payout ratio is deliberately being held down to help its stockholders avoid personal taxes, the fi rm is subject to heavy penal- ties. This factor is relevant primarily to privately owned fi rms.

14-5b Investment Opportunities 1. Number of profi table investment opportunities. As we saw in our discussion of the

residual model, if a fi rm has a large number of profi table investment opportu- nities, this will tend to produce a low target payout ratio and vice versa if the fi rm has few good investment opportunities.

2. Possibility of accelerating or delaying projects. The ability to accelerate or postpone projects permits a fi rm to adhere more closely to a stable dividend policy.

14-5c Alternative Sources of Capital 1. Cost of selling new stock. If a fi rm needs to fi nance a given level of investment, it

can obtain equity by retaining earnings or by issuing new common stock. If fl otation costs (including any negative signaling effects of a stock offering) are high, re will be well above rs, making it better to set a low payout ratio and to fi nance through retention rather than through the sale of new common stock. On the other hand, a high dividend payout ratio is more feasible for a fi rm whose fl otation costs are low. Flotation costs differ among fi rms—for example, the fl otation percentage is especially high for small fi rms, so they tend to set low payout ratios.

2. Ability to substitute debt for equity. A fi rm can fi nance a given level of investment with debt or equity. As noted, low stock fl otation costs permit a more fl exible dividend policy because equity can be raised by retaining earnings or by sell- ing new stock. A similar situation holds for debt policy: If the fi rm can adjust its debt ratio without raising its WACC sharply, it can pay the expected divi- dend, even if earnings fl uctuate, by additional borrowing.

3. Control. If management is concerned about maintaining control, it may be reluctant to sell new stock; hence, the company may retain more earnings than

457Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

it otherwise would. However, if stockholders want higher dividends and a proxy fi ght looms, the dividend might be increased.

14-5d Effects of Dividend Policy on rs The effects of dividend policy on rs may be considered in terms of four factors: (1) stockholders’ desire for current versus future income, (2) the perceived riskiness of dividends versus capital gains, (3) the tax advantage of capital gains, and (4) the information content of dividends (signaling). We discussed each of those factors earlier, so we only note here that the importance of each factor varies from fi rm to fi rm depending on the makeup of its current and possible future stockholders.

It should be apparent that dividend policy decisions are based more on informed judgment than on quantitative analysis. Even so, to make rational divi- dend decisions, fi nancial managers must take account of all the points discussed in the preceding sections.

SEL F TEST Identify the four broad sets of factors that aff ect dividend policy.

What constraints aff ect dividend policy?

How do investment opportunities aff ect dividend policy?

How does the availability and cost of outside capital aff ect dividend policy?

14-6 STOCK DIVIDENDS AND STOCK SPLITS Stock dividends were originally used by fi rms that were short of cash in lieu of regular cash dividends. Today, though, the primary purpose of dividends is to increase the number of shares outstanding and thus to lower the stock’s price in the market. Stock splits have a similar purpose.

Stock dividends and splits can best be explained through an example. We use Porter Electronic Controls Inc., a $700 million electronic components manufac- turer, for this purpose. Since its inception, Porter’s markets have been expanding and the company has enjoyed growth in sales and earnings. Some of its earnings have been paid out in dividends; but some also were retained each year, causing its earnings per share and the stock price to grow. The company began its life with only a few thousand shares outstanding; and after some years of growth, each of Porter’s shares had a very high EPS and DPS. When a “normal” P/E ratio was applied, the resulting market price was so high that few people could afford to buy a “round lot” of 100 shares. This limited demand for the stock and thus kept the fi rm’s total market value below what it would have been if more shares at a lower price had been outstanding. To correct this situation, Porter “split its stock,” as described in the next section.

14-6a Stock Splits Although there is little empirical evidence to support the contention, there is nev- ertheless a widespread belief in fi nancial circles that an optimal price range exists for stocks. Optimal means that if the price is within this range, the price/earnings ratio (and hence the fi rm’s value) will be maximized. Many observers, including Por- ter’s management, believe that the best range for most stocks is from $20 to $80 per

Up-to-date information about changes in stock splits and stock repurchases is now just a few clicks away. A good place to get started is The Online Investor at www.theonlineinvestor .com. The Online Investor’s home page includes recent stock repurchase and stock split announcements at “Buybacks” and “Stock Splits.”

www.theonlineinvestor.com

458 Part 5 Capital Structure and Dividend Policy

share. Accordingly, if the price of Porter’s stock rose to $80, management would probably declare a two-for-one stock split, thus doubling the number of shares outstanding, halving the earnings and dividends per share, and thereby lowering the stock price. Each stockholder would have more shares, but each share would be worth less. In Yogi Berra’s terms (refer to Chapter 13’s feature box “Yogi Berra on the M&M Proposition”), a stock split just divides the corporate value pie into more slices. If the post-split price was $40, Porter’s stockholders would be exactly as well off as they were before the split. However, if the stock price was to stabilize above $40, stockholders would be better off. Stock splits can be of any size—for example, the stock can be split two-for-one, three-for-one, one-and-a-half-for-one, or any other way.11

14-6b Stock Dividends Stock dividends are similar to stock splits because they “divide the pie into smaller slices” without affecting the fundamental position of the current stockholders. On a 5% stock dividend, the holder of 100 shares would receive an additional 5 shares (without cost); on a 20% stock dividend, the same holder would receive 20 new shares; and so forth. Again, the total number of shares is increased; so earnings, dividends, and price per share all decline.

If a fi rm wants to reduce the price of its stock, should it use a stock split or a stock dividend? Stock splits are generally used after a sharp price run-up to pro- duce a large price reduction. Stock dividends used on a regular annual basis keep the stock price more or less constrained. For example, if a fi rm’s earnings and divi- dends were growing at about 10% per year, its stock price would tend to increase at about that same rate and it would soon be outside the desired trading range. A 10% annual stock dividend would maintain the stock price within the optimal trading range. Note, though, that because small stock dividends create bookkeep- ing problems and unnecessary expenses, fi rms use stock splits far more often than stock dividends.12

14-6c Effect on Stock Prices If a company splits its stock or declares a stock dividend, will this increase the market value of its stock? Several empirical studies have addressed this question. Here is a summary of their fi ndings.13

1. On average, the price of a company’s stock rises shortly after it announces a stock split or dividend.

Stock Split An action taken by a firm to increase the number of shares outstanding, such as doubling the number of shares outstanding by giving each stockholder two new shares for each one formerly held.

Stock Dividend A dividend paid in the form of additional shares of stock rather than in cash.

11 Reverse splits, which reduce the shares outstanding, can also be used. For example, a company whose stock sells for $5 might employ a one-for-fi ve reverse split, exchanging one new share for fi ve old ones and raising the value of the shares to about $25, which is within the optimal price range. LTV Corporation did this after several years of losses had driven its stock price below the optimal range. 12 Accountants treat stock splits and stock dividends somewhat diff erently. For example, in a two-for-one stock split, the number of shares outstanding is doubled and the par value is halved, and that is about all there is to it. With a stock dividend, a bookkeeping entry is made transferring “retained earnings” to “common stock.” For example, if a fi rm had 1,000,000 shares outstanding, if the stock price was $10, and if it wanted to pay a 10% stock dividend, (1) each stockholder would be given 1 new share of stock for each 10 shares held and (2) the accounting entries would involve showing 100,000 more shares outstanding and transferring 100,000($10) ! $1,000,000 from “retained earnings” to “common stock.” The retained earnings transfer limits the size of stock dividends, but that is not important because companies can split their stock any way they choose. 13 See Eugene F. Fama, Lawrence Fisher, Michael C. Jensen, and Richard Roll, “The Adjustment of Stock Prices to New Information,” International Economic Review, February 1969, pp. 1–21; Mark S. Grinblatt, Ronald M. Masulis, and Sheridan Titman, “The Valuation Eff ects of Stock Splits and Stock Dividends,” Journal of Financial Economics, December 1984, pp. 461–490; Ravi Dahr, William N. Goetzmann, Shane Shepherd, and Ning Zhu, “The Impact of Clientele Changes: Evidence from Stock Splits,” Yale International Center for Finance Working Paper No. 03-14, March 2004; and Thomas E. Copeland, “Liquidity Changes Following Stock Splits,” Journal of Finance, March 1979, pp. 115–141.

459Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

2. One reason that stock splits and stock dividends may lead to higher prices is that investors often take stock splits/dividends as signals of higher future earnings. Because only companies whose managements believe that things look good tend to split their stocks, the announcement of a stock split is taken as a signal that earnings and cash dividends are likely to rise. Thus, the price increases associated with stock splits/dividends may be the result of a favor- able signal for earnings and dividends.

3. If a company announces a stock split or dividend, its price will tend to rise. However, if during the next few months it does not announce an increase in earnings and dividends, the stock price generally will drop back to the earlier level. This supports the signaling effect discussed earlier.

4. By creating more shares and lowering the stock price, stock splits may also increase the stock’s liquidity. This tends to increase the fi rm’s value.

5. There is also evidence that stock splits change the mix of shareholders. The proportion of trades made by individual investors tends to increase after a stock split, whereas the proportion of trades made by institutional investors tends to fall. We are not sure how this affects the stock’s value.

What do we conclude from all this? From a pure economic standpoint, stock dividends and splits are just additional pieces of paper. However, they provide management with a relatively low-cost way of signaling that the fi rm’s prospects look good. Further, we should note that since few large, publicly owned stocks sell at prices above several hundred dollars, we simply do not know what the effect would be if Chevron, Microsoft, Xerox, Hewlett-Packard, and other highly suc- cessful fi rms had never split their stocks and consequently sold at prices in the thousands or even millions of dollars per share.14

14 It is interesting to note that Berkshire Hathaway, which is controlled by billionaire Warren Buff ett, one of the most successful fi nanciers of the 20th century, has never had a stock split and its stock sold on the NYSE for $123,000 per share in May 2008. But in response to investment trusts that were being formed to sell fractional units of the stock—and thus, in eff ect, to split it—Buff ett himself created a new class of Berkshire Hathaway stock (Class B) worth about 1/30 of a Class A (regular) share.

SEL F TEST What are stock dividends and stock splits?

How do stock dividends and splits aff ect stock prices?

In what situation should a fi rm pay a stock dividend?

In what situation should a fi rm split its stock?

Suppose you have 100 common shares of Tillman Industries. The EPS is $4.00, the DPS is $2.00, and the stock sells for $60 per share. Now Tillman announces a two-for-one split. Immediately after the split, how many shares will you have, what will be the adjusted EPS and DPS, and what would you expect the stock price to be? (200 shares; $2.00; $1.00; probably a little over $30)

14-7 STOCK REPURCHASES Several years ago a Fortune article entitled “Beating the Market by Buying Back Stock” reported that during a one-year period, more than 600 major corporations repurchased signifi cant amounts of their own stock. It also gave illustrations of some specifi c companies’ repurchase programs and the effects of these programs

460 Part 5 Capital Structure and Dividend Policy

on stock prices. The article’s conclusion was that “buybacks have made a mint for shareholders who stay with the companies carrying them out.”

More recently, as we noted in the opening vignette, Microsoft announced plans to establish a dividend and to repurchase shares of its common stock. Microsoft’s recent actions are part of a larger trend in which many leading companies have re- purchased stock. How do stock repurchase programs work, and why have they become so prevalent over the past several years? We discuss these questions in the remainder of this section.

There are three principal types of stock repurchases: (1) situations where the fi rm has cash available for distribution to its stockholders and it distributes this cash by repurchasing shares rather than by paying cash dividends, (2) situations where the fi rm concludes that its capital structure is too heavily weighted with equity and it sells debt and uses the proceeds to buy back its stock, and (3) situations where the fi rm has issued options to employees and it uses open market repurchases to obtain stock for use when the options are exercised.

Stock that has been repurchased by a fi rm is called treasury stock. If some of the outstanding stock is repurchased, fewer shares will remain outstanding. Assuming that the repurchase does not adversely affect the fi rm’s future earn- ings, the earnings per share on the remaining shares will increase, resulting in a higher market price per share. As a result, capital gains will have been substi- tuted for dividends.

14-7a The Effects of Stock Repurchases Many companies have been repurchasing their stock in recent years. Until the 1980s, most repurchases amounted to a few million dollars. But in 1985, Phillips Petroleum announced plans for the largest repurchase on record at that time—81 million of its shares with a market value of $4.1 billion. Even more dramatic, in 2004, Microsoft announced plans for a $30 billion stock repurchase that would take place over a number of years. Other large repurchases have been made by Procter & Gamble, Dell, Home Depot, Texas Instruments, IBM, Coca-Cola, Teledyne, Atlantic Richfi eld, Goodyear, and Xerox. Indeed, since 1985, more shares have been repurchased than issued.

The effects of a repurchase can be illustrated with data on American Develop- ment Corporation (ADC). The company expects to earn $4.4 million in 2009, and 50% of this amount (or $2.2 million) has been allocated for distribution to com- mon shareholders. There are 1.1 million shares outstanding, and the market price is $20 a share. ADC believes that it can use the $2.2 million to repurchase 100,000 of its shares through a tender offer at $22 a share or pay a cash dividend of $2 a share.15

Stock Repurchase A transaction in which a firm buys back shares of its own stock, thereby decreasing shares outstanding, increasing EPS, and often increasing the stock price.

15 Stock repurchases are generally made in one of three ways: (1) A publicly owned fi rm can simply buy its own stock through a broker on the open market. (2) It can make a tender off er, under which it permits stockholders to send in (that is, “tender”) their shares to the fi rm in exchange for a specifi ed price per share. In this case, the fi rm generally indicates that it will buy up to a specifi ed number of shares within a particular time period (usually about 2 weeks); if more shares are tendered than the company wants to purchase, purchases are made on a pro rata basis. (3) The fi rm can purchase a block of shares from one large holder on a negotiated basis. If a negotiated purchase is employed, care must be taken to ensure that this one stockholder does not receive preferential treatment over other stockholders or that any preference given can be justifi ed by “sound business reasons.” A number of years ago Texaco’s management was sued by stockholders who were unhappy over the company’s repurchase of about $600 million of stock from the Bass Brothers at a substantial premium over the market price. The suit charged that Texaco’s management, afraid the Bass Brothers would attempt a takeover, used the buyback to “get them off its back.” Such payments have been dubbed greenmail.

461Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

The effect of the repurchase on the EPS and market price per share of the remaining stock can be analyzed as follows:

1. Current EPS ! Total earnings

_________________ Numbers of shares ! $4.4 million ___________ 1.1 million ! $4.00 per share

2. P/E ratio ! $20 ____ $4 ! 5#

3. EPS after repurchasing 100,000 shares ! $4.4 million ___________ 1 million ! $4.40 per share

4. Expected market price after repurchase ! (P/E)(EPS) ! (5)($4.40) ! $22 per share

It should be noted from this example that in any case, investors would receive before-tax benefi ts of $2 per share either in the form of a $2 cash dividend or a $2 increase in the stock price. This result would occur because we assumed, fi rst, that shares could be repurchased at exactly $22 a share and, second, that the P/E ratio would remain constant. If shares could be bought for less than $22, the operation would be even better for remaining stockholders; but the reverse would hold if ADC had to pay more than $22 a share. Furthermore, the P/E ratio might change as a result of the repurchase operation, rising if investors viewed it favorably and falling if they viewed it unfavorably. Some factors that might affect P/E ratios are considered next.

14-7b Advantages of Repurchases The advantages of repurchases are as follows: 1. A repurchase announcement may be viewed as a positive signal by investors

because repurchases are often motivated by managements’ belief that their fi rms’ shares are undervalued.

2. The stockholders have a choice when the fi rm distributes cash by repurchas- ing stock—they can sell or not sell. With a cash dividend, on the other hand, stockholders must accept a dividend payment and pay the tax. Thus, those stockholders who need cash can sell back some of their shares, while those who do not want additional cash can simply retain their stock. From a tax standpoint, a repurchase permits both types of stockholders to get what they want.

3. A repurchase can remove a large block of stock that is “overhanging” the mar- ket and keeping the price per share down.

4. Dividends are “sticky” in the short run because managements are reluctant to raise the dividend if the increase cannot be maintained in the future— managements dislike cutting cash dividends because of the negative signal a cut gives. Therefore, if excess cash fl ows are expected to be temporary, man- agements may prefer to make distributions as share repurchases rather than to declare increased cash dividends that cannot be maintained.

5. Companies can use the residual model to set a target cash distribution level, then divide the distribution into a dividend component and a repurchase compo- nent. The dividend payout ratio will be relatively low; but the dividend itself will be relatively secure, and it will grow as a result of the declining number of shares outstanding. This gives the company more fl exibility in adjusting the total distribution than if the entire distribution were in the form of cash divi- dends because repurchases can be varied from year to year without giving off adverse signals. This procedure has much to recommend it, and it is an

462 Part 5 Capital Structure and Dividend Policy

important reason for the dramatic increase in the volume of share repurchases. IBM, FPL, and most other large companies use repurchases in this manner.

6. Repurchases can be used to produce large-scale changes in capital structure. For example, a number of years ago Consolidated Edison decided that its debt ratio was so low that it was not minimizing its WACC. It then borrowed $400 million and used the funds to repurchase shares of its common stock. This resulted in an immediate shift from a nonoptimal to an optimal capital structure.

7. Companies that use stock options as an important component of employee compensation can repurchase shares and then reissue those shares when employees exercise their options. This avoids having to issue new shares, which dilutes earnings per share. Microsoft and other high-tech companies have used this procedure in recent years.

14-7c Disadvantages of Repurchases Disadvantages of repurchases include the following: 1. Stockholders may not be indifferent between dividends and capital gains, and

the price of the stock might benefi t more from cash dividends than from repur- chases. Cash dividends are generally dependable, but repurchases are not.

2. The selling stockholders may not be fully aware of all the implications of a repurchase, or they may not have all the pertinent information about the cor- poration’s present and future activities. This is especially true in situations where management has good reason to believe that the stock price is well below its intrinsic value. However, fi rms generally announce repurchase pro- grams before embarking on them to avoid potential stockholder suits.

3. The corporation may pay too high a price for the repurchased stock, to the dis- advantage of remaining stockholders. If its shares are not actively traded and if the fi rm seeks to acquire a relatively large amount of its stock, the price may be bid above its intrinsic value and then fall after the fi rm ceases its repurchase operations.

14-7d Conclusions on Stock Repurchases When all the pros and cons on stock repurchases have been totaled, where do we stand? Our conclusions may be summarized as follows: 1. Because of the deferred tax on capital gains, repurchases have a tax advantage

over dividends as a way to distribute income to stockholders. This advantage is reinforced by the fact that repurchases provide cash to stockholders who want cash but also allow those who do not need current cash to delay its receipt. On the other hand, dividends are more dependable and are thus better suited for those who need a steady source of income.

2. Because of signaling effects, companies should not pay fl uctuating dividends— that would lower investors’ confi dence in the company and adversely affect its cost of equity and its stock price. However, cash fl ows vary over time, as do investment opportunities; so the “proper” dividend in the residual model sense varies. To get around this problem, a company can set its dividend at a level low enough to keep dividend payments from constraining operations and then use repurchases on a more or less regular basis to distribute excess cash. Such a procedure would provide regular, dependable dividends in addi- tion to additional cash fl ows to those stockholders who want it.

3. Repurchases are also useful when a fi rm wants to make a large, rapid shift in its capital structure, wants to distribute cash from a one-time event such as the sale of a division, or wants to obtain shares for use in an employee stock option plan.

463Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

In earlier editions of this book, we argued that companies ought to be doing more repurchasing and paying out less cash as dividends. Increases in the size and frequency of repurchases in recent years suggest that companies have fi nally reached this same conclusion.

SEL F TEST Explain how repurchases can (1) help stockholders hold down taxes and

(2) help fi rms change their capital structures.

What is treasury stock?

What are three procedures a fi rm can use to repurchase its stock?

What are some advantages and disadvantages of stock repurchases?

How can stock repurchases help a company operate in accordance with the residual dividend model?

Once a company becomes profi table, it must decide what to do with the cash it gener- ates. It may choose to retain cash and use it to purchase additional operating assets, to repay outstanding debt, or to acquire other companies. Alternatively, it may choose to return cash to shareholders. Keep in mind that every dollar that management chooses to retain is a dollar that shareholders could have received and invested else- where. Therefore, managers should retain earnings if and only if they can invest the money within the fi rm and earn more than stockholders can earn outside the fi rm. Consequently, high-growth companies with many good projects tend to retain a high percentage of earnings, whereas mature companies with a great deal of cash but lim- ited investment opportunities tend to have generous cash distribution policies.

T YING I T ALL TO GETHER

KEY TERMS Define each of the following terms: a. Target payout ratio; optimal dividend policy b. Dividend irrelevance theory; bird-in-the-hand fallacy c. Information content, or signaling; clientele effect; signal; clienteles d. Residual dividend model e. Low-regular-dividend-plus-extras f. Declaration date; holder-of-record date; ex-dividend date; payment date g. Dividend reinvestment plan (DRIP) h. Stock split; stock dividend i. Stock repurchase

ALTERNATIVE DIVIDEND POLICIES Components Manufacturing Corporation (CMC) has an all-common-equity capital structure. It has 200,000 shares of $2 par value common stock outstanding. When CMC’s founder, who was also its research director and most successful inventor, retired unexpectedly to the South Pacific in late 2008, CMC was left

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

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464 Part 5 Capital Structure and Dividend Policy

suddenly and permanently with materially lower growth expectations and relatively few attractive new investment opportunities. Unfortunately, there was no way to replace the founder’s contributions to the firm. Previously, CMC found it necessary to plow back most of its earnings to finance growth, which averaged 12% per year. Future growth at a 6% rate is considered realistic, but that level would call for an increase in the dividend payout. Further, it now appears that new investment projects with at least the 14% rate of return required by CMC’s stockholders (rs ! 14%) would amount to only $800,000 for 2009 compared to a projected $2,000,000 of net income. If the existing 20% dividend pay- out was continued, retained earnings would be $1.6 million in 2009; but as noted, invest- ments that yield the 14% cost of capital would amount to only $800,000. The one encouraging point is that the high earnings from existing assets are expected to continue, and net income of $2 million is still expected for 2009. Given the dramatically changed circumstances, CMC’s management is reviewing the firm’s dividend policy. a. Assuming that the acceptable 2009 investment projects would be financed entirely by

earnings retained during the year and assuming that CMC uses the residual dividend model, calculate DPS in 2009.

b. What payout ratio does your answer to Part a imply for 2009? c. If a 60% payout ratio is maintained for the foreseeable future, what is your estimate of

the present market price of the common stock? How does this compare with the mar- ket price that should have prevailed under the assumptions existing just before the news about the founder’s retirement? If the two values of P0 are different, comment on why.

d. What would happen to the stock price if the old 20% payout was continued? Assume that if this payout is maintained, the average rate of return on the retained earnings will fall to 7.5% and the new growth rate will be as follows:

g ! (1.0 " Payout ratio)(ROE)

! (1.0 " 0.2)(7.5%)

! (0.8)(7.5%) ! 6.0%

Discuss the pros and cons of having the directors formally announce what a firm’s dividend policy will be in the future.

The cost of retained earnings is less than the cost of new outside equity capital. Consequently, it is totally irrational for a firm to sell a new issue of stock and to pay dividends during the same year. Discuss the meaning of those statements.

Would it ever be rational for a firm to borrow money in order to pay dividends? Explain.

Modigliani and Miller (MM) on the one hand and Gordon and Lintner (GL) on the other hand have expressed strong views regarding the effect of dividend policy on a firm’s cost of capital and value. a. In essence, what are MM’s and GL’s views regarding the effect of dividend policy on

the cost of capital and stock prices? b. How could MM use the information content, or signaling, hypothesis to counter their

opponents’ arguments? If you were debating MM, how would you counter them? c. How could MM use the clientele effect concept to counter their opponents’

arguments? If you were debating MM, how would you counter them?

How would each of the following changes tend to affect aggregate (that is, the average for all corporations) payout ratios, other things held constant? Explain your answers. a. An increase in the personal income tax rate b. A liberalization of depreciation for federal income tax purposes—that is, faster tax

write-offs c. A rise in interest rates d. An increase in corporate profits e. A decline in investment opportunities

QUESTIONSQUESTIONS

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465Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

f. Permission for corporations to deduct dividends for tax purposes as they now deduct interest charges

g. A change in the Tax Code so that realized and unrealized capital gains in any year are taxed at the same rate as dividends

One position expressed in the financial literature is that firms set their dividends as a residual after using income to support new investment. a. Explain what a residual dividend policy implies, illustrating your answer with a table

showing how different investment opportunities can lead to different dividend payout ratios.

b. Think back to Chapter 13 where we considered the relationship between capital structure and the cost of capital. If the WACC-versus-debt-ratio plot was shaped like a sharp V, would this have a different implication for the importance of setting dividends according to the residual policy than if the plot was shaped like a shallow bowl (a flattened U)?

Executive salaries have been shown to be more closely correlated to the size of the firm than to its profitability. If a firm’s board of directors is controlled by management rather than outside directors, this might result in the firm’s retaining more earnings than can be justified from the stockholders’ point of view. Discuss those statements, being sure (a) to discuss the interrelationships among cost of capital, investment opportunities, and new investment and (b) to explain the implied relationship between dividend policy and stock prices.

What is the difference between a stock dividend and a stock split? As a stockholder, would you prefer to see your company declare a 100% stock dividend or a two-for-one split? Assume that either action is feasible.

Most firms like to have their stock selling at a high P/E ratio, and they also like to have extensive public ownership (many different shareholders). Explain how stock dividends or stock splits may help achieve those goals.

Indicate whether the following statements are true or false. If the statement is false, explain why. a. If a firm repurchases its stock in the open market, the shareholders who tender the

stock are subject to capital gains taxes. b. If you own 100 shares in a company’s stock and the company’s stock splits 2-for-1,

you will own 200 shares in the company following the split. c. Some dividend reinvestment plans increase the amount of equity capital available to

the firm. d. The Tax Code encourages companies to pay a large percentage of their net income in

the form of dividends. e. If your company has established a clientele of investors who prefer large dividends,

the company is unlikely to adopt a residual dividend policy. f. If a firm follows a residual dividend policy, holding all else constant, its dividend

payout will tend to rise whenever the firm’s investment opportunities improve.

RESIDUAL DIVIDEND MODEL Axel Telecommunications has a target capital structure that consists of 70% debt and 30% equity. The company anticipates that its capital budget for the upcoming year will be $3,000,000. If Axel reports net income of $2,000,000 and it follows a residual dividend payout policy, what will be its dividend payout ratio?

STOCK SPLIT Gamma Medical’s stock trades at $90 a share. The company is contemplating a 3-for-2 stock split. Assuming that the stock split will have no effect on the market value of its equity, what will be the company’s stock price following the stock split?

STOCK REPURCHASES Beta Industries has net income of $2,000,000, and it has 1,000,000 shares of common stock outstanding. The company’s stock currently trades at $32 a share. Beta is considering a plan in which it will use available cash to repurchase 20% of its shares in the open market. The repurchase is expected to have no effect on net income or the company’s P/E ratio. What will be Beta’s stock price following the stock repurchase?

STOCK SPLIT After a 5-for-1 stock split, Strasburg Company paid a dividend of $0.75 per new share, which represents a 9% increase over last year’s pre-split dividend. What was last year’s dividend per share?

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466 Part 5 Capital Structure and Dividend Policy

EXTERNAL EQUITY FINANCING Northern Pacific Heating and Cooling Inc. has a 6-month backlog of orders for its patented solar heating system. To meet this demand, management plans to expand production capacity by 40% with a $10 million investment in plant and machinery. The firm wants to maintain a 40% debt-to-total-assets ratio in its capital structure. It also wants to maintain its past dividend policy of distributing 45% of last year’s net income. In 2008, net income was $5 million. How much external equity must Northern Pacific seek at the beginning of 2009 to expand capacity as desired? Assume that the firm uses only debt and common equity in its capital structure.

RESIDUAL DIVIDEND MODEL Welch Company is considering three independent projects, each of which requires a $5 million investment. The estimated internal rate of return (IRR) and cost of capital for these projects are presented here:

Project H (high risk): Cost of capital ! 16% IRR ! 20% Project M (medium risk): Cost of capital ! 12% IRR ! 10% Project L (low risk): Cost of capital ! 8% IRR ! 9%

Note that the projects’ costs of capital vary because the projects have different levels of risk. The company’s optimal capital structure calls for 50% debt and 50% common equity. Welch expects to have net income of $7,287,500. If Welch establishes its dividends from the residual model, what will be its payout ratio?

DIVIDENDS Bowles Sporting Inc. is prepared to report the following income statement (shown in thousands of dollars) for the year 2009.

Sales $15,200 Operating costs including depreciation 11,900 EBIT $ 3,300 Interest 300 EBT $ 3,000 Taxes (40%) 1,200 Net income $ 1,800

Prior to reporting this income statement, the company wants to determine its annual dividend. The company has 500,000 shares of stock outstanding, and its stock trades at $48 per share. a. The company had a 40% dividend payout ratio in 2008. If Bowles wants to maintain

this payout ratio in 2009, what will be its per-share dividend in 2009? b. If the company maintains this 40% payout ratio, what will be the current dividend

yield on the company’s stock? c. The company reported net income of $1.5 million in 2008. Assume that the number of

shares outstanding has remained constant. What was the company’s per-share dividend in 2008?

d. As an alternative to maintaining the same dividend payout ratio, Bowles is considering maintaining the same per-share dividend in 2009 that it paid in 2008. If it chooses this policy, what will be the company’s dividend payout ratio in 2009?

e. Assume that the company is interested in dramatically expanding its operations and that this expansion will require significant amounts of capital. The company would like to avoid transactions costs involved in issuing new equity. Given this scenario, would it make more sense for the company to maintain a constant dividend payout ratio or to maintain the same per-share dividend?

ALTERNATIVE DIVIDEND POLICIES Rubenstein Bros. Clothing is expecting to pay an annual dividend per share of $0.75 out of annual earnings per share of $2.25. Currently, Rubenstein Bros.’ stock is selling for $12.50 per share. Adhering to the company’s target capital structure, the firm has $10 million in assets, of which 40% is funded by debt. Assume that the firm’s book value of equity equals its market value. In past years, the firm has earned a return on equity (ROE) of 18%, which is expected to continue this year and into the foreseeable future. a. Based on that information, what long-run growth rate can the firm be expected to

maintain? (Hint: g ! Retention rate × ROE.) b. What is the stock’s required return?

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467Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

c. If the firm changed its dividend policy and paid an annual dividend of $1.50 per share, financial analysts would predict that the change in policy will have no effect on the firm’s stock price or ROE. Therefore, what must be the firm’s new expected long-run growth rate and required return?

d. Suppose instead that the firm has decided to proceed with its original plan of disbursing $0.75 per share to shareholders but the firm intends to do so in the form of a stock dividend rather than a cash dividend. The firm will allot new shares based on the current stock price of $12.50. In other words, for every $12.50 in dividends due to shareholders, a share of stock will be issued. How large will the stock dividend be relative to the firm’s current market capitalization? (Hint: Remember that market capitalization ! P0 # number of shares outstanding.)

e. If the plan in Part d is implemented, how many new shares of stock will be issued and by how much will the company’s earnings per share be diluted?

ALTERNATIVE DIVIDEND POLICIES In 2008, Keenan Company paid dividends totaling $3,600,000 on net income of $10.8 million. Note that 2008 was a normal year and that for the past 10 years, earnings have grown at a constant rate of 10%. However, in 2009, earnings are expected to jump to $14.4 million, and the firm expects to have profitable investment opportunities of $8.4 million. It is predicted that Keenan will not be able to maintain the 2009 level of earnings growth—the high 2009 earnings level is attributable to an exceptionally profitable new product line introduced that year—and the company will return to its previous 10% growth rate. Keenan’s target capital structure is 40% debt and 60% equity. a. Calculate Keenan’s total dividends for 2009 assuming that it follows each of the

following policies: (1) Its 2009 dividend payment is set to force dividends to grow at the long-run

growth rate in earnings. (2) It continues the 2008 dividend payout ratio. (3) It uses a pure residual dividend policy (40% of the $8.4 million investment is

financed with debt and 60% with common equity). (4) It employs a regular-dividend-plus-extras policy, with the regular dividend

being based on the long-run growth rate and the extra dividend being set according to the residual policy.

b. Which of the preceding policies would you recommend? Restrict your choices to the ones listed but justify your answer.

c. Assume that investors expect Keenan to pay total dividends of $9,000,000 in 2009 and to have the dividend grow at 10% after 2009. The stock’s total market value is $180 million. What is the company’s cost of equity?

d. What is Keenan’s long-run average return on equity? [Hint: g ! Retention rate # ROE ! (1.0 " Payout rate)(ROE).]

e. Does a 2009 dividend of $9,000,000 seem reasonable in view of your answers to Parts c and d? If not, should the dividend be higher or lower? Explain your answer.

RESIDUAL DIVIDEND MODEL Buena Terra Corporation is reviewing its capital budget for the upcoming year. It has paid a $3.00 dividend per share (DPS) for the past several years, and its shareholders expect the dividend to remain constant for the next several years. The company’s target capital structure is 60% equity and 40% debt, it has 1,000,000 shares of common equity outstanding, and its net income is $8 million. The company forecasts that it will require $10 million to fund all of its profitable (that is, positive NPV) projects for the upcoming year. a. If Buena Terra follows the residual dividend model, how much retained earnings will

it need to fund its capital budget? b. If Buena Terra follows the residual dividend model, what will be the company’s

dividend per share and payout ratio for the upcoming year? c. If Buena Terra maintains its current $3.00 DPS for next year, how much retained

earnings will be available for the firm’s capital budget? d. Can the company maintain its current capital structure, maintain the $3.00 DPS, and

maintain a $10 million capital budget without having to raise new common stock?

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468 Part 5 Capital Structure and Dividend Policy

e. Suppose that Buena Terra’s management is firmly opposed to cutting the dividend; that is, it wants to maintain the $3.00 dividend for the next year. Also assume that the company was committed to funding all profitable projects and was willing to issue more debt (along with the available retained earnings) to help finance the company’s capital budget. Assume that the resulting change in capital structure has a minimal effect on the company’s composite cost of capital so that the capital budget remains at $10 million. What portion of this year’s capital budget would have to be financed with debt?

f. Suppose once again that Buena Terra’s management wants to maintain the $3.00 DPS. In addition, the company wants to maintain its target capital structure (60% equity and 40% debt) and maintain its $10 million capital budget. What is the minimum dollar amount of new common stock that the company would have to issue to meet each of its objectives?

g. Now consider the case where Buena Terra’s management wants to maintain the $3.00 DPS and its target capital structure, but it wants to avoid issuing new common stock. The company is willing to cut its capital budget to meet its other objectives. Assuming that the company’s projects are divisible, what will be the company’s capital budget for the next year?

h. What actions can a firm that follows the residual dividend policy take when its forecasted retained earnings are less than the retained earnings required to fund its capital budget?

DIVIDEND POLICY Southeastern Steel Company (SSC) was formed 5 years ago to exploit a new continuous casting process. SSC’s founders, Donald Brown and Margo Valencia, had been employed in the research depart- ment of a major integrated-steel company; but when that company decided against using the new process (which Brown and Valencia had developed), they decided to strike out on their own. One advantage of the new process was that it required relatively little capital compared to the typical steel company, so Brown and Valencia have been able to avoid issuing new stock and thus own all of the shares. However, SSC has now reached the stage in which outside equity capital is necessary if the firm is to achieve its growth targets yet still maintain its target capital structure of 60% equity and 40% debt. Therefore, Brown and Valencia have decided to take the company public. Until now, Brown and Valencia have paid themselves reasonable salaries but routinely reinvested all after-tax earnings in the firm; so dividend policy has not been an issue. However, before talking with potential outside investors, they must decide on a dividend policy. Assume that you were recently hired by Arthur Adamson & Company (AA), a national consulting firm, which has been asked to help SSC prepare for its public offering. Martha Millon, the senior AA consultant in your group, has asked you to make a presentation to Brown and Valencia in which you review the theory of dividend policy and discuss the following questions: a. (1) What is meant by the term dividend policy? (2) Explain briefly the dividend irrelevance theory that was put forward by Modigliani and Miller. What

were the key assumptions underlying their theory? (3) Why do some investors prefer high-dividend-paying stocks, while other investors prefer stocks that

pay low or nonexistent dividends? b. Discuss (1) the information content, or signaling, hypothesis; (2) the clientele effect; and (3) their effects on

dividend policy. c. (1) Assume that SSC has an $800,000 capital budget planned for the coming year. You have determined that

its present capital structure (60% equity and 40% debt) is optimal, and its net income is forecasted at $600,000. Use the residual dividend model approach to determine SSC’s total dollar dividend and pay- out ratio. In the process, explain how the residual dividend model works. Then explain what would happen if net income was forecasted at $400,000 and at $800,000.

(2) In general terms, how would a change in investment opportunities affect the payout ratio under the residual payment policy?

(3) What are the advantages and disadvantages of the residual policy? (Hint: Don’t neglect signaling and clientele effects.)

d. What is a dividend reinvestment plan (DRIP), and how does it work? e. Describe the series of steps that most firms take in setting dividend policy in practice. f. What are stock repurchases? Discuss the advantages and disadvantages of a firm’s repurchasing its own shares. g. What are stock dividends and stock splits? What are the advantages and disadvantages of stock dividends

and stock splits?

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IN TEGRATED C ASE SOUTHEASTERN STEEL COMPANY

469Chapter 14 Distributions to Shareholders: Dividends and Share Repurchases

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions.

Microsoft’s Dividend Policy In this chapter’s opening vignette, we discussed Microsoft’s decision to establish a dividend payout pol- icy in 2003. Let’s fi nd out what has happened to Microsoft’s (MSFT) dividend policy since the time of this announcement. We can address this issue by relying on the data that are provided in Thomson ONE.

Discussion Questions 1. To get information about MSFT’s dividend policy, enter its ticker quote (MSFT-O) and select OVERVIEW>FULL

REPORTS>THOMSON FULL REPORTS>FULL COMPANY REPORT. Click on STOCK & EARNINGS DATA and scroll down to the “Annual Historical Data” section. What has happened to MSFT’s dividend per share, dividend yield, and dividend payout over the past 5 years? Provide an explanation for what took place.

2. Compare this information with other firms in the same industry. To see how MSFT stacks up against its peers, select COMPARABLES>OVERVIEWS>PER SHARE DATA to get MSFT’s peers’ last annual dividends. Access- ing COMPARABLES>OVERVIEWS>ABSOLUTE RANKINGS will give their dividend yields. You can also get this information from the VALUATION COMPARISON in this same section. Has MSFT behaved differently from its peers, or have there been industrywide shifts?

3. Refer back to the FULL COMPANY REPORT used in Question 1. Manually plot earnings and dividends over time. In the text, we point out that dividends are often more stable than earnings. Do you see a similar pattern for MSFT? Explain.

4. In the “Interim Financial Data” section of the FULL COMPANY REPORT, identify the dividend declared date, ex-date, and pay date. Explain the significance of those dates. Go back to “Overview” and access the “Interac- tive Price Chart.” Can you observe price shifts around these dates? Explain what price shifts you might expect to see.

5. Investors are more concerned with future dividends than historical dividends, so go to ESTIMATES and scroll down to the “Consensus Estimates” section. Click on the “Available Measures” menu to toggle between earn- ings per share and dividends per share. How do analysts expect MSFT’s payout policy to behave in the future?

6. Refer back to the FULL COMPANY REPORT and scroll down to the “5 Yr Annual Balance Sheet” section. Does it appear that MSFT has been repurchasing any stock, or has it been issuing new stock?

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WORKING CAPITAL MANAGEMENT, FORECASTING,

AND MULTINATIONAL FINANCIAL MANAGEMENT

15 Working Capital Management

16 Financial Planning and Forecasting

17 Multinational Financial Management

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Best Buy Company, North America’s largest consumer electronics retailer, has performed extremely well over the past decade. Its stock sold for $50 in late 2007, up from $2 only 10 years earlier. This excellent performance stemmed from sound financial and operating practices, especially its working capital management, the focus of this chapter.

Working capital management involves find- ing the optimal levels for cash, marketable secu- rities, accounts receivable, and inventory and then financing that working capital for the least cost. Most of Best Buy’s customers use credit cards, so neither in-store cash nor accounts receivable is significant. Therefore, Best Buy’s working capital policy focuses on its inventories. To maintain sales, its stores must be well stocked with the goods customers are seeking at the

time they are shopping. This involves determin- ing what new products are hot, determining where they can be obtained at the lowest cost, and delivering them to stores in a timely manner.

Dramatic improvements in communications and computer technology have transformed the way Best Buy manages its inventories. It now col- lects real-time data from each store on how each product is selling, and its computers place orders automatically to keep the shelves full. Moreover, if sales of an item are slipping, prices are lowered to reduce stocks of that item before the situation gets so bad that drastic price cuts are necessary. After studying this chapter, you will have a good understanding of how working capital should be managed so as to maximize profits and stock prices.

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Chapter 15 Working Capital Management

About 50% of the typical industrial or retail fi rm’s assets are held as working capital, and many students’ fi rst jobs focus on working capital management. This is particu- larly true in smaller businesses, where the majority of new jobs are being created. When you fi nish this chapter, you should be able to: • Explain how diff erent amounts of current assets and current liabilities aff ect fi rms’

profi tability and thus their stock prices. • Discuss how the cash conversion cycle is determined, how the cash budget is con-

structed, and how each is used in working capital management. • Explain how companies decide on the proper amount of each current asset—cash,

marketable securities, accounts receivable, and inventory. • Discuss how companies set their credit policies and explain the eff ect of credit

policy on sales and profi ts. • Describe how the costs of trade credit, bank loans, and commercial paper are

determined and how that information impacts decisions for fi nancing working capital.

• Explain how companies use security to lower their costs of short-term credit.

15-1 BACKGROUND ON WORKING CAPITAL The term working capital originated with the old Yankee peddler who would load up his wagon and go off to peddle his wares. The merchandise was called “work- ing capital” because it was what he actually sold, or “turned over,” to produce his profi ts. The wagon and horse were his fi xed assets. He generally owned the horse and wagon (so they were fi nanced with “equity” capital), but he bought his mer- chandise on credit (that is, by borrowing from his supplier) or with money bor- rowed from a bank. Those loans were called working capital loans, and they had to be repaid after each trip to demonstrate that the peddler was solvent and worthy of a new loan. Banks that followed this procedure were said to be employing “sound banking practices.” The more trips the peddler took per year, the faster his working capital turned over and the greater his profi ts.

This concept can be applied to modern businesses, as we demonstrate in this chapter. We begin with a review of two basic defi nitions that were covered in Chapter 3: 1. Working capital. Current assets are often called working capital because these

assets “turn over” (i.e., are used and then replaced during the year).1

2. Net working capital. When a fi rm buys inventory on credit, its suppliers in effect lend it the money used to fi nance the inventory. The fi rm could have borrowed from its bank or sold stock to obtain the money, but it received the funds from its suppliers. These loans are recorded as accounts payable, and they are typi- cally “free” in the sense that they do not bear interest. Similarly, Allied pays its workers every 2 weeks and pays taxes quarterly, so its labor force and the tax authorities provide it with loans equal to its accrued wages and taxes. If we subtract the sum of payables plus accruals from current assets, the difference is

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1 Any current assets not used in normal operations, such as excess cash held to pay for a plant under construc- tion, are deducted and thus not included in working capital. Allied Food Products uses all of its current assets in operations.

474 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

called net working capital, which represents the amount of money that the fi rm must obtain from nonfree sources to carry its current assets. Here is the 2008 net working capital for Allied Food Products, the fi rm we discussed in Chapter 3:

Net working capital ! (Current assets) " (Payables # Accruals)

! $1,000 " ($60 # $140) ! $800 million SEL

F TEST How did the term working capital originate?

Diff erentiate between working capital and net working capital.

15-2 CURRENT ASSET INVESTMENT POLICIES In this section, we discuss how the amount of current assets held affects profi tabil- ity. To begin, Figure 15-1 shows three alternative policies regarding the size of cur- rent asset holdings. The top line has the steepest slope, which indicates that the

Note: The sales/current assets relationship is shown here as being linear, but the relationship could be curvilinear.

Current Asset Investment Policies (Millions of Dollars)FIGURE 15-1

50 100 150 2000

Current Assets ($)

Sales ($)

Relaxed

Moderate

Restricted

Policy Current Assets per

$100 of Sales Turnover of Current

Assets: Sales/CA Relaxed $30 3.3x Moderate 23 4.3 Restricted 16 6.3

475Chapter 15 Working Capital Management

15-3 CURRENT ASSET FINANCING POLICIES Investments in current assets must be fi nanced; and the primary sources of funds include bank loans, credit from suppliers (accounts payable), accrued liabilities, long-term debt, and common equity. Each of those sources has advantages and disadvantages, so each fi rm must decide which sources are best for it.

To begin, note that most businesses experience seasonal and/or cyclical fl uc- tuations. For example, construction fi rms tend to peak in the summer, retailers peak around Christmas, and the manufacturers who supply both construction companies and retailers follow related patterns. Similarly, the sales of virtually all

SEL F TEST Identify and explain three alternative current asset investment policies.

Use the DuPont equation to show how working capital policy aff ects a fi rm’s expected ROE.

fi rm holds a great deal of cash, marketable securities, receivables, and inventories relative to its sales. When receivables are high, the fi rm has a liberal credit policy, which results in a high level of accounts receivable. This is a relaxed policy. On the other hand, when a fi rm has a restricted (or tight or “lean-and-mean”) policy, hold- ings of current assets are minimized. A moderate policy lies between the two extremes.

We can use the DuPont equation to demonstrate how working capital man- agement affects ROE:

ROE ! Profi t margin $ Total assets turnover $ Leverage factor

! Net income __________ Sales $ Sales ______ Assets $

Assets ______ Equity

A restricted (lean-and-mean) policy means a low level of assets (hence, a high total assets turnover ratio), which results in a high ROE, other things held constant. However, this policy also exposes the fi rm to risks because shortages can lead to work stoppages, unhappy customers, and serious long-run problems. The relaxed policy minimizes such operating problems; but it results in a low turnover, which in turn lowers ROE. The moderate policy falls between the two extremes. The optimal strategy is the one that maximizes the fi rm’s long-run earnings and the stock’s intrinsic value.

Note that changing technologies can lead to changes in the optimal policy. For example, when a new technology makes it possible for a manufacturer to produce a given product in 5 rather than 10 days, work-in-progress inventories can be cut in half. Similarly, retailers such as Wal-Mart and Home Depot have inventory management systems in which bar codes on all merchandise are read at the cash register. This information is transmitted electronically to a computer that records the remaining stock of each item, and the computer automatically places an order with the supplier’s computer when the stock falls to a specifi ed level. This process lowers the “safety stocks” that would otherwise be necessary to avoid running out of stock, which lowers inventories to profi t-maximizing levels.

Relaxed Current Asset Policy Relatively large amounts of cash, marketable securities, and inventories are carried; and a liberal credit policy results in a high level of receivables.

Restricted Current Asset Policy Holdings of cash, marketable securities, inventories, and receivables are constrained.

Moderate Current Asset Policy Between the relaxed and restricted policies.

476 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

businesses increase when the economy is strong; hence, they build up current as- sets at those times but let inventories and receivables fall when the economy weak- ens. Note, though, that current assets rarely drop to zero—companies maintain some permanent current assets, which are the current assets needed at the low point of the business cycle. Then as sales increase during an upswing, current as- sets are increased, and these extra current assets are defi ned as temporary current assets as opposed to permanent current assets. The way these two types of current assets are fi nanced is called the fi rm’s current assets fi nancing policy.

15-3a Maturity Matching, or “Self-Liquidating,” Approach

The maturity matching, or “self-liquidating,” approach calls for matching asset and liability maturities as shown in Panel a of Figure 15-2. All of the fi xed assets plus the permanent current assets are fi nanced with long-term capital, but tempo- rary current assets are fi nanced with short-term debt. Inventory expected to be sold in 30 days would be fi nanced with a 30-day bank loan, a machine expected to last for 5 years would be fi nanced with a 5-year loan, a 20-year building would be fi nanced with a 20-year mortgage bond, and so forth. Actually, two factors prevent an exact maturity matching: (1) There is uncertainty about the lives of assets. For example, a fi rm might fi nance inventories with a 30-day bank loan, expecting to sell the inventories and use the cash to retire the loan. But if sales are slow, the cash would not be forthcoming and the fi rm might not be able to pay off the loan when it matures. (2) Some common equity must be used, and common equity has no maturity. Still, when a fi rm attempts to match asset and liability maturities, this is defi ned as a moderate current asset fi nancing policy.

15-3b Aggressive Approach Panel b of Figure 15-2 illustrates the situation for a more aggressive fi rm that fi nances some of its permanent assets with short-term debt. Note that we used the term relatively in the title of Panel b because there can be different degrees of aggres- siveness. For example, the dashed line in Panel b could have been drawn below the line designating fi xed assets, indicating that all of the current assets—both perma- nent and temporary—and part of the fi xed assets were fi nanced with short-term credit. This policy would be a highly aggressive, extremely nonconservative posi- tion; and the fi rm would be subject to dangers from loan renewal as well as prob- lems with rising interest rates. However, short-term interest rates are generally lower than long-term rates, and some fi rms are willing to sacrifi ce some safety for the chance of higher profi ts.

The reason for adopting the aggressive policy is to take advantage of the fact that the yield curve is generally upward-sloping; hence, short-term rates are gen- erally lower than long-term rates. However, a strategy of fi nancing long-term as- sets with short-term debt is really quite risky. To illustrate, suppose a company borrows $1 million on a 1-year basis and uses the funds to buy machinery that will lower labor costs by $200,000 per year for 10 years.2 Cash fl ows from the equip- ment would not be suffi cient to pay off the loan at the end of only 1 year, so the loan would have to be renewed. If the company encountered temporary fi nancial problems, the lender might refuse to renew the loan, which could lead to bank- ruptcy. Had the fi rm matched maturities and fi nanced the plant with a 10-year

Permanent Current Assets Current assets that a firm must carry even at the trough of its cycles.

Temporary Current Assets Current assets that fluctuate with seasonal or cyclical variations in sales.

Current Asset Financing Policy The way current assets are financed.

Maturity Matching, or “Self-Liquidating,” Approach A financing policy that matches asset and liability maturities. This is a moderate policy.

2 We are oversimplifying here. Few lenders would explicitly lend money for 1 year to fi nance a 10-year asset. What would actually happen is that the fi rm would borrow on a 1-year basis for “general corporate purposes” and then use the money to purchase the 10-year machinery.

477Chapter 15 Working Capital Management

Alternative Current Asset Financing PoliciesFIGURE 15-2

1 2 3 4 5 6 7 8

Temporary Current Assets

Total Permanent

Assets

Dollars Temporary

Current Assets

Long-Term Debt plus Equity plus Spontaneous Current Liabilities

Short-Term, Nonspontaneous Debt Financing

a. Moderate Approach (Maturity Matching)

Time Period

1 2 3 4 5 6 7 8

Dollars Temporary

Current Assets

Long-Term Debt plus Equity plus Spontaneous Current Liabilities

Short-Term, Nonspontaneous Debt Financing

b. Relatively Aggressive Approach

Time Period

1 2 3 4 5 6 7 8

Dollars Marketable Securities

Long-Term Debt plus Equity plus Spontaneous Current Liabilities

Short-Term Financing Requirements

c. Conservative Approach

Time Period

Fixed Assets

Permanent Level of Current Assets

Fixed Assets

Permanent Level of Current Assets

Fixed Assets

Permanent Level of Current Assets

478 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

loan, the required loan payments would have been better matched with the cash fl ows and the loan renewal problem would not have arisen.

15-3c Conservative Approach Panel c of the fi gure shows the dashed line above the line designating permanent current assets, indicating that long-term capital is used to fi nance all the perma- nent assets and to meet some of the seasonal needs. In this situation, the fi rm uses a small amount of short-term credit to meet its peak requirements, but it also meets part of its seasonal needs by “storing liquidity” in the form of marketable securi- ties. The humps above the dashed line represent short-term fi nancings, while the troughs below the dashed line represent short-term security holdings. This is a very safe, conservative fi nancing policy.

15-3d Choosing between the Approaches Because the yield curve is normally upward-sloping, the cost of short-term debt is generally lower than that of long-term debt. However, short-term debt is riskier to the borrowing fi rm for two reasons: (1) If a fi rm borrows on a long-term basis, its inter- est costs will be relatively stable over time. But if it uses short-term credit, its interest expense can fl uctuate widely, perhaps reaching such high levels that prof- its are extinguished. (2) If a fi rm borrows heavily on a short-term basis, a tempo- rary recession may adversely affect its fi nancial ratios and render it unable to repay this debt. Recognizing this point, if the borrower’s fi nancial position is weak, the lender may not renew the loan, which could force the borrower into bankruptcy.

Note too that short-term loans can generally be negotiated much faster than long- term loans. Lenders need to make a more thorough fi nancial examination before extending long-term credit, and the loan agreement must be spelled out in detail because a great deal can happen during the life of a 10- to 20-year loan.

Finally, short-term debt may offer greater fl exibility. If the fi rm thinks that interest rates are abnormally high, it may prefer short-term credit to gain fl exibility in changing the debt contract. Also, if its needs for funds are seasonal or cyclical, it may not want to commit itself to long-term debt because while provisions for repaying long-term debt can be built into the contract, prepayment penalties are generally built into long-term debt contracts to permit the lender to recover its setup costs. Finally, long-term loan agreements generally contain provisions, or covenants, that constrain the fi rm’s future actions in order to protect the lender, whereas short-term credit agreements generally have fewer restrictions.

All things considered, it is not possible to state that long-term or short-term fi nancing is better than the other. The fi rm’s specifi c conditions will affect the choice, as will the preferences of managers. Optimistic and/or aggressive managers will probably lean more toward short-term credit to gain an interest cost advantage, while more conservative managers will lean toward long-term fi nancing to avoid potential renewal problems. The factors discussed here should be considered, but the fi nal decision will refl ect managers’ personal preferences and judgments.

SEL F TEST Diff erentiate between permanent current assets and temporary current

assets.

What does maturity matching mean, and what is the advantage of this fi nancing policy?

What are advantages and disadvantages of short-term versus long-term debt as identifi ed in this chapter?

479Chapter 15 Working Capital Management

15-4 THE CASH CONVERSION CYCLE All fi rms follow a “working capital cycle” in which they purchase or produce inven- tory, hold it for a time, and then sell it and receive cash. This process is similar to the Yankee peddler’s trips, and it is known as the cash conversion cycle (CCC).

15-4a Calculating the Targeted CCC Assume that Great Fashions Inc. (GFI) is a start-up business that buys ladies’ golf outfi ts from a manufacturer in China and sells them through pro shops at high-end golf clubs in the United States, Canada, and Mexico. The company’s business plan calls for it to purchase $100,000 of merchandise at the start of each month and have the merchandise sold within 60 days. The company will have 40 days to pay its sup- pliers, and it will give its customers 60 days to pay for their purchases. GFI expects to just break even during its fi rst few years; so its monthly sales will be $100,000, the same as its purchases. Any funds required to support operations will be obtained from the bank, and those loans must be repaid as soon as cash is available.

This information can be used to calculate GFI’s cash conversion cycle, which nets out the three time periods described below:3

1. Inventory conversion period. For GFI, this is the 60 days it takes to sell the merchandise.4

2. Average collection period (ACP). This is the length of time customers are given to pay for goods following a sale. The ACP is also called the days’ sales outstanding (DSO). GFI’s business plan calls for an ACP of 60 days, which is consistent with its 60-day credit terms.

3. Payables deferral period. This is the length of time GFI’s suppliers give GFI to pay for its purchases (40 days in our example).

On Day 1, GFI buys merchandise and expects to sell the goods and thus convert them to accounts receivable in 60 days. It should take another 60 days to collect the receivables, making a total of 120 days between receiving merchandise and collect- ing cash. However, GFI is able to defer its own payments for 40 days.

We combine these three periods to fi nd the planned cash conversion cycle, shown here as an equation and in Figure 15-3 as a picture.

Inventory Average Payables Cash conversion # collection " deferral ! conversion 15-1 period period period cycle

60 # 60 " 40 ! 80 days

Although GFI must pay $100,000 to its suppliers after 40 days, it will not receive any cash until 60 ! 60 " 120 days into the cycle. Therefore, it will have to borrow the $100,000 cost of the merchandise from its bank on Day 40, and it will not be able to repay the loan until it collects on Day 120. Thus, for 120 # 40 " 80 days—which is the cash conversion cycle (CCC)—it will owe the bank $100,000 and will be paying interest on this debt. The shorter the cash conversion cycle the better because that will lower interest charges.

Note that if GFI could sell goods faster, collect receivables faster, or defer its payables longer without hurting sales or increasing operating costs, its CCC would

Cash Conversion Cycle (CCC) The length of time funds are tied up in working capital or the length of time between paying for working capital and collecting cash from the sale of the working capital.

Inventory Conversion Period The average time required to convert raw materials into finished goods and then to sell them.

Average Collection Period (ACP) The average length of time required to convert the firm’s receivables into cash, that is, to collect cash following a sale.

Payables Deferral Period The average length of time between the purchase of materials and labor and the payment of cash for them.

3 See Verlyn D. Richards and Eugene J. Laughlin, “A Cash Conversion Cycle Approach to Liquidity Analysis,” Financial Management, Spring 1980, pp. 32–38. 4 If GFI were a manufacturer, the inventory conversion period would be the time required to convert raw materials into fi nished goods and then to sell those goods.

480 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

decline, its interest charges would be reduced, and its profi ts and stock price would be improved.

15-4b Calculating the CCC from Financial Statements The preceding section illustrates the CCC in theory; but in practice, we would cal- culate the CCC based on the fi rm’s fi nancial statements. Moreover, the actual CCC would almost certainly differ from the theoretically forecasted value because of real-world complexities such as shipping delays, sales slowdowns, and customer delays in making payments. Moreover, a fi rm such as GFI would start a new cycle before the earlier one ended, and this too would muddy the waters.

To see how the CCC is calculated in practice, assume that GFI has been in busi- ness for several years and is now in a stable position—placing orders, making sales, obtaining collections, and making payments on a recurring basis. The fol- lowing data were taken from its latest fi nancial statements:

Annual sales $1,216,666 Cost of goods sold 1,013,889 Inventory 250,000 Accounts receivable 300,000 Accounts payable 150,000

We begin with the inventory conversion period:

15-2 Inventory conversion period ! Inventory

_______________________ Cost of goods sold per day

! $250,000 ______________ $1,013,889/365 ! 90 days

Thus, it takes GFI an average of 90 days to sell its merchandise, not the 60 days called for in the business plan. Note also that inventory is carried at cost; so the denominator of the equation should be the cost of goods sold, not sales.

The average collection period (or days sales outstanding) is calculated next:

15-3 Average collection period ! Receivables ___________ Sales/365

! $300,000 ______________ $1,216,666/365 ! 90 days

So it takes GFI 90 days after a sale to receive cash, not the 60 days called for in the business plan. Because receivables are recorded at the sales price, we use sales rather than cost of goods sold in the denominator.

The Cash Conversion CycleFIGURE 15-3

Finish Goods and Sell Them

Receive Materials

Pay Cash for Purchased Materials

Collect Cash for Accounts

Receivable

Days

Inventory Conversion

Period (60 Days)

Average Collection

Period (60 Days)

Payables Deferral

Period (40 Days)

Cash Conversion

Period (80 days)

481Chapter 15 Working Capital Management

The payables deferral period is found as follows, again using cost of goods sold in the denominator because payables are recorded at cost:

Payables deferral period ! Payables

________________ Purchases per day ! Payables

____________________ Cost of goods sold/365 15-4

! $150,000 ______________ $1,013,889/365 ! 54 days

GFI is supposed to pay its suppliers after 40 days; but it is a slow payer, delaying payment on average until Day 54.

We can combine the three periods to calculate GFI’s actual cash conversion cycle:

Cash conversion cycle (CCC) ! 90 days # 90 days " 54 days ! 126 days

GFI’s actual 126-day CCC is quite different from the planned 80 days. It takes lon- ger than planned to sell merchandise, customers don’t pay as fast as they should, and GFI pays its suppliers slower than it should. The end result is a CCC of 126 days versus the planned 80 days.

When the planned 80-day CCC is “reasonable,” the actual 126 days is too high. The CFO should push salespeople to speed up sales and the credit manager to accelerate collections. Also, the purchasing department should try to get longer payment terms. If GFI could take those steps without hurting sales and operating costs, the fi rm would help its profi ts and stock price.

Two professors, Hyun-Han Shin and Luc Soenen, studied more than 2,900 companies over a 20-year period. They found that shortening the cash conversion cycle resulted in higher profi ts and better stock price performances.5 Their study demonstrates that good working capital management is important.

5 See Hyun-Han Shin and Luc Soenen, “Effi ciency of Working Capital Management and Corporate Profi tability,” Financial Practice and Education, Fall/Winter 1998, pp. 37–45.

Some fi rms are able to operate with zero or even negative net working capital. Dell and Amazon.com are examples. When customers order computers from Dell’s web site or books from Amazon, they must provide a credit card num- ber. Dell and Amazon then receive next-day cash, even before the product is shipped and they have paid their own suppliers. This results in a negative CCC, which means that working capital provides, does not use, cash.

To grow, companies normally need cash for working capital. However, when the CCC is negative, growth in sales provides cash rather than uses it. This cash can be invested in plant and equipment as well as research and development or used for any other corporate purpose. Analysts recognize this point when they value Dell and Amazon, and it helps the companies’ stock prices.

SOME FIRMS OPERATE WITH NEGATIVE WORKING CAPITAL! SEL

F TEST Defi ne the following terms: inventory conversion period, average collection period, and payables deferral period. Explain how these terms are used to form the cash conversion cycle.

How would a reduction in the cash conversion cycle increase profi tability?

What are some actions a fi rm can take to shorten its cash conversion cycle?

482 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

15-5 THE CASH BUDGET Firms need to forecast their cash fl ows. If they are likely to need additional cash, they should line up funds well in advance. On the other hand, if they are likely to generate surplus cash, they should plan for its productive use. The primary fore- casting tool is the cash budget, illustrated in Table 15-1, which is a printout from the chapter’s Excel model.

Cash Budget A table that shows cash receipts, disbursements, and balances over some period.

4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20

21 22 23 24

27 28 29 30 31 32 33 34

35 36 37

38 39 40 41

A B C D E F G H I J K L M N

20% 70% 10%

0% 2%

70% $ 15 $100 $ 10

May June July August Sept Oct Nov Dec

Input Data Collections during month of sale Collections during 1st month after sale Collections during 2nd month after sale Percent bad debts Discount on first month collections Purchases as a % of next month's sales Lease payments Construction cost for new plant (Oct) Target cash balance Sales adjustment factor (change from base)

THE CASH BUDGET

Collections During month of sale: 0.2(Sales)(0.98) During 1st month after sale: 0.7(prior month's sales) During 2nd month after sale: 0.1(sales 2 months ago)

Total collections

Purchases: 70% of next months sales

Payments Payment for materials: Last month's purchases Wages and salaries Lease payments Other expenses Taxes Payment for plant construction Total payments

Net cash flows: Net cash flow (NCF) for month: Row 25 minus Row 34 Cumulative NCF: Prior month's cum. NCF plus this month's NCF

Cash surplus (or loan requirement) Target cash balance Surplus cash (or loan needed): Row 37 minus Row 39 Maximum required loan (shown as a negative) Maximum available for investment

Sales (gross)

Assumed constant. Don't change. Assumed constant. Don't change. Equal to 100% - (20% + 70%) - Bad debt % Can change to see effects Can change to see effects Can change to see effects Can change to see effects Can change to see effects Can change to see effects % increase or decrease from base to see effects

$200 $250 $300 $400 $500 $350 $250 $200 $59 $78 $98 $69 $49 $39 175 210 280 350 245 175 20 25 30 40 50 35

$254 $313 $408 $459 $344 $249

$210 $280 $350 $245 $175 $140

$210 $280 $350 $245 $175 $140 30 40 50 40 30 30 15 15 15 15 15 15 10 15 20 15 10 10 30 20 100 $265 $350 $465 $415 $230 $215

($11) ($37) ($57) $44 $114 $34 ($11) ($48) ($105) ($61) $53 $87

$10 $10 $10 $10 $10 $10 ($21) ($58) ($115) ($71) $43 $77 ($115) $77

Allied Food Products 2009 Cash Budget (Dollars in Millions)T a b l e 1 5 - 1

Notes: a. Although the budget period is July through December, sales and purchases data for May and June are needed to determine collections and

payments during July and August. b. Firms can both borrow and pay off commercial loans on a daily basis. So the $21 million loan shown for July would likely be borrowed

gradually on a daily basis as needed; and during October, the $115 million loan that existed at the beginning of the month would be reduced daily to the $71 million ending balance, which, in turn, would be completely paid off sometime during November.

483Chapter 15 Working Capital Management

Cash budgets can be of any length, but fi rms typically develop a monthly cash budget like Table 15-1 for the coming year and a daily cash budget at the start of each month. The monthly budget is good for annual planning, while the daily budget gives a more precise picture of the actual cash fl ows and is good for sched- uling actual payments on a day-by-day basis.

The monthly cash budget begins with a forecast of sales for each month and a projection of when actual collections will occur. Then there is a forecast of materi- als purchases, followed by forecasted payments for materials, labor, leases, new equipment, taxes, and other expenses. When the forecasted payments are sub- tracted from the forecasted collections, the result is the expected net cash gain or loss for each month. This gain or loss is added to or subtracted from the beginning cash balance, and the result is the amount of cash the fi rm would have on hand at the end of the month if it neither borrowed nor invested.

We use Allied Foods to illustrate cash budgets. To shorten the example, we deal only with the last half of 2009. Allied sells mainly to grocery chains, and its projected 2009 sales are $3,300 million. As Table 15-1 shows, sales increase during the summer, peak in September, and then decline during the fall. All sales are on terms of 2/10, net 30, meaning that a 2% discount is allowed if payment is made within 10 days. But if the discount is not taken, the full amount is due in 30 days. However, like most companies, Allied fi nds that some customers pay late. Experi- ence shows that 20% of customers pay during the month of the sale—these are the discount customers. Another 70% pay during the month immediately following the sale; and 10% are late, paying in the second month after the sale.6

The costs to Allied for foodstuffs, spices, preservatives, and packaging materi- als average 70% of sales revenues. Purchases are generally made 1 month before the fi rm expects to sell the fi nished products, but Allied’s suppliers allow it to delay payments for 30 days. July sales are forecasted at $300 million; so purchases during June should amount to $210 million, and this amount must be paid in July.

Wages and lease payments are also built into the cash budget, as are Allied’s estimated tax payments—$30 million due September 15 and $20 million due December 15. Also, a $100 million payment for a new plant must be made in Octo- ber, and miscellaneous other required payments are shown in the budget. Allied’s target cash balance is $10 million, and it plans to borrow to meet this target or to invest surplus funds if it generates more cash than is needed.

We use this information at the top of Table 15-1 to forecast monthly cash sur- pluses or shortfalls from July through December, along with the amount Allied will need to borrow or will have available to invest so as to keep the end-of-month cash balance at the target level.

Inputs used in the forecast—which are assumptions that may not be correct— are given on Rows 6 through 15. These values are used in the calculations shown here. Row 20 gives the sales forecast for the period May through December. May and June sales are needed to determine collections for July and August. Rows 22 through 25 relate to collections. Row 22 shows that 20% of the sales during any given month are collected during that month. However, customers who pay the fi rst month take the discount; so collections for that month are reduced by 2%. For example, collections for July are calculated as 20% of the $300 million sales for that month minus the 2% discount, or 0.2($300) # 0.2($300)(0.02) " $58.8 million, rounded to $59 million. Row 23 shows the collections for the previous month’s sales. For example, in July, 70% of the $250 million June sales, or $175 million,

Target Cash Balance The desired cash balance that a firm plans to maintain in order to conduct business.

6 A negligible percentage of sales results in bad debts. The low bad debt losses result from Allied’s careful screen- ing of customers and its generally tight credit policies. However, the cash budget model can show the eff ects of bad debts, so Allied’s CFO could show top management how cash fl ows would be aff ected if the fi rm relaxed its credit policy to stimulate sales.

484 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

should be collected. Row 24 shows collections from sales 2 months earlier. Thus, in July, collections for May sales should be (0.10)($200) " $20 million. The collections during each month are summed and shown on Row 25. Thus, the July collections include 20% of July sales (minus the discount) and 70% of June sales plus 10% of May sales, or $254 million in total.

Raw material costs, which are 70% of next month’s sales, are shown on Row 26. July sales are forecasted at $300 million, so June purchases are 0.7($300) " $210 million. The $210 million must be paid in July, so that amount is shown on Row 28. Continu- ing, forecasted sales for August are $400 million; so Allied must purchase 0.7($400) " $280 million of materials in July, and that amount must be paid in August.

Other required payments—labor costs, lease payments, taxes, construction costs, and miscellaneous expenses—are shown on Rows 29 through 33; and the total of all payments is shown on Row 34.

Next, on Row 36, we show the net cash fl ow (NCF) for each month, calculated as collections on Row 25 minus total payments on Row 34. The NCF for July is #$11 million; and cash fl ows remain negative due to the fall harvest and process- ing until October, when positive cash fl ows begin.

The monthly cash fl ows are then used to calculate the cumulative net cash fl ows as shown on Row 37. Here we add the NCF for each month to the cumula- tive NCF from the prior month. Since there was no prior cumulative NCF at the beginning of July, the cumulative NCF for July is simply the NCF for that month, #$11 million. For August, we add the NCF for that month, #$37 million, to the prior cumulative NCF, the #$11 million at the end of July, to get the #$48 million cumulative NCF at the end of August. There is another negative cash fl ow during September, so the cumulative NCF rises to a peak of #$105 million. However, in October, the NCF is positive; so the cumulative fi gure declines to #61 million, and it changes from negative to positive amounts in November and December.

Allied’s target cash balance is $10 million—it wants to maintain that balance at all times. It plans to borrow $10 million at the start of the analysis, and we show that amount on Row 39. Because there is a projected cash loss of $11 million during July and because Allied borrowed $10 million at the start of the month, at the end of July its loan outstanding will total $21 million as shown on Row 40.7 It will incur additional cash shortfalls in August and September; and the required loan will continue to increase, peaking at $115 million at the end of September. However, positive cash fl ows begin in October; and they will be used to reduce the loan, which will be completely paid off by the end of November, at which time the com- pany will have funds to invest. Indeed, by the end of December, Allied should have no loans outstanding and $77 million available for investment.

Row 41 shows the maximum required loan, $115 million; and Row 42 shows the maximum projected surplus, $77 million. Allied’s treasurer will need to arrange a line of credit so that the fi rm can borrow up to $115 million, increasing the loan over time as funds are needed and repaying it later when cash fl ows become posi- tive. The treasurer would show the cash budget to the bankers when negotiating for the line of credit. Lenders would want to know how much Allied expects to need, when the funds will be needed, and when the loan will be repaid. The lenders—and Allied’s top executives—would question the treasurer about the bud- get. They would want to know how the forecasts would be affected if sales were higher or lower than those projected, how changes would affect the forecasts when customers pay, and the like. The questioning would focus on these two questions: How accurate is the forecast likely to be? What would be the effects of signifi cant errors?

7 If Allied had begun with a positive cash balance, that amount would have been deducted from the initial loan needed. Note too that our cash budget is simplifi ed because it does not show interest expense for the loan or interest income on investments. Those items could be added easily to the cash budget.

485Chapter 15 Working Capital Management

Note that if cash infl ows and outfl ows do not occur uniformly during each month, the actual funds needed might be quite different from the indicated amounts. The data in Table 15-1 show the situation on the last day of each month, and we see that the maximum projected loan is $115 million. However, if all pay- ments had to be made on the 1st of the month but most collections came on the 30th, Allied would have to make $265 million of payments in July before it received the $254 million from collections. In that case, the fi rm would need to borrow about $275 million, not the $21 million shown in Table 15-1. A daily cash budget would reveal that situation.

Table 15-1 was prepared using Excel, which makes it easy to change the as- sumptions. Therefore, we could examine the cash fl ow effects of changes in sales, the target cash balance, customers’ payments, and so forth. Also, the effects of changes in credit policy and inventory management could be examined through the cash budget.

SEL F TEST How could the cash budget be used when the terms of a bank loan are

negotiated?

Suppose a fi rm’s cash fl ows do not occur uniformly throughout the month. What eff ect would this have on the accuracy of the forecasted borrowing requirements based on a monthly cash budget? How could the fi rm deal with this problem?

15-6 CASH AND MARKETABLE SECURITIES When most of us use the term cash, we mean currency (paper money and coins) in addition to bank demand deposits. However, when corporate treasurers use the term, they often mean currency and demand deposits in addition to very safe, highly liquid marketable securities that can be sold quickly at a predictable price and thus be con- verted to bank deposits.8 Therefore, “cash” as reported on balance sheets generally includes short-term securities, which are also called “cash equivalents.”

Note that a fi rm’s marketable security holdings can be divided into two cate- gories: (1) Operating short-term securities, which are held primarily to provide liquidity and are bought and sold as needed to provide funds for operations, and (2) other short-term securities, which are holdings in excess of the amount needed to support normal operations. Highly profi table fi rms such as Microsoft often hold far more securities than are needed for liquidity purposes. Those securities will eventually be liquidated; and the cash will be used for such things as paying a large one-time dividend, repurchasing stock, retiring debt, acquiring other fi rms, or fi nancing major expansions. This breakdown is not reported on the balance sheet, but fi nancial managers know how much of their securities will be needed for operating versus other purposes. In our discussion of net working capital, the focus is on securities held to provide operating liquidity.

8 The reason corporate treasurers think of cash as they do is that from their perspective, there is little diff erence between demand deposits and liquid marketable securities. They can call a dealer, sell securities, and have the proceeds deposited in the fi rm’s bank account in an hour or so. Also, many types of short-term securities are available. Treasury bills are an obvious example; but as we discussed in Chapter 2, there are many other safe, liquid, short-term, marketable securities.

486 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

15-6a Currency Fast-food operators, casinos, hotels, movie theaters, and a few other businesses hold substantial amounts of currency; but the importance of currency has decreased over time due to the rise of credit cards, debit cards, and other payment mecha- nisms. Companies such as McDonald’s need to hold enough currency to support operations; but if they held more, this would raise capital costs and tempt robbers. Each fi rm decides its own optimal level; but even for retailers, currency generally represents a small part of total cash holdings.9

15-6b Demand Deposits Demand (or checking) deposits are far more important than currency for most businesses. These deposits are used for transactions—paying for labor and raw materials, purchasing fi xed assets, paying taxes, servicing debt, paying divi- dends, and so on. However, commercial demand deposits typically earn no interest; so fi rms try to minimize their holdings while still ensuring that they are able to pay suppliers promptly, take trade discounts, and take advantage of bar- gain purchases. The following techniques are used to optimize demand deposit holdings: 1. Hold marketable securities rather than demand deposits to provide liquidity. When

the fi rm holds marketable securities, the need for demand deposits is reduced. For example, if a large bill requiring immediate payment comes in unexpect- edly, the treasurer can simply call a securities dealer, sell some securities, and have funds deposited in the fi rm’s checking account that same day. Securities pay interest whereas demand deposits do not, so holding securities in lieu of demand deposits increases profi ts.

2. Borrow on short notice. Firms can establish lines of credit under which they can borrow with just a telephone call if and when they need extra cash. Note, though, that they may have to pay fees for those commitments and the cost of those fees must be considered when deciding to use borrowing capacity rather than securities to provide liquidity.

3. Forecast payments and receipts better. The better the fi rm can forecast its cash infl ows and outfl ows, the smaller its needs for funds to meet unexpected requirements. Therefore, improving infl ow/outfl ow forecasts lessens the need to hold liquid assets and thus reduces the required amount of working capital. The cash budget is the key tool used to improve cash forecasts.

4. Speed up payments. Firms can take actions to get their cash receipts faster. For example, they can use lockboxes, which are post offi ce boxes operated by banks. Suppose a New York fi rm sells to customers all across the country. If it sends out bills and has customers make payments to its New York headquar- ters, time will be lost in waiting on the mail, in opening envelopes, in deposit- ing checks in the bank, and in waiting for the bank to clear the checks to make sure they are good. To speed up this process, the fi rm can direct customers to send payments to a post offi ce box in the customer’s local area, then have a bank empty the box several times each day and start the collection process. If a fi rm’s receipts average $1 million per day and if the use of lockboxes can reduce the delay in obtaining usable cash from 5 days to 1 day, the fi rm will reduce funds in transit from $5 million to $1 million and thus receive an

Lockbox A post office box operated by a bank to which payments are sent. Used to speed up effective receipt of cash.

9 In “olden days,” currency was also held as a store of value, for use during emergencies, for use in making bargain purchases, and the like. That is true today only in undeveloped parts of the world.

487Chapter 15 Working Capital Management

effective cash infusion of $4 million. This is a one-time benefi t, but the fi rm will be earning a continuing return on the $4 million.10

5. Use credit cards, debit cards, wire transfers, and direct deposits. If a fi rm switches from selling on credit to accepting credit or debit cards, it will receive next-day cash and thus the same cash fl ow benefi ts as described earlier. Similarly, requir- ing customers to pay via wire deposits speeds up collections, increases free cash fl ows, and reduces required cash holdings.

6. Synchronize cash fl ows. If a fi rm can synchronize its cash infl ows and outfl ows, the fi rm will reduce its need for cash balances. For example, utilities, oil com- panies, and department stores generally use “billing cycles” under which dif- ferent customers are billed on different days, causing cash to fl ow in evenly during the month. These fi rms can then set up their own payment schedules to match their infl ows. This reduces average cash balances, just as your per- sonal average monthly balance can be reduced when your income comes in at the same time as your required payments.

Banks have experts who help fi rms optimize their cash management proce- dures. The banks charge a fee for this service, but the benefi ts of a good cash man- agement system are well worth the cost.

15-6c Marketable Securities Marketable securities held for operations are managed in conjunction with demand deposits—the management of one requires coordination with the other. Firms also purchase marketable securities as cash builds up from operations and then sell those securities when they need cash. Microsoft is a good example. It had accumu- lated more than $60 billion of cash (mostly marketable securities) by the end of 2004. It needed to hold some of those securities for liquidity purposes, but mainly the funds built up because Microsoft generated more cash from operations than it needed. Investors urged management to use this “cash” in a more productive manner or to pay it out as dividends so stockholders could invest it. Partly because of this pressure, in the fall of 2004, Microsoft announced a one-time dividend of $30 billion; it also stepped up its stock repurchase program. By the end of 2007, Microsoft’s holdings of cash and equivalents had been reduced to a more “reason- able” $6.6 billion.

Given the size and importance of marketable securities holdings, how they are managed can have a signifi cant effect on profi ts. A trade-off between risk and return is involved—the fi rm wants to earn high returns; but since most marketable securities are held to provide liquidity, treasurers want to hold securities that can be sold very quickly at a known price. That means high-quality, short-term instru- ments. Long-term Treasury bonds are safe, but they are not well suited for the marketable securities portfolio because their prices decline when interest rates rise. Similarly, short-term securities issued by risky companies are not suitable because their prices decline when the issuers’ problems grow worse. Treasury bills, most commercial paper (discussed in Section 15-11), bank certifi cates of deposit, and money market funds are suitable holdings.

It’s worth noting that so-called safe securities don’t always turn out to be safe. In 2007, billions of dollars of Aaa-rated commercial paper was actually backed by

10 We should mention the term fl oat, as it often comes up in connection with cash management. If you write a check and it takes 5 days for the recipient to receive and deposit the check and for it to be deducted from your account, you have 5 days of fl oat, or the use of the money for 5 days before you have to deposit funds in your account. That’s payment fl oat. On the other hand, if someone sends you a check and it takes 6 days for you to receive and deposit it and for the bank to clear the funds, that’s 6 days of collection fl oat. Your “net fl oat” would be –1 day. Positive net fl oat is good, but negative net fl oat is bad from the standpoint of minimizing required cash holdings.

488 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

subprime mortgages; and when those mortgages started defaulting, this commer- cial paper caused their holders a great deal of trouble. One issue of commercial paper was downgraded from Aaa to Ba in just one day, and those people holding what they thought was safe and highly liquid paper found it to be totally illiquid and of doubtful value. As you might guess, before it defaulted, the mortgage- backed commercial paper paid a somewhat higher return, about 3.505% versus about 3.467% for paper backed by T-bills. Those seeking higher returns generally have to accept more risk.

A fi rm’s relationship with its bank—especially its ability to borrow on short notice—can have a signifi cant effect on its need for both demand deposits and marketable securities. If a company has a fi rmly committed line of credit under which it can obtain funds with a simple telephone call, it won’t need much in the way of liquid reserves.

Finally, larger corporations shop for securities all around the world, buying wherever risk-adjusted rates are highest. This shopping tends to equalize world- wide rates—if interest rates in Europe are higher than rates in the United States for equally risky securities, companies will buy European securities, driving their prices up and their yields down, until an equilibrium has been established. We truly live in a global economy.11

11 Companies can also buy securities that are denominated in diff erent currencies. Thus, if a fi rm’s treasurer thinks that the euro is likely to appreciate against the dollar, he or she might purchase securities denominated in euros; and if things work out as expected, the fi rm will earn interest and enjoy an additional gain from the change in exchange rates. Again, these actions help to keep world fi nancial markets in equilibrium.

SEL F TEST What two defi nitions of cash are commonly encountered?

Diff erentiate between marketable securities held for operating (transactions) purposes and securities held for other reasons.

How has the development of credit and debit cards aff ected fi rms’ currency holdings?

How would the use of credit cards aff ect a fi rm’s cash conversion cycle as- suming it previously allowed customers 30 days to pay for their purchases?

How does a fi rm’s ability to borrow aff ect its optimal holdings of cash and securities?

Common stocks that are traded on the NYSE are liquid in the sense that they can be sold and converted to cash on short notice. Are stocks a good choice for a fi rm’s marketable securities portfolio? Explain.

15-7 INVENTORIES Inventories, which can include (1) supplies, (2) raw materials, (3) work in process, and (4) fi nished goods, are an essential part of virtually all business operations. Optimal inventory levels depend on sales, so sales must be forecasted before target inventories can be established. Moreover, because errors in setting inventory levels lead to lost sales or excessive carrying costs, inventory management is quite important. There- fore, fi rms use sophisticated computer systems to monitor their inventory holdings.

Retailers such as Best Buy, Wal-Mart, and Home Depot use computers to keep track of each inventory item by size, shape, and color; and bar code information collected at checkout updates inventory records. When inventories shown in the

489Chapter 15 Working Capital Management

computer decline to a set level, the computer sends an order to the supplier’s com- puter, specifying exactly what is needed. The computer also reports how fast items are moving. If an item is moving too slowly, the computer will suggest a price cut to lower the inventory stock before the item becomes obsolete. Manufacturers such as GE use similar systems to keep track of items and to place orders as they are needed.

Although inventory management is important, it is under the operational control of production managers and marketing people rather than fi nancial managers. Still, fi nancial managers are involved in several ways. First, it is expensive to install and maintain the computer systems used to track inventories; and the capital budgeting analysis discussed earlier in the text must be used to determine which system is best. Second, if the fi rm decides to increase its inventory holdings, the fi nancial manager must raise the capital needed to acquire the additional inventory. And third, the fi nancial manager is responsible for identifying any area of weakness that affects the fi rm’s overall profi tability, using ratios and other procedures for comparing the fi rm to its benchmark companies. Therefore, the CFO will compare the fi rm’s inventory- to-sales ratio with those of its benchmarks to see if things look “reasonable.”

Since inventory management is outside the mainstream of fi nance, we cover it in Web Appendix 15A rather than in the text chapter. However, “Supply Chain Management,” provided at the top of this page, discusses how inventories are managed by modern corporations.

Herman Miller, Inc., manufactures a wide variety of offi ce furni- ture; and a typical order from a single customer might require work at fi ve diff erent plants. Each plant uses components from diff erent suppliers, and each plant works on orders for many customers. Imagine all the coordination that’s required. The sales force generates the order, the purchasing department orders components from suppliers, and the suppliers must order materials from their own suppliers. Then the suppliers ship the components to the appropriate Herman Miller plant, the plants build the products, the diff erent products are gath- ered together to complete the order, and the order is shipped to the customer. If one part of that process malfunctions, the entire order will be delayed, inventory will pile up, and extra costs to expedite the order will be incurred. Moreover, the company’s reputation will be damaged, hurting future sales. To prevent such consequences, Herman Miller employs a process called supply chain management (SCM). The key

element in SCM is sharing information all the way from the point of sale at the retailer to suppliers and even back to sup- pliers’ suppliers. SCM requires sophisticated software; but even more important, SCM requires cooperation among the diff erent companies and departments in the supply chain. A new culture of open communication is required, and this is often diffi cult for many companies because they are reluc- tant to divulge operating information. Many of Herman Miller’s suppliers were initially wary of these new relation- ships. However, SCM has been a win-win situation, with increases in value for Herman Miller and its suppliers. SCM enabled Herman Miller to sharply reduce its inven- tory, to cut 2 weeks off delivery times to customers, and to operate its plants at a 20% higher volume without further capital expenditures. The results were much higher earnings, cash fl ows, and stock price.

Sources: Elaine L. Appleton, “Supply Chain Brain,” CFO, July 1997, pp. 51–54; Kris Frieswick, “Up Close and Virtual,” CFO, April 1998, pp. 87–91.

SUPPLY CHAIN MANAGEMENT SEL

F TEST What are the three primary tasks of the fi nancial manager regarding inventory management?

490 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

15-8 ACCOUNTS RECEIVABLE Although some sales are made for cash, today the vast majority of sales are on credit. Thus, in the typical situation, goods are shipped, inventories are reduced, and an account receivable is created.12 Eventually, the customer pays, the fi rm receives cash, and its receivables decline. The fi rm’s credit policy is the primary determinant of accounts receivable, and it is under the administrative control of the CFO. Moreover, credit policy is a key determinant of sales, so sales and mar- keting executives are concerned with this policy. Therefore, we begin our discus- sion of accounts receivable by discussing credit policy.

15-8a Credit Policy Credit policy consists of these four variables: 1. Credit period is the length of time buyers are given to pay for their purchases.

For example, the credit period might be 30 days. Customers prefer longer credit periods, so lengthening the period will stimulate sales. However, a lon- ger credit period lengthens the cash conversion cycle; hence, it ties up more capital in receivables, which is costly. Also, the longer a receivable is outstand- ing, the higher the probability that the customer will default and that the account will end up as a bad debt.

2. Discounts are price reductions given for early payment. The discount speci- fi es what the percentage reduction is and how rapidly payment must be made to be eligible for the discount. For example, a 2% discount is often given if the customer pays within 10 days. Offering discounts has two benefi ts. First, the discount amounts to a price reduction, which stimulates sales. Second, dis- counts encourage customers to pay earlier than they otherwise would, which shortens the cash conversion cycle. However, discounts mean lower prices— and lower revenues unless the quantity sold increases by enough to offset the price reduction. The benefi ts and costs of discounts must be balanced when credit policy is being established.

3. Credit standards refer to the required fi nancial strength of acceptable credit cus- tomers. With regard to credit standards, factors considered for business custom- ers include ratios such as the customer’s debt and interest coverage ratios, the customer’s credit history (has the customer paid on time in the past or tended to be delinquent), and the like. For individual customers, their credit score as developed by credit rating agencies is the key item. In both cases, the key ques- tion is this: Is the customer likely to be willing and able to make the required payment on schedule? Note that when standards are set too low, bad debt losses will be too high; on the other hand, when standards are set too high, the fi rm will lose too many sales and thus profi ts. So a balance must be struck between the costs and benefi ts of tighter credit standards.

4. Collection policy refers to the procedures used to collect past due accounts, including the toughness or laxity used in the process. At one extreme, the fi rm might write a series of polite letters after a fairly long delay; at the other extreme, delinquent accounts may be turned over to a collection agency rela- tively quickly. Firms should be somewhat fi rm, but excessive pressure can

Account Receivable Funds due from a customer.

Credit Policy A set of rules that includes the firm’s credit period, discounts, credit standards, and collection procedures offered.

Credit Period The length of time customers have to pay for purchases.

Discounts Price reductions given for early payment.

Credit Standards The financial strength customers must exhibit to qualify for credit.

Collection Policy Degree of toughness in enforcing the credit terms.

12 Whenever goods are sold on credit, two accounts are created—an asset item entitled account receivable appears on the books of the selling fi rm, and a liability item called an account payable appears on the books of the purchaser. At this point, we are analyzing the transaction from the viewpoint of the seller; so we are focusing on the variables under the seller’s control—in this case, receivables. In Section 15-9, we will examine the transaction from the viewpoint of the purchaser when we discuss accounts payable as a source of funds and consider their cost relative to the cost of funds obtained from other sources.

491Chapter 15 Working Capital Management

13 Credit analysts use procedures ranging from highly sophisticated computerized “credit-scoring” systems, which calculate the statistical probability that a given customer will default, to informal procedures, which involve going through a checklist of factors that should be considered when a credit application is processed. The credit- scoring systems use various fi nancial ratios, such as the current ratio and the debt ratio (for businesses), and income, years with the same employer, and the like (for individuals), to determine the statistical probability of default. Credit is then granted to those with low default probabilities. The informal procedures often involve examining the “5 Cs of Credit”: character, capacity, capital, collateral, and conditions. Character is obvious; capacity is a subjective estimate of ability to repay; capital means how much net worth the borrower has; collateral means assets pledged to secure the loan; and conditions refers to business conditions, which aff ect ability to repay.

lead customers whose business is profi table to take their business elsewhere. Again, a balance must be struck between the costs and benefi ts of different collection policies.

Firms generally publish their credit terms, defi ned as a statement of their credit period and discount policy. Thus, Allied Foods might have stated credit terms of 2/10, net 30, which means that it allows a 2% discount if payment is received within 10 days of the purchase; if the discount is not taken then, the full amount is due in 30 days. Credit standards and collection policies are relatively subjective, so they are not generally discussed in the published credit terms.

15-8b Setting and Implementing the Credit Policy Credit policy is important for three main reasons: (1) It has a major effect on sales, (2) it infl uences the amount of funds tied up in receivables, and (3) it affects bad debt losses. Because of the importance of the policy, the fi rm’s executive committee, which normally consists of the president in addition to the vice presidents of fi nance and marketing, has the fi nal say on setting the credit policy. Once the policy has been established, the credit manager, who typically works under the CFO, must carry it out and monitor its effects. Managing a credit department requires fast, accurate, and up-to-date information. Several organizations, including Experian, Equifax, and TransUnion, use computer-based networks to collect, store, and distribute credit information. For businesses, Dun & Bradstreet provides detailed credit reports over the Internet for a fee. The reports include the following information: 1. A summary balance sheet and income statement 2. A number of key ratios with trend information 3. Data obtained from the fi rm’s suppliers telling whether it pays promptly or

slowly and whether it has recently failed to make any payments 4. A verbal description of the physical condition of the fi rm’s operations 5. A verbal description of the backgrounds of the fi rm’s owners, including any

previous bankruptcies, lawsuits, or divorce settlement problems 6. A summary rating ranging from A for the best credit risks to F for fi rms that

are deemed likely to default

For individuals, credit scores, which are numerical scores from 0 to 10 that are based on a statistical analysis, provide a summary assessment of the likelihood that a potential customer will default on a required payment. Computerized ana- lytical systems assist in making better credit decisions; but in the fi nal analysis, most credit decisions are exercises in informed judgment.13

We have emphasized the costs of granting credit. However, if it is possible to sell on credit and to impose a carrying charge on the receivables that are outstanding, credit sales can actually be more profi table than cash sales. This is especially true for consumer durables (e.g., automobiles and appliances), but it is also true for certain types of industrial equipment. Thus, GM’s General Motors Acceptance Corporation (GMAC) unit, which fi nances automobiles, is highly profi table, as are other companies’ credit

Credit Terms Statement of the credit period and any discount offered.

Credit Score A numerical score from 1 to 10 that indicates the likelihood that a person or business will pay on time.

492 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

subsidiaries.14 Some companies actually earn more on credit than cash sales, and their salespeople earn higher commissions when they make a credit sale.

The carrying charges on outstanding consumer credit are generally about 18% on a nominal basis: 1.5% per month, so 1.5% $ 12 " 18%. This is equivalent to an effective annual rate of (1.015)12 # 1.0 " 19.6%. Having receivables outstanding that earn more than 18% is highly profi table unless there are too many bad debt losses.

Legal considerations must also be taken into account when setting credit pol- icy. Under the Robinson-Patman Act, it is illegal for a fi rm to charge prices that discriminate between customers unless the different prices are cost-justifi ed. The same holds true for credit—it is illegal to offer more favorable credit terms to one customer or class of customers than to another unless the differences are cost-justifi ed.

15-8c Monitoring Accounts Receivable The total amount of accounts receivable outstanding at any given time is deter- mined by the volume of credit sales and the average length of time between sales and collections. For example, suppose Boston Lumber Company (BLC), a whole- sale distributor of lumber products, has sales of $1,000 per day (all on credit) and it requires payment after 10 days. BLC has no bad debts or slow-paying customers. Under those conditions, it must have the capital to carry $10,000 of receivables:

15-5 Accounts receivable ! Sales per day $ Length of collection period

! $1,000 $ 10 days ! $10,000

If either sales or the collection period changes, so will accounts receivable. For example, if sales doubled to $2,000/day, receivables would also double; and the fi rm would need an additional $10,000 to fi nance this increase. Similarly, if the col- lection period lengthened to 20 days, this too would double the receivables and require additional capital.

If management is not careful, the collection period will creep up, as good cus- tomers take longer to pay and as sales are made to weaker customers, who tend to pay slowly or not at all and thus create bad debts. So it is important to monitor re- ceivables. One easy-to-use monitoring technique employs the DSO. Here’s Allied Foods’ DSO as calculated back in Chapter 4:

DSO ! Days

sales outstanding

! Receivables ___________________ Average sales per day ! Receivables _______________ Annual sales/365

! $375 __________ $3,000/365 ! $375 _______ $8.2192 ! 45.625 days ≈ 46 days

Industry average ! 36 days

Allied has an average daily sales (ADS) of $8.2192 million, and those sales are out- standing for 45.625 days. If we multiply the DSO by the average daily sales, we determine the capital tied up in receivables:

Receivables ! (ADS)(DSO) ! ($8.2192)(45.625) ! $375 million

14 Companies that do a large volume of sales fi nancing typically set up subsidiary companies called captive fi nance companies to do the actual fi nancing. For example, General Motors, Chrysler, and Ford have captive fi nance com- panies, as do Sears, IBM, and General Electric.

493Chapter 15 Working Capital Management

15 Another technique used to monitor receivables is the Aging Schedule, which shows the dollar amount and percentage of receivables that have been outstanding for diff erent lengths of time. See Brigham and Daves, Intermediate Financial Management, 9th edition (Mason, OH: Thomson-SouthWestern, 2007), Chapter 21, pp. 737–738.

Note, though, that if Allied collected its receivables faster and reduced its DSO to the 36-day industry average, its receivables would decline to $295.89 million, or by $79.11 million. The DSO can also be compared to the fi rm’s own credit terms. Allied sells on terms of net 30, so its DSO should be no greater than 30 days. Obviously, some customers are paying late, so there is room for improvement in its collections policy and practices.15

SEL F TEST What are credit terms?

What are the four credit policy variables?

Defi ne days sales outstanding (DSO). What can be learned from it, and how is it aff ected by seasonal sales fl uctuations?

What is credit quality, and how is it assessed?

How does collection policy infl uence sales, the collection period, and the bad debt loss percentage?

How can cash discounts be used to infl uence sales volume and the DSO?

How do legal considerations aff ect a fi rm’s credit policy?

15-9 ACCOUNTS PAYABLE (TRADE CREDIT) Firms generally make purchases from other fi rms on credit and record the debt as an account payable. Accounts payable, or trade credit, is the largest single category of short-term debt, representing about 40% of the average corporation’s current liabilities. This credit is a spontaneous source of fi nancing in the sense that it arises spontaneously from ordinary business transactions. For example, if a fi rm makes a purchase of $1,000 on terms of net 30, it must pay for goods 30 days after the invoice date. This instantly and spontaneously provides $1,000 of credit for 30 days. If the fi rm purchases $1,000 of goods each day, on average, it will be receiving 30 times $1,000, or $30,000, of credit from its suppliers. If sales, and consequently purchases, double, its accounts payable also will double, to $60,000. So simply by growing, the fi rm spontaneously generates another $30,000 of fi nancing. Similarly, if the terms under which it buys are extended from 30 to 40 days, its accounts pay- able will expand from $30,000 to $40,000. Thus, expanding sales and lengthening the credit period generate additional fi nancing.

Trade credit may be free, or it may be costly. If the seller does not offer dis- counts, the credit is free in the sense that there is no cost for using it. However, if discounts are available, a complication arises. To illustrate, suppose PCC Inc. buys 20 microchips each day with a list price of $100 per chip on terms of 2/10, net 30. Under these terms, the “true” price of the chips is 0.98($100) " $98 because the chips can be purchased for only $98 by paying within 10 days. Thus, the $100 list price has two components:

List price ! $98 “true” price # $2 fi nance charge

Trade Credit Debt arising from credit sales and recorded as an account receivable by the seller and as an account payable by the buyer.

494 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

If PCC decides to take the discount, it will pay at the end of Day 10 and show $19,600 of accounts payables:16

Accounts payable(Take discounts) ! (10 days)(20 chips) ($98 per chip)

! $19,600

If it decides to delay payment until the 30th day, its trade credit will be $58,800:

Accounts payable(No discounts) ! (30 days)(20 chips)($98 per chip)

! $58,800

By not taking discounts, PCC can obtain an additional $39,200 of trade credit, but this $39,200 is costly credit because the fi rm must give up the discounts to get it. There- fore, PCC must answer this question: Could we obtain the additional $39,200 at a lower cost from some other source (e.g., a bank)?

To illustrate the situation, assume that PCC operates 365 days per year and buys 20 chips per day at a “true” price of $98 per chip. Therefore, its total chip pur- chases are 20($98)(365) " $715,400 per year. If it does not take discounts, its chips will cost 20($100)(365) " $730,000, or an additional $14,600. This $14,600 is the annual cost of the $39,200 of extra credit. Dividing the $14,600 cost by the $39,200 additional credit yields the nominal annual cost of the additional trade credit, 37.24%:

Nominal annual cost of trade credit ! $14,600 _______ $39,200 ! 37.24%

If PCC can borrow from its bank or some other source for less than 37.24%, it should take the discount and use only $19,600 of trade credit.

The same result can be obtained with the following equation:

15-6 Nominal annual

cost of trade credit

! Discount % ________________ 100 " Discount % $ 365 ______________________ Days credit is

outstanding " Discount

period

! 2 ___ 98 $ 365 ____ 20 ! 2.04% $ 18.25 ! 37.24%

The numerator of the fi rst term, Discount %, is the cost per dollar of credit, while the denominator, 100 – Discount %, represents the funds made available by not tak- ing the discount. Thus, the fi rst term, 2.04%, is the cost per period for the trade credit. The denominator of the second term is the number of days of extra credit obtained by not taking the discount. So the entire second term shows how many times per year the cost is incurred, 18.25 times in this example.17

16 A question arises here: Should accounts payable refl ect gross purchases or purchases net of discounts? Generally accepted accounting principles permit either treatment if the diff erence is not material; but if the discount is material, the account payable must be recorded net of discounts, or at the “true” price. Then the cost of not taking discounts is reported as an additional expense called “discounts lost.” This procedure highlights the often high cost of not taking discounts. In PCC’s case, it would record payables of 20($98) " $1,960, not $2,000, per day; and if it did not take the discount and had to pay the full $2,000, it would show the $40 discount lost per day as an expense. 17 The nominal annual cost formula does not take account of compounding; and in eff ective annual interest terms, the cost of trade credit is even higher. The discount is equivalent to interest; and with terms of 2/10, net 30, the fi rm gains the use of funds for 30 #10 " 20 days. So there are 365/20 " 18.25 “interest periods” per year. Remember that the fi rst term in Equation 15-6, (Discount %)/(100 # Discount %) " 0.02/0.98 " 0.0204, is the periodic interest rate. That rate is paid 18.25 times each year, so the eff ective annual cost of trade credit is 44.6%:

Eff ective annual rate " (1.0204)18.25 # 1.0 " 1.4459 # 1.0 " 44.6%

Thus, the 37.2% nominal cost calculated with Equation 15-6 understates the eff ective cost.

495Chapter 15 Working Capital Management

With this background, we can defi ne two types of trade credit: free and costly: 1. Free trade credit is the trade credit that is obtained without a cost, and it con-

sists of all trade credit that is available without giving up discounts. In PCC’s case, when it buys on terms of 2/10, net 30, the fi rst 10 days of purchases, or $19,600, are free.

2. Costly trade credit is any trade credit over and above the free trade credit. For PCC, the additional 20 days, or $39,200, are not free because getting additional credit means giving up the discount.

Firms should always use the free component, but they should use the costly com- ponent only if they cannot obtain funds at a lower cost from another source.18

Free Trade Credit Credit received during the discount period.

Costly Trade Credit Credit taken in excess of free trade credit, whose cost is equal to the discount lost.

18 Note that the cost of trade credit can be reduced by paying late. If PCC could get away with paying in 60 days rather than the specifi ed 30 days, the eff ective credit period would become 60 # 10 " 50 days, the number of times the discount would be lost would fall to 365/50 " 7.3, and the nominal cost would drop from 37.2% to 2.04% $ 7.3 " 14.9%. This is called stretching accounts payable, and it damages the fi rm’s reputation and can cause problems later. 19 Sometimes the note will also specify that the fi rm must maintain a compensating balance equal to 10% to 20% of the face amount of the loan. This balance generally has the eff ect of increasing the eff ective cost of the loan. Compensating balances are much less common today than they were a few years ago.

SEL F TEST What is trade credit?

What is the diff erence between free trade credit and costly trade credit?

What is the formula for fi nding the nominal annual cost of trade credit?

Does the nominal cost of trade credit understate the eff ective cost? Explain.

15-10 BANK LOANS The key features of bank loans, another important source of short-term fi nancing for businesses and individuals, are discussed in this section.

15-10a Promissory Note The terms of a bank loan are spelled out in a promissory note. Here are some key features of most promissory notes:19

1. Amount. The amount borrowed is indicated. 2. Maturity. Although banks do make longer-term loans, the bulk of their lending is

on a short-term basis—about two-thirds of all bank loans mature in a year or less. Long-term loans always have a specifi c maturity date, while a short-term loan may or may not have a specifi ed maturity. For example, a loan may mature in 30 days, 90 days, 6 months, or 1 year; or it may call for payment “on demand,” in which case the loan can remain outstanding as long as the bor- rower wants to continue using the funds and the bank agrees. Bank loans to businesses are frequently written as 90-day notes, so the loan must be repaid or renewed at the end of 90 days. It is often expected that the loan will be renewed; but if the borrower’s fi nancial position deteriorates, the bank can refuse to renew it. This can lead to bankruptcy. Because banks usually don’t

Promissory Note A document specifying the terms and conditions of a loan, including the amount, interest rate, and repayment schedule.

496 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

demand payment unless the borrower’s creditworthiness has deteriorated, some “short-term loans” remain outstanding for years, with the interest rate fl oating with rates in the economy.

3. Interest rate. The interest rate can be fi xed or fl oating. For larger loans, it is typi- cally indexed to the bank’s prime rate, to the T-bill rate, or to the London Interbank Offer Rate (LIBOR). The note will also indicate whether the bank uses a 360- or 365-day year for purposes of calculating interest. The indicated rate is a nominal rate, and the effective annual rate is generally higher.

4. Interest only versus amortized. Loans are either interest only, meaning that only interest is paid during the life of the loan, with all principal repaid when the loan matures, or amortized, meaning that some of the principal is repaid on each payment date. Amortized loans are also called installment loans.

5. Frequency of interest payments. If the note is on an interest-only basis, it will indicate how frequently interest must be paid. Interest is typically calculated daily but paid monthly.

6. Discount interest. Most loans call for interest to be paid only after it has been earned; but banks also lend on a discount basis, where interest is paid in advance. On a discount loan, the borrower actually receives less than the face amount of the loan; and this increases its effective cost. We discuss discount loans in Web Appendix 15B.

7. Add-on loans. Auto loans and other consumer installment loans are generally set up on an “add-on basis,” which means that interest charges over the life of the loan are calculated and then added to the face amount of the loan. Thus, the borrower signs a promissory note calling for payment of the funds received plus all interest that must be paid over the life of the loan. The add-on feature raises the effective cost of a loan.

8. Collateral. If a loan is secured by equipment, buildings, accounts receivable, or inventories, this fact is indicated in the note. Security for loans is discussed in more detail in Section 15-13.

9. Restrictive covenants. The note may also specify that the borrower must main- tain certain ratios at or better than specifi ed levels, and it spells out what hap- pens if the borrower defaults on those covenants. Default provisions often allow the lender to demand immediate payment of the entire loan balance. Also, the interest rate on the loan might be increased.

10. Loan guarantees. If the borrower is a small corporation, the bank will probably insist that its larger stockholders personally guarantee the loan. Troubled companies’ owners have been known to divert assets from the company to relatives or other entities they own, so banks protect themselves by obtaining personal guarantees.

15-10b Line of Credit A line of credit is an agreement between a bank and a borrower indicating the maximum amount of credit the bank will extend to the borrower. For example, in December, a bank loan offi cer might indicate to a fi nancial manager that the bank regards the fi rm as being “good for” up to $80,000 during the coming year, provided the borrower’s fi nancial condition does not deteriorate. If on January 10 the fi nancial manager signs a promissory note for $15,000 for 90 days, this would be called “taking down” $15,000 of the credit line. The $15,000 would be credited to the fi rm’s checking account; and before it was repaid, the fi rm could borrow an additional $65,000 for a total of $80,000. Such a line of credit would be informal and nonbinding; but formal and binding lines are available, as dis- cussed next.

Line of Credit An arrangement in which a bank agrees to lend up to a specified maximum amount of funds during a designated period.

497Chapter 15 Working Capital Management

15-10c Revolving Credit Agreement A revolving credit agreement is a formal line of credit. To illustrate, in 2008, a Texas petroleum company negotiated a revolving credit agreement for $100 million with a group of banks. The banks were formally committed for 4 years to lend the fi rm up to $100 million if the funds were needed. The company, in turn, paid an annual commitment fee of one-fourth of 1% on the unused balance of the commit- ment to compensate the banks for making the commitment. Thus, if the fi rm did not take down any of the $100 million commitment during a year, it would still be required to pay a $250,000 annual fee, normally in monthly installments of $20,833.33. If it borrowed $50 million on the fi rst day of the agreement, the unused portion of the line of credit would fall to $50 million and the annual fee would fall to $125,000. Of course, interest would also have to be paid on the money the fi rm actually borrowed. In this case, the interest rate on the “revolver” was pegged to the LIBOR rate, being set at LIBOR minus 0.5 percentage point; so the cost of the loan would vary over time as interest rates change.20

Note that a revolving credit agreement is similar to an informal line of credit, but with an important difference: The bank has a legal obligation to honor a revolv- ing credit agreement, and it receives a commitment fee. Neither the legal obliga- tion nor the fee exists under informal lines of credit.

15-10d Costs of Bank Loans The costs of bank loans vary for different types of borrowers at any given point in time and for all borrowers over time. Interest rates are higher for riskier borrowers, and rates are higher on smaller loans because of the fi xed costs involved in making and servicing loans. If a fi rm can qualify as a “prime credit” because of its size and fi nancial strength, it can borrow at the prime rate, which at one time was the low- est rate banks charged. Rates on other loans are generally scaled up from the prime rate. But loans to large, strong customers are made at rates tied to LIBOR; and the costs of such loans are generally well below prime:

Rates on April 28, 2008: Prime: 5.25%. 1-Year LIBOR: 3.17875%. The rate to smaller, riskier borrowers is generally stated something like “prime plus 2.5%”; but for a larger borrower such as the Texas oil company, it is generally stated something like “LIBOR plus 2.5%.”

Bank rates vary widely over time depending on economic conditions and Federal Reserve policy. When the economy is weak, loan demand is usually slack, infl ation is low, and the Fed makes plenty of money available to the system. As a result, rates on all types of loans are relatively low. Conversely, when the economy is booming, loan demand is typically strong, the Fed restricts the money supply to fi ght infl ation, and the result is high interest rates. As an indication of the kinds of fl uctuations that can occur, the prime rate during 1980 rose from 11% to 21% in just 4 months; and it rose from 6% to 9% during 1994.

Calculating Banks’ Interest Charges: Regular (or Simple) Interest Banks calculate interest in several different ways. In this section, we explain the procedure used for most business loans. We discuss procedures used for consumer and small business loans in Web Appendix 15B. For illustrative purposes, we

Revolving Credit Agreement A formal, committed line of credit extended by a bank or another lending institution.

Prime Rate A published interest rate charged by commercial banks to large, strong borrowers.

20 Each bank sets its own prime rate; but because of competitive forces, most banks’ prime rates are identical. Further, most banks follow the rate set by the large New York City banks.

In recent years, many banks have been lending to large, strong companies at rates below the prime rate. As we discuss in Section 15-11, larger fi rms have ready access to the commercial paper market and if banks want to do business with these companies, they must match (or at least come close to) the commercial paper rate.

498 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

assume a loan of $10,000 at the prime rate (currently 5.25%) with a 360-day year. Interest must be paid monthly, and the principal is payable “on demand” if and when the bank wants to end the loan. Such a loan is called a regular, or simple, interest loan.

We begin by dividing the nominal interest rate (5.25% in this case) by 360 to get the rate per day. The rate is expressed as a decimal fraction, not as a percentage:

Simple interest rate per day ! Nominal rate ____________ Days in year

! 0.0525/360 ! 0.00014583333

To fi nd the monthly interest payment, the daily rate is multiplied by the amount of the loan, then by the number of days during the payment period. For our illustrative loan, the daily interest charge would be $1.458333333 and the total for a 30-day month would be $43.75:

Interest charge for month ! (Rate per day)(Amount of loan)(Days in month)

! (0.00014583333)($10,000)(30 days) ! $43.75

The effective interest rate on a loan depends on how frequently interest must be paid—the more frequently interest is paid, the higher the effective rate. If interest is paid once a year, the nominal rate also will be the effective rate. However, if interest must be paid monthly, the effective rate will be (1 ! 0.0525/12)12 – 1 " 5.3782%.

Calculating Banks’ Interest Charges: Add-On Interest Banks and other lenders typically use add-on interest for automobiles and other types of installment loans. The term add-on means that the interest is calculated and then added to the amount borrowed to determine the loan’s face value. To illustrate, suppose you borrow $10,000 on an add-on basis at a nominal rate of 7.25% to buy a car, with the loan to be repaid in 12 monthly installments. At a 7.25% add-on rate, you would make total interest payments of $10,000(0.0725) " $725. However, since the loan is paid off in monthly installments, you would have the use of the full $10,000 for only the fi rst month; and the outstanding balance would decline until, during the last month, only 1/12 of the original loan was still outstanding. Thus, you would be paying $725 for the use of only about half the loan’s face amount, as the average usable funds would be only about $5,000. There- fore, we can calculate the approximate annual rate as 14.5%:

15-7 Approximate annual rateAdd-on ! Interest paid __________________ (Amount received)/2

! $725 _________ $10,000/2 ! 14.5%

The annual percentage rate (APR) the bank provides to the borrower would be 13.12%, and the true effective annual rate would be 13.94%. Both of those rates are far higher than the nominal 7.25%.21

Regular, or Simple, Interest The situation when only interest is paid monthly.

Add-On Interest Interest that is calculated and added to funds received to determine the face amount of an installment loan.

21 To fi nd the annual percentage rate and the eff ective rate on an add-on loan, we fi rst fi nd the payment per month, $10,725/12 " $893.75. With a fi nancial calculator, enter N " 12, PV " 10000, PMT " #893.75, and FV " 0; then press I/YR to obtain 1.093585%. This is a monthly rate; so multiply by 12 to get 13.12%, which is the APR the bank would report to the borrower. The eff ective annual rate would be (1.010936)12 # 1 " 13.94%, quite a bit above the APR.

499Chapter 15 Working Capital Management

SEL F TEST What is a promissory note, and what terms are normally included in a

promissory note?

What is a line of credit? a revolving credit agreement?

What’s the diff erence between simple interest and add-on interest as bankers use these terms?

If a fi rm borrowed $500,000 at a rate of 10% simple interest with monthly interest payments and a 365-day year, what would be the required interest payment for a 30-day month? If interest must be paid monthly, what would be the eff ective annual rate? ($4,109.59; 10.47%)

If this loan had been made on a 10% add-on basis payable in 12 end-of-month installments, what would be the monthly payments? What is the annual per- centage rate? the eff ective annual rate? ($45,833.33; 17.97% 19.53%)

How does the cost of costly trade credit generally compare with the cost of short-term bank loans?

15-11 COMMERCIAL PAPER Commercial paper is a promissory note issued by a large, strong fi rm—most often a fi nancial institution—that wants to borrow on a short-term basis. Commercial paper is sold primarily to other business fi rms, insurance companies, pension funds, money market mutual funds, and banks in denominations of at least $100,000. It is generally unsecured; but “asset-backed paper” secured by credit card debt and other small, short-term loans has also been issued. Also (and with very bad consequences) in 2007, subsidiaries of fi nancial institutions such as Merrill Lynch and Citigroup sold a great deal of commercial paper and used it to buy bonds backed by subprime mortgages. This created a situation where short- term commercial paper was backed by long-term debt—and very poor quality debt at that. When the real situation was learned, holders of commercial paper refused to roll it over when it matured and the fi nancial institutions that had sold it were forced to sell the mortgages that backed the paper, often at huge losses. That forced Citi, Merrill, and other institutions to bail out their subsidiaries and to take losses in the tens of billions of dollars.

A large majority of the commercial paper outstanding has been issued by fi nancial institutions. Nonfi nancial companies also issue a great deal of paper, but they generally rely more heavily on bank loans for short-term funding. For exam- ple, in March 2008, the Federal Reserve reported that commercial paper issued by nonfi nancial fi rms totaled slightly more than $177 billion—that same month the total amount of commercial and industrial loans held by commercial banks was nearly 1.5 trillion dollars.

Commercial Paper Unsecured, short-term promissory notes of large firms, usually issued in denominations of $100,000 or more with an interest rate somewhat below the prime rate.

SEL F TEST What is commercial paper?

What types of companies use commercial paper to meet their short-term fi nancing needs?

500 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

15-12 ACCRUALS (ACCRUED LIABILITIES) As we discussed in Chapter 3, fi rms generally pay employees on a weekly, biweekly, or monthly basis; so the balance sheet typically shows some accrued wages. Simi- larly, the fi rm’s own estimated income taxes, Social Security and income taxes withheld from employee payrolls, and sales taxes collected are generally paid on a weekly, monthly, or quarterly basis. Therefore, the balance sheet typically shows some accrued wages and taxes, which we refer to as accruals.

Accruals arise automatically from a fi rm’s operations; hence, they are spontaneous funds. For example, if sales grow by 50%, accrued wages and taxes should also grow by about 50%. Accruals are “free” in the sense that no interest is paid on them. However, fi rms cannot control their accruals because the timing of wage payments is set by contract or industry custom and tax pay- ments are set by law. Thus, fi rms use all the accruals they can, but they have little control over their levels.

Accruals Continually recurring short-term liabilities, especially accrued wages and accrued taxes.

Spontaneous Funds Funds that are generated spontaneously as the firm expands.

SEL F TEST What types of short-term credit are classifi ed as accrued liabilities?

What is the cost of accrued liabilities? If accruals have such a low cost, why don’t fi rms use them even more?

15-13 USE OF SECURITY IN SHORT-TERM FINANCING Other things held constant, borrowers prefer to use unsecured short-term debt because the bookkeeping costs associated with secured loans are high. However, fi rms may fi nd that they can borrow only if they put up collateral to protect the lender or that securing the loan enables them to borrow at a lower rate.

Stocks and bonds, equipment, inventory, accounts receivable, land, and build- ings can be used as collateral. However, few fi rms that need loans hold portfolios of stocks and bonds. Land, buildings, and equipment are good forms of collateral; but they are generally used to secure long-term loans rather than short-term work- ing capital loans. Therefore, most secured short-term business loans use accounts receivable and inventories as collateral.

To understand the use of security, consider the case of a Chicago hardware dealer who wanted to modernize and expand his store. He requested a $200,000 loan. After examining his fi nancial statements, the bank indicated that it would lend him a maximum of $100,000 on an unsecured basis and that the interest rate would be 10%. However, the company had about $300,000 of accounts receivable that could be used as collateral; and with the receivables as security, the bank agreed to lend the full $200,000 and at the prime rate of 5.25%. Processing costs for administering the loan were fairly high; but even so, the secured loan was less expensive than an unsecured loan would have been.22

Secured Loan A loan backed by collateral, often inventories or accounts receivable.

22 The term asset-based fi nancing is often used as a synonym for secured fi nancing. In recent years, accounts receivable have been used as security for long-term bonds, which has permitted corporations to borrow from lenders such as pension funds rather than being restricted to banks and other traditional short-term lenders.

501Chapter 15 Working Capital Management

SEL F TEST From the borrower’s standpoint, what are the advantages and disadvan-

tages of securing a loan?

What two types of current assets are frequently used as security for short- term loans?

How could borrowers take advantage of lenders if UCC-1s did not exist?

This chapter discussed the management of current assets, including cash, market- able securities, inventory, and receivables. Current assets are essential, but there are costs associated with holding them. So if a company can reduce its current assets without hurting sales, this will increase its profi tability. The investment in current assets must be fi nanced; and this fi nancing can be in the form of long-term debt, common equity, and/or short-term credit. Firms typically use trade credit and accru- als; they also may use bank debt or commercial paper.

Although current assets and procedures for fi nancing them can be analyzed as we did in this chapter, decisions are normally made within the context of the fi rm’s overall fi nancial plan. We take up fi nancial planning in the next chapter; hence, we continue our discussion of working capital there.

T YING I T ALL TO GETHER

KEY TERMS Define each of the following terms: a. Working capital; net working capital b. Relaxed current asset policy; restricted current asset policy; moderate current asset

policy c. Permanent current assets; temporary current assets d. Current asset financing policy; maturity matching (self-liquidating) approach to

financing working capital e. Cash conversion cycle; inventory conversion period; average collection period;

payables deferral period f. Cash budget; target cash balance g. Lockbox; account receivable

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

When the collateral securing a loan is to be kept on the borrower’s premises, a form called a UCC-1 (Uniform Commercial Code Form 1) is fi led with the secre- tary of the state in which the collateral is located, along with a Security Agreement (also part of the Uniform Commercial Code) that describes the nature of the agree- ment. The UCC-1 prevents the borrower from using the same collateral to secure loans from different lenders, and the security agreement spells out conditions under which the lender can seize the collateral.

502 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

h. Credit policy; credit period; discounts; credit standards; collection policy; credit terms; credit score

i. Trade credit; free versus costly trade credit j. Promissory note; line of credit; revolving credit agreement k. Prime rate; simple interest; add-on interest l. Commercial paper; accruals; spontaneous funds m. Secured loan

WORKING CAPITAL POLICY Calgary Company is thinking of modifying its working capi- tal assets policy. Fixed assets are $600,000, sales are projected at $3 million, the EBIT/sales ratio is projected at 15%, the interest rate is 10% on all debt, the federal-plus-state tax rate is 40%, and Calgary plans to maintain a 50% debt-to-assets ratio. Three alternative current asset policies are under consideration: 40%, 50%, and 60% of projected sales. What is the expected return on equity under each alternative?

CURRENT ASSET FINANCING Vanderheiden Press Inc. and Herrenhouse Publishing Company had the following balance sheets as of December 31, 2008 (thousands of dollars):

Vanderheiden Press Herrenhouse Publishing

Current assets $100,000 $ 80,000 Fixed assets (net) 100,000 120,000 Total assets $200,000 $200,000

Current liabilities $ 20,000 $ 80,000 Long-term debt 80,000 20,000 Common stock 50,000 50,000 Retained earnings 50,000 50,000 Total liabilities and equity $200,000 $200,000

Earnings before interest and taxes for both firms are $30 million, and the effective federal- plus-state tax rate is 40%. a. What is the return on equity for each firm if the interest rate on current liabilities is

10% and the rate on long-term debt is 13%? b. Assume that the short-term rate rises to 20%. While the rate on new long-term debt

rises to 16%, the rate on existing long-term debt remains unchanged. What would be the returns on equity for Vanderheiden Press and Herrenhouse Publishing under these conditions?

c. Which company is in a riskier position? Why?

What are some pros and cons of holding high levels of current assets in relation to sales? Use the DuPont equation to help explain your answer.

Define cash conversion cycle (CCC). Explain why, holding other things constant, a firm’s profitability would increase if it lowered its CCC.

What are the two definitions of cash, and why do corporate treasurers often use the second definition?

What is a cash budget, and how can this statement be used to help reduce the amount of cash that a firm needs to carry? What are the advantages and disadvantages of daily over monthly cash budgets, and how might a cash budget be used when a firm is negotiating a loan from its bank?

ST-2ST-2

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QUESTIONSQUESTIONS

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503Chapter 15 Working Capital Management

What are the four key factors in a firm’s credit policy? How would an easy policy differ from a tight policy? Give examples of how the four factors might differ between the two policies. How would the easy versus the tight policy affect sales? profits?

What does it mean to adopt a maturity matching approach to financing assets, including current assets? How would a more aggressive or a more conservative approach differ from the maturity matching approach, and how would each affect expected profits and risk? In general, is one approach better than the others?

Why is some trade credit called free while other credit is called costly? If a firm buys on terms of 2/10, net 30, pays at the end of the 30th day, and typically shows $300,000 of accounts payable on its balance sheet, would the entire $300,000 be free credit, would it be costly credit, or would some be free and some costly? Explain your answer. No calculations are necessary.

Define each of the following loan terms, and explain how they are related to one another: the prime rate, the rate on commercial paper, the simple interest rate on a bank loan calling for interest to be paid monthly, and the rate on an installment loan based on add-on interest. If the stated rate on each of these loans was 6%, would they all have equal, effective annual rates? Explain.

Why are accruals called spontaneous sources of funds, what are their costs, and why don’t firms use more of them?

Indicate using a (!), (–), or (0) whether each of the following events would probably cause accounts receivable (A/R), sales, and profits to increase, decrease, or be affected in an indeterminate manner:

A/R Sales Profits

The firm tightens its credit standards. The terms of trade are changed from 2/10, net 30, to 3/10, net 30. The terms are changed from 2/10, net 30, to 3/10, net 40. The credit manager gets tough with past due accounts.

CASH CONVERSION CYCLE Primrose Corp has $15 million of sales, $2 million of inventories, $3 million of receivables, and $1 million of payables. Its cost of goods sold is 80% of sales, and it finances working capital with bank loans at an 8% rate. What is Primrose’s cash conversion cycle (CCC)? If Primrose could lower its inventories and receivables by 10% each and increase its payables by 10%, all without affecting sales or cost of goods sold, what would be the new CCC, how much cash would be freed up, and how would that affect pre-tax profits?

RECEIVABLES INVESTMENT Lamar Lumber Company has sales of $10 million per year, all on credit terms calling for payment within 30 days; and its accounts receivable are $2 million. What is Lamar’s DSO, what would it be if all customers paid on time, and how much capital would be released if Lamar could take action that led to on-time payments?

COST OF TRADE CREDIT AND BANK LOAN Lamar Lumber buys $8 million of materials (net of discounts) on terms of 3/5, net 60; and it currently pays after 5 days and takes discounts. Lamar plans to expand, which will require additional financing. If Lamar decides to forgo discounts, how much additional credit could it get and what would be the nominal and effective cost of that credit? If the company could get the funds from a bank at a rate of 10%, interest paid monthly, based on a 365-day year, what would be the effective cost of the bank loan, and should Lamar use bank debt or additional trade credit? Explain.

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PROBLEMS PROBLEMS

15-115-1Easy Problems 1–3 Easy Problems 1–3

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504 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

CASH CONVERSION CYCLE Zocco Corporation has an inventory conversion period of 75 days, an average collection period of 38 days, and a payables deferral period of 30 days. a. What is the length of the cash conversion cycle? b. If Zocco’s annual sales are $3,421,875 and all sales are on credit, what is the invest-

ment in accounts receivable? c. How many times per year does Zocco turn over its inventory?

RECEIVABLES INVESTMENT McDowell Industries sells on terms of 3/10, net 30. Total sales for the year are $912,500; 40% of the customers pay on the 10th day and take discounts, while the other 60% pay, on average, 40 days after their purchases. a. What is the days’ sales outstanding? b. What is the average amount of receivables? c. What is the percentage cost of trade credit to customers who take the discount? d. What is the percentage cost of trade credit to customers who do not take the discount

and pay in 40 days? e. What would happen to McDowell’s accounts receivable if it toughened up on its

collection policy with the result that all nondiscount customers paid on the 30th day?

WORKING CAPITAL INVESTMENT Prestopino Corporation produces motorcycle batteries. Prestopino turns out 1,500 batteries a day at a cost of $6 per battery for materials and labor. It takes the firm 22 days to convert raw materials into a battery. Prestopino allows its customers 40 days in which to pay for the batteries, and the firm generally pays its suppliers in 30 days. a. What is the length of Prestopino’s cash conversion cycle? b. At a steady state in which Prestopino produces 1,500 batteries a day, what amount of

working capital must it finance? c. By what amount could Prestopino reduce its working capital financing needs if it was

able to stretch its payables deferral period to 35 days? d. Prestopino’s management is trying to analyze the effect of a proposed new

production process on its working capital investment. The new production process would allow Prestopino to decrease its inventory conversion period to 20 days and to increase its daily production to 1,800 batteries. However, the new process would cause the cost of materials and labor to increase to $7. Assuming the change does not affect the average collection period (40 days) or the payables deferral period (30 days), what will be the length of its cash conversion cycle and its working capital financing requirement if the new production process is implemented?

WORKING CAPITAL CASH FLOW CYCLE Christie Corporation is trying to determine the effect of its inventory turnover ratio and days sales outstanding (DSO) on its cash flow cycle. Christie’s 2008 sales (all on credit) were $150,000; and it earned a net profit of 6%, or $9,000. It turned over its inventory 6 times during the year, and its DSO was 36.5 days. The firm had fixed assets totaling $35,000. Christie’s payables deferral period is 40 days. a. Calculate Christie’s cash conversion cycle. b. Assuming Christie holds negligible amounts of cash and marketable securities,

calculate its total assets turnover and ROA. c. Suppose Christie’s managers believe that the inventory turnover can be raised to 7.3

times. What would Christie’s cash conversion cycle, total assets turnover, and ROA have been if the inventory turnover had been 7.3 for 2008?

WORKING CAPITAL POLICY Rentz Corporation is investigating the optimal level of current assets for the coming year. Management expects sales to increase to approximately $2 million as a result of an asset expansion presently being undertaken. Fixed assets total $1 million, and the firm plans to maintain a 60% debt ratio. Rentz’s interest rate is currently 8% on both short-term and longer-term debt (which the firm uses in its permanent structure). Three alternatives regarding the projected current asset level are under consideration: (1) a tight policy where current assets would be only 45% of projected sales, (2) a moderate policy where current assets would be 50% of sales, and (3) a relaxed policy where current assets would be 60% of sales. Earnings before interest and taxes should be 12% of total sales, and the federal-plus-state tax rate is 40%. a. What is the expected return on equity under each current asset level? b. In this problem, we assume that expected sales are independent of the current asset

policy. Is this a valid assumption? Why or why not? c. How would the firm’s risk be affected by the different policies?

15-415-4Intermediate Problems 4–6 Intermediate Problems 4–6

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15-715-7Challenging Problems 7–10 Challenging Problems 7–10

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505Chapter 15 Working Capital Management

LOCKBOX SYSTEM Hardin-Gehr Corporation (HGC) began operations 5 years ago as a small firm serving customers in the Detroit area. However, its reputation and market area grew quickly. Today HGC has customers all over the United States. Despite its broad customer base, HGC has maintained its headquarters in Detroit and it keeps its central billing system there. On average, it takes 5 days from the time customers mail in payments until HGC can receive, process, and deposit them. HGC would like to set up a lockbox collection system, which it estimates would reduce the time lag from customer mailing to deposit by 3 days—bringing it down to 2 days. HGC receives an average of $1,400,000 in payments per day. a. How much free cash would HGC generate if it implemented the lockbox system?

Would this be a one-time cash flow or a recurring one, assuming the company ceases to grow? How would growth affect your answer?

b. If HGC has an opportunity cost of 10%, how much is the lockbox system worth on an annual basis?

c. What is the maximum monthly charge HGC should pay for the lockbox system?

CASH BUDGETING Helen Bowers, owner of Helen’s Fashion Designs, is planning to re- quest a line of credit from her bank. She has estimated the following sales forecasts for the firm for parts of 2009 and 2010:

May 2009 $180,000

June 180,000

July 360,000

August 540,000

September 720,000

October 360,000

November 360,000

December 90,000

January 2010 180,000

Estimates regarding payments obtained from the credit department are as follows: collected within the month of sale, 10%; collected the month following the sale, 75%; collected the second month following the sale, 15%. Payments for labor and raw materials are made the month after these services were provided. Here are the estimated costs of labor plus raw materials:

May 2009 $ 90,000

June 90,000

July 126,000

August 882,000

September 306,000

October 234,000

November 162,000

December 90,000

General and administrative salaries are approximately $27,000 a month. Lease payments under long-term leases are $9,000 a month. Depreciation charges are $36,000 a month. Miscellaneous expenses are $2,700 a month. Income tax payments of $63,000 are due in September and December. A progress payment of $180,000 on a new design studio must be paid in October. Cash on hand on July 1 will be $132,000, and a minimum cash balance of $90,000 should be maintained throughout the cash budget period. a. Prepare a monthly cash budget for the last 6 months of 2009. b. Prepare monthly estimates of the required financing or excess funds—that is, the

amount of money Bowers will need to borrow or will have available to invest. c. Now suppose receipts from sales come in uniformly during the month (that is, cash

receipts come in at the rate of 1/30 each day), but all outflows must be paid on the 5th. Will this affect the cash budget? That is, will the cash budget you prepared be valid under these assumptions? If not, what could be done to make a valid estimate of the

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506 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

peak financing requirements? No calculations are required, although if you prefer, you can use calculations to illustrate the effects.

d. Bowers’ sales are seasonal; and her company produces on a seasonal basis, just ahead of sales. Without making any calculations, discuss how the company’s current and debt ratios would vary during the year if all financial requirements were met with short-term bank loans. Could changes in these ratios affect the firm’s ability to obtain bank credit? Explain.

CASH BUDGETING Rework Problem 15-10 using a spreadsheet model. After completing Parts a through d, respond to the following: If Bowers’ customers began to pay late, collections would slow down, thus increasing the required loan amount. If sales declined, this also would have an effect on the required loan. Do a sensitivity analysis that shows the effects of these two factors on the maximum loan requirement.

COMPREHENSIVE/SPREADSHEET PROBLEMCOMPREHENSIVE/SPREADSHEET PROBLEM

15-1115-11

MANAGING CURRENT ASSETS Dan Barnes, financial manager of Ski Equipment Inc. (SKI), is excited, but ap- prehensive. The company’s founder recently sold his 51% controlling block of stock to Kent Koren, who is a big fan of EVA (Economic Value Added). EVA is found by taking the after-tax operating profit and subtracting the dollar cost of all the capital the firm uses:

EVA ! EBIT(1 " T) " Capital costs

! EBIT(1 " T) " WACC(Capital employed).

If EVA is positive, the firm is creating value. On the other hand, if EVA is negative, the firm is not covering its cost of capital and stockholders’ value is being eroded. Koren rewards managers handsomely if they create value, but those whose operations produce negative EVAs are soon looking for work. Koren frequently points out that if a company can generate its current level of sales with fewer assets, it will need less capital. That would, other things held constant, lower capital costs and increase EVA.

Shortly after he took control of SKI, Koren met with SKI’s senior executives to tell them of his plans for the company. First, he presented some EVA data that convinced everyone that SKI had not been creating value in re- cent years. He then stated, in no uncertain terms, that this situation must change. He noted that SKI’s designs of skis, boots, and clothing are acclaimed throughout the industry but that something is seriously amiss elsewhere in the company. Costs are too high, prices are too low, or the company employs too much capital; and he wants SKI’s managers to correct the problem.

Barnes has long believed that SKI’s working capital situation should be studied—the company may have the optimal amounts of cash, securities, receivables, and inventories; but it may also have too much or too little of these items. In the past, the production manager resisted Barnes’s efforts to question his holdings of raw materials inventories, the marketing manager resisted questions about finished goods, the sales staff resisted questions about credit policy (which affects accounts receivable), and the treasurer did not want to talk about her cash and securities balances. Koren’s speech made it clear that such resistance would no longer be tolerated.

Barnes also knows that decisions about working capital cannot be made in a vacuum. For example, if inven- tories could be lowered without adversely affecting operations, less capital would be required, the dollar cost of capital would decline, and EVA would increase. However, lower raw materials inventories might lead to pro- duction slowdowns and higher costs, while lower finished goods inventories might lead to the loss of profitable sales. So before inventories are changed, it will be necessary to study operating as well as financial effects. The situation is the same with regard to cash and receivables.

a. Barnes plans to use the ratios in Table IC15-1 as the starting point for discussions with SKI’s operating execu- tives. He wants everyone to think about the pros and cons of changing each type of current asset and the

15-1215-12

IN TEGRATED C ASE SKI EQUIPMENT INC.

507Chapter 15 Working Capital Management

way changes would interact to affect profits and EVA. Based on the data in Table IC15-1, does SKI seem to be following a relaxed, moderate, or restricted working capital policy?

b. How can we distinguish between a relaxed but rational working capital policy and a situation where a firm has a large amount of current assets simply because it is inefficient? Does SKI’s working capital policy seem appropriate?

c. SKI tries to match the maturity of its assets and liabilities. Describe how SKI could adopt a more aggressive or a more conservative financing policy.

d. Assume that SKI’s payables deferral period is 30 days. Now calculate the firm’s cash conversion cycle. e. What might SKI do to reduce its cash and securities without harming operations?

In an attempt to better understand SKI’s cash position, Barnes developed a cash budget. Data for the first 2 months of the year are shown in Table IC15-2. (Note that Barnes’s preliminary cash budget does not account for interest income or interest expense.) He has the figures for the other months, but they are not shown in Table IC15-2.

f. In his preliminary cash budget, Barnes has assumed that all sales are collected and, thus, that SKI has no bad debts. Is this realistic? If not, how would bad debts be dealt with in a cash budgeting sense? (Hint: Bad debts affect collections but not purchases.)

g. Barnes’s cash budget for the entire year, although not given here, is based heavily on his forecast for monthly sales. Sales are expected to be extremely low between May and September but then increase dramatically in the fall and winter. November is typically the firm’s best month, when SKI ships equipment to retailers for the holiday season. Interestingly, Barnes’s forecasted cash budget indicates that the company’s cash hold- ings will exceed the targeted cash balance every month except October and November, when shipments will be high but collections will not be coming in until later. Based on the ratios in Table IC15-1, does it appear that SKI’s target cash balance is appropriate? In addition to possibly lowering the target cash balance, what actions might SKI take to better improve its cash management policies and how might that affect its EVA?

h. Is there any reason to think that SKI may be holding too much inventory? If so, how would that affect EVA and ROE?

i. If the company reduces its inventory without adversely affecting sales, what effect should this have on the company’s cash position (1) in the short run and (2) in the long run? Explain in terms of the cash budget and the balance sheet.

j. Barnes knows that SKI sells on the same credit terms as other firms in the industry. Use the ratios presented in Table IC15-1 to explain whether SKI’s customers pay more or less promptly than those of its competitors. If there are differences, does that suggest that SKI should tighten or loosen its credit policy? What four vari- ables make up a firm’s credit policy, and in what direction should each be changed by SKI?

k. Does SKI face any risks if it tightens its credit policy? Explain. l. If the company reduces its DSO without seriously affecting sales, what effect will this have on its cash posi-

tion (1) in the short run and (2) in the long run? Answer in terms of the cash budget and the balance sheet. What effect should this have on EVA in the long run?

m. Assume that SKI buys on terms of 1/10, net 30, but that it can get away with paying on the 40th day if it chooses not to take discounts. Also assume that it purchases $3 million of components per year, net of dis- counts. How much free trade credit can the company get, how much costly trade credit can it get, and what is the percentage cost of the costly credit? Should SKI take discounts? Why or why not?

n. Suppose SKI decided to raise an additional $100,000 as a 1-year loan from its bank, for which it was quoted a rate of 8%. What is the effective annual cost rate assuming simple interest and add-on interest on a 12-month installment loan?

SKI Industry Current 1.75 2.25 Debt/assets 58.76% 50.00% Turnover of cash and securities 16.67 22.22 Days sales outstanding (365-day basis) 45.63 32.00 Inventory turnover 4.82 7.00 Fixed assets turnover 11.35 12.00 Total assets turnover 2.08 3.00 Profit margin 2.07% 3.50% Return on equity (ROE) 10.45% 21.00%

Selected Ratios: SKI and Industry AverageT a b l e I C 1 5 - 1

508 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Nov Dec Jan Feb Mar Apr I. COLLECTIONS AND PURCHASES

WORKSHEET (1) Sales (gross) $71,218 $68,212 $65,213.00 $52,475.00 $42,909 $30,524 Collections (2) During month of sale

(0.2 $ 0.98 $ month’s sales) 12,781.75 10,285.10 (3) During first month after sale

(0.7 $ previous month’s sales) 47,748.40 45,649.10 (4) During second month after sale

(0.1 $ sales 2 months ago) 7,121.80 6,821.20 (5) Total collections (Lines 2 ! 3 ! 4) $67,651.95 $62,755.40 Purchases (6) (0.85 $ forecasted sales 2 months

from now) $44,603.75 $36,472.65 $25,945.40 (7) Payments (1-month lag) 44,603.75 36,472.65 II. CASH GAIN OR LOSS FOR MONTH (8) Collections (from Section I) $67,651.95 $62,755.40 (9) Payments for purchases (from

Section I) 44,603.75 36,472.65 (10) Wages and salaries 6,690.56 5,470.90 (11) Rent 2,500.00 2,500.00 (12) Taxes (13) Total payments $53,794.31 $44,443.55 (14) Net cash gain (loss) during month

(Line 8 – Line 13) $13,857.64 $18,311.85 III. CASH SURPLUS OR LOAN

REQUIREMENT (15) Cash at beginning of month if no

borrowing is done $3,000.00 $16,857.64 (16) Cumulative cash [cash at start

! gain or # loss " (Line 14 ! Line 15)] $16,857.64 $35,169.49

(17) Target cash balance 1,500.00 1,500.00 (18) Cumulative surplus cash or

loans outstanding to maintain $1,500 target cash balance (Line 16 # Line 17) $15,357.64 $33.669.49

SKI’s Cash Budget for January and FebruaryT a b l e I C 1 5 - 2

T h e M i s s T h a t H i t L i ke a B o m b s h e l l

16 CHAPTER

509

In March 2008, CEO Jeffrey Immelt announced to security analysts that all of GE’s divisions were hitting their earnings targets and that the firm would enjoy double-digit growth for the year. According to Immelt, GE’s global portfolio of businesses, which ranged from nuclear power plants to TV networks and movie stu- dios, stabilized earnings and protected the company from economic shocks such as the subprime mortgage debacle. GE’s stock responded nicely, rising from $32 to $38 per share. However, less than a month later Immelt held another televised news conference where he announced that GE’s first-quarter earnings were down 5.8%, with similar declines likely for the rest of 2008. GE’s stock plunged, lowering stockholder wealth by about $50 billion in just one day.

Immelt’s announcement delivered a blow to GE’s reputation and credibility. Investors set stock prices based on information and recommenda- tions from the security analysts who work for the

large investment banks and brokerages. Analysts study historical data, but they recognize that companies’ managers have the best information about future earnings. Therefore, if a company is “credible” and can be trusted, analysts base their forecasts heavily on information like Immelt pro- vided in his March forecast. Each analyst pro- duces a “target price,” which is essentially his or her estimate of the stock’s intrinsic value. The brokers of the analysts’ firms then use that infor- mation when they make recommendations to their customers. Immelt’s initial forecast led to buy recommendations and GE purchases, but the quick retraction led to substantial losses and unhappy customers. Those customers let their brokers know how they felt, and those feelings were relayed to the analysts and then to Immelt; and he probably called some of his subordinates to task. The whole episode was embarrassing to Immelt and to GE. GE’s board must have been unhappy, which is not good for a CEO in an era when CEOs can be easily replaced.

Financial Planning and Forecasting

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510 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Yogi Berra, the former player and manager for the New York Yankees, once said, “If you don’t know where you’re going, you probably won’t get there.” That’s certainly true for a company—it needs a plan, one that starts with the fi rm’s general goals and details the steps that will be taken to get there. When you fi nish this chapter, you should be able to: • Discuss the importance of strategic planning and the central role that fi nancial

forecasting plays in the overall planning process. • Explain how fi rms forecast sales. • Use the Additional Funds Needed (or AFN) equation and discuss the relationship

between asset growth and the need for funds. • Explain how spreadsheets are used in the forecasting process, starting with his-

torical statements, ending with projected statements, and including a set of fi nan- cial ratios based on those projected statements.

• Discuss how planning is an iterative process. Financial planners begin with a set of assumptions, see what is likely to happen

based on those assumptions, and then see if modifi cations can help the fi rm achieve better results. GE’s critics suggest that the company should make forecasts based on its current structure and on an “if broken up” basis, then go forward with the breakup if that indicates the higher shareholder value.1

Although we focus on forecasting from the corporation’s standpoint, top security analysts go through the same process. Analysts with hedge and private equity funds are especially active as forecasters, and they are particularly interested in the itera- tive process of forecasting.

GE was founded to commercialize Thomas Edison’s inventions in lightbulb and power plant technologies, but today its divisions extend far beyond its base. A number of analysts have questioned GE’s diversification strategy and have argued that the company should spin off unrelated units and return to its roots. They point out that GE’s stock price in 2008 is about 30% below its 2001 level; and they ask why, if the company has such a good strategic plan, its stock price has not done better. Here’s the comment of one analyst, Citigroup’s Jeff Sprague: “We believe the evidence is mount- ing that GE is too big and complex to manage effectively.”

Sprague and others believe that stockholders would be better served if GE were split into several smaller, more focused companies. Then each company’s CEO would pre- sumably understand his or her particular business and could focus exclusively on running it. Businesses that are related could be kept together, but unrelated ones would be spun off. If that were done, perhaps forecasting would be easier, Immelt would end up less chagrined, and GE’s stockholders would be wealthier.

Source: “GE Shocks Market with Profit Drop, Shares Tumble,” April 11, 2008, http://moneycentral.msn.com.

PU T TING THINGS IN PER SPECTIVE

1 GE’s executives have undoubtedly done these analyses. However, since executive compensation is a function of the size of the corporation, there is a bias against voluntary divestitures. Hedge funds and buyout funds have no such bias, so the majority of breakups are led by activist investors.

http://moneycentral.msn.com

511Chapter 16 Financial Planning and Forecasting

16-1 STRATEGIC PLANNING Management textbooks often list the following as the key elements of a strategic plan: • Mission Statement. Many but not all fi rms articulate a mission statement. GE

does not have one, but it states that its chairman’s letter in the annual report serves this purpose. In his letter, Jeff Immelt discusses his goals for GE’s major businesses and for the fi rm as a whole. Not surprisingly, Immelt indicated that he wants the various businesses to achieve high growth rates, high profi t mar- gins, and high rates of return on invested capital, all with the ultimate goal of increasing GE’s stock price.

• Corporate Scope. Corporate scope defi nes the lines of business the fi rm plans to pursue and the geographic areas in which it will operate. Some fi rms deliber- ately limit their scope on the theory that it is better for top managers to focus sharply on a narrow range of functions as opposed to spreading the company over many different types of businesses. Academics have studied which is the better choice. Some studies suggest that investors generally value focused fi rms more highly than diversifi ed ones.2 However, if a fi rm is successful in combining a group of diversifi ed businesses so that they help one another, as GE tries to do, the result may be synergistic effects that raise the value of the overall enterprise.3 In any event, the stated corporate scope should be logical and consistent with the fi rm’s capabilities.

• Statement of Corporate Objectives. A fi rm’s statement of coporate objectives is that part of the corporate plan that sets forth the specifi c goals that operating managers are expected to meet. Like most fi rms, GE has both qualitative and quantitative objectives. For example, here is a key statement from Immelt’s 2006 letter to stockholders:

We expect our businesses to achieve 10%+ earnings growth most years, with long-term returns on equity of 20%. We expect our businesses to be industry leaders in market share, value, and profi tability.

GE has a history of selling off units that do not meet its objectives and of replac- ing underperforming managers, but GE also rewards managers generously when they meet their targets.

• Corporate Strategies. GE has several broad corporate strategies. One is to be highly diversifi ed by both products and geographic scope in order to achieve earnings stability and fi nancial strength. Its management believes that fi nancial strength will lead to a low cost of capital, which will benefi t all its units. Also, since GE’s management believes that the company should be at the forefront in

Mission Statement A condensed version of a firm’s strategic plan.

Corporate Scope Defines a firm’s lines of business and geographic areas of operation.

Statement of Corporate Objectives Sets forth specific goals to guide management.

Corporate Strategies Broad approaches developed for achieving a firm’s goals.

2 See, for example, Philip G. Berger and Eli Ofek, “Diversifi cation’s Eff ect on Firm Value,” Journal of Financial Economics, Vol. 37, no. 1 (1995), pp. 39–66, and Larry Lang and René Stulz, “Tobin’s Q, Corporate Diversifi cation, and Firm Performance,” Journal of Political Economy, Vol. 102, Issue 6 (1994), pp. 1248–1280. 3 The dictionary defi nition of synergy is a situation where the whole is greater than the sum of the parts, and it’s sometimes called the 2 ! 2 " 5 eff ect. GE has a jet engine business and another business that produces gas turbines for electric power generation. Those businesses are similar enough so that new developments in one can benefi t the other. One has to wonder, though, how GE’s jet engine business benefi ts its Universal-NBC entertainment unit. GE’s management argues that its diversifi cation stabilizes its revenues and profi ts, and that this resulted in a triple-A bond rating and a relatively low cost of capital for all its businesses. A number of academic studies dispute this conclusion, though, with the academics arguing that it is easy for stockholders to diversify and better to have top managers focus on one business. Interestingly, GE’s April 2008 earnings shortfall brought forth calls for the company to be broken up into more cohesive units whose managers could focus on products and markets that they knew very well.

512 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

addressing environmental issues, it is investing heavily in infrastructure tech- nologies to purify air and water. Immelt expects to “do good by doing good.”

• Operating Plan. Each of GE’s units must develop a detailed operating plan that is consistent with the corporate strategy to help it achieve the fi rm’s objectives. Operating plans can be developed for any time horizon, but most companies use a 5-year horizon. The plan explains in considerable detail those people responsible for each particular function, deadlines for specifi c tasks, sales and profi t targets, and the like.

• Financial Plan. Financial planning is a multi-step process. Allied’s fi nancial plan involves four steps. First, assumptions are made about the future levels of sales, costs, interest rates, and so forth, for use in the forecast. Second, a set of projected fi nancial statements is developed. Third, projected ratios such as those we discussed in Chapter 4 are calculated and analyzed. Fourth, the entire plan is reexamined, the assumptions are reviewed, and the management team considers how additional changes in operations might improve results. This last step requires reconsideration of all the earlier parts of the overall plan, from the mission statement to the operating plan. Thus, the fi nancial plan ties the entire planning process together.

Financial planning as described previously is often called “value-based management,” meaning that the effects of various decisions on the fi rm’s fi nancial position and value are studied by simulating their effects within the fi rm’s fi nancial model. For example, if GE was considering a shift in appliance manufacturing from Kentucky to Mexico, it would simulate the effects through its fi nancial model and then make the move if it appeared that profi ts and thus shareholder wealth would be increased.4

Operating Plan Provides management with detailed implementation guidance based on the corporate strategy to help meet the corporate objectives.

Financial Plan The document that includes assumptions, projected financial statements, and projected ratios and ties the entire planning process together.

4 Note, though, that there would surely be political ramifi cations to such a move. These eff ects would be studied by use of the model, and the computer-generated results would be an input in the decision. However, the ulti- mate decision would be made by GE’s top executives and board, not, in essence, by a computer. 5 Note that you need 5 years of data to fi nd the 4-year growth rate from 2004 to 2008.

SEL F TEST What are the key elements of a corporation’s strategic plan?

How is the fi nancial plan related to the other parts of a fi rm’s overall strategic plan?

How can the fi nancial plan be used to help management provide guidance to security analysts?

16-2 THE SALES FORECAST Financial plans generally begin with a sales forecast, which starts with a review of sales during the past 5 years, shown as a graph such as the one in Figure 16-1 for Allied Foods. These numbers are based on Allied’s fi nancial statements, which were fi rst presented in Chapter 3. The data below the graph show 5 years of historical sales.

Allied had its ups and downs from 2004 to 2008. In 2006, poor weather in California’s fruit-producing regions resulted in below-average crops, which caused 2006 sales to fall below the 2005 level. Then a bumper crop in 2007 pushed sales up by 15%, an unusually high growth rate for a mature food processor. As shown in the chapter’s Excel model, the compound annual growth rate over the 4-year period was 9.88%.5 Due to planned new products, planned increased production,

513Chapter 16 Financial Planning and Forecasting

planned distribution capacity, a new advertising campaign, and other factors, management expects the growth rate to increase slightly, to 10%, in 2009. There- fore, sales should rise from $3,000 million to $3,300 million.

Of course, management likes higher sales growth, but not at any cost. For example, sales could be increased by cutting prices, spending more on advertising, granting easier credit, and the like. However, all of those actions would have a cost. Also, sales growth cannot occur without a concurrent increase in capacity, and that too is costly. So the sales growth must be balanced against the cost of achieving that growth.

If the sales forecast is off, the consequences can be serious. First, if the market expands by more than Allied expects, it will not be able to meet demand, its cus- tomers will buy from competitors, and it will lose market share. On the other hand, if its projections are overly optimistic, Allied could end up with too much plant, equipment, and inventory, leading to low turnover ratios, high costs for deprecia- tion and storage, and write-offs of spoiled inventory. This would result in low profi ts and a depressed stock price. Moreover, if Allied fi nanced its expansion with debt, high interest charges would compound the fi rm’s problems.

Finally, note that the sales forecast is the most important input in the fi rm’s forecast of fi nancial statements, including the projected EPS, which we will cover in Section 16-4. The importance of the sales forecast is highlighted when we fore- cast the fi nancial statements.

Allied Food Products: 2009 Sales Projection (Millions of Dollars)FIGURE 16-1

3,000

2,000

1,000

Net Sales ($)

2004 2005 2006 2007 2008 2009

Projected

Regression Line

Year Sales 2004 $2,058 2005 2,534 2006 2,472 2007 2,850 2008 3,000 2009 3,300 (Projected)

SEL F TEST Why is an accurate sales forecast critical for fi nancial planning?

514 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

16-3 THE AFN EQUATION We saw in Chapter 3 that in 2008, Allied had assets of $2,000 million and sales of $3,000 million. Thus, it required $2,000/$3,000 " $0.6667 of assets to generate each dollar of sales. Moreover, the company plans to increase sales by 10%, or $300 mil- lion, in 2009:

Increase in Sales ! "Sales ! 0.10($3,000 million) ! $300 million

Assuming the assets-to-sales ratio remains constant, Allied will need an additional $200 million of assets to support the $300 million increase in sales:

Required increase in assets ! 0.6667("Sales) ! 0.6667($300) ! $200 million

Note that if growth is low (say, 0%), #Sales will be zero and there will be no required increase in assets. On the other hand, if sales grow very rapidly, the requirement for additional assets will be large. Thus, the increase in assets is fun- damentally dependent on the growth rate in sales.

Naturally, if assets are to grow by $200 million, liabilities and equity must also grow by the same amount—the balance sheet must balance. But where will this capital come from? Here are a fi rm’s primary capital sources: 1. Spontaneous Increases in Accounts Payable and Accruals. Allied must make addi-

tional purchases to increase its inventories, and it must hire more workers. Its purchases will automatically lead to additional accounts payable, which amount to “loans” from its suppliers. Also, hiring more workers will automatically lead to higher accrued wages, which amount to short-term “loans” from its workers. Hence, some of the required $200 million will come spontaneously from suppliers and workers—this is called spontaneously generated funds. Also, assuming profi t margins are maintained, higher sales will mean higher profi ts and thus higher taxes and accrued taxes. So “spontaneous” increases in payables, accrued wages, and accrued taxes will take care of part of the required $200 million.

2. Addition to Retained Earnings. Assuming Allied has positive earnings and does not pay out all of those earnings as dividends, its retained earnings will grow. The addition to retained earnings depends on the fi rm’s profi t margin and its retention ratio, which is the proportion of net income that is reinvested in the fi rm. This addition to retained earnings will help fi nance growth.

3. AFN: Additional Funds Needed. It is possible that spontaneous funds and addi- tional retained earnings will offset the forecasted increase in assets. Normally, though, that situation does not occur—normally, there is a shortfall, called Addi- tional Funds Needed (AFN), which has to be made up by additional borrowing and/or the sale of new stock. Note, though, that if a company is growing very slowly and thus not increasing assets very much, its spontaneous funds plus its addition to retained earnings may be larger than the required increase in assets. In that case, the AFN is negative, indicating that a surplus of capital is forecasted.

We can combine these concepts to develop Equation 16-1, the AFN equation. AFN is the total amount of new interest-bearing debt and preferred and common stock the fi rm must issue to support its planned growth.6

Spontaneously Generated Funds Funds that arise out of normal business operations from its suppliers, employees, and the government (such as accounts payable and accrued wages and taxes) that reduce the firm’s need for external financing.

Retention Ratio The proportion of net income that is reinvested in the firm and is calculated as 1 minus the dividend payout ratio.

Additional Funds Needed (AFN) The amount of external capital (interest-bearing debt and preferred and common stock) needed to acquire the needed assets.

AFN Equation An equation that shows the relationship of external funds needed by a firm to its projected increase in assets, the spontaneous increase in liabilities, and its increase in retained earnings.

6 The term additional funds needed was developed to show how much additional capital a fi rm needs to support its planned growth. However, as we see later, a fi rm may be able to grow without any additional outside capital. In fact, the fi rm may even generate excess capital that can be used to retire debt, repurchase stock, and raise the dividend. In this case, the calculated AFN will be negative. Also, in this chapter, we do quite a few calculations and generally round when we show results. This may lead to minor “rounding diff erences,” which you should disregard.

515Chapter 16 Financial Planning and Forecasting

7 The CFO also loaded the Excel model on his laptop so he could do on-the-spot sensitivity analyses. For exam- ple, he could change the growth rate and instantly fi nd the new AFN. Similarly, he could change the dividend payout ratio, the profi t margin, and the other variables to see how those changes would aff ect the fi rm’s capital requirements. Still, the analysis in Table 16-1 provided a useful starting point.

Additional

funds needed, or AFN

! Projected

increase in assets

# Spontaneous

increase in liabilites

# Increase in

retained earnings

16-1

! (A0*/S0)"S # (L0*/S0)"S # MS1(1 – Payout)

Allied Foods’ CFO used Equation 16-1 in the following manner. Every fall the company’s Executive Committee, which includes the CEO, the CFO, and other top executives, meets to consider plans for the coming year. The meeting this year is especially important for two reasons: (1) The national credit crunch is constraining the fi rm’s ability to raise capital, so the amounts needed and available must be determined. (2) Corporate raiders and private equity fi rms have targeted a num- ber of food processors; and when they take over, heads roll in the acquired fi rm. Allied’s executives are aware of both factors.

Allied’s CFO plans to proceed in two steps. First, he will use the AFN equation to give the others an idea of how much new capital the fi rm will need to support the targeted 10% growth rate, assuming the various operating ratios remain constant. Second, he will present the results of a full-scale fi nancial planning model. The model will show forecasted fi nancial statements in addition to a set of forecasted ratios like those discussed in Chapter 4, along with an estimate of the 2009 EPS. The CFO hopes the EPS forecast will help the company avoid the embarrassment suf- fered by GE’s Jeff Immelt, which was discussed in this chapter’s opening vignette.

The CFO brought copies of Table 16-1, which is based on Equation 16-1, and data from the fi nancial statements presented in Chapter 3 to the Executive Com- mittee.7 Part I of the table picks up selected data from the 2008 balance sheet and income statement. Part II uses the Part I data to calculate inputs for Equation 16-1. Note that all the calculations in Part II assume that the company’s operating ratios in 2009 continue at 2008 levels. Part III uses the items calculated in Part II to calcu- late the AFN. To increase sales by $300 million, Allied must increase assets by $200 million. The asset increase will be supported by $20 million from spontaneous increases in payables and accruals, and another $66 million will come from retained earnings. In total, $114 million of new outside funds will be needed; and since Allied does not use preferred stock, the amount must come from interest-bearing debt in addition to new common stock.

As noted, the AFN equation assumes that the 2009 ratios will remain constant at the 2008 levels. If economic conditions or managerial decisions cause the ratios to change, the forecasted AFN will change. Part IV of the table shows how some specifi c input changes will change the forecasted AFN. For example, if the target growth rate was increased from 10% to 15% with other things held constant, the AFN would increase from $114 million to $201 million. On the other hand, if the target growth rate was lowered to 5%, the AFN would be only $27 million. Also, as shown in Part V, if the company grew at a rate of 3.45% while other things were held constant, AFN would be zero. Thus 3.45% is called Allied’s sustainable growth rate.

Finally, note that if the growth rate slowed and other inputs were changed in the manner specifi ed in Part IV of the table, Allied would end up with a large negative AFN, indicating that retained earnings and spontaneous capital were far more than suffi cient to fi nance the now smaller amount of additional assets needed.

Sustainable Growth Rate The maximum achievable growth rate without the firm having to raise external funds. In other words, it is the growth rate at which the firm’s AFN equals zero.

516 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

A B C D E F G H JI

Part I. 2008 Data from Chapter 3, Tables 3-1 and 3-2 A0* = Assets at 12/31/08; all assets were needed for 2008 sales S0 = 2008 Sales 2008 Net Income 2008 Dividends L0* = 2008 payables + accruals, which increase spontaneously with sales Part II. Data Used in the AFN Equation: 2008 Ratios Held Constant

AFN = Additional Funds Needed to buy assets needed to support growth. AFN is in addition to funds raised internally (i.e., AFN represents required external funds). g = Target growth rate in sales A0*/S0 = Assets required per $1 of sales = $2,000/$3,000. Shows the required new assets for the coming year when multiplied by the increase in sales. Also called the capital intensity ratio. The higher this ratio, the more new assets the firm will need to support a given amount of growth. S1 = 2009 Sales = (1+g)(S0) = (1.1)($3,000) ∆S = Growth in sales = S1 - S0 = $3,300 - $3,000. It can also be found as ∆S = g(S0). L0*/S0 = Spontaneously generated funds per dollar of new sales. When multiplied by ∆S, we find the new payables and accruals that are available to support growth. M = Profit margin on sales = 2008 net income/S0 = $117.5/$3,000. Multiply by S1 (not S0) to find the net income available in 2009 for dividends or growth. RR = Retention Rate = (1 - Dividend Payout Ratio) = (1 - Dividends/Net Income) = (1 - $57.5/$117.50). The higher the retention rate, the greater the proportion of net income that is retained to support growth. Part III. The AFN Equation AFN = Required increase in – Spontaneous – Funds obtained as new assets increase in Payables Retained Earnings. and Accruals Based on 2009 Sales = (A0*/S0)∆S - (L0*/S0)∆S - MS1(RR) = 0.6667($300) - 0.0667($300) - 0.0392($3,300)(0.5106) = $200 - $20 - $66 AFN = $114 million

Part IV. Sensitivity Analysis: AFN with Changed Input Values

$2,000 $3,000 $117.5

$57.5 $200

Base Case: 2008 Data

10.00%

0.6667 $3,300

$300

0.0667

0.0392

0.5106

15%, up from 10%. With faster growth, the firm needs more new assets. 5%, down from 10%. With slower growth, the firm needs less new assets. At g < 3.45%, new retained earnings plus spontaneous funds exceed required new assets. 0.5000, down from 0.6667. This factor is called the capital intensity ratio. We lowered it in this example; and with a lower value, fewer assets are required for any given level of sales. If Allied's management can increase the total assets turnover ratio, the A0*/S0 ratio will decline, which will reduce AFN. 0.0800, up from 0.0667. Allied spontaneously generates funds from accounts payable and accruals; and the larger the L0*/S0 ratio, the smaller the need for external financing. With a higher value, more spontaneous funds are available; so the AFN declines.

AFN (Old = $114)

Change: New New - Old

Higher Growth:

Lower Growth:

A0*/S0:

L0*/S0:

$201

$27

$64

$110

$87

–$87

–$50

–$4

Additional Funds Needed (AFN) Model ($ in Millions)T a b l e 1 6 - 1

(Continued)

517Chapter 16 Financial Planning and Forecasting

16-3a Excess Capacity Adjustments The AFN equation includes the term A0*/S0, which is called the capital intensity ratio. For Allied, this ratio is calculated as $2,000/$3,000 " 0.6667. When multiplied by #S " $300 million, this ratio indicated that Allied must increase its assets by $200 million. However, the CFO thought that in 2008, Allied had more fi xed assets than it really needed; he wanted to demonstrate to the Executive Committee how excess capacity adjustments might affect the fi rm’s need for external funds. He noted that Allied had $1,000 million of current assets and $1,000 million of fi xed assets; so he broke A0*/S0 into two parts, one for fi xed assets and one for current assets:

Current assets: A0*C/S0 " $1,000/$3,000 " 0.333 " 33.3% Fixed assets: A0*F/S0 " $1,000/$3,000 " 0.333 " 33.3%

Now suppose that the current assets were used at full capacity but that fi xed assets had been used at only 96% of capacity in 2008. Therefore, if fi xed assets had been used to full capacity, sales could have reached $3,125 million before any ad- ditions to fi xed assets were required versus the actual $3,000 million of sales. In this example, the calculated $3,125 million sales is Allied’s full capacity sales:

Full capacity sales ! Actual sales ____________________

Percentage of capacity

at which fi xed assets were operated

! $3,000 million/0.96 ! $3,125 million

This indicates that Allied’s Target fi xed assets/Sales ratio should be 32% rather than the indicated 33.3% calculated previously:

Target fi xed assets/Sales ! Actual fi xed assets ________________ Full capacity sales

! $1,000/$3,125 ! 0.32 ! 32%

Under these conditions, sales could increase to $3,125 million with no increase in fi xed assets and a sales increase to $3,300 million would require only $1,056 mil- lion of fi xed assets, or an additional $56 million of fi xed assets:

Required level of fi xed assets

! (Target fi xed assets/Sales)(Projected sales)

! 0.32($3,300) ! $1,056 million

Capital Intensity Ratio The ratio of assets required per dollar of sales (A0*/S0 ).

Excess Capacity Adjustments Changes made to the existing asset forecast because the firm is not operating at full capacity.

0.1000, up from 0.0392. If the profit margin increases, more earnings will be available to support growth and thus the smaller the AFN. With a higher profit margin, more net income is earned; so the AFN declines. 20%, down from 48.94%. If Allied lowers the dividend payout ratio, more of its earnings will be retained and thus the smaller the AFN. Here we lower the payout, so the AFN declines.

Change all variables simultaneously to g = 5% and the other values as indicated above. The result is a large but negative AFN, indicating that the firm is generating a substantial amount of capital—more than sufficient to meet its forecasted asset requirements.

Part V. Sustainable Growth Rate. Maximum achievable growth rate without raising external funds (i.e., g that forces AFN = 0, holding other variables at base-case levels). Use g = 3.45%, and you will see that AFN = 0.

Payout:

$12

$77

–$189

–$102

–$303

3.45%

–$37

Additional Funds Needed (AFN) Model ($ in Millions)T a b l e 1 6 - 1

518 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Earlier estimate of AFN ! 1.1($1,000) ! $1,100 million Diff erence ! #$44 million

Thus, the existence of excess capacity would lower Allied’s required AFN from $114 million to $114 million $ $44 million " $70 million.

A similar situation could occur with respect to inventories, cash, or any other asset. Moreover, the L0*/S0 ratio could be increased if the fi rm negotiated longer credit terms for its purchases. Similarly, it might be possible for Allied to improve its profi t margin or to lower its dividend payout ratio. Because so many conditions can change, it is useful to go beyond the AFN equation analysis and construct Allied’s forecasted fi nancial statements, the topic of the next section. Also, we want to know how good or bad the fi rm’s fi nancial ratios will be and what the impact will be on its EPS. The AFN tells us nothing about those things, but the forecasted fi nancial statements do.

Forecasted Financial Statements Financial statements that project the company’s financial position and performance over a period of years.

8 This section is relatively straightforward, but it does involve a number of steps. The table can be developed with a calculator, but it’s far easier to do using Excel. We recommend that everyone read the section and look at Table 16-2 while doing so. Finance majors should read the section especially carefully. It also would help if they accessed the chapter model and worked through it.

SEL F TEST If the key ratios are expected to remain constant, the AFN equation can be

used to forecast the need for external funds. Write out the equation and explain its logic.

How would an increase in each of the following factors aff ect the AFN? (1) Payout ratio (2) Capital intensity ratio, A0*/S0 (3) Profi t margin (4) Days sales outstanding, DSO (5) Sales growth rate

Is it possible for the AFN to be negative? If so, what would that indicate?

If excess capacity exists, how would that aff ect the calculated AFN?

16-4 FORECASTED FINANCIAL STATEMENTS8 The AFN equation provides useful insights into the forecasting process—if you understand the AFN, you will fi nd it easier to understand forecasted fi nancial statements. Therefore, Allied’s CFO used the AFN calculations in Table 16-1 as a warm-up for his presentation of the forecasted 2009 fi nancial statements. We describe how he developed the forecast presented in Table 16-2 in this section. Following is a brief discussion of the table.

16-4a Part I. Inputs Rows 2 through 9 show the basic inputs, or assumptions, used in the forecast. The CFO had met previously with the CEO and other top executives. They had reviewed the ratio analysis developed in Chapter 4 and concluded that improve- ments must be made in 2009. Otherwise, a private equity buyer or hedge fund might decide to take over the fi rm; and if that occurred, the executives would probably lose their jobs.

519Chapter 16 Financial Planning and Forecasting

Adjustable Inputs The inputs in Column C show key 2008 ratios that management controls and that may be adjusted in the future. Column D gives the values the CFO used for the initial 2009 forecast, and Column E gives industry average numbers. The fi rst input shown is the growth rate. This number can be changed; but throughout Table 16-2, a 10% growth rate is assumed. Next, we have the Operating costs/Sales ratio. Allied’s ratio in 2008 was 90.54%, which is higher than the industry’s 87% ratio. A reduction toward the industry average would lead to a substantial improvement in net income, and the CFO used as a tentative target for 2009 a ratio of 89.5%. Next, we saw in Chapter 4 that Allied’s receivables and inventories were too high relative to its sales. If those accounts can be reduced, the result will be lower bad debts and storage costs and thus increased profi ts. Also, the excess capital invested in receivables and inven- tories can be released and used to pay off debt and/or to repurchase common stock,

1 2 3 4 5 6 7 8 9

11 12 13 14 15 16 17 18 19

21 22 23 24 25 26

27 28 29 30 31 32 33 34 35 36

A B C D E F G

Part I. Inputs

Part II. Income Statements Sales Operating costs (includes depreciation) Earnings before interest and taxes (EBIT) Less interest expense Earnings before taxes (EBT) Taxes Net income (NI) Dividends Addition to retained earnings

Part III. Balance Sheets

Assets Cash Accounts receivable Inventories Fixed assets (grow with sales) Total assets

Liabilities and Equity Payables + accruals (both grow with sales) Short-term bank loans Total current liabilities Long-term bonds Total debt Common stock Retained earnings Total common equity Total liabilities and equity

Growth rate, g Operating costs/Sales

Receivables/Sales Inventories/Sales

Debt ratio Payout ratio

2008 NA

90.54% 12.50% 20.50% 53.00% 48.94%

Industry NA 87.00%

9.86% 9.17%

40.00% 45.00%

Fixed Inputs Tax rate (T)

Interest rate Shares out'ing Price per share

FA/Sales

2008 $3,000.0

2,716.2 $ 283.8

88.0 $ 195.8

78.3 $ 117.5 $ 57.5 $ 60.0

Change (1 + g) 0.895

See notes

EBT(T)

NI(Payout)

40% 10.00%

50 $23.06

33.33%

2009 $3,300.0

2,953.5 $ 346.5

80.9 $ 265.6

106.2 $ 159.3 $ 74.9 $ 84.4

2008

$ 10.0 375.0 615.0

1,000.0 $2,000.0

$ 200.0 110.0

$ 310.0 750.0

$1,060.0 130.0 810.0

$ 940.0 $2,000.0

Change

(1 + g) 0.1100 0.1900 (1 + g)

(1 + g) See notes

See notes

See notes $84.4

2009

$ 11.0 363.0 627.0

1,100.0 $2,101.0

$ 220.0 103.5

$ 323.5 706.0

$1,029.5 177.1 894.4

$1,071.5 $2,101.0

2009 10.00%

89.50% 11.00% 19.00% 49.00% 47.00%

Adjustable Inputs

Forecasted Financial Statements (Total Dollars and Shares in Millions)T a b l e 1 6 - 2

(Continued)

520 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

both of which would improve the fi rm’s ROE and EPS. Again, the CFO set initial tar- gets between Allied’s 2008 ratios and the industry averages.

In addition, Allied’s debt ratio, at 53%, greatly exceeds the 40% industry aver- age; and the fi rm’s bankers have complained and indicated that the cost of debt would decline if this ratio were lowered. Security analysts also have stated that Allied’s stock is riskier than it would be if it had less debt, and that adversely affects its price/earnings (P/E) ratio.

Similarly, Allied’s dividend payout ratio is above average, and the CEO and several board members think that it should be lowered. This would provide more funds to support growth, which stockholders may want.

38 39 40 41 42 43 44 45 46 47 48 49 50

52 53 54

56 57 58 59 60 51 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Part IV. Ratios and EPS Operating costs/Sales Receivables/Sales Inventory/Sales Debt ratio Payout ratio Inventory turnover Days sales outstanding (DSO) Total assets turnover Assets/Equity (equity multiplier) Times interest earned (TIE) Profit margin Return on assets (ROA) Return on equity (ROE)

DuPont Calculations

Actual for 2008 Forecasted for 2009 Industry average data

Earnings per share (EPS)

Part V. Notes on Calculations Assets in 2009 will change to this amount, from the balance sheet Target debt ratio Resulting total debt: (Target ratio)( 2009 Assets) Less: Payables and accruals Bank loans and bonds (= Interest-bearing debt) Allocated to bank loans, based on 2008 proportions Allocated to bonds, based on 2008 proportions Interest expense: (Interest rate)(2009 Bank loans plus bonds) Target equity ratio = 1 – Target debt ratio Required total equity: (2009 Assets)(Target equity ratio) Retained earnings, from 2009 balance sheet Required common stock = Required equity – Retained earnings Old shares outstanding (millions) Increase in common stock = 2009 Stock – 2008 Stock Initial price per share from input section Change in shares = Change in stock/Initial price per share New shares outstanding = Old shares + ∆ Shares Old EPS = 2008 Net income/Old shares outstanding New EPS = 2009 Net income/New shares outstanding

2008 90.54%

12.50% 20.50% 53.00% 48.94%

4.88 45.63

1.50 2.13 3.23

3.92% 5.88%

12.50%

× days × × ×

2009E 89.50% 11.00% 19.00% 49.00% 47.00%

5.26 40.15

1.57 1.96 4.28

4.83% 7.58%

14.87%

Industry 87.00%

9.86% 9.17%

40.00% 45.00%

10.90 36.00

1.80 1.67 6.00

5.00% 9.00%

15.00%

Equity Multiplier

(A/E)

Total Assests Turnover

(S/A)

Profit Margin N/S

= ROE

3.92% 4.83% 5.00%

1.50 1.57 1.80

2.13 1.96 1.67

12.5% 14.9% 15.0%

$2,101.0 49.00%

$1,029.5 -$ 220.0 $ 809.5 $ 103.5 $ 706.0 $ 80.9

51% $1,071.5 $ 894.4 $ 177.1

50 $ 47.1 $ 23.06

2.04 52.04

$ 2.35 $ 3.06

12.79% 87.21%

$2.35 $3.06

Forecasted Financial Statements (Total Dollars and Shares in Millions)T a b l e 1 6 - 2

521Chapter 16 Financial Planning and Forecasting

Fixed Inputs. Some other inputs required for the forecast are not under man- agement’s direct control or are not expected to change. These inputs are shown in Column G—the tax rate; the interest rate; the shares initially outstanding; the ini- tial stock price; and the Fixed assets/Sales ratio, which the CFO concluded was fi ne. The number of shares outstanding will change in 2009 depending on how much new equity the fi rm must raise; but in this analysis, the other variables are held constant. Of course, management hopes the stock price will increase as a result of the fi rm’s actions and improved fi nancial position, but the CFO wisely decided not to make a prediction at this point.

16-4b Part II. Forecasted Income Statement The forecasted 2009 income statement starts with the 2008 income statement, but forecasts that 2009 sales grow by 10%. Next, the assumed new operating cost ratio is multiplied by the new sales level to calculate the forecasted 2009 operating costs, which are subtracted from sales to obtain the forecasted EBIT. Interest expenses are calculated in Part V, the Notes section, after the interest- bearing debt has been determined in the balance sheet developed in Part III. Once the interest expense has been calculated and entered in the income state- ment, the forecasted net income is determined. Dividends for 2009 are found by multiplying the target payout ratio by the 2009 forecasted net income. Divi- dends are then subtracted from net income to fi nd the 2009 addition to retained earnings.

16-4c Part III. Forecasted Balance Sheet The forecasted 2009 balance sheet is developed from the 2008 statement. Cash and fi xed assets are multiplied by 1.1 because they increase at the same rate as sales growth. Accounts receivable are found by multiplying the assumed 11% Receiv- ables/Sales ratio (given in Part I) by sales, and inventories are found by multiply- ing the 19% Inventories/Sales ratio (also given in Part I) by sales. We then sum the four asset accounts to fi nd forecasted 2009 total assets.

On the liabilities side, because payables and accruals grow at the same rate as sales, we multiply the 2008 values by 1.10. Also, 2009 retained earnings are found by adding the 2009 addition to retained earnings from the income statement to 2008 retained earnings. To complete the balance sheet, we need to fi nd the amounts for short-term bank debt, bonds, and new common stock. To obtain those values, we skip down to Part V, the Notes section. Here we multiply the target debt ratio times the just calculated total assets to obtain the forecasted total debt amount. We then subtract payables and accruals from this amount to fi nd the forecast for interest-bearing debt (which includes bank loans and bonds). Next, we multiply the interest-bearing debt by the 2008 proportions of bank debt and long-term bonds to fi nd the forecasted amounts for those two items. Similarly, we fi nd the re- quired amount of 2009 total equity by multiplying (1 – target debt ratio) times the forecasted assets. We then subtract forecasted retained earnings to fi nd 2009 com- mon stock, which we insert in the balance sheet. When we sum the liability and equity accounts, the total matches the forecasted assets, which it must.

16-4d Part IV. Ratios and EPS With the 2009 income statement and balance sheet forecasted, we can calculate the forecasted 2009 ratios and EPS; those calculations are done in Part IV. The fi rst fi ve ratios shown are the same ones given in the Part I Inputs section. We calculated them from the forecasted statement as a check on the accuracy of the model.

522 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

SEL F TEST What advantages does the forecasted fi nancial statement method have over

the AFN equation for forecasting fi nancial requirements?

Why should a marketing or management major be interested in fi nancial forecasting? Would fi nancial forecasting be relevant for such people when they graduate and enter the work force? Explain.

An interesting aspect of Part IV is the DuPont calculations. In 2008, Allied’s profi t margin and turnover were quite low, but its equity multiplier was relatively high. The result was a low but risky 12.5% ROE. The forecast for 2009 shows im- provements in the profi t margin and turnover, which boost ROE, and a lowering of the equity multiplier, which holds down the ROE but indicates less fi nancial risk. The result is a much better and less risky 14.9% ROE, which is very close to the industry average.

The fi nal item in Part IV is the forecasted EPS, which jumps from $2.35 in 2008 to $3.06 in 2009. The CFO calculated the following data for use in his talk but de- cided not to include it in the table:

P/E ratio 9.8% versus 11.3% for the industry Current stock price $23.06

Allied’s estimated stock price is then calculated by multiplying its forecasted EPS by the industry average P/E ratio:

$3.06 (11.3) " $34.58

Percentage gain: $34.58/$23.06 $ 1 " 49.96%, or approximately 50%

16-4e Using the Forecast to Improve Operations Allied’s CFO generated Table 16-2 with a straightforward Excel model. The table could have been worked with a calculator, but it was easier to do the work using Excel. Moreover and very importantly, once he set up the model, he could make all kinds of changes to see the forecasted results under alternative scenarios. It’s trivi- ally easy to change the growth rate and the fi ve key input variables in Part I. It would be easy to change the fi nancing assumptions, perhaps using more bank debt and fewer bonds. It also would be easy to show the results of fi nancing only with debt or only with stock. With any such input changes, the model instantly provides modifi ed results. Indeed, the CFO had the model on his laptop, took it to the meeting, and answered a number of “what if” questions.

Of course, it’s much easier to change inputs in a spreadsheet model than it is to change actual operations so that the forecasted results are generated. How- ever, as we said earlier in the chapter, if you don’t know where you’re going, it’s hard to get there. Allied’s ratio analysis in Chapter 4 pointed out the fi rm’s weak- nesses, and the model shown in Table 16-2 demonstrates how improvements in the driver variables will affect the fi rm’s ROE, its EPS, and (of course) its stock price. Allied’s managers’ compensation is partly based on the fi rm’s fi nancial re- sults, including its ROE and stock price, so they are keenly interested in the model and its results. The threat of fi ring is also a strong motivator, and getting poor results while operating good assets makes the fi ring of management a real possibility.

523Chapter 16 Financial Planning and Forecasting

16-5 USING REGRESSION TO IMPROVE FORECASTS9 In fi nancial statement forecasts, it is often appropriate to assume that most of the assets increase at the same rate as sales. However, that is often not the case. We noted in our discussion of the AFN equation that excess capacity might exist, in which case assets would increase less rapidly than sales. Similarly, economies of scale might exist, and this too could enable sales to increase less rapidly than assets. We can use regression techniques to investigate the existence of such situations and thus improve the fi nancial forecasts.

To illustrate regression analysis, consider Figure 16-2, which shows Allied’s sales, inventories, and receivables during the last 5 years and scatter diagrams of inventories and receivables versus sales. Estimated regression equations, found with a fi nancial calculator or spreadsheet, can be developed. For example, here is the estimated relationship between inventories and sales (in millions of dollars):

Inventories ! #$35.7 $ 0.186(Sales)

We can use the regression equation to estimate the 2009 inventory level. Since 2009 sales are projected at $3,300 million, according to the regression, 2009 inventories should be $578 million:

Inventories ! #$35.7 $ 0.186($3,300) ! $578 million

Regression Analysis A statistical technique that fits a line to observed data points so that the resulting equation can be used to forecast other data points.

9 This section is relatively technical, but it can be omitted without loss of continuity.

Allied Food Products: Regression Models (Millions of Dollars)FIGURE 16-2

400

500

600

700

300

Inventories ($)

0 2,000 2,250 2,750 3,0002,500 Sales ($)

Inventories = –35.7 + 0.186 (Sales) R2 = 0.51

R2 = 0.81 250

300

350

400

200

Receivables ($)

0 2,000 2,250 2,750 3,0002,500 Sales ($)

Receivables = 62 + 0.097 (Sales)

Year Sales Inventories Accounts Receivable 2004 $2,058 $387 $268 2005 2,534 398 297 2006 2,472 409 304 2007 2,850 415 315 2008 3,000 615 375 2009 3,300 (Projected)

524 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

This is $49 million less than the $627 million forecast used in the projected fi nancial statements. Note also that although our graph shows a linear relationship, we could have used a nonlinear regression model had we believed that such a relationship was more appropriate. Also, we could have used a multiple regression equation, which would have brought other factors that affect inventories into the picture.

SEL F TEST Examine the following statement: Using regression to predict items such

as inventories is better than basing such predictions on last year’s Inventory/Sales ratio because regression helps smooth out the effects of random fluctuations. Do you agree or disagree? Explain.

16-6 ANALYZING THE EFFECTS OF CHANGING RATIOS When we forecasted the 2009 fi nancial statements, we assumed that the 2009 oper- ating ratios would move closer to the industry averages and we based asset levels on those assumptions. However, it is often preferable to base forecasted assets on a regression analysis. Also, it is often useful to examine specifi c asset ratios to get a better idea of the effects on the fi rm’s fi nancial position given various changes to these ratios. In this section, we explore the effects of modifying receivable and inventory ratios.

16-6a Modifying Accounts Receivable In Table 16-2, Allied’s DSO is projected to be 40.15 days versus an industry average 36 days. Its sales per day are projected to be $3,300/365 = $9.04 million. If Allied could operate at the industry-average DSO, its receivables would be reduced by

Receivables at 40.15 days ! 40.15($9.04) ! $363.0 million Receivables at 36.00 days ! 36.00($9.04) ! $325.5 million Receivables reduction ! Additional 2009 FCF ! $ 37.5 million

Thus, receivables could be reduced by another $37.5 million if Allied’s credit man- ager could achieve the industry-average DSO. That would mean $37.5 million of additional free cash fl ow to the fi rm in 2009, plus additional FCF going forward as Allied grows. The CFO could use this example in a discussion with Allied’s credit manager.

16-6b Modifying Inventories Inventories can be analyzed in a similar manner. First, note that Allied’s forecasted inventory turnover is 5.26 times versus 10.9 times for the industry. Moreover, in Table 16-2 Allied’s forecasted 2009 inventory is $627 million versus $3,300 million of sales. Given this information, we can fi nd Allied’s inventories if Allied is able to achieve the industry-average inventory turnover:

Currently forecasted inventory turnover ! $3,300/5.26 ! $627 million Inventory at industry-average turnover ! $3,300/10.9 ! $303 million Inventory reduction ! Additional 2009 FCF ! $324 million

525Chapter 16 Financial Planning and Forecasting

Thus, inventories could be reduced by another $324 million if Allied’s inventory turnover could be increased to the industry average. That would mean another $324 million of free cash fl ow in 2009, plus further additions going forward. Again, the CFO could use this example in a discussion with the inventory manager.

16-6c Other “Special Studies” Once a fi rm has developed a model to forecast its fi nancial statements, it can do all types of special “what if” studies. For example, the model that Allied’s CFO used to make Table 16-2 (which is part of the chapter Excel model) could be used to fi nd the results shown in the two preceding sections for receivables and inventories. The model also could be used to estimate the effects of changing the dividend pol- icy on the statements and on the required AFN. Indeed, the AFN equation could be modifi ed to obtain a “quick and dirty” estimate of the effects of the dividend payout on the AFN. As we saw earlier in Section 16-3 in the discussion of the AFN equation, Allied has a payout ratio of 0.4894; and when that number was used in the equation, an AFN of $114 million resulted:

AFN ! 0.6667("S) # 0.06667("S) # 0.0392(S1)(0.5106) ! 0.6667($300) # 0.06667($300) # 0.0392($3,300)(0.5106)

! $200 # $20 # $66 ! $114 million

Now suppose Allied anticipated problems raising $114 million to carry out its business plan. The CFO might then suggest to the directors a reduction of the pay- out ratio to 20%. That would result in an AFN of about $77 million (shown in Part IV of Table 16-1), which is about $37 million less than the original AFN calculated. Of course, as we saw in the dividend chapter, lowering the dividend might create problems of its own; but at times, such an action may be necessary to maximize a fi rm’s intrinsic value and long-run stock price.

This chapter described techniques for forecasting fi nancial statements, which is a crucial part of the fi nancial planning process. Both investors and corporations regu- larly use forecasting techniques to help value a company’s stock; to estimate the benefi ts of potential projects; and to estimate how changes in capital structure, divi- dend policy, and working capital policy infl uence shareholder value.

The type of forecasting described in this chapter is important for several reasons. First, if the projected operating results are unsatisfactory, management can “go back to the drawing board,” reformulate its plans, and develop more reasonable targets for the coming year. Second, the funds required to meet the sales forecast may not be obtainable. If so, it is obviously better to know this in advance and to scale back projected operations than to suddenly run out of cash and have operations grind to an abrupt halt. And third, fi rms often give guidance to analysts regarding likely fu- ture earnings; and as GE’s Jeff Immelt learned, it is benefi cial to be able to provide reasonably accurate forecasts.

T YING I T ALL TO GETHER

526 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

KEY TERMS Define each of the following terms: a. Mission statement; corporate scope; statement of corporate objectives; corporate

strategies b. Operating plan; financial plan c. Spontaneously generated funds d. Additional Funds Needed (AFN); AFN equation e. Capital intensity ratio; sustainable growth rate f. Forecasted financial statements; retention ratio g. Excess capacity adjustments h. Regression analysis

SUSTAINABLE GROWTH RATE Weatherford Industries Inc. has the following ratios: A0*/S0 " 1.6; L0*/S0 " 0.4; profit margin " 0.10; and retention ratio " 0.55, or 55%. Sales last year were $100 million. Assuming that these ratios will remain constant, use the AFN equation to determine the maximum growth rate (the sustainable growth rate) Weatherford can achieve without having to employ nonspontaneous external funds.

ADDITIONAL FUNDS NEEDED Suppose Weatherford’s financial consultants report (1) that the inventory turnover ratio is Sales/Inventory " 3 times versus an industry average of 4 times and (2) that Weatherford can reduce inventories and thus raise its turnover to 4 without affecting sales, the profit margin, or the other asset turnover ratios. Under those conditions, use the AFN equation to determine the amount of additional funds Weatherford will require next year if sales grow by 20%.

What are the key factors on which external financing depends, as indicated in the AFN equation?

Assume that an average firm in the office supply business has a 6% profit margin, a 40% debt/assets ratio, a total assets turnover of 2 times, and a dividend payout ratio of 40%. Is it true that if such a firm is to have any sales growth (g & 0), it will be forced to borrow or to sell common stock (that is, it will need some nonspontaneous external capital even if g is very small)?

Would you agree that computerized corporate planning models were a fad during the 1990s but that because of a need for flexibility in corporate planning, they are no longer used by most firms?

Certain liability and net worth items generally increase spontaneously with increases in sales. Put a check mark (✓) next to those items that typically increase spontaneously.

Accounts payable Notes payable to banks Accrued wages Accrued taxes Mortgage bonds Common stock Retained earnings

Suppose a firm makes the following policy changes. If the change means that external nonspontaneous financial requirements (AFN) will increase, indicate this with a (!),

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

ST-3ST-3

QUESTIONSQUESTIONS

16-116-1

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527Chapter 16 Financial Planning and Forecasting

indicate a decrease with a ($), and indicate an indeterminate or negligible effect with a (0). Think in terms of the immediate short-run effect on funds requirements. a. The dividend payout ratio is increased. b. Rather than produce computers in advance, a computer company

decides to produce them only after an order has been received. c. The firm decides to pay all suppliers on delivery, rather than

after a 30-day delay, to take advantage of discounts for rapid payment.

d. The firm begins to sell on credit. (Previously, all sales had been on a cash basis.)

e. The firm’s profit margin is eroded by increased competition; sales are steady.

f. Advertising expenditures are stepped up. g. A decision is made to substitute long-term mortgage bonds for

short-term bank loans. h. The firm begins to pay employees on a weekly basis. (Previously

it had paid employees at the end of each month.)

AFN EQUATION Carter Corporation’s sales are expected to increase from $5 million in 2008 to $6 million in 2009, or by 20%. Its assets totaled $3 million at the end of 2008. Carter is at full capacity, so its assets must grow in proportion to projected sales. At the end of 2008, current liabilities are $1 million, consisting of $250,000 of accounts payable, $500,000 of notes payable, and $250,000 of accrued liabilities. Its profit margin is forecasted to be 5%, and the forecasted retention ratio is 30%. Use the AFN equation to forecast the additional funds Carter will need for the coming year.

AFN EQUATION Refer to Problem 16-1. What additional funds would be needed if the company’s year-end 2008 assets had been $4 million? Assume that all other numbers are the same. Why is this AFN different from the one you found in Problem 16-1? Is the company’s “capital intensity” the same or different? Explain.

AFN EQUATION Refer to Problem 16-1 and assume that the company had $3 million in assets at the end of 2008. However, now assume that the company pays no dividends. Under these assumptions, what additional funds would be needed for the coming year? Why is this AFN different from the one you found in Problem 16-1?

PRO FORMA INCOME STATEMENT Austin Grocers recently reported the following 2008 income statement (in millions of dollars):

Sales $700 Operating costs including depreciation 500 EBIT $200 Interest 40 EBT $160 Taxes (40%) 64 Net income $ 96 Dividends $ 32 Addition to retained earnings $ 64

This year the company is forecasting a 25% increase in sales; and it expects that its year- end operating costs, including depreciation, will equal 70% of sales. Austin’s tax rate, interest expense, and dividend payout ratio are all expected to remain constant. a. What is Austin’s projected 2009 net income? b. What is the expected growth rate in Austin’s dividends?

PROBLEMS PROBLEMS

16-116-1Easy Problems 1–6 Easy Problems 1–6

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528 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

EXCESS CAPACITY Walter Industries has $5 billion in sales and $1.7 billion in fixed assets. Currently, the company’s fixed assets are operating at 90% of capacity. a. What level of sales could Walter Industries have obtained if it had been operating at

full capacity? b. What is Walter’s Target fixed assets/Sales ratio? c. If Walter’s sales increase 12%, how large of an increase in fixed assets will the

company need to meet its Target fixed assets/Sales ratio?

REGRESSION AND INVENTORIES Jasper Furnishings has $300 million in sales. The company expects that its sales will increase 12% this year. Jasper’s CFO uses a simple linear regression to forecast the company’s inventory level for a given level of projected sales. On the basis of recent history, the estimated relationship between inventories and sales (in millions of dollars) is as follows:

Inventories ! $25 $ 0.125(Sales)

Given the estimated sales forecast and the estimated relationship between inventories and sales, what are your forecasts of the company’s year-end inventory level and its inventory turnover ratio?

PRO FORMA INCOME STATEMENT At the end of last year, Roberts Inc. reported the following income statement (in millions of dollars):

Sales $3,000 Operating costs excluding depreciation 2,450 EBITDA $ 550 Depreciation 250 EBIT $ 300 Interest 125 EBT $ 175 Taxes (40%) 70 Net income $ 105

Looking ahead to the following year, the company’s CFO has assembled this information: • Year-end sales are expected to be 10% higher than the $3 billion in sales generated last

year. • Year-end operating costs, excluding depreciation, are expected to equal 80% of year-

end sales. • Depreciation is expected to increase at the same rate as sales. • Interest costs are expected to remain unchanged. • The tax rate is expected to remain at 40%.

On the basis of that information, what will be the forecast for Roberts’ year-end net income?

LONG-TERM FINANCING NEEDED At year-end 2008, total assets for Ambrose Inc. were $1.2 million and accounts payable were $375,000. Sales, which in 2008 were $2.5 million, are expected to increase by 25% in 2009. Total assets and accounts payable are proportional to sales, and that relationship will be maintained; that is, they will grow at the same rate as sales. Ambrose typically uses no current liabilities other than accounts payable. Common stock amounted to $425,000 in 2008, and retained earnings were $295,000. Ambrose plans to sell new common stock in the amount of $75,000. The firm’s profit margin on sales is 6%; 60% of earnings will be retained. a. What was Ambrose’s total debt in 2008? b. How much new long-term debt financing will be needed in 2009? (Hint: AFN $ New

stock " New long-term debt.)

SALES INCREASE Pierce Furnishings generated $2 million in sales during 2008, and its year-end total assets were $1.5 million. Also, at year-end 2008, current liabilities were $500,000, consisting of $200,000 of notes payable, $200,000 of accounts payable, and $100,000 of accrued liabilities. Looking ahead to 2009, the company estimates that its assets must increase by $0.75 for every $1.00 increase in sales. Pierce’s profit margin is 5%, and its retention ratio is 40%. How large a sales increase can the company achieve without having to raise funds externally?

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16-716-7Intermediate Problems 7–12 Intermediate Problems 7–12

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529Chapter 16 Financial Planning and Forecasting

REGRESSION AND RECEIVABLES Edwards Industries has $320 million in sales. The company expects that its sales will increase 12% this year. Edwards’ CFO uses a simple linear regression to forecast the company’s receivables level for a given level of projected sales. On the basis of recent history, the estimated relationship between receivables and sales (in millions of dollars) is as follows:

Receivables ! $9.25 $ 0.07(Sales)

Given the estimated sales forecast and the estimated relationship between receivables and sales, what are your forecasts of the company’s year-end balance for receivables and its year-end days sales outstanding (DSO) ratio? Assume that DSO is calculated on the basis of a 365-day year.

REGRESSION AND INVENTORIES Charlie’s Cycles Inc. has $110 million in sales. The company expects that its sales will increase 5% this year. Charlie’s CFO uses a simple linear regression to forecast the company’s inventory level for a given level of projected sales. On the basis of recent history, the estimated relationship between inventories and sales (in millions of dollars) is as follows:

Inventories ! $9 $ 0.0875(Sales)

Given the estimated sales forecast and the estimated relationship between inventories and sales, what are your forecasts of the company’s year-end inventory level and its inventory turnover ratio?

EXCESS CAPACITY Edney Manufacturing Company has $2 billion in sales and $0.6 billion in fixed assets. Currently, the company’s fixed assets are operating at 80% of capacity. a. What level of sales could Edney have obtained if it had been operating at full capacity? b. What is Edney’s Target fixed assets/Sales ratio? c. If Edney’s sales increase 30%, how large of an increase in fixed assets will the

company need to meet its Target fixed assets/Sales ratio?

ADDITIONAL FUNDS NEEDED Morrissey Technologies Inc.’s 2008 financial statements are shown here.

Morrissey Technologies Inc.: Balance Sheet as of December 31, 2008

Cash $ 180,000 Accounts payable $ 360,000 Receivables 360,000 Notes payable 56,000 Inventories 720,000 Accrued liabilities 180,000 Total current assets $1,260,000 Total current liabilities $ 596,000

Long-term debt 100,000 Fixed assets 1,440,000 Common stock 1,800,000

Retained earnings 204,000 Total assets $2,700,000 Total liabilities and equity $2,700,000

Morrissey Technologies Inc.: Income Statement for December 31, 2008

Sales $3,600,000 Operating costs including depreciation 3,279,720 EBIT $ 320,280 Interest 20,280 EBT $ 300,000 Taxes (40%) 120,000 Net income $ 180,000 Per Share Data: Common stock price $45.00 Earnings per share (EPS) $ 1.80 Dividends per share (DPS) $ 1.08

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16-1316-13Challenging Problems 13–14

Challenging Problems 13–14

530 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Suppose that in 2009, sales increase by 10% over 2008 sales. The firm currently has 100,000 shares outstanding. It expects to maintain its 2008 dividend payout ratio and believes that its assets should grow at the same rate as sales. The firm has no excess capacity. However, the firm would like to reduce its Operating costs/Sales ratio to 87.5% and increase its total debt ratio to 30%. (It believes that its current debt ratio is too low relative to the industry average.) The firm will raise 30% of 2009 forecasted total debt as notes payable, and it will issue long-term bonds for the remainder. The firm forecasts that its before-tax cost of debt (which includes both short-term and long-term debt) is 12.5%. Assume that any common stock issuances or repurchases can be made at the firm’s current stock price of $45. a. Construct the forecasted financial statements assuming that these changes are made.

What are the firm’s forecasted notes payable and long-term debt balances? What is the forecasted addition to retained earnings?

b. If the profit margin remains at 5% and the dividend payout ratio remains at 60%, at what growth rate in sales will the additional financing requirements be exactly zero? In other words, what is the firm’s sustainable growth rate? (Hint: Set AFN equal to zero and solve for g.)

EXCESS CAPACITY Krogh Lumber’s 2008 financial statements are shown here.

Krogh Lumber: Balance Sheet as of December 31, 2008 (Thousands of Dollars)

Cash $ 1,800 Accounts payable $ 7,200 Receivables 10,800 Notes payable 3,472 Inventories 12,600 Accrued liabilities 2,520 Total current assets $25,200 Total current liabilities $13,192

Mortgage bonds 5,000 Net fixed assets 21,600 Common stock 2,000

Retained earnings 26,608 Total assets $46,800 Total liabilities and equity $46,800

Krogh Lumber: Income Statement for December 31, 2008 (Thousands of Dollars)

Sales $36,000 Operating costs including depreciation 30,783 Earnings before interest and taxes $ 5,217 Interest 1,017 Earnings before taxes $ 4,200 Taxes (40%) 1,680 Net income $ 2,520 Dividends (60%) $ 1,512 Addition to retained earnings $ 1,008

a. Assume that the company was operating at full capacity in 2008 with regard to all items except fixed assets; fixed assets in 2008 were being utilized to only 75% of capacity. By what percentage could 2009 sales increase over 2008 sales without the need for an increase in fixed assets?

b. Now suppose 2009 sales increase by 25% over 2008 sales. Assume that Krogh cannot sell any fixed assets. All assets other than fixed assets will grow at the same rate as sales; however, after reviewing industry averages, the firm would like to reduce its Operating costs/Sales ratio to 82% and increase its debt ratio to 42%. The firm will maintain its 60% dividend payout ratio, and it currently has 1 million shares outstanding. The firm plans to raise 35% of its 2009 total debt as notes payable, and it will issue bonds for the remainder. Its before-tax cost of debt is 11%. Any stock issuances or repurchases will be made at the firm’s current stock price of $40. Develop the projected financial statements as shown in Table 16-2. What are the balances of notes payable, bonds, common stock, and retained earnings?

16-1416-14

531Chapter 16 Financial Planning and Forecasting

FORECASTING FINANCIAL STATEMENTS Use a spreadsheet model to forecast the financial statements in Problems 16-13 and 16-14.

COMPREHENSIVE/SPREADSHEET PROBLEM COMPREHENSIVE/SPREADSHEET PROBLEM

16-1516-15

FINANCIAL FORECASTING Sue Wilson, the new financial manager of New World Chemicals (NWC), a California producer of specialized chemicals for use in fruit orchards, must prepare a formal financial forecast for 2009. NWC’s 2008 sales were $2 billion, and the marketing department is forecasting a 25% increase for 2009. Wilson thinks the company was operating at full capacity in 2008, but she is not sure. The first step in her forecast was to assume that key ratios would remain unchanged and that it would be “business as usual” at NWC. The 2008 financial statements, the 2009 initial forecast, and a ratio analysis for 2008 and the 2009 initial forecast are given in Table IC16-1.

Assume that you were recently hired as Wilson’s assistant and that your first major task is to help her develop the formal financial forecast. She asks you to begin by answering the following questions.

a. Assume (1) that NWC was operating at full capacity in 2008 with respect to all assets, (2) that all assets must grow at the same rate as sales, (3) that accounts payable and accrued liabilities also will grow at the same rate as sales, and (4) that the 2008 profit margin and dividend payout will be maintained. Under those conditions, what would the AFN equation predict the company’s financial requirements to be for the coming year?

b. Consultations with several key managers within NWC, including production, inventory, and receivable managers, have yielded some very useful information.

(1) NWC’s high DSO is largely due to one significant customer who battled through some hardships the past 2 years but who appears to be financially healthy again and is generating strong cash flow. As a re- sult, NWC’s accounts receivable manager expects the firm to lower receivables enough to make the DSO equal to 34 days without adversely affecting sales.

(2) NWC was operating a little below capacity; but its forecasted growth will require a new facility, which is expected to increase NWC’s net fixed assets to $700 million.

(3) A relatively new inventory management system (installed last year) has taken some time to catch on and to operate efficiently. NWC’s inventory turnover improved slightly last year, but this year NWC expects even more improvement as inventories decrease and inventory turnover is expected to rise to 10×.

Incorporate that information into the 2009 initial forecast results, as these adjustments to the initial forecast represent the final forecast for 2009. (Hint: Total assets do not change from the initial forecast.)

c. Calculate NWC’s forecasted ratios based on its final forecast and compare them with the company’s 2008 historical ratios, the 2009 initial forecast ratios, and the industry averages. How does NWC compare with the average firm in its industry, and is the company’s financial position expected to improve during the coming year? Explain.

d. Based on the final forecast, calculate NWC’s free cash flow for 2009. How does this FCF differ from the FCF forecasted by NWC’s initial “business as usual” forecast?

e. Initially, some NWC managers questioned whether the new facility expansion was necessary, especially since it results in increasing net fixed assets from $500 million to $700 million (a 40% increase). However, after extensive discussions about NWC needing to position itself for future growth and being flexible and competitive in today’s marketplace, NWC’s top managers agreed that the expansion was necessary. Among the issues raised by opponents was that NWC’s fixed assets were being operated at only 85% of capacity. Assuming that its fixed assets were operating at only 85% of capacity, by how much could sales have in- creased, both in dollar terms and in percentage terms, before NWC reached full capacity?

f. How would changes in these items affect the AFN: (1) the dividend payout ratio, (2) the profit margin, (3) the capital intensity ratio, and (4) NWC beginning to buy from its suppliers on terms that permit it to pay after 60 days rather than after 30 days? (Consider each item separately and hold all other things constant.)

16-1616-16

IN TEGRATED C ASE NEW WORLD CHEMICALS INC.

532 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

A. Balance Sheets 2008 2009E

Cash and equivalents $ 20 $ 25 Accounts receivable 240 300 Inventories 240 300 Total current assets $ 500 $ 625 Net fixed assets 500 625 Total assets $1,000 $1,250

Accounts payable and accrued liabilities $ 100 $ 125 Notes payable 100 190 Total current liabilities $ 200 $ 315 Long-term debt 100 190 Common stock 500 500 Retained earnings 200 245 Total liabilities and equity $1,000 $1,250

Financial Statements and Other Data on NWC (Millions of Dollars)T a b l e I C 1 6 - 1

B. Income Statements 2008 2009E

Sales $2,000.00 $2,500.00 Less: Variable costs 1,200.00 1,500.00 Fixed costs 700.00 875.00 Earnings before interest and taxes (EBIT) $ 100.00 $ 125.00 Interest 16.00 16.00 Earnings before taxes (EBT) $ 84.00 $ 109.00 Taxes (40%) 33.60 43.60 Net income $ 50.40 $ 65.40 Dividends (30%) $ 15.12 $ 19.62 Addition to retained earnings $ 35.28 $ 45.78

C. Key Ratios NWC(2008) NWC(2009E) Industry Comment

Basic earning power 10.00% 10.00% 20.00% Profit margin 2.52 2.62 4.00 Return on equity 7.20 8.77 15.60 Days sales outstanding (365 days) 43.80 days 43.80 days 32.00 days Inventory turnover 8.33% 8.33% 11.00% Fixed assets turnover 4.00 4.00 5.00 Total assets turnover 2.00 2.00 2.50 Debt/assets 30.00% 40.34% 36.00% Times interest earned 6.25% 7.81% 9.40% Current ratio 2.50 1.99 3.00 Payout ratio 30.00% 30.00% 30.00%

533Chapter 16 Financial Planning and Forecasting

Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions.

Forecasting the Future Performance of Abercrombie & Fitch Clothing retailer Abercrombie & Fitch enjoyed phenomenal success in the late 1990s. Between 1996 and 2000, its sales grew almost fourfold—from $335 million to more than $1.2 billion—and its stock price soared by more than 500%. However, in 2002, its growth rate had begun to slow down and Abercrombie had a hard time meeting its quarterly earnings targets. As a result, the stock price in late 2002 was about half of what it was 3 years earlier. Abercrombie’s struggles resulted from increased competition, a slug- gish economy, and the challenges of staying ahead of the fashion curve. Since 2002, the company’s stock has rebounded strongly, but questions remain about the fi rm’s long-term growth prospects.

Given the questions about Abercrombie’s future growth rate, analysts have focused on the company’s earnings reports. Thomson ONE provides a convenient and detailed summary of the company’s recent earnings history along with a summary of analysts’ earnings forecasts.

To access this information, we begin by entering the company’s ticker symbol, ANF, on Thomson ONE’s main screen and then selecting “GO.” This takes us to an overview of the company’s recent per- formance. After checking out the overview, you should click on “Estimates.” Click on “View Forecasts” (in the middle of your screen) to see details of the EPS summary report. On both of these screens, you will fi nd a wide range of information about the company’s past and projected earnings.

Discussion Questions 1. What are the mean and median forecasts for Abercrombie’s earnings per share over the next fiscal year? 2. Based on analysts’ forecasts, what is the expected long-term growth rate in earnings? 3. Have analysts made any significant changes to their forecasted earnings for Abercrombie & Fitch in the past

few months? Explain. 4. Historically, have Abercrombie’s reported earnings generally met, exceeded, or fallen short of analysts’ fore-

casted earnings? 5. How has Abercrombie’s stock performed this year relative to the S&P 500?

few months? Explain. 4. Historically, have Abercrombie’s reported earnings generally met, exceeded, or fallen short of analysts’ fore-

casted earnings? 5. How has Abercrombie’s stock performed this year relative to the S&P 500?

U . S . Fi r m s Lo o k O ve r s e a s t o E n h a n ce S h a r e h o l d e r Va l u e

Multinational Financial Management1

AR K

BA SS

ET T/

AL AM

17 CHAPTER

534

From the end of World War II until the 1970s, the United States dominated the world economy. However, that situation no longer exists. Raw materials, finished goods, services, and money flow freely across most national boundaries, as do innovative ideas and new technologies. World- class U.S. companies are making breakthroughs in foreign labs, obtaining capital from foreign investors, and putting foreign employees on the fast track to the top. Dozens of top U.S. manufac- turers, including Dow Chemical, Colgate- Palmolive, IBM, and Hewlett-Packard, sell more of their products outside the United States than they do at home. Likewise, service firms such as Citigroup, McDonald’s, and AFLAC receive more than half their revenues from foreign sales.

The trend is even more pronounced in profits. In recent years, Coca-Cola and many other com- panies have made more money in the Pacific Rim and Western Europe than in the United States. All told, Coca-Cola now reports that more than 75%

of its operating profits come from outside North America. As a result, economic events around the globe and changing exchange rates now have a profound effect on the company’s bottom line. In particular, profits earned in foreign currencies are worth more when the U.S. dollar declines. Conse- quently, the sharp decline in the U.S. dollar in recent years has helped boost Coca-Cola’s profits and helps explain why the stock has outper- formed the overall stock market.

Successful global companies such as Coca- Cola must conduct business in different econo- mies, and they must be sensitive to the many subtleties of different cultures and political sys- tems. Accordingly, they find it useful to blend into the foreign landscape to help win product acceptance and avoid political problems. At the same time, foreign-based multinationals are arriving on American shores in ever greater num- bers. Sweden’s ABB, the Netherlands’s Philips, France’s Thomson, and Japan’s Fujitsu and

1 This chapter was coauthored with Professor Roy Crum of the University of Florida.

Chapter 17 Multinational Financial Management

Managers of multinational companies must deal with a wide range of issues that are not present when a company operates in a single country. In this chapter, we high- light the key diff erences between multinational and domestic corporations and we discuss the impact these diff erences have on the fi nancial management of multina- tional businesses. By the time you complete this chapter, you should be able to: • Identify the primary reasons companies choose to go “global.” • Explain how exchange rates work and interpret diff erent exchange rate quotations. • Discuss the intuition behind interest rate parity and purchasing power parity. • Explain the diff erent opportunities and risks that investors face when they invest

overseas. • Identify some specifi c challenges that a multinational corporation faces and dis-

cuss how they infl uence its capital budgeting, capital structure, and working capi- tal policies.

17-1 MULTINATIONAL OR GLOBAL CORPORATIONS The term multinational, or global, corporation describes a fi rm that operates in an integrated fashion in a number of countries. During the past 20 years, a new and fundamentally different form of international commercial activity has developed that has greatly increased worldwide economic and political interdependence. Rather than merely buy resources from and sell goods to foreign nations, multina- tional fi rms now make direct investments in fully integrated operations—from extraction of raw materials through the manufacturing process and fi nally to the distribution of products to consumers throughout the world. Today multinational corporate networks control a large and growing share of the world’s technological, marketing, and productive resources.

Companies, both U.S. and foreign, go “global” for seven primary reasons: 1. To seek production effi ciency. As competition increases in their domestic market-

place and as demand increases in other markets, companies often conclude that they must produce their products overseas. Companies based in high-cost countries have strong incentives to shift production to lower-cost regions, assuming an adequate supply of labor with the requisite skills and an ade- quate transportation infrastructure. For example, GE has production and

Multinational, or Global, Corporation A firm that operates in an integrated fashion in a number of countries.

Honda are all waging campaigns to be identified as Ameri- can companies that employ Americans, transfer technology to America, and help the U.S. trade balance.

The emergence of “world companies” raises a host of questions for governments. For example, should domestic firms be favored, or does it make no difference what a com- pany’s nationality is as long as the firm provides domestic jobs? Should a company make an effort to keep jobs in its home country, or should it produce where total production costs are lowest? What nation controls the technology developed by a multinational corporation, particularly when

the technology can be used in military applications? Must a multinational company adhere to rules imposed in its home country with respect to its operations outside the home country? And if a U.S. firm such as Xerox produces copiers in Japan and then ships them to the United States, should they be reflected in the trade deficit in the same way as Toshiba copiers imported from Japan? Keep those ques- tions in mind as you read this chapter. When you finish, you should have a better appreciation of the problems that governments face and the difficult but profitable opportu- nities that managers of multinational companies face.

PU T TING THINGS IN PER SPECTIVE

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536 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

assembly plants in Mexico, South Korea, and Singapore. Even Japanese manu- facturers have started to shift some of their production to lower-cost countries in the Pacifi c Rim and the Americas. BMW, in response to high production costs in Germany, has built assembly plants in the United States, among other coun- tries. Those examples illustrate how companies strive to remain competitive by locating manufacturing facilities wherever in the world they can produce and transport their products to meet the demand in their major markets at the lowest total unit landed costs.

2. To avoid political, trade, and regulatory hurdles. Governments sometimes impose tariffs, quotas, and other restrictions on imported goods and services. They often do so to raise revenues, to protect domestic industries, and to pursue various political and economic policy objectives. To circumvent government hurdles, fi rms often develop production facilities abroad. For example, the pri- mary reason Japanese auto companies moved production to the United States was to get around U.S. import quotas. Now Honda, Nissan, Toyota, Mazda, and Mitsubishi are assembling vehicles in the United States. This was also the situation in the 1970s when India followed a development strategy to compete domestically with imported products. One reason that prompted U.S. phar- maceutical maker SmithKline and Britain’s Beecham to merge was to avoid licensing and regulatory delays in their largest markets, Western Europe and the United States. GlaxoSmithKline (the result of a 2000 merger between Glaxo Wellcome and SmithKline Beecham) now identifi es itself as an inside player in Europe and the United States.

3. To broaden their markets. After a company’s home market matures, growth opportunities are often better in foreign markets. According to economic prod- uct life-cycle theory, a fi rm fi rst produces in its home market, where it can bet- ter develop its product and satisfy local customers. This attracts competitors; but when the home market is expanding rapidly, new customers provide the necessary sales growth. However, as the home market matures and the growth of total demand slows, competition becomes more intense. At the same time, demand for the product develops abroad, which creates conditions favoring production in foreign countries to satisfy foreign demand and to cut produc- tion and transportation costs so that the company can remain competitive. Thus, such homegrown fi rms as IBM, Coca-Cola, and McDonald’s are aggres- sively expanding into overseas markets. In addition, foreign fi rms such as Sony and Toshiba now play an important role in the U.S. consumer electronics market. Also, as products become more complex and development becomes more expensive, it is necessary to sell more units to cover overhead costs; so larger markets are critical.

4. To seek raw materials and new technology. Supplies of many essential raw materi- als are geographically dispersed; so companies must go where the materials are found, no matter how challenging it may be to operate in some of the loca- tions. For example, major deposits of oil are located on the northern coast of Alaska, in Siberia, in the deserts of the Middle East, and in the Canadian tar sands, all of which present unique challenges. Thus, U.S. oil companies such as ExxonMobil need major production facilities around the world to ensure access to the basic input resources needed to sustain the companies in the future. Because ExxonMobil has refi neries, distribution facilities, and oil pro- duction fi elds, this type of investment is referred to as a vertically integrated investment, whereby the fi rm undertakes an investment to secure its supply of inputs at stable prices.

5. To protect processes and products. Firms often possess special intangible assets such as brand names, technological and marketing know-how, managerial

Vertically Integrated Investment Occurs when a firm undertakes an investment to secure its input supply at stable prices.

537Chapter 17 Multinational Financial Management

expertise, and superior research and development (R&D) capabilities. Unfor- tunately, property rights involving intangible assets are often diffi cult to protect, particularly in foreign markets. Firms sometimes invest abroad rather than license local foreign fi rms in order to protect the secrecy of their production processes, distribution systems, or the product itself. Once a fi rm’s formula or production process is revealed to other local fi rms, those fi rms may more easily develop similar products or processes, which will hurt the original fi rm’s sales. For example, to protect its formula, Coca-Cola builds bottling plants and distribution networks in foreign markets but imports the concen- trate or syrup required to make the product from the United States. In the 1960s, Coca-Cola faced strong pressure from the Indian government to reveal its formula in order to continue its operations in India. Rather than reveal its formula, the company withdrew its operations from India until the foreign investment climate improved.

6. To diversify. By establishing worldwide production facilities and markets, fi rms can cushion the effect of adverse economic conditions in any single country. For example, in recent years, the decline in the U.S. dollar has benefi ted U.S. corporations with signifi cant overseas operations, which helps soften the blow from a weakening U.S. economy. In general, geographic diversifi cation of inputs and outputs works because the economic fl uctuations or political vaga- ries of different countries are not perfectly correlated. Therefore, companies investing overseas can benefi t from diversifi cation in the same way that indi- viduals benefi t from investing in a broad portfolio of stocks. However, because individual shareholders can diversify their investments internationally on their own, it makes less sense for fi rms to undertake foreign investments solely for diversifi cation purposes. Note, though, that in countries that place con- straints on foreign stock ownership or that do not have internationally traded companies, corporate diversifi cation might make sense because then compa- nies can do something that shareholders cannot easily duplicate in their indi- vidual portfolios.

7. To retain customers. If a company goes abroad and establishes production or distribution operations, it will need inputs and services at the new locations. If it can obtain what it needs from a supplier that also operates in the same set of countries, managing the relationship will be much easier and econo- mies of scale and other synergies will likely be obtained. Therefore, suppli- ers of inputs or services can better retain the business of their customers who are “going global” if they follow their customers abroad. Large U.S. banks such as Citibank and JPMorgan Chase initially expanded abroad to supply banking services to their long-time customers, although they quickly capi- talized on their global network to develop new customer relationships. The same history is also true for accounting, law, advertising, and similar service providers.

The past 10 to 20 years has seen an increasing amount of investment in the United States by foreign corporations and in foreign nations by U.S. corporations. This trend is shown in Figure 17-1, and it is important because of its implications for eroding the traditional doctrine of independence and self-reliance that has been a hallmark of U.S. policy. Just as U.S. corporations with extensive overseas opera- tions are said to use their economic power to exert substantial economic and politi- cal infl uence over host governments in many parts of the world, it is feared that foreign corporations are gaining similar sway over U.S. policy. These develop- ments suggest an increasing degree of mutual infl uence and interdependence among business enterprises and nations, to which the United States is not immune.

538 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

17-2 MULTINATIONAL VERSUS DOMESTIC FINANCIAL MANAGEMENT

In theory, the concepts and procedures discussed in the fi rst 16 chapters are valid for both domestic and multinational operations. However, some additional factors need to be considered when fi rms operate globally. Five of these factors are listed here: 1. Different currency denominations. Cash fl ows in various parts of a multinational

corporate system will be denominated in different currencies. Hence, exchange rates must be included in all fi nancial analyses.

2. Political risk. Nations are free to place constraints on the transfer or use of cor- porate resources, and they can change regulations and tax rules at any time. They can even expropriate assets within their boundaries. Therefore, political risks can take on many forms. Of course, political risks are present for compa- nies operating in a single country. But for multinational fi rms, political risks exist in various forms from country to country; and they must be addressed explicitly in any fi nancial analysis.

Sources: Marilyn Ibarra and Jennifer Koncz, “Direct Investment Positions for 2006: Country and Industry De- tail,” Survey of Current Business, July 2007, pp. 21–36; Elena L. Nguyen, “The International Investment Position of the United States at Yearend 2002,” Survey of Current Business, July 2003, pp. 12–21; Patricia E. Abaroa, “The International Investment Position of the United States at Yearend 2003,” Survey of Current Business, July 2004, pp. 30–39; and Bureau of Economic Analysis, “U.S. Net International Investment Position at Yearend 2004,” BEA News, June 30, 2005.

Direct Investment Positions on a Current-Cost Basis, 1982–2006FIGURE 17-1

0 1982 1986 1990 1994 1998 2002 2006

500

1,000

1,500

2,000

2,500

3,000 $ Billions

U.S. Direct Investment Abroad Foreign Direct Investment in U.S.

SEL F TEST What is a multinational corporation?

Why do companies “go global”?

Discuss the following statement: The U.S. is not immune to the infl uence of foreign corporations over U.S. economic and political policies.

539Chapter 17 Multinational Financial Management

3. Economic and legal ramifi cations. Each country has its own unique economic and legal systems, and these differences can cause signifi cant problems when a corporation tries to coordinate and control its worldwide operations. For example, differences in tax laws among countries can cause a given economic transaction to have strikingly different after-tax consequences depending on where the transaction occurs. Similarly, differences in legal systems of host nations, such as the Common Law of Great Britain versus the French Civil Law, complicate matters ranging from the simple recording of business trans- actions to the role the judiciary plays in resolving confl icts. Such differences can restrict multinational corporations’ fl exibility in deploying resources and make procedures that are required in one part of the company illegal in others. These differences also make it diffi cult for executives trained in one country to move easily to another.

4. Role of governments. Most fi nancial models developed in the United States assume the existence of a competitive marketplace in which the participants determine the terms of trade. The government, through its power to establish basic ground rules, is involved in the process; but other than taxes, its role is minimal. Thus, the market provides the primary barometer of success, and it gives the best clues about what must be done to remain competitive. This view of the process is reasonably correct for the United States and Western Europe, but it does not accurately describe the situation in the rest of the world. Although market imperfections can complicate the decision process, they can also be valuable to the extent that they can be overcome by one fi rm but still serve as barriers to entry by competitors. Frequently, the terms under which companies compete, the actions that must be taken or avoided, and the terms of trade on various transactions are determined not in the marketplace, but by direct negotiation between host governments and multinational enterprises. This is essentially a political process, and it must be treated as such. Thus, tra- ditional fi nancial models have to be recast to include political and other non- economic aspects of the decision.

5. Language and cultural differences. The ability to communicate is critical in all business transactions. In this regard, U.S. citizens are often at a disadvantage because they generally are fl uent only in English. On the other hand, Euro- pean and Japanese businesspeople are usually fl uent in several languages, including English. At the same time, even within geographic regions that are considered relatively homogenous, different countries have unique cultural heritages that shape values and infl uence the conduct of business. Multina- tional corporations fi nd that matters such as defi ning the appropriate goals of the fi rm and attitudes toward risk, performance evaluation and compensation systems, interactions with employees, and the ability to curtail unprofi table operations vary dramatically from one country to the next.

Those fi ve factors complicate fi nancial management and increase the risks that multinational fi rms face. However, the prospects for high returns and other factors make it worthwhile for fi rms to accept these risks and learn how to manage them.

SEL F TEST Identify and briefl y discuss fi ve major factors that complicate fi nancial man-

agement in multinational fi rms.

540 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

17-3 THE INTERNATIONAL MONETARY SYSTEM Every nation has a monetary system and a monetary authority. In the United States, the Federal Reserve is the monetary authority; and its task is to hold down infl ation while promoting economic stability and growth. If countries are to trade with one another, some sort of system must be designed to facilitate payments between nations. The international monetary system is the framework within which exchange rates are determined; and it ties global currency, money, capital, real estate, commodity, and real asset markets into a network of institutions and instruments regulated by intergovernmental agreements and driven by each coun- try’s unique political and economic objectives.2

17-3a International Monetary Terminology In a discussion of the international monetary system, it is useful to begin by intro- ducing some important concepts and terminology: 1. An exchange rate is the price of one country’s currency in terms of another

country’s currency. For example, on Monday, May 26, 2008, 1 U.S. dollar would buy 0.5046 British pound, 0.6340 euro, or 0.9919 Canadian dollar.

2. A spot exchange rate is the quoted price for a unit of foreign currency to be delivered “on the spot” or within a very short period of time. The pound rate quoted, £0.5046/$, is a spot rate as of the close of business on May 26, 2008.

3. A forward exchange rate is the quoted price for a unit of foreign currency to be delivered at a specifi ed date in the future. If today was May 26, 2008, and we wanted to know how many pounds we could expect to receive for a dollar on November 26, 2008, we would look at the 6-month forward rate, which was £0.5122/$ versus the £0.5046/$ spot rate. Thus, the dollar is expected to appre- ciate relative to the British pound during the next 6 months. Note also that the forward exchange contract on May 26 would lock in this exchange rate but no money would change hands until November 26. The spot rate on November 26 might be quite different from £0.5122, in which case we would have a profi t or a loss on the forward purchase.

4. A fi xed exchange rate for a currency is set by the government and is allowed to fl uctuate only slightly (if at all) around the desired rate, which is called the par value. For example, Belize has fi xed the exchange rate for the Belizean dollar at BZD 2.00/$1, and it has maintained this fi xed rate for the past few years.

5. A fl oating or fl exible exchange rate is not regulated by the government, so supply and demand in the market determine the currency’s value. The U.S. dollar and the euro are examples of free-fl oating currencies. If U.S. customers are import- ing more goods from Europe than they are exporting to Europe, they will have to make net purchases of euros and sales of dollars, which will cause the euro to appreciate relative to the dollar. Note, though, that central banks do inter- vene in the market from time to time to nudge exchange rates up or down even though they basically fl oat.

6. Devaluation or revaluation of a currency is the technical term referring to the decrease or increase in the stated par value of a currency whose value is fi xed.

International Monetary System The framework within which exchange rates are determined. It is the blueprint for international trade and capital flows.

Exchange Rate The number of units of a given currency that can be purchased for one unit of another currency.

2 For a comprehensive history of the international monetary system and details of how it has evolved, consult one of the many economics books on the subject, including Robert Carbaugh, International Economics, 11th edition (Mason, OH: Thomson South-Western, 2007); Mordechai Kreinin, International Economics: A Policy Approach, 10th ed. (Mason, OH: Thomson South-Western, 2006); Beth V. Yarbrough and Robert M. Yarbrough, The World Economy: Trade and Finance, 7th edition (Mason, OH: Thomson South-Western, 2006); and Joseph P. Daniels and David D. VanHoose, Global Economic Issues and Policies with Economic Applications (Mason, OH: Thomson South-Western, 2004).

For a listing of world currencies, currency symbols, and their regimes, go to the University of British Columbia Sauder School of Business Pacific Exchange Rate Service web site at http://fx.sauder .ubc.ca/currencies.html.

http://fx.sauder.ubc.ca/currencies.html

541Chapter 17 Multinational Financial Management

This decision is made by the government, usually without warning. For example, on July 21, 2005, the Chinese government suddenly announced that it was revaluing the yuan to make it 2.1% stronger against the U.S. dollar. (The new exchange rate was CNY 8.1097/$.) Even though it was widely believed that the yuan was signifi cantly undervalued, this revaluation caught many by surprise since the exchange rate had been pegged at a fi xed rate of CNY 8.2781/$ for nearly a decade. Just as importantly, on that date, the Chinese government abandoned the strict peg to the U.S. dollar and instead adopted a more fl exible system where the yuan is now linked to a basket of foreign currencies including the dollar. Since then, the yuan has steadily appreciated relative to the U.S. dollar. On May 26, 2008, the exchange rate was CNY 6.9365/$; so it cost 14.5% fewer yuan to buy a dollar than previously.

7. Depreciation or appreciation of a currency refers to a decrease or increase, respec- tively, in the foreign exchange value of a fl oating currency. These changes are caused by market forces rather than by governments.

17-3b Current Monetary Arrangements At the most basic level, we can divide currency regimes into two broad groups: fl oating rates and fi xed rates. Within the two regimes, there are gradations among subregimes in terms of how rigidly they adhere to the basic positions. Looking fi rst at the fl oating-rate category, the two main subgroups are as follows: 1. Freely fl oating. Here the exchange rate is determined by the supply and demand

for the currency. Under a freely-fl oating regime, governments may occasion- ally intervene in the market to buy or sell their currency to stabilize fl uctua- tions, but they do not attempt to alter the absolute level of the rate. This policy exists at one end of the continuum of exchange-rate regimes. For example, the currencies of Australia, Brazil, and the Philippines, among many others, are allowed to fl oat with a minimum of intervention.

2. Managed fl oating. Here there is signifi cant government intervention to manage the exchange rate by manipulating the currency’s supply and demand. For example, the governments of Colombia, Israel, and Poland manage their respective currency’s fl oat. Governments rarely reveal their target exchange rate levels when they use a managed-fl oat regime because doing so would make it too easy for currency speculators to profi t.

Most developed countries follow either a freely-fl oating or a managed-fl oat regime. A few developing countries do so as well, often reluctantly and as a result of a market that forces them to abandon a fi xed-rate regime.

Types of fi xed-exchange-rate regimes include the following: 1. No local currency. The most extreme position is for the country to have no local

currency of its own, using another country’s currency as its legal tender (such as the U.S. dollar in the Panama Canal Zone, in Ecuador, and in the Turks and Caicos Islands) or belonging to a group of countries that shares a common cur- rency (such as the euro). With this arrangement, the local government surren- ders the ability to use exchange rates to tinker with its economy.

2. Currency board arrangement. Under a variation of the fi rst subregime, a country technically has its own currency but commits to exchange it for a specifi ed for- eign money unit at a fi xed exchange rate. This requires the country to impose domestic currency restrictions unless it has enough foreign currency reserves to cover all requested exchanges. This is called a currency board arrangement. Argentina had a currency board arrangement before its crisis of January 2002, when it was forced to devalue the peso and default on its debt.

Freely-Floating Regime Occurs when the exchange rate is determined by supply and demand for the currency.

Managed-Float Regime Occurs when there is significant government intervention to control the exchange rate via manipulation of the currency’s supply and demand.

Currency Board Arrangement Occurs when a country has its own currency but commits to exchange it for a specified foreign money unit at a fixed exchange rate and legislates domestic currency restrictions unless it has the foreign currency reserves to cover requested exchanges.

542 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

3. Fixed peg arrangement. In a fi xed-peg arrangement, the country locks, or “pegs,” its currency to another currency or basket of currencies at a fi xed exchange rate. This allows the currency to vary only slightly from its desired rate; and if it moves outside the specifi ed limits (often set at !1% of the target rate), its central bank intervenes to force the currency back within the limits. An example is China, where the yuan is no longer pegged to the U.S. dollar but rather to a bas- ket of currencies. Additional examples include Bhutan’s ngultrum, which is pegged to the Indian rupee; the Falkland Islands’ pound, which is pegged to the British pound; and Barbados’s dollar, which is pegged to the U.S. dollar.

Other variations have been used, and new ones are developed from time to time. A majority of the world’s countries employ a system that includes a fi xed- exchange-rate arrangement along with occasional interventions. So while the most important currencies (as measured by volume of transactions) are allowed to fl oat and the international monetary system is often called a fl oating regime, most cur- rencies are partially fi xed but occasionally are manipulated in some manner.

Fixed-Peg Arrangement Occurs when a country locks its currency to a specific currency or basket of currencies at a fixed exchange rate.

SEL F TEST What is an international monetary system?

What is the diff erence between spot and forward exchange rates?

What is the basic diff erence between fl oating- and fi xed-exchange rates?

Diff erentiate between devaluation/revaluation of a currency and deprecia- tion/appreciation of a currency.

What are the two broad categories of the various currency regimes? What are the subgroups of those two broad categories?

17-4 FOREIGN EXCHANGE RATE QUOTATIONS Foreign exchange rate quotations can be found in The Wall Street Journal and in other leading print publications and on web sites. Exchange rates are given in two differ- ent ways. As shown in Table 17-1, which is an excerpt from The Wall Street Journal Online, in Column 1, they are quoted as “USD equivalent”; in Column 2, they are quoted as “Currency per USD.” For example, 1 Canadian dollar is worth (or can be exchanged for) 1.0082 U.S. dollars, or 1 U.S. dollar can buy 0.9919 Canadian dollar.

Note that if the foreign exchange markets are in equilibrium, which is usually the case for the major traded currencies, the two quotations must be reciprocals of each other, as shown here for the Canadian dollar.

Canadian dollar: 1/1.0082 ! 0.9919 1/0.9919 ! 1.0082

17-4a Cross Rates All of the exchange rates given in Table 17-1 are relative to the U.S. dollar. Suppose, though, that a German executive is fl ying to Tokyo on business. The exchange rate in which he or she is interested is not euros or yen per dollar—rather, the issue is how many yen can be purchased with a euro. This is called a cross rate, and it can be calculated from the following data from Column 2 of Table 17-1:

Spot Rate

Euro €0.6340/$1

Yen ¥103.44/$1

Cross Rate The exchange rate between any two currencies.

For up-to-date currency quotations on the Web, visit two popular sites: www .bloomberg .com/markets/ currencies/fxc.html and http://finance.yahoo .com/currency.

wwwbloomberg.com/markets/currencies/fxc.html

http://finance.yahoo.com/currency

543Chapter 17 Multinational Financial Management

Because the quotations have the same denominator—one U.S. dollar—we can calculate the cross rate between these (and other) currencies by using the Column 2 quotations. For our German national, the cross rates are found as follows:

Euro/yen exchange rate ! Euro/$ ______ Yen/$

And when we cancel the dollar signs, we are left with the number of euros that one yen could purchase:

€0.6340/¥103.44 ! €0.0061/¥

Alternatively, we could fi nd the number of yen that one euro could buy:

Yen/euro exchange rate ! Yen/$ ______ Euro/$

¥103.44/€0.6340 ! ¥163.15/€

Note that those two cross rates are reciprocals of each other. Financial publications such as The Wall Street Journal and web sites such as

Bloomberg, Yahoo, and The Wall Street Journal Online provide tables of key cur- rency cross rates. Table 17-2 gives the table from The Wall Street Journal Online for May 26, 2008. Notice that there may be slight differences when you calculate cross rates due to the rounding of individual quotations. Currency traders carry quota- tions out to 12 decimal places.

17-4b Interbank Foreign Currency Quotations The quotations from The Wall Street Journal Online given in Tables 17-1 and 17-2 are suffi cient for many purposes. For other purposes, however, additional terminol- ogy and conventions are useful. There are two ways to state the exchange rate between two currencies, in either American or European terms. Accordingly, we need to designate one of the currencies as the “home” currency and the other as the “foreign” currency. This designation is arbitrary. The home currency price of

American Terms The foreign exchange rate quotation that represents the number of American dollars that can be bought with one unit of local currency.

European Terms The foreign exchange rate quotation that represents the units of local currency that can be bought with one U.S. dollar. “European” is intended as a generic term that applies globally.

Direct Quotation: U.S. Dollars Required to Buy

One Unit of Foreign Currency (1)

Indirect Quotation: Number of Units of Foreign

Currency per U.S. Dollar (2)

Brazilian real $0.6028 1.6589 British pound 1.9816 0.5046 Canadian dollar 1.0082 0.9919 Chinese yuan 0.1442 6.9365 Danish krone 0.2114 4.7304 Euro 1.5772 0.6340 Hungarian forint 0.006456 154.89 Israeli shekel 0.3018 3.3135 Japanese yen 0.009667 103.44 Mexican peso 0.0962 10.3983 South African rand 0.1299 7.6982 Swedish krona 0.1693 5.9067 Swiss franc 0.9760 1.0246 Venezuelan bolivar fuerte 0.46628742 2.1446

Note: Column 2 equals 1.0 divided by Column 1. However, rounding differences do occur.

Source: Adapted from The Wall Street Journal Online, http://online.wsj.com, May 27, 2008.

Sample Exchange Rates: Monday, May 26, 2008T a b l e 1 7 - 1

http://online.wsj.com

544 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

one unit of the foreign currency is called a direct quotation. Thus, to a person who considers the United States to be “home,” American terms represent a direct quo- tation. On the other hand, the foreign currency price of one unit of the home currency is called an indirect quotation. European terms represent indirect quotations to people in the United States. Note that if the perspective changes and the “home” currency is no longer the U.S. dollar, the designations of direct and indirect will change. For the remainder of this chapter unless specifi cally stated otherwise, we will assume that the United States is the “home” country and thus that the U.S. dollar is the home currency.

Direct Quotation The home currency price of one unit of the foreign currency.

Indirect Quotation The foreign currency price of one unit of the home currency.

Key Currency Cross RatesT a b l e 1 7 - 2

USDollar (1)

Euro (2)

Pound (3)

SFranc (4)

Peso (5)

Yen (6)

CdnDlr (7)

Canada 0.9919 1.5644 1.9655 0.9681 0.0954 0.0096 — Japan 103.44 163.15 204.99 100.96 9.9483 — 104.29 Mexico 10.398 16.400 20.605 10.149 — 0.1005 10.484 Switzerland 1.0246 1.6160 2.0303 — 0.0985 0.0099 1.0330 United Kingdom 0.5046 0.7959 — 0.4925 0.0485 0.0049 0.5088 Euro 0.6340 — 1.2564 0.6188 0.0610 0.0061 0.6392 United States — 1.5772 1.9816 0.9760 0.0962 0.0097 1.0082

Note: Column 1 shows how many units of each foreign currency a U.S. dollar will buy, Column 2 shows how many units a euro will buy, and so forth. Source: Adapted from “Key Currency Cross Rates,” The Wall Street Journal Online, http://online.wsj.com, May 27, 2008.

SEL F TEST Explain the diff erence between direct and indirect quotations.

What is a cross rate?

Assume that today 1 Canadian dollar is worth 0.75 U.S. dollar. How many Canadian dollars would you receive for 1 U.S. dollar? (1.333)

Assume that 1 U.S. dollar can be exchanged for 105 Japanese yen or for 0.80 euro. What is the euro/yen exchange rate? (€0.007619/¥)

17-5 TRADING IN FOREIGN EXCHANGE Importers, exporters, tourists, and governments buy and sell currencies in the for- eign exchange market. For example, when a U.S. trader imports automobiles from Japan, payment is probably made in Japanese yen. The importer buys yen (through its bank) in the foreign exchange market, much as one buys common stocks on the New York Stock Exchange or pork bellies on the Chicago Mercantile Exchange. However, whereas stock and commodity exchanges have organized trading fl oors, the foreign exchange market consists of a network of brokers and banks based in New York, London, Tokyo, and other fi nancial centers. Most buy and sell orders are conducted by computer and telephone.3

3 For a more detailed explanation of exchange rate determination and operations of the foreign exchange mar- ket, see Roy L. Crum, Eugene F. Brigham, and Joel F. Houston, Fundamentals of International Finance (Mason, OH: Thomson South-Western, 2005).

http://online.wsj.com

545Chapter 17 Multinational Financial Management

17-5a Spot Rates and Forward Rates The exchange rates shown earlier in Tables 17-1 and 17-2 are known as spot rates, which means the rate paid for delivery of the currency “on the spot” or, in reality, no more than 2 days after the day of the trade. For most of the world’s major currencies, it also is possible to buy (or sell) currencies for delivery at some agreed- upon future date, usually 30, 90, or 180 days from the day the transaction is negotiated. This rate is known as the forward exchange rate.

For example, suppose a U.S. fi rm must pay 500 million yen to a Japanese fi rm in 30 days and the current spot rate is 103.44 yen per dollar. Unless spot rates change, the U.S. fi rm will pay the Japanese fi rm the equivalent of $4.834 million (500 million yen divided by 103.44 yen per dollar) in 30 days. But if the spot rate falls to 100 yen per dollar, for example, the U.S. fi rm will have to pay the equiva- lent of $5 million. The treasurer of the U.S. fi rm can avoid this risk by entering into a 30-day forward exchange contract. This contract promises delivery of yen to the U.S. fi rm in 30 days at a guaranteed price of 103.26 yen per dollar. No cash changes hands at the time the treasurer signs the forward contract, although the U.S. fi rm might have to put down some collateral as a guarantee against default. Because the fi rm can use an interest-bearing instrument for the collateral, though, this requirement is not costly. The counterparty to the forward contract must de- liver the yen to the U.S. fi rm in 30 days, and the U.S. fi rm is obligated to purchase the 500 million yen at the previously agreed-upon rate of 103.26 yen per dollar. Therefore, the treasurer of the U.S. fi rm is able to lock in a payment equivalent to $4.842 million no matter what happens to spot rates. This technique is called “hedging.”

Forward rates for 30-, 90-, and 180-day delivery, along with the current spot rates for some commonly traded currencies, are given in Table 17-3. If we can ob- tain more of the foreign currency for a dollar in the forward market than in the spot market, the forward currency is less valuable than the spot currency and the for- ward currency is said to be selling at a discount. Conversely, if we can obtain less of the foreign currency for a dollar in the forward market than in the spot market, the forward currency is more valuable than the spot currency and the forward cur- rency is said to be selling at a premium. Thus, because a dollar buys fewer yen and Swiss francs in the forward than in the spot market, the forward yen and Swiss francs are selling at a premium. On the other hand, a dollar buys more pounds and

Spot Rate The effective exchange rate of a foreign currency for delivery on (approximately) the current day.

Forward Exchange Rate An agreed-upon price at which two currencies will be exchanged at some future date.

Discount on Forward Rate The situation when the spot rate is less than the forward rate.

Premium on Forward Rate The situation when the spot rate is greater than the forward rate.

Spot Rate

Forward Rates Forward Rate at a Premium or Discount30 Days 90 Days 180 Days

British pound 0.5046 0.5060 0.5084 0.5122 Discount Canadian dollar 0.9919 0.9925 0.9930 0.9938 Discount Japanese yen 103.44 103.26 102.95 102.48 Premium Swiss franc 1.0246 1.0244 1.0241 1.0241 Premium

Notes: a. These are representative quotes as provided by a sample of New York banks. Forward rates for other currencies and for other lengths of time

can often be negotiated. b. When it takes more units of a foreign currency to buy one dollar in the future, the value of the foreign currency is less in the forward market

than in the spot market; hence, the forward rate is at a discount to the spot rate. Likewise, when it takes less units of a foreign currency to buy one dollar in the future, the value of the foreign currency is more in the forward market than in the spot market; hence, the forward rate is at a premium to the spot rate.

Source: Adapted from The Wall Street Journal Online, http://online.wsj.com, May 27, 2008.

Selected Spot and Forward Exchange Rates (Number of Units of Foreign Currency per U.S. Dollar)

T a b l e 1 7 - 3

http://online.wsj.com

546 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

17-6 INTEREST RATE PARITY Market forces determine whether a currency sells at a forward premium or dis- count, and the general relationship between spot and forward exchange rates is specifi ed by a concept called “interest rate parity.”

Interest rate parity holds that investors should earn the same return on interest-bearing investments in all countries after adjusting for risk. It recognizes that when you invest in a country other than your home country, you are affected by two forces—returns on the investment itself and changes in the exchange rate. It follows that your overall return will be higher than the investment’s stated return if the currency in which your investment is denominated appreciates relative to your home currency. Likewise, your overall return will be lower if the foreign currency you receive declines in value.

The relationship between spot and forward exchange rates and interest rates, which is known as interest rate parity, is expressed in the following equation:

Forward exchange rate

____________________ Spot exchange rate ! (1 " rh) _______ (1 " rf)

Both the forward and spot rates are expressed in terms of the amount of home currency received per unit of foreign currency; and rh and rf are the periodic interest rates in the home country and the foreign country, respectively. If this relationship does not hold, currency traders will buy and sell currencies—that is, engage in arbitrage—until it does hold.

To illustrate interest rate parity, consider the case of a U.S. investor who can buy default-free 90-day Japanese bonds that promise a 4% nominal return. The 90-day in- terest rate, rf, is 4%/4 " 1% because 90 days is one-fourth of a 360-day year. Assume also that the spot exchange rate is $0.009667, which means that you can exchange 0.009667 dollar for 1 yen, or 103.44 yen per dollar. Finally, assume that the 90-day for- ward exchange rate is $0.009713, which means that you can exchange 1 yen for 0.009713 dollar, or receive 102.95 yen per dollar exchanged, 90 days from now.

The U.S. investor can receive a 4% annualized return denominated in yen; but if he or she ultimately wants to consume goods in the United States, those yen must be converted to dollars. The dollar return on the investment depends, therefore, on what happens to exchange rates over the next 3 months. However, the investor can lock in the dollar return by selling the foreign currency in the forward market. For example, the investor can do the following simultaneously: • Convert $1,000 to 103,440 yen in the spot market. • Invest the 103,440 yen in 90-day Japanese bonds that have a 4% annualized return

or a 1% quarterly return and hence will pay (103,440)(1.01) " 104,474.40 yen in 90 days.

Interest Rate Parity Specifies that investors should expect to earn the same return in all countries after adjusting for risk.

SEL F TEST Explain what it means for a forward currency to sell at a discount and at a

premium.

Suppose a U.S. fi rm must pay 200 million Swiss francs to a Swiss fi rm in 90 days. Briefl y explain how the fi rm would use forward exchange rates to “lock in” the price of the payable due in 90 days.

Canadian dollars in the forward market than in the spot market, so the forward pounds and Canadian dollars are selling at a discount.

547Chapter 17 Multinational Financial Management

• Agree today to exchange the 104,474.40 yen 90 days from now at the 90-day forward exchange rate of 102.95 yen per dollar, for a total of $1,014.81.

This investment, therefore, has an expected 90-day return of $14.81/$1,000 " 1.481%, which translates into a nominal return of 4(1.481%) " 5.92%. In this case, 4% of the expected 5.92% return is coming from the bond itself and 1.92% arises because the market believes the yen will strengthen relative to the dollar. Note that by locking in the forward rate today, the investor has eliminated any exchange rate risk. And because the Japanese bond is assumed to be default-free, the investor is assured of earning a 5.92% dollar return.

Interest rate parity implies that an investment in the United States with the same risk as a Japanese bond should have an annual return of 5.92%. Solving for rh in the parity equation, we indeed fi nd that the predicted annual interest rate in the United States is 5.92%.

Interest rate parity shows why a particular currency might be at a forward premium or discount. Note that a currency is at a forward premium whenever do- mestic interest rates are higher than foreign interest rates. Discounts will prevail if domestic interest rates are lower than foreign interest rates. If these conditions do not hold, arbitrage will soon force interest rates back to parity.

17-7 PURCHASING POWER PARITY We have discussed exchange rates in some detail, and we have considered the relationship between spot and forward exchange rates. However, we have not yet addressed this fundamental question: What determines the spot level of exchange rates in each country? While exchange rates are infl uenced by a multitude of fac- tors that are diffi cult to predict, particularly on a day-to-day basis, over the long run, market forces work to ensure that similar goods sell for similar prices in dif- ferent countries after exchange rates are taken into account. This relationship is known as “purchasing power parity.”

Purchasing power parity (PPP), sometimes referred to as the law of one price, implies that the level of exchange rates adjusts so as to cause identical goods to cost the same amount in different countries. For example, if a pair of tennis shoes costs $100 in the United States and 50 pounds in Britain, PPP implies that the exchange rate will be $2 per pound. Consumers can purchase the shoes in Britain for 50 pounds, or they can exchange their 50 pounds for $100 and pur- chase the same shoes in the United States at the same effective cost, assuming

Purchasing Power Parity (PPP) The relationship in which the same products cost roughly the same amount in different countries after the exchange rate is taken into account.

What is interest rate parity?

Assume that interest rate parity holds. When a currency trades at a forward premium, what does that imply about domestic rates relative to foreign in- terest rates? when a currency trades at a forward discount?

Assume that 90-day U.S. securities have a 3.5% annualized interest rate, whereas 90-day Canadian securities have a 4% annualized interest rate. In the spot market, 1 U.S. dollar can be exchanged for 1.4 Canadian dollars. If interest rate parity holds, what is the 90-day forward exchange rate between U.S. and Canadian dollars? ($0.7134/C$ or C$1.40173/$) On the basis of your answer to the previous question, is the Canadian dollar selling at a premium or discount on the forward rate? (Discount)

SEL F TEST

548 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

no transactions or transportation costs. The equation for purchasing power parity is shown here:

Ph ! (Pf)(Spot rate)

Spot rate ! Ph __ Pf

Purchasing power parity (PPP) implies that the same product will sell for the same price in every country after adjusting for current exchange rates. One problem when testing to see if PPP holds is that it assumes that goods consumed in diff er- ent countries are of the same quality. For example, if you fi nd that a product is more expensive in Switzerland than it is in Canada, one explanation is that PPP fails to hold; but another explanation is that the product sold in Switzerland is of a higher quality and therefore deserves a higher price.

One way to test for PPP is to fi nd goods that have the same quality worldwide. With this in mind, The Economist magazine occasionally compares the prices of a well-known good whose quality is the same in 120 diff erent countries: the McDonald’s Big Mac hamburger.

The tables shown in Panels A and B on the next page provide information collected during 2007. The Panel A table gives the price of a Big Mac in each country’s local currency and the actual dollar exchange rate when these data were collected. In Panel B, the fi rst numeric column calculates the price of the Big Mac in terms of the U.S. dollar—this is obtained by dividing the local price by the actual exchange rate at that time. For example, a Big Mac costs 6.30 Swiss francs in Zurich, which is shown in Panel A. Given an exchange rate of 1.21 Swiss francs per dollar (as shown in Panel A), this implies that the dollar price of a Big Mac is 6.30 Swiss francs/1.21 Swiss francs per dollar ≈ $5.20, shown in Panel B.

The second numeric column in Panel B backs out the implied exchange rate that would hold under PPP. This is obtained by dividing the price of the Big Mac in each local currency by its U.S. price. For example, as shown in Panel A, a Big Mac costs 52 rubles in Russia and $3.41 in the United States. If PPP holds, the exchange rate should be approxi- mately 15.2 rubles per dollar (52 rubles/$3.41), which is shown in Panel B.

Comparing the implied exchange rate (shown in Panel B) to the actual exchange rate (shown in Panel A), we see the

extent to which the local currency is under- or overvalued relative to the dollar. Given that the actual exchange rate at the time was 25.6 rubles per dollar, this rate implies that the ruble was 41% undervalued, which is shown in the last col- umn of Panel B.

The evidence suggests that strict PPP does not hold, but recent research suggests that the Big Mac test may shed some insights about where exchange rates are headed. The average price of a Big Mac in the European Monetary Union (EMU) is 3.06 euros. This implies that the euro’s PPP is $1.12; so at its current rate of $1.36, the euro is overvalued by 22%.

Norway, Sweden, Switzerland, and Denmark—four Euro- pean countries that are not part of the EMU—have curren- cies that are signifi cantly overvalued against the dollar. The Norwegian kroner is overvalued by 102%, the Swedish krona is overvalued by 42%, the Swiss franc is overvalued by 53%, and the Danish krone is overvalued by 49%. In contrast, the Japanese yen is the most undervalued rich-world currency— by 33%.

According to the Big Mac Index, relative to the U.S. dol- lar, the euro is overvalued by 22%. A particularly bad year for the U.S. dollar was 2007. At year-end, the U.S. dollar was at its lowest point in a decade. This decline occurred primarily because the U.S. had imported so much more than it had exported, paying for the defi cit by borrowing from foreign- ers. At some point, we will have to pay off that debt, which means selling dollars and buying foreign currencies. Those transactions will lower the value of the dollar relative to the values of foreign currencies. The Big Mac Index anticipates those actions.

One last benefi t of the Big Mac test is that it tells us the cheapest places to fi nd a Big Mac. According to the data, if you are looking for a Big Mac, head to China but avoid Iceland because the Chinese yuan is the most undervalued currency and the Icelandic kronur is the most overvalued.

Sources: Adapted from “Sizzling: The Big Mac Index (Food for Thought about Exchange Rate Controversies), The Economist, Vol. 384, July 7, 2007, pp. 74–76, and Li Lian Ong, “Burgernomics: The Economics of the Big Mac Standard,” Journal of International Money and Finance, Vol. 16, no. 6 (1997), pp. 867–878.

HUNGRY FOR A BIG MAC? GO TO CHINA!

549Chapter 17 Multinational Financial Management

PANEL A PANEL B

Big Mac Prices

in Local Currency

Actual Dollar

Exchange Rate, 7/2/07

Big Mac Prices

in Dollarsb

Implied PPP

of the

Dollar c

Under (#) Over (")

Valuation against

the Dollar, %

United Statesa $3.41 — United Statesa $3.41 — — Argentina Peso8.25 3.09 Argentina 2.67 2.42 –22 Australia A$3.45 1.17 Australia 2.95 1.01 –14 Brazil Real6.90 1.91 Brazil 3.61 2.02 6 Britain £1.99 2.01d Britain 4.01 1.71d 18 Canada C$3.88 1.05 Canada 3.68 1.14 8 Chile Peso1,565 527 Chile 2.97 459 –13 China Yuan11.0 7.60 China 1.45 3.23 –58 Czech Republic Koruna52.9 21.1 Czech Republic 2.51 15.5 –27 Denmark DKr27.75 5.46 Denmark 5.08 8.14 49 Egypt Pound9.54 5.69 Egypt 1.68 2.80 –51 Euro area €3.06 1.36f Euro area 4.17e 1.12f 22 Hong Kong HK$12.0 7.82 Hong Kong 1.54 3.52 –55 Hungary Forint600 180 Hungary 3.33 176 –2 Iceland Kronur469 61.7 Iceland 7.61 138 123 Indonesia Rupiah15,900 9,015 Indonesia 1.76 4,663 –48 Japan ¥280 122 Japan 2.29 82.1 –33 Malaysia Ringgit5.50 3.43 Malaysia 1.60 1.61 –53 Mexico Peso29.0 10.8 Mexico 2.69 8.50 –21 New Zealand NZ4.60 1.28 New Zealand 3.59 1.35 5 Norway Kroner40.0 5.81 Norway 6.88 11.7 102 Peru NewSol9.50 3.17 Peru 3.00 2.79 –12 Philippines Peso85.0 45.9 Philippines 1.85 24.9 –46 Poland Zloty6.90 2.75 Poland 2.51 2.02 –26 Russia Rouble52.0 25.6 Russia 2.03 15.2 –41 Singapore S$3.95 1.52 Singapore 2.59 1.16 –24 South Africa Rand15.5 6.97 South Africa 2.22 4.55 –35 South Korea Won2,900 923 South Korea 3.14 850 –8 Sweden SKr33.0 6.79 Sweden 4.86 9.68 42 Switzerland SFr6.30 1.21 Switzerland 5.20 1.85 53 Taiwan NT$75.0 32.8 Taiwan 2.29 22.0 –33 Thailand Baht62.0 34.5 Thailand 1.80 18.2 –47 Turkey Lira4.75 1.30 Turkey 3.66 1.39 7 Venezuela Bolivar7,400 2,147 Venezuela 3.45 2,170 1

Notes: a Average of New York, Chicago, San Francisco, and Atlanta. b At current exchange rate. c Purchasing power parity: Local price divided by price in the United States. d Dollars per pound. e Weighted average of member countries. f Dollars per euro. Sources: McDonald’s; and “Sizzling: The Big Mac Index (Food for Thought about Exchange Rate Controversies),” The Economist, Vol. 384, July 7, 2007, pp. 74–76.

550 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Note that the spot market exchange rate is expressed as the number of units of home currency that can be exchanged for one unit of foreign currency ($2 per pound).

PPP assumes that market forces will eliminate situations in which the same product sells at a different price overseas. For example, if the tennis shoes cost $90 in the United States, trading companies could purchase them in the United States for $90, sell them for 50 pounds in Britain, exchange the 50 pounds for $100 in the foreign exchange market, and earn a profi t of $10 on every pair of shoes. Ulti- mately, this trading activity would increase the demand for tennis shoes in the United States and thus raise Ph, increase the supply of tennis shoes in Britain and thus reduce Pf, and increase the demand for dollars in the foreign exchange market and thus reduce the spot rate. Each of those actions works to restore PPP.

Note that PPP assumes that there are no transportation or transactions costs (or import restrictions) that would limit the ability to ship goods between coun- tries. In many cases, these assumptions are incorrect, which explains why PPP is often violated. An additional complication, when empirically testing to see whether PPP holds, is that products in different countries are rarely identical. Frequently, there are real or perceived differences in quality, which can lead to price differ- ences in different countries.

Still, the concepts of interest rate parity and purchasing power parity are criti- cally important to those engaged in international activities. Companies and inves- tors must anticipate changes in interest rates, infl ation, and exchange rates; and they often try to hedge the risks of adverse movements in those factors. The parity relationships are extremely useful when anticipating future conditions.

Ph " Price of the good in the home country ($100, assuming the United States is the home country)

Pf " Price of the good in the foreign country (50 pounds) SEL

F TEST What is purchasing power parity?

A television set sells for $1,000 U.S. dollars. In the spot market, $1 " 110 Japa- nese yen. If purchasing power parity holds, what should be the price (in yen) of the same television set in Japan? (¥110,000)

Price diff erences in “similar” products in diff erent countries often exist. What can explain those diff erences?

17-8 INFLATION, INTEREST RATES, AND EXCHANGE RATES Relative infl ation rates, or the rates of infl ation in foreign countries compared with that in the home country, have two key implications for multinational fi rms: (1) Relative infl ation rates infl uence future production costs at home and abroad, and (2) infl ation has an important effect on relative interest rates and exchange rates. Both of those factors infl uence multinational corporations’ fi nancing deci- sions and the profi tability of foreign investments.

The currencies of countries with higher infl ation rates than the U.S. infl ation rate, by defi nition, depreciate over time against the dollar. Countries in which this

Here:

551Chapter 17 Multinational Financial Management

has occurred include Mexico and all the South American nations. On the other hand, the currencies of Switzerland and Japan, which have had less infl ation than the United States, have appreciated against the dollar. In fact, a foreign currency will, on average, depreciate or appreciate at a percentage rate approximately equal to the amount by which its infl ation rate is over or under the U.S. infl ation rate.

Relative infl ation also affects interest rates. Indeed, the interest rate in any country is largely determined by its infl ation rate. So countries with higher infl a- tion rates than the U.S. infl ation rate also have higher interest rates, and the reverse is true for countries with lower infl ation rates.

It is tempting for a multinational corporation to borrow in countries with the lowest interest rates. However, this is not always a good strategy. Suppose, for ex- ample, that interest rates in Switzerland are lower than those in the United States be- cause of Switzerland’s lower infl ation rate. A U.S. multinational fi rm could therefore reduce its interest expense by borrowing in Switzerland. However, because of rela- tive infl ation rates, the Swiss franc will probably appreciate in the future, causing the dollar cost of annual interest and principal payments on Swiss debt to rise over time. Thus, the lower interest rate could be more than offset by losses from currency appreciation. Similarly, multinational corporations should not necessarily avoid borrowing in a country such as Brazil, where interest rates have been very high, because future de- preciation of the Brazilian real could make such borrowing relatively inexpensive.

SEL F TEST What eff ects do relative infl ation rates have on relative interest rates?

What happens over time to the currencies of countries with higher infl ation rates than U.S. infl ation rates? To countries with lower infl ation rates?

Why might a multinational corporation decide to borrow in a country such as Brazil, where interest rates are high, rather than in a country such as Switzerland, where interest rates are low?

17-9 INTERNATIONAL MONEY AND CAPITAL MARKETS One way for U.S. citizens to invest in world markets is to buy the stocks of U.S. mul- tinational corporations that invest directly in foreign countries. Another way is to purchase foreign securities—stocks, bonds, or money market instruments issued by foreign companies. Security investments are known as portfolio investments, and they are distinguished from direct investments in physical assets by U.S. corporations.

For a time after World War II, the U.S. capital markets dominated world mar- kets. Today, however, the value of U.S. securities represents less than one-fourth of the value of all securities. Given this situation, it is important for both corporate managers and investors to understand international markets. Moreover, these markets often offer better opportunities for raising or investing capital than are available domestically.

17-9a International Credit Markets There are three major types of international credit markets. The fi rst type is the market for fl oating-rate bank loans, called Eurocredits, whose rates are tied to LIBOR, which stands for London Interbank Offer Rate. LIBOR is the interest rate offered by the largest and strongest banks on large deposits. On May 26, 2008, the 3-month LIBOR rate was 2.65%. Eurocredits tend to be issued for a fi xed term with no early repayment. The oldest example of a Eurocredit is a Eurodollar deposit,

Eurocredits Floating-rate bank loans that are available in most major trading currencies and that are tied to LIBOR.

Eurodollar A U.S. dollar deposited in a bank outside the United States.

552 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

which is a U.S. dollar deposited in a bank outside the United States. Today Eurocredits exist for most major trading currencies.

The second type of market is the Eurobond market. A eurobond is an interna- tional bond underwritten by an international bank and sold to investors in coun- tries other than the one in whose currency the bond is denominated. Thus, U.S. dollar-denominated eurobonds are not sold in the United States, pound eurobonds are not sold in the United Kingdom, and yen eurobonds are not sold in Japan. These bonds are true international debt instruments and are usually issued in bearer form, which means that the owner’s identity is not registered and thus is not known. To receive interest payments, the owner must clip a coupon and pres- ent it for payment at one of the designated payor banks. Most eurobonds are not rated by the rating agencies such as S&P and Moody’s, although a number of eurobonds are starting to be rated. Eurobonds can be issued with either a fi xed- coupon rate or a fl oating-rate coupon depending on the preferences of the issuer, and they have medium- or long-term maturities.

The third type of market is the foreign bond market. Foreign bonds are issued in the country in whose currency the bond is denominated, and they are under- written by investment banks in that country. However, the borrower is headquar- tered in a different country. For instance, a Canadian company might issue a U.S. dollar-denominated bond in New York to fund its U.S. operations. Foreign bonds issued in the United States are sometimes called “Yankee bonds.” Similarly,

Eurobond An international bond underwritten by an international syndicate of banks and sold to investors in countries other than the one in whose money unit the bond is denominated.

Foreign Bond A type of international bond issued in the domestic capital market of the country in whose currency the bond is denominated and underwritten by investment banks from the same country.

In Chapter 2, we described the major U.S. stock market indi- ces. As discussed herein, similar market indices also exist for each major world fi nancial center. The accompanying fi gure compares four of these indices (Japan, Germany, Great Britain, and India) against the U.S. Dow Jones Industrial Average.

Hong Kong In Hong Kong, the primary stock index is the Hang Seng. Cre- ated by HSI Services Limited, the Hang Seng index refl ects the performance of the Hong Kong stock market. It is com- prised of 33 domestic stocks (accounting for about 70% of the market’s capitalization), which are divided into four sub- indices: Commerce and Industry, Finance, Utilities, and Properties.

Germany The major indicator of the German stock market, the XETRA DAX, is comprised of 30 German blue chip stocks. These stocks are listed on the Frankfurt exchange, and they are representative of the industrial structure of the German economy.

Great Britain The FT-SE 100 Index (pronounced “footsie”) is the most widely followed indicator of equity investments in Great Britain. It is a value-weighted index comprised of the 100 largest companies on the London Stock Exchange, and its value is calculated every minute during the trading session.

Japan In Japan, the principal barometer of stock performance is the Nikkei 225 Index. The index’s value, which is calculated every minute throughout daily trading, consists of a collection of highly liquid equity issues thought to be representative of the Japanese economy.

Chile The Santiago Stock Exchange has three main share indices: the General Stock Price Index (IGPA), the Selective Stock Price Index (IPSA), and the INTER-10 Index. The IPSA, which refl ects the price variations of the most active stocks, is comprised of 40 of the most actively traded stocks on the exchange.

India Of the 22 stock exchanges in India, the Bombay Stock Exchange (BSE) is the largest, with more than 6,000 listed stocks and approximately two-thirds of the country’s total trading volume. Established in 1875, the exchange is also the oldest in Asia. Its yardstick is the BSE Sensex, an index of 30 publicly traded Indian stocks that account for one-fi fth of the BSE’s market capitalization.

Spain In Spain, the IBEX 35 is the offi cial index for measuring equity market performance. This index is comprised of the 35 most actively traded securities on the Joint Stock Exchange Sys- tem (comprising the four Spanish stock exchanges).

STOCK MARKET INDICES AROUND THE WORLD

553Chapter 17 Multinational Financial Management

Source: Adapted from Yahoo Finance historical quotes obtained from the web site at http://fi nance.yahoo.com.

1/95 1/96 1/97 1/98 1/99 1/00 1/01 1/02 1/03 1/04 1/05 1/06 1/07

300

Relative Value (%)

250

India

Germany

United States

Great Britain

Japan

200

150

100

–50

–100

Selected International Stock Indices—Compound Returns Since January 1995

“bulldogs” are foreign bonds issued in London, and “samurai bonds” are foreign bonds issued in Tokyo. Foreign bonds can have a fi xed-rate coupon or a fl oating- rate coupon, and they have the same maturities as the purely domestic bonds with which they must compete for funds.

17-9b International Stock Markets New issues of stock are sold in international markets for a variety of reasons. For example, a Turkish fi rm might sell an equity issue in the United States because it can tap a much larger source of capital than in its home country. Also, a U.S. fi rm might tap the Turkish market because it wants to create an equity market presence to accom- pany its operations in that country. Occasionally, large multinational companies also issue new stock simultaneously in multiple countries. For example, Alcan Aluminum, a Canadian company, simultaneously issued new stock in Canada, Europe, and the United States using different underwriting syndicates in each market.

In addition to new issues, outstanding stocks of large multinational companies are occasionally listed on several international exchanges. For example, Coca- Cola’s stock is traded on six stock exchanges in the United States, four exchanges in Switzerland, and the Frankfurt exchange in Germany. Some 500 foreign stocks are

http://finance.yahoo.com

554 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

17-10 INVESTING OVERSEAS Investors should consider additional risk factors if they invest overseas. First, there is country risk, which refers to the risk involved in investing in a particular coun- try. This risk depends on the country’s economic, political, and social environ- ment. Some countries provide a safer investment climate and therefore less country risk than others. Examples of country risk include the risk that property will be expropriated without adequate compensation in addition to risks associated with changes in tax rates, regulations, and currency repatriation. Country risk also includes changes in host-country requirements regarding local production and employment as well as the danger of damage due to internal strife, ranging from crippling strikes to terrorism and civil war.

It is especially important to keep in mind when investing overseas that securi- ties are often denominated in a currency other than the dollar, which means that returns on the investment depend on what happens to exchange rates. This is known as exchange rate risk. For example, if a U.S. investor purchases a Japanese bond, interest will probably be paid in yen, which must then be converted into dollars before the investor can spend his or her money in the United States. If the yen weakens relative to the dollar, it will buy fewer dollars; hence, fewer dollars will be received when funds are repatriated. However, if the yen strengthens, the effective investment return will increase. It therefore follows that returns on a for- eign investment depend on the in-country performance of the foreign security and on changes in exchange rates.

Country Risk The risk that arises from investing or doing business in a particular country.

Exchange Rate Risk The risk that exchange rate changes will reduce the number of dollars provided by a given amount of a foreign currency.

SEL F TEST What are the three major types of international credit markets?

What is LIBOR?

What are ADRs?

SEL F TEST What is country risk?

What is exchange rate risk?

On what two factors does the return on a foreign investment depend?

listed in the United States—one example is Royal Dutch Petroleum, which is listed on the NYSE. U.S. investors also can invest in foreign companies through American Depository Receipts (ADRs), which are certifi cates representing ownership of for- eign stock held in trust. About 1,700 ADRs are now available in the United States, with most of them traded on the over-the-counter (OTC) market. However, more and more ADRs are being listed on the New York Stock Exchange, including England’s British Airways, Japan’s Honda Motors, and Italy’s Fiat Group.

American Depository Receipts (ADRs) Certificates representing ownership of foreign stock held in trust.

555Chapter 17 Multinational Financial Management

Various forecasting services measure the level of country risk in diff erent countries and provide indexes that indicate factors such as each country’s expected economic perfor- mance, access to world capital markets, political stability, and level of internal confl ict. Country risk analysts use sophisticated models to measure risk, thus providing corpo- rate managers and investors with a way to judge both the relative and absolute risk of investing in diff erent countries. A sample of recent country risk estimates compiled by Insti- tutional Investor is presented in the accompanying table. The higher a country’s score, the lower its country risk. The maximum possible score is 100.

Rank Country Total Score 1 Switzerland 96.4 7 Germany 94.8

11 France 94.1 12 United Kingdom 94.0 13 United States 93.8 17 Japan 91.4 29 South Korea 79.9 33 Chile 77.4 34 China 76.5 44 Russia 69.4

Rank Country Total Score 46 Mexico 69.3 52 South Africa 65.8 55 India 62.7 60 Brazil 60.6 70 Turkey 52.0 84 Argentina 41.9 92 Iran 35.7

118 Tanzania 27.9 161 Iraq 13.9 174 Zimbabwe 5.8

The countries with the least country risk have strong market- based economies, ready access to worldwide capital mar- kets, relatively little social unrest, a stable political climate, relatively low infl ation, and a sound currency. Switzerland’s top ranking may surprise you, but that country’s ranking is the result of its strong economic performance and political stability. You also may be surprised that the United States was ranked 13th. At the lower end of the range, there are fewer surprises. Each of those countries has considerable social and political unrest and no market-based economic system. An investment in any of these countries is clearly a risky proposition.

MEASURING COUNTRY RISK

Source: Excerpted from Harvey P. Shapiro, “Feeling the U.S.’s Pain,” Institutional Investor, March 2008, pp. 107–110.

The U.S. stock market represents approximately 35% of the world stock market; as a result, many U.S. investors hold at least some foreign stock. Analysts have long touted the benefi ts of investing overseas, arguing that foreign stocks improve diver- sifi cation and provide good growth opportunities. When investing in international stocks, you need to rec- ognize that you are investing in both the foreign market and the foreign currency. Table 17-4 indicates how stocks in each country performed in 2007. Column 2 indicates how stocks in each country performed in terms of the U.S. dollar, while Column 3 shows how the country’s stocks performed in terms of its local currency. For example, in 2007, Brazilian stocks rose

by 42.6%, but the Brazilian real increased by about 20% versus the U.S. dollar. Therefore, if a U.S. investor had bought Brazilian stocks, he or she would have made 42.6% in Brazilian real terms; but those Brazilian reals would have bought 20% more U.S. dollars, so the eff ective return would have been 71.1%. Thus, the results of foreign investments depend on the foreign market and on what happens to the exchange rate. Indeed, when you invest overseas, you are making two bets: (1) that foreign stocks will increase in their local markets and (2) that the currencies in which you will be paid will rise relative to the dollar. For Brazil and most of the other countries shown in Table 17-4, both of those factors were favorable in 2007.

INVESTING IN INTERNATIONAL STOCKS

(Continued)

556 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Source: “Ups and Downs Around the World,” The Wall Street Journal, January 2, 2008, p. R4.

Country Return in U.S. Dollars Return in Local Currency Brazil #71.1% #42.6% Malaysia #44.6 #35.5 Hong Kong #44.5 #44.9 Thailand #39.0 #29.5 Indonesia #39.0 #45.1 Finland #39.0 #25.3 Philippines #36.7 #15.1 South Korea #33.6 #34.5 Germany #30.5 #17.7 Greece #29.8 #17.1 Singapore #27.6 #19.7 Canada #27.1 #7.8 Norway #26.8 #10.6 Australia #25.3 #12.4 Portugal #24.5 #12.3 Chile #23.0 #15.1 Spain #17.8 #6.2 Denmark #17.6 #6.1 Iceland #13.1 $0.2 South Africa #12.6 #9.1 Netherlands #12.0 #1.0 France #11.3 #0.4 Mexico #10.8 #11.7 Taiwan #6.5 #6.0 Belgium #5.6 $4.7 Switzerland #5.6 $2.0 United Kingdom #3.8 #2.1 United States #3.8 #3.8 New Zealand #2.2 $6.4 Italy #1.7 $8.3 Austria #1.6 $8.4 Sweden $3.1 $8.5 Japan $6.0 $11.9 Ireland $19.2 $27.1

World #8.4 — World except U.S. #11.8 —

Dow Jones Global Stock Indexes in 2007 (Ranked by Performance in U.S.-Dollar Terms)

T a b l e 1 7 - 4

17-11 INTERNATIONAL CAPITAL BUDGETING Up to now, we have discussed the general environment in which multinational fi rms operate. In the remainder of the chapter, we discuss how international factors affect key corporate decisions. We begin with capital budgeting. Although the same basic principles of capital budgeting apply to both foreign and domestic operations, there are some key differences. First, cash fl ow estimation is more complex for overseas investments. Most multinational fi rms set up separate

557Chapter 17 Multinational Financial Management

subsidiaries for each foreign country in which they operate, and the relevant cash fl ows for the parent company are the dividends and royalties paid by the subsid- iaries to the parent. Second, these cash fl ows must be converted into the parent company’s currency, so they are subject to exchange rate risk. For example, General Motors’ German subsidiary may make a profi t of 100 million euros in 2008, but the value of this profi t to GM will depend on the dollar/euro exchange rate: How many dollars will 100 million euros buy?

Dividends and royalties are normally taxed by both foreign and home-country governments. Furthermore, a foreign government may restrict the repatriation of earnings to the parent company. For example, some governments place a ceiling, often stated as a percentage of the company’s net worth, on the amount of cash dividends that a subsidiary can pay to its parent. Such restrictions are normally intended to force multinational fi rms to reinvest earnings in the foreign country, although restrictions are sometimes imposed to prevent large currency outfl ows that might disrupt the exchange rate.

Whatever the host country’s motivation for blocking repatriation of profi ts, the result is that the parent corporation cannot use cash fl ows blocked in the for- eign country to pay dividends to its shareholders or to invest elsewhere in the business. Hence, from the perspective of the parent organization, the cash fl ows that are relevant for foreign investment analysis are those that the subsidiary is actually ex- pected to send back to the parent. The present value of those cash fl ows is found by applying an appropriate discount rate, and this present value is then compared with the parent’s required investment to determine the project’s NPV.

In addition to the complexities of the cash fl ow analysis, the cost of capital may be different for a foreign project than for an equivalent domestic project because foreign projects may be more or less risky. Higher risks might arise from (1) exchange rate risk and (2) political risk. A lower risk might result from the benefi ts of international diversifi cation.

The foreign currency cash fl ows to be turned over to the parent must be con- verted into U.S. dollars by translating them at expected future exchange rates. An analysis should be conducted to ascertain the effects of exchange rate variations; and on the basis of this analysis, an exchange rate risk premium should be added to the domestic cost of capital to refl ect this risk. It is sometimes possible to hedge against exchange rate fl uctuations; but this may not be possible, especially on long-term projects. If hedging is used, the costs of doing so must be subtracted from the project’s cash fl ows.

Political risk refers to potential actions by a host government that would reduce the value of a company’s investment. It includes at one extreme the expropriation without compensation of the subsidiary’s assets; but it also includes less drastic ac- tions that reduce the value of the parent fi rm’s investment in the foreign subsidiary, including higher taxes, tighter repatriation or currency controls, and restrictions on prices charged. The risk of expropriation is small in traditionally friendly and stable countries such as Great Britain and Switzerland. However, in Latin America, Africa, the Far East, and Eastern Europe, the risk may be substantial. Past expropriations in- clude those of ITT and Anaconda Copper in Chile; Gulf Oil in Bolivia; Occidental Petroleum in Libya; and the assets of many companies in Iraq, Iran, and Cuba.

Note that companies can take several steps to reduce the potential loss from expropriation: (1) fi nance the subsidiary with local capital, (2) structure operations so that the subsidiary has value only as a part of the integrated corporate system, and (3) obtain insurance against economic losses due to expropriation from a source such as the Overseas Private Investment Corporation (OPIC). In the latter case, insurance premiums would have to be added to the project’s cost.

Several organizations rate the country risk, or the risk associated with invest- ing in a particular country. These ratings are based on the country’s social, politi- cal, and economic environment—its business climate. Perhaps surprisingly, many

Repatriation of Earnings The process of sending cash flows from a foreign subsidiary back to the parent company.

Political Risk Potential actions by a host government that would reduce the value of a company’s investment.

Business Climate Refers to a country’s social, political, and economic environment.

558 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

of these studies suggest that the United States does not have the lowest level of country risk. This is particularly signifi cant because even though people in the United States often assume that its bonds have no country risk, others do not agree. Foreign investors are concerned about how changes in U.S. policies (e.g., tax or Federal Reserve policies) might affect their investments. To the extent that these perceptions about U.S. country risk infl uence investors’ willingness to hold U.S. securities, they will have an effect on U.S. interest rates.

SEL F TEST List some key diff erences in capital budgeting as applied to foreign versus

domestic operations.

What are the relevant cash fl ows for an international investment—the cash fl ows produced by the subsidiary in the country in which it operates or the cash fl ows in dollars that it sends to its parent company? Explain.

Why might the cost of capital for a foreign project diff er from that of an equivalent domestic project? Could it be lower? Explain.

What adjustments might be made to the domestic cost of capital for a for- eign investment due to exchange rate risk, political risk, and country risk?

17-12 INTERNATIONAL CAPITAL STRUCTURES Capital structures vary across countries. For example, the Organization for Eco- nomic Cooperation and Development (OECD) recently reported that, on average, Japanese fi rms have 85% debt to total assets (in book value terms), German fi rms have 64%, and U.S. fi rms have 55%. One problem, however, when interpreting these numbers is that different countries often use different accounting conven- tions with regard to (1) reporting assets on a historical-cost versus a replacement- cost basis, (2) treating leased assets, (3) reporting pension plan liabilities, and (4) capitalizing versus expensing R&D costs. These differences make it diffi cult to compare capital structures.

A study by Raghuram Rajan and Luigi Zingales of the University of Chicago attempted to control for different accounting practices. In their study, Rajan and Zingales used a database that covers fewer fi rms than the OECD but one that pro- vides a more complete breakdown of balance sheet data. They concluded that dif- ferences in accounting practices can explain much but not all of the cross-country variations.

Rajan and Zingales’s results are summarized in Table 17-5. There are a number of different ways to measure capital structure. One way is the average ratio of total liabilities to total assets—this is similar to the measure used by the OECD, and it is reported in Column 1. Based on this measure, German and Japanese fi rms appear to be more highly levered than U.S. fi rms. However, if you look at Column 2, where capital structure is measured by interest-bearing debt to total assets, it appears that German fi rms use less leverage than U.S. and Japanese fi rms. What explains this difference? Rajan and Zingales argue that much of this difference is explained by the way German fi rms account for pension liabilities. German fi rms generally include all pension liabilities (and their offsetting assets) on the balance sheet, whereas fi rms in other countries (including the United States) generally “net out” pension assets and liabilities on their balance sheets. To see the importance of this difference, consider a fi rm with $10 million in liabilities (not including pension liabilities) and $20 million in assets (not including pension assets). Assume that the fi rm has $10 million in pension liabilities that are fully funded by $10 million in

559Chapter 17 Multinational Financial Management

pension assets. Therefore, net pension liabilities are zero. If this fi rm was in the United States, it would report a ratio of total liabilities to total assets equal to 50% ($10 million/$20 million). By contrast, if this fi rm operated in Germany, both its pension assets and liabilities would be reported on the balance sheet. The fi rm would have $20 million in liabilities and $30 million in assets—or a 67% ($20 mil- lion/$30 million) ratio of total liabilities to total assets. Total debt is the sum of short-term debt and long-term debt and excludes other liabilities including pen- sion liabilities. Therefore, the measure of total debt to total assets provides a more comparable measure of leverage across different countries.

Rajan and Zingales also make a variety of adjustments that attempt to control for other differences in accounting practices. The effects of these adjustments are reported in Columns 3 and 4. Overall, the evidence suggests that companies in Germany and the United Kingdom tend to have less leverage, whereas fi rms in Canada appear to have more leverage relative to fi rms in the United States, France, Italy, and Japan. This conclusion is supported by data in the fi nal column, which shows the average times-interest-earned ratio for fi rms in a number of different countries. Recall from Chapter 4 that the TIE ratio is the ratio of operating income (EBIT) to interest expense. This measure indicates how much cash the fi rm has available to service its interest expense. In general, fi rms with more leverage have a lower times-interest-earned ratio. The data indicate that this ratio is highest in the United Kingdom and Germany and lowest in Canada.

Median Capital Structures among Large Industrialized Countries (Measured In Terms of Book Value)

T a b l e 1 7 - 5

Country

Total Liabilities to Total Assets (Unadjusted

for Accounting Differences)

(1)

Debt to Total Assets (Unadjusted

for Accounting Differences)

(2)

Total Liabilities to Total Assets

(Adjusted for

Accounting Differences)

(3)

Debt to Total Assets

(Adjusted for

Accounting Differences)

(4)

Times Interest

Earned (TIE) Ratio

(5) Canada 56% 32% 48% 32% 1.55% France 71 25 69 18 2.64 Germany 73 16 50 11 3.20 Italy 70 27 68 21 1.81 Japan 69 35 62 21 2.46 United Kingdom 54 18 47 10 4.79 United States 58 27 52 25 2.41 Mean 64% 26% 57% 20% 2.69% Standard deviation 8% 7% 10% 8% 1.07%

Source: Raghuram Rajan and Luigi Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data,” Journal of Finance, Vol. 50, no. 5 (December 1995), pp. 1421–1460. Used with permission.

SEL F TEST Do international diff erences in fi nancial leverage exist? Explain.

560 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

Over the past two decades, the global economy has become increasingly integrated and more companies generate more of their profi ts from overseas operations. In many respects, the concepts developed in the fi rst 16 chapters still apply to multina- tional fi rms. However, multinational companies have more opportunities but also face diff erent risks than do companies that operate only in their home market. The chapter discussed many of the key trends aff ecting the global markets today, and it described the most important diff erences between multinational and domestic fi - nancial management.

T YING I T ALL TO GETHER

KEY TERMS Define each of the following terms: a. Multinational, or global, corporation b. Vertically integrated investment c. International monetary system d. Exchange rate e. Freely-floating regime; managed-float regime f. Currency board arrangement g. Fixed-peg arrangement h. Cross rate i. American terms; European terms j. Direct quotation; indirect quotation k. Spot rate; forward exchange rate l. Discount on forward rate; premium on forward rate m. Interest rate parity; purchasing power parity n. Eurocredits; Eurodollar o. Eurobond; foreign bond p. American Depository Receipts (ADRs); repatriation of earnings q. Country risk; exchange rate risk; political risk; business climate

CROSS RATES Suppose the exchange rate between the U.S. dollar and the EMU euro is €0.65" $1.00 and the exchange rate between the U.S. dollar and the Canadian dollar is $1.00 " C$0.98. What is the cross rate of euros to Canadian dollars?

Why do U.S. corporations build manufacturing plants abroad when they can build them at home?

If the euro depreciates against the U.S. dollar, can a dollar buy more or fewer euros as a result?

If the United States imports more goods from abroad than it exports, foreigners will tend to have a surplus of U.S. dollars. What will this do to the value of the dollar with respect to foreign currencies? What is the corresponding effect on foreign investments in the United States?

SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A)

ST-1ST-1

ST-2ST-2

QUESTIONSQUESTIONS

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561Chapter 17 Multinational Financial Management

Should firms require higher rates of return on foreign projects than on identical projects located at home? Explain.

Does interest rate parity imply that interest rates are the same in all countries?

Why might purchasing power parity fail to hold?

What is a Eurodollar? If a French citizen deposits $10,000 in Chase Manhattan Bank in New York, have Eurodollars been created? What if the deposit is made in Barclay’s Bank in London? Chase Manhattan’s Paris branch? Does the existence of the Eurodollar market make the Federal Reserve’s job of controlling U.S. interest rates easier or more difficult? Explain.

EXCHANGE RATE If British pounds sell for $2 (U.S.) per pound, what should dollars sell for in pounds per dollar?

CROSS RATES A currency trader observes that in the spot exchange market, 1 U.S. dollar can be exchanged for 3.50 Israeli shekels or for 104.00 Japanese yen. What is the cross- exchange rate between the yen and the shekel; that is, how many yen would you receive for every shekel exchanged?

INTEREST RATE PARITY Six-month T-bills have a nominal rate of 7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5%. In the spot exchange market, 1 yen equals $0.009. If interest rate parity holds, what is the 6-month forward exchange rate?

PURCHASING POWER PARITY A television costs $500 in the United States. The same television costs 312.5 euros. If purchasing power parity holds, what is the spot exchange rate between the euro and the dollar?

EXCHANGE RATES Table 17-1 lists foreign exchange rates for May 26, 2008. On that day, how many dollars would be required to purchase 1,000 units of each of the following: British pounds, Canadian dollars, EMU euros, Japanese yen, Mexican pesos, and Swedish kronas?

EXCHANGE RATES Look up the six currencies in Problem 17-5 in the foreign exchange section of a current issue of The Wall Street Journal. a. What is the current exchange rate for changing dollars into 1,000 units of pounds,

Canadian dollars, euros, yen, Mexican pesos, and Swedish kronas? b. What is the percentage gain or loss between the May 26, 2008, exchange rate and the

current exchange rate for each of the currencies in Part a?

CURRENCY APPRECIATION Suppose that 1 Danish krone could be purchased in the foreign exchange market today for $0.20. If the krone appreciated 10% tomorrow against the dollar, how many krones would a dollar buy tomorrow?

CROSS RATES Suppose the exchange rate between the U.S. dollar and the Swedish krona was 6 krona " $1 and the exchange rate between the dollar and the British pound was £1 " $2. What was the exchange rate between Swedish kronas and pounds?

CROSS RATES Look up the three currencies in Problem 17-8 in the foreign exchange section of a current issue of The Wall Street Journal. What is the current exchange rate between Swedish kronas and pounds?

INTEREST RATE PARITY Assume that interest rate parity holds. In both the spot market and the 90-day forward market, 1 Japanese yen " 0.0086 dollar. And 90-day risk-free securities yield 4.6% in Japan. What is the yield on 90-day risk-free securities in the United States?

PURCHASING POWER PARITY In the spot market, 10.5 Mexican pesos can be exchanged for 1 U.S. dollar. A compact disc costs $15 in the United States. If purchasing power parity (PPP) holds, what should be the price of the same disc in Mexico?

INTEREST RATE PARITY Assume that interest rate parity holds and that 90-day risk-free securities yield 5% in the United States and 5.3% in Britain. In the spot market, 1 pound " $2. a. Is the 90-day forward rate trading at a premium or a discount relative to the spot rate? b. What is the 90-day forward rate?

17-417-4

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PROBLEMS PROBLEMS

17-117-1Easy Problems 1–4 Easy Problems 1–4

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17-317-3

17-417-4

17-517-5Intermediate Problems 5–11 Intermediate Problems 5–11

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17-817-8

17-917-9

17-1017-10

17-1117-11

17-1217-12Challenging Problems 12–17

Challenging Problems 12–17

562 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

SPOT AND FORWARD RATES Chamberlain Canadian Imports has agreed to purchase 15,000 cases of Canadian beer for 4 million Canadian dollars at today’s spot rate. The firm’s financial manager, James Churchill, has noted the following current spot and forward rates:

U.S. Dollar/Canadian Dollar Canadian Dollar/U.S. Dollar Spot 1.0526 0.9500 30-day forward 1.0504 0.9520 90-day forward 1.0471 0.9550 180-day forward 1.0444 0.9575

On the same day, Churchill agrees to purchase 15,000 more cases of beer in 3 months at the same price of 4 million Canadian dollars. a. What is the price of the beer in U.S. dollars if it is purchased at today’s spot rate? b. What is the cost in U.S. dollars of the second 15,000 cases if payment is made in

90 days and the spot rate at that time equals today’s 90-day forward rate? c. If the exchange rate for the Canadian dollar is 0.90 to $1 in 90 days, how much will

Churchill have to pay for the beer (in U.S. dollars)?

EXCHANGE GAINS AND LOSSES You are the vice president of International InfoXchange, headquartered in Chicago, Illinois. All shareholders of the firm live in the United States. Earlier this month you obtained a loan of 5 million Canadian dollars from a bank in Toronto to finance the construction of a new plant in Montreal. At the time the loan was received, the exchange rate was $1.05 to the Canadian dollar. By the end of the month, it has unexpectedly dropped to 95 cents. Has your company made a gain or a loss as a result, and by how much?

RESULTS OF EXCHANGE RATE CHANGES Early in September 1983, it took 245 Japanese yen to equal $1. Nearly 25 years later, in May 2008, that exchange rate had fallen to 103.5 yen to $1. Assume that the price of a Japanese-manufactured automobile was $9,000 in September 1983 and that its price changes were in direct relation to exchange rates. a. Has the price, in dollars, of the automobile increased or decreased during the 25-year

period because of changes in the exchange rate? b. What would the dollar price of the automobile be in May 2008, again assuming that

the car’s price changes only with exchange rates?

FOREIGN INVESTMENT ANALYSIS After all foreign and U.S. taxes, a U.S. corporation expects to receive 3 pounds of dividends per share from a British subsidiary this year. The exchange rate at the end of the year is expected to be $2 per pound, and the pound is expected to depreciate 5% against the dollar each year for an indefinite period. The dividend (in pounds) is expected to grow at 10% a year indefinitely. The parent U.S. corporation owns 10 million shares of the subsidiary. What is the present value in dollars of its equity ownership of the subsidiary? Assume a cost of equity capital of 15% for the subsidiary.

FOREIGN CAPITAL BUDGETING Solitaire Machinery is a Swiss multinational manufacturing company. Currently, Solitaire’s financial planners are considering undertaking a 1-year project in the United States. The project’s expected dollar- denominated cash flows consist of an initial investment of $1,000 and a cash inflow the following year of $1,200. Solitaire estimates that its risk-adjusted cost of capital is 14%. Currently, 1 U.S. dollar will buy 1.025 Swiss francs. In addition, 1-year risk-free securities in the United States are yielding 7.25%, while similar securities in Switzerland are yielding 4.5%. a. If this project was instead undertaken by a similar U.S.-based company with the same

risk-adjusted cost of capital, what would be the net present value and rate of return generated by this project?

b. What is the expected forward exchange rate 1 year from now? c. If Solitaire undertakes the project, what is the net present value and rate of return of

the project for Solitaire?

MULTINATIONAL FINANCIAL MANAGEMENT Yohe Telecommunications is a multinational corporation that produces and distributes telecommunications technology. Although its corporate headquarters are located in Maitland, Florida, Yohe usually buys its raw materials in several different foreign countries using several different foreign

17-1317-13

17-1417-14

17-1517-15

17-1617-16

17-1717-17

COMPREHENSIVE/SPREADSHEET PROBLEMCOMPREHENSIVE/SPREADSHEET PROBLEM

17-1817-18

563Chapter 17 Multinational Financial Management

MULTINATIONAL FINANCIAL MANAGEMENT Citrus Products Inc. is a medium-sized producer of citrus juice drinks with groves in Indian River County, Florida. Until now, the company has confined its operations and sales to the United States; but its CEO, George Gaynor, wants to expand into the Pacific Rim. The first step is to set up sales subsidiaries in Japan and Australia, then to set up a production plant in Japan, and finally to distrib- ute the product throughout the Pacific Rim. The firm’s financial manager, Ruth Schmidt, is enthusiastic about the plan; but she is worried about the implications of the foreign expansion on the firm’s financial management pro- cess. She has asked you, the firm’s most recently hired financial analyst, to develop a 1-hour tutorial package that explains the basics of multinational financial management. The tutorial will be presented at the next board of directors meeting. To get you started, Schmidt has given you the following list of questions.

a. What is a multinational corporation? Why do firms expand into other countries? b. What are the five major factors that distinguish multinational financial management from financial manage-

ment as practiced by a purely domestic firm? c. Consider the following illustrative exchange rates:

U.S. Dollars Required to Buy One Unit of Foreign Currency

Japanese yen 0.009 Australian dollar 0.650

(1) Are these currency prices direct quotations or indirect quotations? (2) Calculate the indirect quotations for yen and Australian dollars. (3) What is a cross rate? Calculate the two cross rates between yen and Australian dollars. (4) Assume that Citrus Products can produce a liter of orange juice and ship it to Japan for $1.75. If the firm

wants a 50% markup on the product, what should the orange juice sell for in Japan? (5) Now assume that Citrus Products begins producing the same liter of orange juice in Japan. The product

costs 250 yen to produce and ship to Australia, where it can be sold for 6 Australian dollars. What is the U.S. dollar profit on the sale?

(6) What is exchange rate risk?

17-1917-19

IN TEGRATED C ASE CITRUS PRODUCTS INC.

currencies. The matter is further complicated because Yohe often sells its products in other foreign countries. One product in particular, the SY-20 radio transmitter, draws Component X, Component Y, and Component Z (its principal components) from Switzerland, France, and England, respectively. Specifically, Component X costs 165 Swiss francs, Component Y costs 20 euros, and Component Z costs 105 British pounds. The largest market for the SY-20 is Japan, where the product sells for 38,000 Japanese yen. Naturally, Yohe is intimately concerned with economic conditions that could adversely affect dollar exchange rates. You will find Tables 17-1, 17-2, and 17-3 useful for completing this problem. a. How much in dollars does it cost Yohe to produce the SY-20? What is the dollar sale

price of the SY-20? b. What is the dollar profit that Yohe makes on the sale of the SY-20? What is the per-

centage profit? c. If the U.S. dollar was to weaken by 10% against all foreign currencies, what would be

the dollar profit for the SY-20? d. If the U.S. dollar was to weaken by 10% only against the Japanese yen and remained

constant relative to all other foreign currencies, what would be the dollar and per- centage profits for the SY-20?

e. Using the 180-day forward exchange information from Table 17-3, calculate the return on 1-year securities in Switzerland assuming the rate of return on 1-year securities in the United States is 4.9%.

f. Assuming that purchasing power parity (PPP) holds, what would be the sale price of the SY-20 if it was sold in England rather than Japan?

564 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management

d. Briefly describe the current international monetary system. What are the different types of exchange rate systems?

e. What is the difference between spot rates and forward rates? When is the forward rate at a premium to the spot rate? at a discount?

f. What is interest rate parity? Currently, you can exchange 1 yen for 0.0095 U.S. dollar in the 30-day forward market, and the risk-free rate on 30-day securities is 4% in both Japan and the United States. Does interest rate parity hold? If not, which securities offer the highest expected return?

g. What is purchasing power parity (PPP)? If grapefruit juice costs $2 a liter in the United States and purchas- ing power parity holds, what should be the price of grapefruit juice in Australia?

h. What effect does relative inflation have on interest rates and exchange rates? i. (1) Briefly explain the three major types of international credit markets. (2) Briefly explain how ADRs work. j. To what extent do average capital structures vary across different countries? k. What is the effect of multinational operations on capital budgeting decisions?

APPEND IX A

SOLUTIONS TO SELF-TEST QUESTIONS AND PROBLEMS Note: Except for Chapter 1, we do not show an answer for ST-1 problems because they are verbal rather than quantitative in nature.

Chapter 1 Refer to the marginal glossary defi nitions or relevant chapter sections to check your responses.

Chapter 3 a. EBIT $5,000,000

Interest 1,000,000 EBT $4,000,000 Taxes (40%) 1,600,000 Net income $2,400,000

b. NWC ! Current assets " (Payables # Accruals) ! $14,000,000 " ($3,000,000 # $1,000,000)

! $10,000,000

c. FCF ! EBIT(1 " T) # Depreciation " ! Capital expenditures # Increase in net working capital " ! [$5,000,000(0.6) # $1,000,000] " [$3,000,000 # 0]

! $4,000,000 " $3,000,000

! $1,000,000

d. Retained earnings at the end of the year can be calculated as follows:

Balance of retained earningsBOY $4,500,000 Add: Net income* 2,400,000 Less: Common dividends 1,200,000 Balance of retained earningsEOY $5,700,000

*Net income was calculated in Part a.

Chapter 4 Billingsworth paid $2 in dividends and retained $2 per share. Since total retained earnings rose by $12 million, there must be 6 million shares outstanding. With a book value of $40 per share, total common equity must be $40(6 million) ! $240 million. Since Billingsworth has $120 million of debt, its debt ratio must be 33.3%:

Debt ______ Assets ! Debt _____________ Debt # Equity !

$120 million ________________________ $120 million # $240 million

! 0.333 ! 33.3%

a. In answering questions such as this, always begin by writing down the relevant defi nitional equations, then start fi lling in numbers. Note that the extra zeros in- dicating millions have been deleted in the following calculations.

ST-1ST-1

ST-2ST-2

ST-3ST-3

A-1

A-2 Appendix A Solutions to Self-Test Questions and Problems

(1) DSO ! Accounts receivable __________________ Sales/365

40.55 ! A/R _________ Sales/365

A/R ! 40.55($2.7397) ! $111.1 million

(2) Current ratio ! Current assets _______________ Current liabilities ! 3.0

! Current assets _____________ $105.5 ! 3.0

Current assets ! 3.0($105.5) ! $316.50 million

(3) Total assets ! Current assets # Fixed assets ! $316.5 # $283.5 ! $600 million

(4) ROA ! Profi t margin $ Total assets turnover

! Net income __________ Sales $ Sales __________ Total assets

! $50 ______ $1,000 $ $1,000 ______ $600

! 0.05 $ 1.667 ! 0.083333 ! 8.3333%

(5) ROE ! ROA $ Assets ______ Equity

12.0% ! 8.3333% $ $600 ______ Equity

Equity ! (8.3333%)($600) _______________ 12.0%

! $416.67 million

(6) Current assets ! Cash and equivalents # Accounts receivable # Inventories $316.5 ! $100.0 # $111.1 # Inventories Inventories ! $105.4 million

Quick ratio ! Current assets " Inventories _________________________ Current liabilities

! $316.5 " $105.4 _______________ $105.5 ! 2.00

(7) Total assets ! Total claims ! $600 million

Current liabilities # Long-term debt # Equity ! $600 million $105.5 # Long-term debt # $416.67 ! $600 million Long-term debt ! $600 " $105.5 " $416.67 ! $77.83 million

Note: We could have found equity as follows:

ROE ! Net income __________ Equity

12.0% ! $50 ______ Equity

Equity ! $50/0.12 ! $416.67 million

Then we could have gone on to fi nd long-term debt.

b. Kaiser’s average sales per day were $1,000/365 ! $2.74 million. Its DSO was 40.55, so A/R ! 40.55($2.74) ! $111.1 million. Its new DSO of 30.4 would cause A/R ! 30.4($2.74) ! $83.3 million. The reduction in receivables would be $111.1 – $83.3 ! $27.8 million, which would equal the amount of cash generated.

A-3Appendix A Solutions to Self-Test Questions and Problems

(1) New equity ! Old equity " Stock bought back ! $416.7 " $27.8 ! $388.9 million

Thus,

New ROE ! Net income __________ New equity

! $50 ______ $388.9

! 12.86% (versus old ROE of 12.0%)

(2) New ROA ! Net income ____________________________ Total assets " Reduction in A/R

! $50 ____________ $600 " $27.8

! 8.74% (versus old ROA of 8.33%)

(3) The old debt is the same as the new debt:

Debt ! Total claims " Equity ! $600 " $416.7 ! $183.3 million

New total assets ! Old total assets " Reduction in A/R ! $600 " $27.8 ! $572.2 million

Therefore,

Debt ______________ Old total assets ! $183.3 ______ $600 ! 30.6%

while

New debt _______________ New total assets ! $183.3 ______ $572.2 ! 32.0%

Chapter 5 a.

$1,000 is being compounded for 3 years; so your balance on January 1, 2012, is $1,259.71:

FVN ! PV(1 # I) N ! $1,000(1 # 0.08)3 ! $1,259.71

Alternatively, using a fi nancial calculator, input N ! 3, I/YR ! 8, PV ! "1000, PMT ! 0, and FV ! ? Solve for FV ! $1,259.71.

FVN ! PV ! 1 # I NOM ____ M " NM

! FV12 ! $1,000(1.02) 12 ! $1,268.24

Alternatively, using a fi nancial calculator, input N ! 12, I/YR ! 2, PV ! "1000, PMT ! 0, and FV ! ? Solve for FV ! $1,268.24.

ST-2ST-2 8%

FV = ?

1/1/09 1/1/12

!1,000

1/1/10 1/1/11 8%

FV = ?

1/1/09 1/1/12

!1,000

1/1/10 1/1/11

FV = ?

1/1/10 1/1/09 1/1/11 1/1/12

!1,000

FV = ?

1/1/10 1/1/09 1/1/11 1/1/12

!1,000

A-4 Appendix A Solutions to Self-Test Questions and Problems

Using a fi nancial calculator, input N ! 3, I/YR ! 8, PV ! 0, PMT ! "333.333, and FV ! ? Solve for FV ! $1,082.13.

Using a fi nancial calculator in begin mode, input N ! 3, I/YR ! 8, PV ! 0, PMT ! "333.333, and FV ! ? Solve for FV ! $1,168.70.

Using a fi nancial calculator, input N ! 3, I/YR ! 8, PV ! 0, FV ! 1259.71, and PMT ! ? Solve for PMT ! "$388.03. Therefore, you would have to make 3 payments of $388.03 each beginning on January 1, 2010.

a. Set up a time line like the one in the preceding problem:

Note that your deposit will grow for 4 years at 8%. The deposit on January 1, 2009, is the PV; and the FV is $1,000. Using a fi nancial calculator, input N ! 4, I/YR ! 8, PMT ! 0, FV ! 1000, and PV ! ? Solve for PV ! "$735.03.

PV ! FV N _______ (1 # I) N !

$1,000 ______ (1.08) 4 ! $735.03

Here we are dealing with a 4-year annuity whose fi rst payment occurs 1 year from today, on 1/1/10, and whose future value must equal $1,000. You should modify the time line to help visualize the situation. Using a fi nancial calculator, input N ! 4, I/YR ! 8, PV ! 0, FV ! 1000, and PMT ! ? Solve for PMT ! "$221.92.

c. This problem can be approached in several ways. Perhaps the simplest way is to ask this question: If I received $750 on 1/1/10 and deposited it to earn 8%, would I have the required $1,000 on 1/1/13? The answer is no.

FV3 ! $750(1.08)(1.08)(1.08) ! $944.78

8% 1/1/10 1/1/111/1/09 1/1/12

!333.333 !333.333 !333.333 FV = ?

8% 1/1/10 1/1/111/1/09 1/1/12

!333.333 !333.333 !333.333 FV = ?

8% 1/1/10 1/1/111/1/09 1/1/12

!333.333 !333.333 FV = ?!333.333

8% 1/1/10 1/1/111/1/09 1/1/12

!333.333 !333.333 FV = ?!333.333

8% 1/1/10 1/1/111/1/09 1/1/12

? ? ? FV = 1,259.71

8% 1/1/10 1/1/111/1/09 1/1/12

? ? ? FV = 1,259.71

ST-3ST-3

8% 1/1/10 1/1/111/1/09 1/1/12 1/1/13

FV = 1,000PV = ?

8% 1/1/10 1/1/111/1/09 1/1/12 1/1/13

FV = 1,000PV = ?

8% 1/1/10 1/1/111/1/09 1/1/12

? ? ?

1/1/13

? FV = 1,000

8% 1/1/10 1/1/111/1/09 1/1/12

? ? ?

1/1/13

? FV = 1,000

8% 1/1/10 1/1/111/1/09 1/1/12

!750

1/1/13

FV = ?

8% 1/1/10 1/1/111/1/09 1/1/12

!750

1/1/13

FV = ?

A-5Appendix A Solutions to Self-Test Questions and Problems

This indicates that you should let your father make the payments of $221.92 rather than accept the lump sum of $750. You could also compare the $750 with the PV of the payments as shown here:

Using a fi nancial calculator, input N ! 4, I/YR ! 8, PMT ! "221.92, FV ! 0, and PV ! ? Solve for PV ! $735.03. This is less than the $750 lump sum offer, so your initial reaction might be to accept the lump sum of $750. However, that would be a mistake. The prob- lem is that when you found the $735.03 PV of the annuity, you were fi nding the value of the annuity today, on January 1, 2009. You were comparing $735.03 today with the lump sum of $750 one year from now, which is, of course, in- valid. What you should have done was take the $735.03; recognize that this is the PV of an annuity as of January 1, 2009; multiply $735.03 by 1.08 to get $793.83; and compare $793.83 with the lump sum of $750. You would then take your father’s offer to make the payments of $221.92 rather than take the lump sum on January 1, 2010.

Using a fi nancial calculator, input N ! 3, PV ! "750, PMT ! 0, FV ! 1000, and I/YR ! ? Solve for I/YR ! 10.0642%.

Using a fi nancial calculator, input N ! 4, PV ! 0, PMT ! "200, FV ! 1000, and I/YR ! ? Solve for I/YR ! 15.09%. You might be able to fi nd a borrower willing to offer you a 15% interest rate, but there would be some risk involved—he or she might not actually pay you the $1,000!

Find the future value of the original $400 deposit:

FV6 ! PV(1.04) 6 ! $400(1.2653) ! $506.13

This means that on January 1, 2013, you need an additional sum of $493.87:

$1,000.00 " $506.13 ! $493.87

This will be accumulated by your making 6 equal payments that earn 8% com- pounded semiannually, or 4% each 6 months. Using a fi nancial calculator, input N ! 6, I/YR ! 4, PV ! 0, FV ! 493.87, and PMT ! ? Solve for PMT ! "$74.46. Alternatively, input N ! 6, I/YR ! 4, PV ! "400, FV ! 1000, and PMT ! ? Solve for PMT ! "$74.46.

8% 1/1/10 1/1/111/1/09 1/1/12

!221.92 PV = ?

!221.92 !221.92 !221.92

1/1/13 8%

1/1/10 1/1/111/1/09 1/1/12

!221.92 PV = ?

!221.92 !221.92 !221.92

1/1/13

I = ? 1/1/10 1/1/111/1/09 1/1/12

!750 1,000

1/1/13 I = ?

1/1/10 1/1/111/1/09 1/1/12

!750 1,000

1/1/13

I = ? 1/1/10 1/1/111/1/09 1/1/12

!200 !200 !200 !200 FV = 1,000

1/1/13 I = ?

1/1/10 1/1/111/1/09 1/1/12

!200 !200 !200 !200 FV = 1,000

1/1/13

4% 1/1/10 1/1/111/1/09 1/1/12

!400

1/1/13

? FV = 1,000

?????

4% 1/1/10 1/1/111/1/09 1/1/12

!400

1/1/13

? FV = 1,000

?????

A-6 Appendix A Solutions to Self-Test Questions and Problems

g. Eff ective annual rate ! ! 1 # I NOM ____ M " M

" 1.0

! ! 1 # 0.08 ____ 2 " 2 " 1 ! (1.04) 2 " 1

! 1.0816 " 1 ! 0.0816 ! 8.16%

APR ! IPER $ M ! 0.04 $ 2 ! 0.08 ! 8%

Bank A’s effective annual rate is 8.24%:

Eff ective annual rate ! ! 1 # 0.08 ____ 4 " 4 " 1.0

! (1.02)4 " 1 ! 1.0824 " 1 ! 0.0824 ! 8.24%

Now Bank B must have the same effective annual rate:

! 1 # I NOM ____ 12 " 12

"1.0 ! 0.0824

! 1 # I NOM ____ 12 " 12

! 1.0824

1 # I NOM ____ 12 ! (1.0824)

1/12

1 # I NOM ____ 12 ! 1.00662

I NOM ____ 12 ! 0.00662

INOM ! 0.07944 ! 7.94%

Thus, the two banks have different quoted rates—Bank A’s quoted rate is 8%, while Bank B’s quoted rate is 7.94%; however, both banks have the same effec- tive annual rate of 8.24%. The difference in their quoted rates is due to the dif- ference in compounding frequency.

Chapter 6 a. Average infl ation over 4 years ! (2% # 2% # 2% # 4%)/4 ! 2.5%

b. T4 ! rRF # MRP4 ! r* # IP4 # MRP4 ! 3% # 2.5% # (0.1)3% ! 5.8%

c. C4, BBB ! r* # IP4 # MRP4 # DRP # LP ! 3% # 2.5% # 0.3% # 1.3% # 0.5% ! 7.6%

d. T8 ! r* # IP8 # MRP8 ! 3% # (3 $ 2% # 5 $ 4%)/8 # 0.7% ! 3% # 3.25% # 0.7% ! 6.95%

e. C8, BBB ! r* # IP8 # MRP8 # DRP # LP ! 3% # 3.25% # 0.7% # 1.3% # 0.5% ! 8.75%

ST-4ST-4

ST-2ST-2

A-7Appendix A Solutions to Self-Test Questions and Problems

f. T9 ! r* # IP9 # MRP9 7.3% ! 3% # IP9 # 0.8% IP9 ! 3.5%

3.5% ! (3 $ 2% # 5 $ 4% # X)/9 31.5% ! 6% # 20% # X 5.5% ! X

X ! Inf lation in Year 9 ! 5.5%

T1 ! 6%; T2 ! 6.2%; T3 ! 6.3%; MRP ! 0

a. Yield of 1-year security 1 year from now is calculated as follows:

2 $ 6.2% ! 6% # X 12.4% ! 6% # X 6.4% ! X

b. Yield of 1-year security 2 years from now is calculated as follows:

3 $ 6.3% ! 2 $ 6.2% # X 18.9% ! 12.4% # X 6.5% ! X

c. Yield of 2-year security 1 year from now is calculated as follows:

3 $ 6.3% ! 6% # 2X 18.9% ! 6% # 2X 12.9% ! 2X 6.45% ! X

Chapter 7 a. Pennington’s bonds were sold at par; therefore, the original YTM equaled the

coupon rate of 12%.

b. VB ! # t!1

$120/2 __________ ! 1 # 0.10 ____ 2 "

t # $1,000 __________

! 1 # 0.10 ____ 2 " 50

With a fi nancial calculator, input the following: N ! 50, I/YR ! 5, PMT ! 60, FV ! 1000, and PV ! ? Solve for PV ! $1,182.56.

c. Current yield ! Annual coupon payment/Price ! $120/$1,182.56 ! 0.1015 ! 10.15%

Capital gains yield ! Total yield " Current yield ! 10% " 10.15% ! "0.15%

Total return ! 10%

d. With a fi nancial calculator, input the following: N ! 13, PV ! "916.42, PMT ! 60, FV ! 1000, and rd/2 ! I/YR ! ? Calculator solution ! rd/2 ! 7.00%; therefore, rd ! YTM ! 14.00%.

Current yield ! $120/$916.42 ! 13.09%

Capital gains yield ! 14% " 13.09% ! 0.91%

e. The following time line illustrates the years to maturity of the bond:

7/1/08 1/1/091/1/08 12/31/147/1/09

3/1/08

1/1/10 …

ST-3ST-3

ST-2ST-2

A-8 Appendix A Solutions to Self-Test Questions and Problems

Thus, on March 1, 2008, 132/3 periods were left before the bond matured. Bond traders actually use the following procedure to determine the price of the bond: (1) Find the price of the bond on the next coupon date, July 1, 2008. Using a

fi nancial calculator, input N ! 13, I/YR ! 7.75, PMT ! 60, FV ! 1000, and PV ! ? Solve for PV ! $859.76.

(2) Add the coupon, $60, to the bond price to get the total value, TV, of the bond on the next interest payment date: TV ! $859.76 $ $60.00 ! $919.76.

(3) Discount this total value back to the purchase date (March 1, 2008): Using a fi nancial calculator, input N ! 4/6, I/YR ! 7.75, PMT ! 0, FV ! 919.76, and PV ! ? Solve for PV ! $875.11.

(4) Therefore, you would have written a check for $875.11 to complete the transaction. Of that amount, $20 ! (1/3)($60) would represent accrued in- terest and $855.11 would represent the bond’s basic value. This break- down would affect your taxes and the seller’s taxes.

(5) This problem could be solved very easily using a spreadsheet or a fi nan- cial calculator with a bond valuation function, such as the HP-12C or the HP-17BII. This is explained in the calculator manual under the heading “Bond Calculations.”

a. (1) $100,000,000/10 ! $10,000,000 per year, or $5 million each 6 months. Since the $5 million will be used to retire bonds immediately, no interest will be earned on it.

(2) VDC will purchase bonds on the open market if they’re selling at less than par. So the sinking fund payment will be less than $5,000,000 each period.

b. The debt service requirements will decline. As the amount of bonds outstanding declines, so will the interest requirements (amounts given in millions of dollars). If the bonds are called at par, the total bond service payments are calculated as follows:

Semiannual Payment

Period Sinking Fund

Payment

Outstanding Bonds on

Which Interest Is Paid

Interest Paymenta

Total Bond

Service (1) (2) (3) (4) (2) # (4) ! (5)

1 $5 $100 $6.0 $11.0

2 5 95 5.7 10.7

3 5 90 5.4 10.4

# # # # # 20 5 5 0.3 5.3

a Interest is calculated as (0.5)(0.12) (Column 3). For example: Interest in Period 2 ! (0.5) (0.12)($95) ! $5.7.

The company’s total cash bond service requirement will be $21.7 million per year for the fi rst year. For both options, interest will decline by 0.12($10,000,000) ! $1,200,000 per year for the remaining years. The total debt service requirement for the open market purchases cannot be precisely determined, but the amounts will be less than what’s shown in Column 5 of the preceding table.

c. Here we have a 10-year 7% annuity whose compound value is $100 million and we are seeking the annual payment, PMT. The solution can be obtained with a fi nancial calculator. Input N ! 10, I/YR ! 7, PV ! 0, and FV ! 100000000 and press the PMT key to obtain $7,237,750. This amount is not known with

ST-3ST-3

A-9Appendix A Solutions to Self-Test Questions and Problems

certainty as interest rates over time will change; the amount may be higher (if interest rates fall) or lower (if interest rates rise).

d. Annual debt service costs will be $100,000,000(0.12) $ $7,237,750 ! $19,237,750.

e. If interest rates rose, causing the bond’s price to fall, the company would use open market purchases. This would reduce its debt service requirements.

Chapter 8 a. The average rate of return for each stock is calculated simply by averaging the

returns over the 5-year period. The average return for Stock A is as follows:

rAvg A ! ("24.25% # 18.50% # 38.67% #14.33% # 39.13%)/5 ! 17.28%

The average return for Stock B is as follows:

rAvg B ! (5.50% # 26.73% # 48.25% # "4.50% # 43.86%)/5 ! 23.97%

The realized rate of return on a portfolio made up of Stock A and Stock B would be calculated by fi nding the average return in each year as rA(% of Stock A) $ rB(% of Stock B) and then averaging these annual returns.

Year Portfolio AB’s Return, rAB 2004 (9.38%)

2005 22.62

2006 43.46

2007 4.92

2008 41.50

rAvg ! 20.62%

b. The standard deviation of returns is estimated using Equation 8-2a as follows:

Estimated σ !

√ ____________

# t!1

( _ r t "

_ r Avg)

2 ___________

N " 1 8-2a

For Stock A, the estimated σ is 25.84%:

σA ! √ ____________________________________________________________________________________________________

("24.25% " 17.28%) 2 # (18.50% " 17.28%)2 # (38.67% " 17.28%)2 # (14.33% " 17.28%)2 # (39.13% " 17.28%)2 ___________________________________________________________________________________________________ 5 " 1

! 25.84%

The standard deviations of returns for Stock B and for the portfolio are simi- larly determined, and they are as follows:

Stock A Stock B Portfolio AB

Standard deviation 25.84% 23.15% 22.96%

c. Since the risk reduction from diversifi cation is small (σAB falls only to 22.96%), the most likely value of the correlation coeffi cient is 0.8. If the corre- lation coeffi cient was "0.8, the risk reduction would be much larger. In fact, the correlation coeffi cient between Stocks A and B is 0.76.

ST-2ST-2

A-10 Appendix A Solutions to Self-Test Questions and Problems

d. If more randomly selected stocks were added to a portfolio, σp would decline to somewhere in the vicinity of 20%. (See Figure 8-6.) σp would remain con- stant only if the correlation coeffi cient was $1.0, which is most unlikely. σp would decline to zero only if the correlation coeffi cient, ρ, was equal to zero and a large number of stocks was added to the portfolio, or if the proper pro- portions were held in a two-stock portfolio with ρ ! "1.0.

a. b ! (0.6)(0.70) # (0.25)(0.90) # (0.1) (1.30) # (0.05)(1.50) ! 0.42 # 0.225 # 0.13 # 0.075 ! 0.85

b. rRF ! 6%; RPM ! 5%; b ! 0.85 rp ! 6% # (5%)(0.85) ! 10.25%

c. bN ! (0.5)(0.70) # (0.25)(0.90) # (0.1)(1.30) # (0.15)(1.50) ! 0.35 # 0.225 # 0.13 # 0.225 ! 0.93

r ! 6% # (5%)(0.93) ! 10.65%

Chapter 9 a. This is not necessarily true. Because G plows back two-thirds of its earnings, its

growth rate should exceed that of D; but D pays higher dividends ($3 versus $1). We cannot say which stock should have the higher price.

b. Again, we do not know which price would be higher. c. This is false. The changes in rd and rs would have a greater effect on G; its price

would decline more. d. The total expected return for D is r̂D ! D1/P0 $ g ! 12% $ 0% ! 12%. The

total expected return for G will have D1/P0 less than 12% and g greater than 0%, but r̂G should be neither greater nor smaller than D’s total expected return, 12%, because the two stocks are stated to be equally risky.

e. We have eliminated a, b, c, and d; so e should be correct. On the basis of the available information, D and G should sell at about the same price, $25; thus, r̂s ! 12% for both D and G. G’s current dividend yield is $1/$25 ! 4%. There- fore, g ! 12% " 4% ! 8%.

The fi rst step is to solve for g, the unknown variable, in the constant growth equation. Since D1 is unknown but D0 is known, substitute D0(1 $ g) for D1 as follows:

P̂0 ! P0 ! D1 _____ rs " g

! D0(1 # g) ________ rs " g

$36 ! $2.40(1 # g) __________ 0.12 " g

Solving for g, we fi nd the growth rate to be 5%:

$4.32 " $36g ! $2.40 # $2.40g $38.4g ! $1.92 g ! 0.05 ! 5% The next step is to use the growth rate to project the stock price 5 years hence:

P̂5 ! D0(1 # g)

________ rs " g

! $2.40(1.05)6 __________ 0.12 " 0.05

! $45.95

(Alternatively, P̂5 ! $36(1.05) 5 ! $45.95.)

Therefore, the fi rm’s expected stock price 5 years from now, P̂5, is $45.95.

ST-3ST-3

ST-2ST-2

ST-3ST-3

A-11Appendix A Solutions to Self-Test Questions and Problems

a. (1) Calculate the PV of the dividends paid during the supernormal growth period:

D1 ! $1.1500(1.15) ! $1.3225 D2 ! $1.3225(1.15) ! $1.5209 D3 ! $1.5209(1.13) ! $1.7186

PV D ! $1.3225 _______ 1.12

# $1.5209 _______ (1.12)2

# $1.7186 _______ (1.12)3

! $1.1808 # $1.2125 # $1.2233 ! $3.6166 ≈ $3.62 (2) Find the PV of the fi rm’s stock price at the end of Year 3:

P̂3 ! D4 ______ rs " g

! D3(1 # g) _________ rs " g

! $1.7186(1.06) ____________ 0.12 " 0.06

! $30.36

PV P̂3 ! $30.36 ______ (1.12)3

! $21.61

(3) Sum the two components to fi nd the value of the stock today:

P̂0 ! $3.62 # $21.61 ! $25.23

Alternatively, the cash fl ows can be placed on a time line as follows:

1 20 3

1.3225 1.5209 1.7186 1.8217

4 12%

g = 15% g = 13% g = 6%

30.3617

32.0803

$1.8217 0.12 ! 0.06=

Enter the cash fl ows into the cash fl ow register and I/YR ! 12 and press the NPV key to obtain P0 ! $25.23.

b. P̂1 ! $1.5209 _______

1.12 # $1.7186 _______

(1.12)2 # $30.36 ______

(1.12)2

! $1.3579 # $1.3701 # $24.2028

! $26.9308 ≈ $26.93

(Calculator solution: $26.93)

P̂2 ! $1.7186 _______

1.12 # $30.36 ______

1.12

! $1.5345 # $27.1071 ! $28.6416 ≈ $28.64

(Calculator solution: $28.64) c.

Year Dividend Yield # Capital Gains Yield ! Total Return

1 $1.3225 _______ $25.23 $ 5.24% $26.93 " $25.23 ______________ $25.23 $ 6.74% $ 12%

2 $1.5209 _______ $26.93 $ 5.65% $28.64 " $26.93 ______________ $26.93 $ 6.35% $ 12%

3 $1.7186 _______ $28.64 $ 6.00% $30.36 " $28.64 ______________ $28.64 $ 6.00% $ 12%

ST-4ST-4

A-12 Appendix A Solutions to Self-Test Questions and Problems

Chapter 10 a. Component costs are as follows:

Common: rs ! D1 __ P0

# g ! D0(1 # g) _________ P0

# g

! $3.60(1.09) __________ $54

# 0.09

! 0.0727 # 0.09 ! 16.27%

Preferred: rp ! Preferred dividend _________________ Pp ! $11 ____

$95 ! 11.58%

Debt at rd ! 12%: rd(1 " T) ! 12%(0.6) ! 7.20%

b. WACC calculation: WACC ! wdrd(1 " T) # wprp # wcrs ! 0.25(7.2%) # 0.15(11.58%) # 0.60(16.27%) ! 13.30%

c. LEI should accept Projects A, B, C, and D. It should reject Project E because its rate of return does not exceed the WACC of funds needed to fi nance it.

Chapter 11 a. Net present value (NPV):

NPVX ! "$10,000 # $6,500 ______ (1.12)1

# $3,000 ______ (1.12)2

# $3,000 ______ (1.12)3

# $1,000 ______ (1.12)4

! $966.01

NPVY ! "$10,000 # $3,500 ______ (1.12)1

# $3,500 ______ (1.12)2

# $3,500 ______ (1.12)3

# $3,500 ______ (1.12)4

! $630.72

Alternatively, using a fi nancial calculator, input the cash fl ows into the cash fl ow register, enter I/YR ! 12, and then press the NPV key to obtain NPVX ! $966.01 and NPVY ! $630.72.

Internal rate of return (IRR): To solve for each project’s IRR, fi nd the discount rates that equate each NPV to zero:

IRRX ! 18.0% IRRY ! 15.0%

Modifi ed internal rate of return (MIRR): To obtain each project’s MIRR, begin by fi nding each project’s terminal value (TV) of cash infl ows:

TVX ! $6,500(1.12) 3 # $3,000(1.12)2 # $3,000(1.12)1 # $1,000 ! $17,255.23

TVY ! $3,500(1.12) 3 # $3,500(1.12)2 # $3,500(1.12)1 # $3,500 ! $16,727.65

Now each project’s MIRR is the discount rate that equates the PV of the TV to each project’s cost, $10,000:

MIRRX ! 14.61% MIRRY ! 13.73%

Payback: To determine the payback, construct the cumulative cash fl ows for each project.

CUMULATIVE CASH FLOWS Year Project X Project Y

0 ($10,000) ($10,000) 1 (3,500) (6,500) 2 (500) (3,000) 3 2,500 500 4 3,500 4,000

ST-2ST-2

A-13Appendix A Solutions to Self-Test Questions and Problems

PaybackX ! 2 # $500 ______

$3,000 ! 2.17 years

PaybackY ! 2 # $3,000

______ $3,500

! 2.86 years

Discounted payback: To determine the discounted payback, construct the cumulative discounted

cash fl ows at the fi rm’s WACC of 12% for each project:

Project X Years

Cash Flow Discounted Cash Flow Cumulative Discounted Cash Flow

!10,000 !10,000

6,500 5,803.57

!4,196.43!10,000

3,000 2,391.58

!1,804.85

3,000 2,135.34 "330.49

1,000 635.52

"966.01

0 1 2 3 4

Discounted PaybackX ! 2 # $1,804.85/$2,135.34 ! 2.85 years

Project Y Years

Cash Flow Discounted Cash Flow Cumulative Discounted Cash Flow

!10,000 !10,000

3,500 3,125.00

!6,875.00!10,000

3,500 2,790.18

!4,084.82

3,500 2,491.23

!1,593.59

3,500 2,224.31 "630.72

0 1 2 3 4

Discounted PaybackY ! 3 # $1,593.59/$2,224.31 ! 3.72 years

b. The following table summarizes the project rankings by each method:

Project That Ranks Higher

NPV X

IRR X

MIRR X

Payback X

Discounted payback X

Note that all methods rank Project X over Project Y. In addition, both projects are acceptable under the NPV, IRR, and MIRR criteria. Thus, both projects should be accepted if they are independent.

c. In this case, we would choose the project with the higher NPV at r ! 12%, or Project X.

d. To determine the effects of changing the cost of capital, plot the NPV profi les of each project. The crossover rate occurs at about 6% to 7% (6.2%). See the graph on the next page.

If the fi rm’s cost of capital is less than 6.2%, a confl ict exists because NPVY % NPVX, but IRRX % IRR Y. Therefore, if r is 5%, a confl ict exists. Note, however, that when r ! 5.0%, MIRRX ! 10.64% and MIRRY ! 10.83%; hence, the modifi ed IRR ranks the projects correctly even if r is to the left of the crossover point.

e. The basic cause of the confl ict is differing reinvestment rate assumptions be- tween NPV and IRR. NPV assumes that cash fl ows can be reinvested at the cost of capital, while IRR assumes reinvestment at the (generally) higher IRR. The high reinvestment rate assumption under IRR makes early cash fl ows es- pecially valuable; hence, short-term projects look better under IRR.

A-14 Appendix A Solutions to Self-Test Questions and Problems

NPV Profi les for Projects X and Y

NPV ($)

4,000

2,000

3,000

1,000

!1,000

15 20105 0

NPV

Crossover Rate = 6.2%

NPV

Cost of Capital (%)

IRRx YIRR

Cost of Capital NPVX NPVY 0% $3,500 $4,000

4 2,545 2,705 8 1,707 1,592 12 966 631 16 307 (206) 18 5 (585)

Chapter 12 a. Estimated investment requirements:

Price ($55,000) Installation ( 10,000) Change in net working capital ( 2,000) Total investment ($67,000)

b. Depreciation schedule: Equipment cost ! $65,000; MACRS 3-year class

YEARS

1 2 3 MACRS depreciation rates 33% 45% 15% Equipment depreciation expense $21,450 $29,250 $9,750

Note that the remaining book value of the equipment at the end of the project’s life is 0.07 & $65,000 ! $4,550.

ST-2ST-2

A-15Appendix A Solutions to Self-Test Questions and Problems

c. Year 0 Year 1 Year 2 Year 3 Equipment purchase ($65,000) Change in NWC (2,000) Revenues (4,000 × $50) $200,000 $200,000 $200,000 Variable costs (70%) 140,000 140,000 140,000 Fixed costs 30,000 30,000 30,000 Depreciation 21,450 29,250 9,750 EBIT $ 8,550 $ 750 $ 20,250 Taxes (40%) 3,420 300 8,100 AT operating income $ 5,130 $ 450 $ 12,150 Add back: Depreciation 21,450 29,250 9,750 Salvage value 10,000 Tax on salvage value (2,180) Recovery of NWC 2,000 Project cash flows ($67,000) $ 26,580 $ 29,700 $ 31,720

26,580 29,700 31,720!67,000

0 111% 2 3

d. From the time line shown in Part c, the project’s NPV can be calculated as follows:

NPV ! "$67,000 # $26,580/(1.11)1 # $29,700/(1.11)2 # $31,720/(1.11)3

! $4,245

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000, CF1 ! 26580, CF2 ! 29700, CF3 ! 31720, and I/YR ! 11 and then solve for NPV ! $4,245.

Since the NPV is positive, the project should be accepted.

e. Project analysis if unit sales turned out to be 20% below forecast: Initial projection ! 4,000 units; however, if unit sales turn out to be only 80%

of forecast, unit sales ! 3,200.

Year 0 Year 1 Year 2 Year 3 Equipment purchase ($65,000) Change in NWC (2,000) Revenues (3,200 $ $50) $160,000 $160,000 $160,000 Variable costs (70%) 112,000 112,000 112,000 Fixed costs 30,000 30,000 30,000 Depreciation 21,450 29,250 9,750 EBIT ($ 3,450) ($ 11,250) $ 8,250 Taxes (40%) (1,380) (4,500) 3,300 AT operating income ($ 2,070) ($ 6,750) $ 4,950 Add back: Depreciation 21,450 29,250 9,750 Salvage value 10,000 Tax on salvage value (2,180) Recovery of NWC 2,000 Project cash flows ($67,000) $ 19,380 $ 22,500 $ 24,520

19,380 22,500 24,520!67,000

0 111% 2 3 NPV Calculation:

A-16 Appendix A Solutions to Self-Test Questions and Problems

NPV ! "$67,000 # $19,380/(1.11)1 # $22,500/(1.11)2 # $24,520/(1.11)3

! "$13,350

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000, CF1 ! 19380, CF2 ! 22500, CF3 ! 24520, and I/YR ! 11 and then solve for NPV ! "$13,350. Since the NPV is negative, the project should not be accepted. If unit sales were 20% below the forecasted level, the project would no longer be accepted.

f. Best-case scenario: Unit sales ! 4,800, Variable cost % ! 65%

Year 0 Year 1 Year 2 Year 3 Equipment purchase ($65,000) Change in NWC (2,000) Revenues (4,800 $ $50) $240,000 $240,000 $240,000 Variable costs (65%) 156,000 156,000 156,000 Fixed costs 30,000 30,000 30,000 Depreciation 21,450 29,250 9,750 EBIT $ 32,550 $ 24,750 $ 44,250 Taxes (40%) 13,020 9,900 17,700 AT operating income $ 19,530 $ 14,850 $ 26,550 Add back: Depreciation 21,450 29,250 9,750 Salvage value 10,000 Tax on salvage value (2,180) Recovery of NWC 2,000 Project cash flows ($67,000) $ 40,980 $ 44,100 $ 46,120

40,980 44,100 46,120!67,000

0 Project NPV:

111% 2 3

NPV ! "$67,000 # $40,980/(1.11)1 # $44,100/(1.11)2 # $46,120/(1.11)3

! $39,434

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000 CF1 ! 40980, CF2 ! 44100, CF3 ! 46120, and I/YR ! 11 and then solve for NPV ! $39,434. Base-case scenario: The NPV was calculated in Part d as $4,245. Worst-case scenario: Unit sales ! 3,200, Variable cost % ! 75%

Year 0 Year 1 Year 2 Year 3 Equipment purchase ($65,000) Change in NWC (2,000) Revenues (3,200 $ $50) $ 160,000 $ 160,000 $160,000 Variable costs (75%) 120,000 120,000 120,000 Fixed costs 30,000 30,000 30,000 Depreciation 21,450 29,250 9,750 EBIT ($ 11,450) ($ 19,250) $ 250 Taxes (40%) (4,580) (7,700) 100 AT operating income ($ 6,870) ($ 11,550) $ 150 Add back: Depreciation 21,450 29,250 9,750 Salvage value 10,000 Tax on salvage value (2,180) Recovery of NWC 2,000 Project cash flows ($67,000) $ 14,580 $ 17,700 $ 19,720

A-17Appendix A Solutions to Self-Test Questions and Problems

14,580 17,700 19,720!67,000

0 Project NPV:

111% 2 3

NPV ! "$67,000 # $14,580/(1.11)1 # $17,700/(1.11)2 # $19,720/(1.11)3

! "$25,080

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000, CF1 ! 14580, CF2 ! 17700, CF3 ! 19720, and I/YR ! 11 and then solve for NPV ! "$25,080.

Scenario Probability NPV Best case 25% $ 39,434 Base case 50 4,245 Worst case 25 "25,080

Expected NPV ! $ 5,711

σNPV ! [0.25($39,434 " $5,711)2 # 0.50($4,245 " $5,711)2 # 0.25("$25,080 " $5,711)2]1/2

σNPV ! [$284,310,182 # $1,074,578 # $237,021,420]1/2

σNPV ! $22,856

CVNPV ! $22,856/$5,711 ! 4.0

g. The project’s CV ! 4.0, which is signifi cantly larger than the fi rm’s typical project CV. So the WACC for this project should be adjusted upward, 11% $ 3% ! 14%. To calculate the expected NPV, standard deviation, and coeffi cient of variation, you would recalculate each scenario’s NPV by discounting the project cash fl ows by 14% rather than 11%.

40,980 44,100 46,120!67,000

0 Best-case scenario:

114% 2 3

NPV ! "$67,000 # $40,980/(1.14)1 # $44,100/(1.14)2 # $46,120/(1.14)3

! $34,011

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000, CF1 ! 40980, CF2 ! 44100, CF3 ! 46120, and I/YR ! 14 and then solve for NPV ! $34,011.

26,580 29,700 31,720!67,000

0 Base-case scenario:

114% 2 3

NPV ! "$67,000 # $26,580/(1.14)1 # $29,700/(1.14)2 # $31,720/(1.14)3

! $579

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000, CF1 ! 26580, CF2 ! 29700, CF3 ! 31720, and I/YR ! 14 and then solve for NPV ! $579.

14,580 17,700 19,720–67,000

0 Worst-case scenario:

114% 2 3

A-18 Appendix A Solutions to Self-Test Questions and Problems

NPV ! "$67,000 # $14,580/(1.14)1 # $17,700/(1.14)2 # $19,720/(1.14)3

! "$27,281

Alternatively, using a fi nancial calculator, you would enter CF0 ! "67000, CF1 ! 14580, CF2 ! 17700, CF3 ! 19720, and I/YR ! 14 and then solve for NPV ! "$27,281.

Scenario Probability NPV

Best case 25% $ 34,011

Base case 50 579

Worst case 25 "27,281

Expected NPV ! $ 1,972

σNPV ! [0.25($34,011 " $1,972)2 # 0.50($579 " $1,972)2 # 0.25("$27,281 " $1,972)2]1/2

σNPV ! [$256,624,380 # $970,225 # $213,934,502]1/2

σNPV ! $21,715

CVNPV ! $21,715/$1,972 ! 11.01

Because the expected NPV of the project is still positive, the project will be accepted; but it is risky.

Chapter 13 a. The following information is given in the problem:

Q ! Units of output (sales) ! 5,000

P ! Average sales price per unit of output ! $100

F ! Fixed operating costs ! $200,000

V ! Variable costs per unit ! $50

EBIT ! Operating income ! $50,000 Total assets ! $500,000 Common equity ! $500,000

(1) Determine the new EBIT level if the change is made:

New EBIT ! P2(Q2) " F2 " V2(Q2) New EBIT ! $95(7,000) " $250,000 " $40(7,000) ! $135,000

(2) Determine the incremental EBIT:

∆EBIT ! $135,000 " $50,000 ! $85,000

(3) Estimate the approximate rate of return on the new investment:

∆ROA ! ∆EBIT __________ Investment ! $85,000 ________ $400,000 ! 21.25%

Since the ROA exceeds Olinde’s average cost of capital, this analysis suggests that the fi rm should go ahead and make the investment.

b. The change would increase the break-even point. Still, with a lower sales price, it might be easier to achieve the higher new break-even volume.

Old: QBE ! F _____ P " V !

$200,000 __________ $100 " $50 ! 4,000 units

New: QBE ! F ______ P2 " V2

! $250,000 _________ $95 " $40 ! 4,545 units

ST-2ST-2

A-19Appendix A Solutions to Self-Test Questions and Problems

c. The incremental ROA is:

ROA ! ∆Profi t ______ ∆Sales $ ∆Sales _______ ∆Assets

Using debt fi nancing, the incremental profi t associated with the investment is equal to the incremental profi t found in Part a minus the interest expense in- curred as a result of the investment:

∆Profi t ! New profi t " Old profi t " Interest ! $135,000 " $50,000 " 0.10($400,000) ! $45,000

The incremental sales is calculated as:

∆Sales ! P2Q2 " P1Q1 ! $95(7,000) " $100(5,000) ! $665,000 " $500,000 ! $165,000

ROA ! $45,000 ________ $165,000 $ $165,000 ________ $400,000 ! 11.25%

The return on the new investment still exceeds the average cost of capital, so the fi rm should make the investment.

a. EBIT $4,000,000 Interest ($2,000,000 $ 0.10) 200,000 Earnings before taxes (EBT) $3,800,000 Taxes (35%) 1,330,000 Net income $2,470,000

EPS ! $2,470,000/600,000 ! $4.1167

P0 ! $4.1167/0.15 ! $27.44

b. Equity ! 600,000 $ $10 ! $6,000,000 Debt ! $2,000,000 Total capital ! $8,000,000 WACC ! wdrd(1 " T) # wcrs ! (2/8)(10%)(1 " 0.35) # (6/8)(15%) ! 1.625% # 11.25% ! 12.875%

c. EBIT $4,000,000 Interest ($10,000,000 $ 0.12) 1,200,000 Earnings before taxes (EBT) $2,800,000 Taxes (35%) 980,000 Net income $1,820,000

Shares bought and retired:

∆N ! ∆Debt/P0 ! $8,000,000/$27.44 ! 291,545

New outstanding shares:

N1 ! N0 " ∆N ! 600,000 " 291,545 ! 308,455

New EPS:

EPS ! $1,820,000/308,455 ! $5.90

New price per share:

P0 ! $5.90/0.17 ! $34.71 versus $27.44

Therefore, Gentry should change its capital structure.

ST-3ST-3

A-20 Appendix A Solutions to Self-Test Questions and Problems

d. In this case, the company’s net income would be higher by (0.12 – 0.10) ($2,000,000) (1 – 0.35) ! $26,000 because its interest charges would be lower. The new price would be as follows:

P0 ! ($1,820,000 # $26,000)/308,455 ____________________________ 0.17 ! $35.20

In the fi rst case, in which debt had to be refunded, the bondholders were com- pensated for the increased risk of the higher debt position. In the second case, the old bondholders were not compensated; their 10% coupon perpetual bonds would now be worth $100/0.12 ! $833.33, or $1,666,667 in total, down from the old $2 million, or a loss of $333,333. The stockholders would have a gain as follows:

($35.20 " $34.71)(308,455) ! $151,143

This gain would, of course, be at the expense of the old bondholders. (There is no reason to think that bondholders’ losses would exactly offset stockholders’ gains.)

e. TIE ! EBIT ____ I

Original TIE ! $4,000,000 __________ $200,000 ! 20 times

New TIE ! $4,000,000 __________ $1,200,000 ! 3.33 times

Chapter 14 a. Projected net income $2,000,000

Less projected capital investments 800,000 Available residual $1,200,000

Shares outstanding 200,000

DPS ! $1,200,000/200,000 shares ! $6 ! D1

b. EPS ! $2,000,000/200,000 shares ! $10 Payout ratio ! DPS/EPS ! $6/$10 ! 60%, or Total dividends/NI ! $1,200,000/$2,000,000 ! 60%

c. Currently, P0 ! D1 _____ rs " g

! $6 __________ 0.14 " 0.06 ! $6 ____ 0.08 ! $75.00

Under the former circumstances, D1 would be based on a 20% payout on $10 EPS, or $2. With rs ! 14% and g ! 12%, we solve for P0:

P0 ! D1 _____

rs " g ! $2 __________

0.14 " 0.12 ! $2 ____

0.02 ! $100

Although CMC has suffered a severe setback, its existing assets will continue to provide a good income stream. More of these earnings should be passed on to the shareholders, as the slowed internal growth has reduced the need for funds. However, the net result is a 25% decrease in the value of the shares.

d. If the payout ratio was continued at 20%, even after internal investment opportunities had declined, the price of the stock would drop to $2/(0.14 " 0.06) ! $25 rather than $75.00. Thus, an increase in the dividend payout is consistent with maximizing shareholder wealth. Because of the diminishing nature of profi table investment opportunities, the greater the fi rm’s level of investment, the lower the average ROE. Thus,

ST-2ST-2

A-21Appendix A Solutions to Self-Test Questions and Problems

the more money CMC retains and invests, the lower its average ROE will be. We can determine the average ROE under different conditions as follows: Old situation (with founder active and a 20% payout):

g ! (1.0 " Payout ratio)(Average ROE) 12% ! (1.0 " 0.2)(Average ROE) Average ROE ! 12%/0.8 ! 15% % rs ! 14%

Note that the average ROE is 15%, whereas the marginal ROE is presumably equal to 14%.

New situation (with founder retired and a 60% payout as explained in Part c:

g ! 6% ! (1.0 " 0.6)(ROE) ROE ! 6%/0.4 ! 15% % rs ! 14%

This suggests that a new payout of 60% is appropriate and that the fi rm is tak- ing on investments down to the point at which marginal returns are equal to the cost of capital. Note that if the 20% payout was maintained, the average ROE would be only 7.5%, which would imply a marginal ROE far below the 14% cost of capital.

Chapter 15 The Calgary Company: Alternative Balance Sheets

Restricted (40%)

Moderate (50%)

Relaxed (60%)

Current assets $1,200,000 $1,500,000 $1,800,000 Fixed assets 600,000 600,000 600,000 Total assets $1,800,000 $2,100,000 $ 2,400,000 Debt $ 900,000 $1,050,000 $1,200,000 Equity 900,000 1,050,000 1,200,000 Total liabilities and equity $1,800,000 $2,100,000 $ 2,400,000

The Calgary Company: Alternative Income Statements

Restricted Moderate Relaxed Sales $3,000,000 $3,000,000 $3,000,000

EBIT 450,000 450,000 450,000 Interest (10%) 90,000 105,000 120,000 Earnings before taxes $ 360,000 $ 345,000 $ 330,000 Taxes (40%) 144,000 138,000 132,000 Net income $ 216,000 $ 207,000 $ 198,000 ROE 24.0% 19.7% 16.5%

a. and b. Income Statements for Year Ended December 31, 2008 (Thousands of Dollars)

Vanderheiden Press Herrenhouse Publishing a b a b

EBIT $ 30,000 $ 30,000 $ 30,000 $ 30,000 Interest 12,400 14,400 10,600 18,600 Taxable income $ 17,600 $ 15,600 $ 19,400 $ 11,400 Taxes (40%) 7,040 6,240 7,760 4,560 Net income $ 10,560 $ 9,360 $ 11,640 $ 6,840

Equity $100,000 $100,000 $100,000 $100,000 ROE 10.56% 9.36% 11.64% 6.84%

ST-2ST-2

ST-3ST-3

A-22 Appendix A Solutions to Self-Test Questions and Problems

Vanderheiden Press has a higher ROE when short-term interest rates are high, whereas Herrenhouse Publishing does better when rates are lower.

c. Herrenhouse’s position is riskier. First, its profi ts and return on equity are more volatile than Vanderheiden’s. Second, Herrenhouse must renew its large short-term loan every year; and if the renewal comes up at a time when money is tight, when its business is depressed, or both, Herrenhouse could be denied credit, which could put it out of business.

Chapter 16 To solve this problem, we defi ne ∆S as the change in sales and g as the growth rate in sales; then we use the following three equations:

∆S ! S0g S1 ! S0(1 # g) AFN ! (A0*/S0)(∆S) " (L0*/S0)(∆S) " MS1(RR)

Set AFN ! 0; substitute known values for A0*/S0, L0*/S0, M, RR, and S0; and solve for g:

0 ! 1.6($100g) " 0.4($100g) " 0.10[$100(1 # g)](0.55) 0 ! $160g " $40g " 0.055($100 # $100g) 0 ! $160g " $40g " $5.5 " $5.5g $114.5g ! $5.5 g ! $5.5/$114.5 ! 0.048 ! 4.8% ! Maximum growth rate without external fi nancing

Assets consist of cash, marketable securities, receivables, inventories, and fi xed assets. Therefore, we can break the A0*/S0 ratio into its components—cash/sales, invento- ries/sales, and so forth. Then,

A0 * ____ S0

! A0 * " Inventories ________________ S0

# Inventories __________ S0 ! 1.6

We know that the inventory turnover ratio is Sales/Inventories ! 3 times, so In- ventories/Sales ! 1/3 ! 0.3333. Further, if the inventory turnover ratio can be in- creased to 4 times, the Inventory/Sales ratio will fall to 1/4 ! 0.25, a difference of 0.3333 – 0.2500 ! 0.0833. This, in turn, causes the A0*/S0 ratio to fall from A0*/S0 ! 1.6 to A0*/S0 ! 1.6 – 0.0833 ! 1.5167.

This change has two effects: First, it changes the AFN equation. Second, it means that Weatherford currently has excessive inventories. Because it is costly to hold excess inventories, Weatherford will want to reduce its inventory holdings by not replacing inventories until the excess amounts have been used. We can account for this by setting up the revised AFN equation (using the new A0*/S0 ratio), esti- mating the funds that will be needed next year if no excess inventories are cur- rently on hand, and subtracting the excess inventories that are currently on hand: Present conditions:

Sales __________ Inventories ! $100 __________ Inventories ! 3,

Inventories ! $100/3 ! $33.3 million at present.

ST-2ST-2

ST-3ST-3

A-23Appendix A Solutions to Self-Test Questions and Problems

New conditions:

Sales __________ Inventories ! $100 __________ Inventories ! 4,

New level of inventories ! $100/4 ! $25 million.

Therefore,

Excess inventories ! $33.3 " $25 ! $8.3 million.

Forecast of funds needed:

∆S ! 0.2($100 million) ! $20 million

AFN ! 1.5167($20) " 0.4($20) " 0.1($120)(0.55) " $8.3 ! $30.3 " $8 " $6.6 " $8.3 ! $7.4 million

Chapter 17 Euros _____ C$ !

Euros _____ US$ $ US$ ____ C$

! 0.65 ____ $1 $ $1 ____ 0.98 !

0.65 ____ 0.98 ! 0.6633 euro per Canadian dollar

ST-2ST-2

A-24

APPEND IX B

ANSWERS TO SELECTED END-OF-CHAPTER PROBLEMS

We present some intermediate steps and fi nal an- swers to selected end-of-chapter problems. Please note that your answer may differ slightly due to rounding differences. Also, some of the problems may have more than one correct solution depending on what assumptions are made in working the prob- lem. Finally, many of the problems involve verbal discussion as well as numerical calculations; the ver- bal material is not presented here.

3-2 $2,500,000 3-4 a, possibly c 3-6 a. $50,000 b. $115,000 3-8 $12,681,482 3-10 a. NWC08 ! $192,000,000

NWC07 ! $210,000,000 b. FCF ! $58,000,000

4-2 D/A ! 58.33% 4-4 M/B ! 4.2667 4-6 ROE ! 8% 4-8 15.31% 4-10 NI/S ! 2%; D/A ! 40% 4-12 TIE ! 3.86 4-14 ∆ROE ! "5.54%; QR ! 1.2 4-16 a 4-18 $262,500 4-20 $50 4-22 a. Current ratio ! 1.98; DSO ! 76.3

days; Total assets turnover ! 1.70; Debt ratio ! 61.9%

5-2 PV ! $1,292.10 5-4 N ! 11.01 years 5-6 FVA5 ! $1,725.22; FVA5 Due ! $1,845.99 5-8 PMT ! $444.89; EAR ! 12.6825% 5-10 a. $895.42 b. $1,552.92 c. $279.20 d. $499.99; $867.13 5-12 a. 7% b. 7% c. 9% d. 15% 5-14 a. $6,374.97 b. $1,105.13

c. $2,000.00 d(1). $7,012.47 d(2). $1,160.38 d(3). $2,000.00 5-16 PV7% ! $1,428.57; PV14% ! $714.29 5-18 a. Stream A: $1,251.25

Stream B: $1,300.32 b. Stream A and Stream B: $1,600 5-20 Contract 2; PV ! $10,717,847.14 5-22 a. $802.43 b. Pymt 1: Int ! $500 and Princ pymt !

$302.43; Pymt 2: Int ! $484.88 and Princ pymt ! $317.55

c. $984.88 5-24 a. $279.20 b. $276.84 c. $443.72 5-26 $17,290.89; $19,734.26 5-28 INOM ! 7.8771% 5-30 a. E ! 63.74 yrs; K ! 41.04 yrs b. $35,825.33 5-32 $496.11 5-34 a. PMT ! $10,052.87 b. Yr 3: Int/Pymt ! 9.09%; Princ/Pymt

! 90.91% 5-36 a. $5,308.12 b. $4,877.09 5-38 $309,015 5-40 $9,385

6-2 2.25% 6-4 1.5% 6-6 21.8% 6-8 8.5% 6-10 6.0% 6-12 0.35% 6-14 a. r1 in Year 2 ! 6% b. I1 ! 2%; I2 ! 5% 6-16 14% 6-18 a. r1 ! 9.20%; r5 ! 7.20%

7-2 a. 7.22% b. $988.46 7-4 YTM ! 6.62%; YTC ! 6.49%; most likely

yield ! 6.49%

A-25Appendix B Answers to Selected End-of-Chapter Problems

7-6 a. C0 ! $1,012.79; Z0 ! $693.04 C1 ! $1,010.02; Z1 ! $759.57 C2 ! $1,006.98; Z2 ! $832.49 C3 ! $1,003.65; Z3 ! $912.41 C4 ! $1,000.00; Z4 ! $1,000.00

7-8 15.03% 7-10 a. YTM ! 9.69% b. CY ! 8.875%; CGY ! 0.816% 7-12 a. YTM ! 8%; YTC ! 6.1% 7-14 a. 5 years b. YTC ! 6.47% 7-16 $1,067.95 7-18 a. TI ! 6.1%; UPS ! 3.65%

8-2 bp ! 1.12 8-4 rM ! 11%; r ! 12.2% 8-6 a. r̂Y ! 14% b. σX ! 12.20% 8-8 b ! 1.33 8-10 4.2% 8-12 a. ri ! 15.5% b(1). rM ! 15%; ri ! 16.5% b(2). rM ! 13%; ri ! 14.5% c(1). ri ! 18.1% c(2). ri ! 14.2% 8-14 bN ! 1.16 8-16 rp ! 11.75% 8-18 a. $0.5 million d(1). $75,000 d(2). 15% 8-20 a. rA ! 11.30%; rB ! 11.30% b. rp Avg ! 11.30% c. σA ! 20.8%; σB ! 20.8%; σp ! 20.1% d. CVA ! CVB ! 1.84; CVp ! 1.78

9-2 P̂0 ! $6.25 9-4 a. end of Year 2 b. $37.80 c. $34.09 9-6 rp ! 8.33% 9-8 a. $125 b. $83.33 9-10 $23.75 9-12 a(1). $9.50 a(2). $13.33 a(3). $21.00 a(4). $44.00 b(1). Undefi ned b(2). #$48.00, which is nonsense 9-14 P0 ! $19.89 9-16 6.25% 9-18 a. P0 ! $54.11; D1/P0 ! 3.55%;

CGY ! 6.45% 9-20 $35.00

10-2 rp ! 8% 10-4 a. rs ! 15% b. re ! 16.11% 10-6 a. rs ! 16.3% b. rs ! 15.4% c. rs ! 16% d. rs Avg ! 15.9% 10-8 rs ! 16.51%; WACC ! 12.79% 10-10 WACC ! 11.4% 10-12 a. rs ! 14.40% b. WACC ! 10.62% c. Project A 10-14 11.94% 10-16 a. g ! 8% b. D1 ! $2.81 c. rs ! 15.81% 10-18 a. rd(1 – T) ! 7%; rp ! 10.20%;

rs ! 15.72% b. WACC ! 13.86% c. Projects 1 and 2 will be accepted. 10-20 a. rd(1 – T) ! 5.4%; rs ! 14.6% b. WACC ! 10.92%

11-2 IRR ! 16% 11-4 4.34 years 11-6 a. 5%: NPVA ! $3.52; NPVB ! $2.87 10%: NPVA ! $0.58; NPVB ! $1.04 15%: NPVA ! #$1.91; NPVB ! #$0.55 b. IRRA ! 11.10%; IRRB ! 13.18% c. 5%: Choose A; 10%: Choose B; 15%:

Choose neither one. 11-8 a. Without mitigation: NPV ! $12.10

million and IRR ! 19.86%; With mitigation: NPV ! $5.70 million and IRR ! 15.24%

11-10 Project A; NPVA ! $30.16 11-12 IRRL ! 11.74% 11-14 a. HCC; PV of costs ! #$805,009.87 c. LCC; PV of costs ! #$686,627.14 11-16 a. NPVA ! $14,486,808; NPVB !

$11,156,893; IRRA ! 15.03%; IRRB ! 22.26%

b. Crossover rate ! 12% 11-18 a. No; PVOld ! #$89,910.08;

PVNew ! #$94,611.45 b. $2,470.80 c. 22.94% 11-20 $10,239.20 11-22 $250.01

12-2 a. $2,600,000 b. $2,000,000 c. $2,700,000 12-4 Yes, NPV ! $15,301.10

A-26 Appendix B Answers to Selected End-of-Chapter Problems

12-6 E(NPV) ! $3,000,000; σNPV ! $23.622 mil- lion; CV ! 7.874

12-8 b. #$126,000 c. $42,518; $47,579; $85,628 d. NPV ! $10,841; Purchase 12-10 Yes, NPV ! $22,329.39. 12-12 NPV5 ! $2,211; NPV4 !

#$2,081; NPV8 ! $13,329; E(NPV) ! $4,486.46

12-14 a. #$98,500 b. CF1 ! $46,675; CF2 ! $52,975;

CF3 ! $37,225; CF4 ! $33,025; CF5 ! $22,850

c. Yes, NPV ! $34,073.20.

13-2 30% debt and 70% equity 13-4 bU ! 1.0435 13-6 a(1). #$60,000 a(2). $40,000 b. QBE ! 14,000 c. QBE ! 8,750 d. QBE ! 17,500 13-8 rs ! 17% 13-10 a. FCA ! $80,000; VA ! $4.80/unit;

PA ! $8.00/unit; FCB ! $120,000; VB ! $4.00/unit; PB ! $8.00/unit

b. Firm B c. 50,000 units 13-12 a. EPSOld ! $2.04; New: EPSD ! $4.74

and EPSS ! $3.27 b. 339,750 units c. QOld ! 316,957 units; QNew, Debt !

272,250 units; QNew, Stock ! 204,750 units

14-2 P0 ! $60 14-4 D0 ! $3.44 14-6 Payout ! 31.39% 14-8 a. 12% b. 18% c. g ! 6%; rs ! 18% d. 6% e. 28,800 new shares; $0.13 per share

15-2 73 days; 30 days; $1,178,082 15-4 a. 83 days b. $356,250 c. 4.87$ 15-6 a. 32 days b. $288,000 c. $45,000 d(1). 30 d(2). $378,000 15-8 a. ROE T ! 11.75%; ROEM ! 10.80%;

ROER ! 9.16% 15-10 a. Oct. loan ! $22,800

16-2 AFN ! $610,000 16-4 a. $133.50 million b. 39.06% 16-6 $67 million; 5.01$ 16-8 a. $480,000 b. $18,750 16-10 $34.338 million; 34.97 ! 35 days 16-12 a. $2,500,000,000 b. 24% c. $24,000,000 16-14 a. 33% b. NP ! $3,553.2; Bonds ! $6,598.8;

Stock ! $2,514; RE ! $28,284

17-2 29.7143 yen per shekel 17-4 1 euro ! $1.6 or $1 ! 0.625 euro 17-8 12 kronas per pound 17-10 rNOM-U.S. ! 4.6% 17-12 a. Discount b. $1.9985 17-14 "$500,000 17-16 $586,046,512

APPEND IX C

SELECTED EQUATIONS AND TABLES Chapter 3 Stockholders’ equity ! Paid-in capital " Retained earnings

Stockholders’ equity ! Total assets # Total liabilities

Net working capital ! Current assets # (Payables " Accruals)

Operating income (or EBIT) ! Sales revenues # Operating costs

FCF ! EBIT(1 # T) " Depreciation # ! Capital expenditures " Increase in net working capital "

Individual Tax Rates in April 2008

Single Individuals

If Your Taxable Income Is

You Pay This Amount on the

Base of the Bracket

Plus This Percentage on the Excess over the Base (Marginal Rate)

Average Tax Rate at

Top of Bracket Up to $7,825 $ 0 10.0% 10.0% $7,825–$31,850 782.50 15.0 13.8 $31,850–$77,100 4,386.25 25.0 20.4 $77,100–$160,850 15,698.75 28.0 24.3 $160,850–$349,700 39,148.75 33.0 29.0 Over $349,700 101,469.25 35.0 35.0

Married Couples Filing Joint Returns

If Your Taxable Income Is

You Pay This Amount on the

Base of the Bracket

Plus This Percentage on the Excess over the Base (Marginal Rate)

Average Tax Rate at

Top of Bracket Up to $15,650 $ 0 10.0% 10.0% $15,650–$63,700 1,565.00 15.0 13.8 $63,700–$128,500 8,772.50 25.0 19.4 $128,500–$195,850 24,972.50 28.0 22.4 $195,850–$349,700 43,830.50 33.0 27.0 Over $349,700 94,601.00 35.0 35.0

Corporate Tax Rates as of January 2008

If a Corporation’s Taxable Income Is

It Pays This Amount on the

Base of the Bracket

Plus This Percentage on the Excess over the Base (Marginal Rate)

Average Tax Rate at

Top of Bracket Up to $50,000 $ 0 15% 15.0% $50,000–$75,000 7,500 25 18.3 $75,000–$100,000 13,750 34 22.3 $100,000–$335,000 22,250 39 34.0 $335,000–$10,000,000 113,900 34 34.0 $10,000,000–$15,000,000 3,400,000 35 34.3 $15,000,000–$18,333,333 5,150,000 38 35.0 Over $18,333,333 6,416,667 35 35.0

A-27

A-28 Appendix C Selected Equations and Tables

Chapter 4 Current ratio ! Current assets _______________ Current liabilities

Quick, or acid test, ratio ! Current assets # Inventories _________________________ Current liabilities

Inventory turnover ratio ! Sales __________ Inventories

Days sales outstanding (DSO) ! Receivables ___________________ Average sales per day ! Receivables _______________ Annual sales/365

Fixed assets turnover ratio ! Sales ______________ Net fi xed assets

Total assets turnover ratio ! Sales __________ Total assets

Debt ratio ! Total debt __________ Total assets

Times-interest-earned (TIE) ratio ! EBIT ______________ Interest charges

D/E ! D/A _______ 1 # D/A and D/A ! D/E _______ 1 " D/E

EBITDA coverage ! EBITDA " Lease payments

___________________________________________ Interest " Principal payments " Lease payments

Operating margin ! Operating income (EBIT)

______________________ Sales

Profi t margin ! Net income __________ Sales

Return on total assets (ROA) ! Net income __________ Total assets

Basic earning power (BEP) ! EBIT __________ Total assets

Return on investors’ capital (ROIC) ! Net income " Interest ____________________ Debt " Equity

Return on common equity (ROE) ! Net income ______________ Common equity

Price/Earnings (P/E) ratio ! Price per share ________________ Earnings per share

Book value per share ! Common equity

_________________ Shares outstanding

Market/book ratio (M/B) ! Market price per share ____________________ Book value per share

ROE ! Profi t margin $ Total assets turnover $ Equity multiplier

! Net income __________ Sales $ Sales __________ Total assets $

Total assets ___________________ Total common equity

EVA ! EBIT(1 # Corporate tax rate) # (Total investors’ capital) $ (After-tax cost of capital) EVA ! Net income # (Equity capital) $ (Cost of equity capital) ! (Equity capital)[Net income/Equity capital # Cost of equity capital] ! (Equity capital)(ROE # Cost of equity capital)

Chapter 5 Future value ! FVN ! PV(1 " I)

Present value ! PV ! FVN _______ (1 " I)N

FVAN ! PMT(1 " I) N-1 " PMT(1 " I)N-2 " PMT(1 " I)N-3 " . . . " PMT(1 " I)0

! PMT [ (1 " I)N # 1 __________ I ]

A-29Appendix C Selected Equations and Tables

FVAdue ! FVAordinary(1 " I) PVAN ! PMT/(1 " I)

1 " PMT/(1 " I)2 " . . . " PMT/(1 " I)N

! PMT [ 1 # 1 _______ (1 " I)N __________ I ] PVAdue ! PVAordinary(1 " I)

PV of a perpetuity ! PMT ____ I

PV ! CF1 ______ (1 " I)1 "

CF2 ______ (1 " I)2 " . . . "

CFN _______ (1 " I)N ! ! t!1 N

CFt ______ (1 " I)t

Periodic rate (IPER) ! Stated annual rate __________________________ Number of payments per year ! I/M

Number of periods ! (Number of years)(Periods per year) ! NM

Eff ective annual rate (EFF%) ! ! 1 " INOM ____ M " M

# 1.0

Chapter 6 Quoted interest rate (r) ! r* " IP " DRP " LP " MRP

! rRF " DRP " LP " MRP

rT-bill ! rRF ! r* " IP

rT-bond ! r*t " IPt " MRPt rC-bond ! r*t " IPt " MRPt " DRPt " LPt rRF with cross-product term ! r* " I " (r* $ I)

Chapter 7 Bond’s value (VB) !

INT _______ (1 " rd) 1 "

INT _______ (1 " rd) 2 " . . . "

INT _______ (1 " rd) N "

M _______ (1 " rd) N

! ! t!1

INT _______ (1 " rd) t "

M _______ (1 " rd) N

Price of callable bond ! ! t!1

INT _______ (1 " rd) t "

Call price ________ (1 " rd) N

VB ! ! t!1

INT/2 _________ (1 " rd/2) t "

M __________ (1 " rd/2) 2N

Chapter 8 Expected rate of return (r̂) ! P1r1 " P2r2 " . . . " PNrN

! ! i!1

Pi ri

Standard deviation ! σ ! √ ___________

! i!1

(ri # r̂) 2 Pi

Estimated σ ! √ ____________

! t!1

(r̄t # r̄Avg) 2

____________ N " 1

Coeffi cient of variation ! CV ! σ __ r̂

r̂p ! w1r̂1 " w2r̂2 " . . . " wNr̂N

! ! i!1

wi r̂i

A-30 Appendix C Selected Equations and Tables

bp ! w1b1 " w2b2 " . . . " wNbN

! ! i!1

wi bi

RPi ! (RPM)bi ri ! rRF " (rM # rRF)bi

Chapter 9 Value of stock (P̂0) ! PV of expected future dividends

! D1 _______ (1 " rs)

1 " D2 ________ (1 " rs )

2 " . . . " D

% ________ (1 " rs ) %

! ! t!1

Dt _______ (1 " rs )

Constant growth stock: P̂0 ! D0(1 " g)

_________ (1 " rs ) 1 "

D0(1 " g) 2

_________ (1 " rs ) 2 " . . . "

D0(1 " g) %

_________ (1 " rs) %

! D0(1 " g) ________ rs # g

! D1 _____ rs # g

Expected rate of return

! Expected dividend yield " Expected growth rate, or capital gains yield

r̂s ! D1 __ P0

" g

Growth rate ! (1 – Payout ratio)ROE

Zero growth stock: P̂0 ! D __ rs

Horizon value ! P̂N ! DN " 1 _____ rs # g

Nonconstant: P̂0 ! D1 _______ (1 " rs)

1 " D2 _______ (1 " rs)

2 " . . . " DN _______ (1 " rs)

N " DN"1 _________ (1 " rs)

N"1 " . . . " D

% _______ (1 " rs) %

! D1 ________ (1 " rs )

1 " D2 ________ (1 " rs )

2 " . . . " DN ________ (1 " rs )

N " P̂N ________ (1 " rs )

! PV of nonconstant dividends " PV of horizon value, P̂N

Market value of company (VCompany ) ! PV of expected future free cash fl ows

! FCF1 ___________ (1 " WACC)1 "

FCF2 ___________ (1 " WACC)2 " . . . "

FCF % ___________ (1 " WACC)%

Horizon value (VCompany at t!N) ! FCFN"1/(WACC # gFCF)

Market value of equity ! Book value " PV of all future EVAs

Vp ! Dp ___ rp

r̂p ! Dp ___ Vp

Chapter 10

WACC ! ! % of debt " ! After-tax cost of debt " " !

% of preferred stock " ! Cost of preferred stock " " ! % of common equity " ! Cost of common equity "

! wdrd(1 – T) " wprp " wcrs

A-31Appendix C Selected Equations and Tables

After-tax cost of debt ! Interest rate on new debt – Tax savings ! rd – rdT ! rd(1 – T)

Component cost of preferred stock ! rp ! Dp ___ Pp

Required rate of return ! Expected rate of return rs ! rRF " RP ! D1/P0 " g ! r̂s

rs ! rRF " (RPM)bi ! rRF " (rM – rRF)bi

P̂0 ! D1 _______ (1 " rs)

1 " D2 _______ (1 " rs)

2 " . . . " D

% _______ (1 " rs) %

! ! t!1

Dt _______ (1 " rs)

P̂0 ! D1 _____ rs # g

rs ! r̂s ! D1 __ P0

" Expected g

Cost of equity from new stock ! re ! D1 ________ P0 (1 # F)

" g

Retained earnings breakpoint

Addition to retained earnings for the year ____________________________________ Equity fraction

Chapter 11 NPV ! CF0 "

CF1 _______ (1 " r)1 " CF2 _______ (1 " r)2 "

. . . " CFN _______ (1 " r)N

! ! t!0

CFt ______ (1 " r)t

CF0 " CF1 _________ (1 " IRR)1 "

CF2 _________ (1 " IRR)2 " . . . "

CFN _________ (1 " IRR)N ! 0

! t!0

CFt ________ (1 " IRR)t ! 0

! t!0

COFt ______ (1 " r)t !

! t!0

CIFt(1 " r) N#t ______________ (1 " MIRR)N

PV costs ! TV ___________ (1 " MIRR)N

Payback ! Number of years prior to full recovery "

Unrecovered cost at start of year ______________________________ Cash fl ow during full recovery year

Chapter 13 EBIT ! PQ – VQ – F ! 0

QBE ! F _____ P # V

bL ! bU[1 " (1 # T)(D/E)]

bU ! bL/[1 " (1 # T)(D/E)]

A-32 Appendix C Selected Equations and Tables

Chapter 14 Dividends ! Net income # Retained earnings required to help fi nance new investements

! Net income # [(Target equity ratio)(Total capital budget)]

Chapter 15

Inventory conversion period

" Average collection period

# Payables deferral period

! Cash conversion cycle

Inventory conversion period ! Inventory

_______________________ Cost of goods sold per day

Average collection period (ACP or DSO) ! Receivables ___________ Sales/365

Payables deferral period ! Payables

________________ Purchases per day ! Payables

____________________ Cost of goods sold/365

Accounts receivable ! Sales per day $ Length of collection period

Receivables ! (ADS)(DSO)

Nominal annual cost of trade credit ! Discount % ________________ 100 # Discount % $ 365 ______________________

Days credit is outstanding # Discount period

Simple interest rate per day ! Nominal rate ____________ Days in year

Interest charge for month ! (Rate per day)(Amount of loan)(Days in month)

Approximate annual rateAdd-on ! Interest paid __________________ (Amount received)/2

Chapter 16 Projected Spontaneous Increase in AFN ! asset # liabilities # retained increase increase earnings

! (A0*/S0)&S # (L0*/S0)&S # MS1(1 – Payout)

Full capacity sales !

Actual sales

____________________

Percentage of capacity at which fi xed assets were operated

Target fi xed assets/Sales ! Actual fi xed assets ________________ Full capacity sales

Required level of fi xed assets ! (Target fi xed assets/Sales)(Projected sales)

Chapter 17 Direct quotation: US$ required ______________________ 1 unit of foreign currency

Indirect quotation: Units of foreign currency

______________________ 1 US$

Forward exchange rate

____________________ Spot exchange rate ! (1 " rh) _______ (1 " rf)

Ph ! (Pf)(Spot rate)

Spot rate ! Ph __ Pf

INDE X

A Abandonment option, 383–384 Abercrombie & Fitch, 533 Accounting income vs. cash

fl ow, 365 Accounting standards, global, 97 Accounts payable, 493–495 Accounts receivable, 490–493

modifying, 524 Accruals, 500 Accrued liabilities, 500 Actual (realized) rate of return

(r̄), 276 Additional funds needed

(AFN), 514 Add-on interest, 498 AFLAC, 534 AFN equation, 514–518 After-tax cost of debt, rd(1 – T), 311 Agency theory, 18 Aggressive approach, 476 Aging schedule, 493 Airbus, 335, 355 Allied Components Company, 362 Allied Food Products, 69, 87, 105,

108, 195, 197, 256, 279, 289, 307–309, 316, 394, 473, 482–485, 492, 493, 512–525

balance sheet, 58 summary of ratios, 104

Allocation, capital, 28–29 Alternative estimates, averaging

the, 317 Alternative minimum tax

(AMT), 72 Amazon.com, 270 American Depository Receipts

(ADRs), 554 American Development

Corporation (ADC), 460 American Stock Exchange, 38 American terms, 543 Amortization, 63 Amortization schedule, 152 Amortized loan, 151–152 Annual compounding, 146–148 Annual depreciation rates, 397 Annual percentage rate

(APR), 148 Annual report, 55 Annuity, 134–135 Annuity due, 135

future rate of, 137 Annuity payments (PMT),

fi nding, 139

Apple Computer, 9, 10, 60, 270, 287, 368

Appreciation of currency, 541, 551 Arbitrage, 546 Ask price, 40 Asset-based fi nancing, 500 Asset management ratios, 89–92 Assets, opportunity costs

association with, 367 Asymmetric information, 423 AT&T, 16, 19 Atlantic Richfi eld, 460 Auction rate securities (ARS), 173 Average collection period

(ACP), 479 Average stock’s beta, 245 Average tax rate, 70

B Balance sheet, 57–61

Allied Food, 58 forecasted, 519

Bank, commercial, 34 investment, 34

Bank loans, 495–499 cost of, 497

Bank of America, 34, 36 Bankruptcy,

and reorganization, 219 effect on capital structure, 421

Base-case NPV, 376 Base-case scenario, 378 Basic earning power (BEP)

ratio, 98 Before-tax cost of debt, 310 Behavioral fi nance theory, 49 Behavioral fi nance, 49 Benchmarking, 105–106 Best Buy Company, 472, 488 Best-case scenario, 378 Beta and CAPM, concerns

about, 257 Beta coeffi cient, 245 Beta coeffi cient, changes in, 256 Beta risk, within-fi rm

and, 381–382 Bid-ask spread, 40 Bid price, 40 Billingham Corporation, 215 Bird-in-the-hand fallacy, 443 Boeing, 335, 355 Bond(s), 195

and valuation, 194

bankruptcy and reorganization, 219

characteristics of, 196–200 issuers, 195–196 other features, 199–200 risk in market, 194 with semiannual

coupons, 209–210 Bond markets, 220 Bond ratings, 215

changes in, 218 criteria for, 216 importance of, 217

Bond riskiness, assessing, 210–214 Bond valuation, 200–203 Bond values, changes over time,

206–209 Bond yields, 203–205 Bondholders vs. stockholders, 20 Bond-yield-plus-risk-premium

approach, 315 Budgeting methods, conclusions,

355–356 Business

activity, 185 climate, 557 decisions, interest rates and,

185–187 ethics, 15–18

company behavior, 15 unethical behavior, 16

organization, forms of, 6–8 risk, 402, 403–413 trends, important, 14

C Call provision, 198 Campus Deli Inc., 435 Cannibalization, 367, 371 Capital,

alternative sources of, 456 external, cost of raising, 319 increased cost of, 318

Capital allocation process, 28–29 Capital asset pricing model

(CAPM), 240 Capital budget, optimal, 385 Capital budgeting, 336

Asian/Pacifi c region, 380 basics of, 335 competition in aircraft

industry, 335 decision criteria, 356 international, 556–558

I-1

Index

Capital budgeting (continued) overview, 336–338 risk analysis in, 374–375

Capital budgeting methods, conclusions, 355–356

Capital component, 309 Capital gain(s),

reasons preferred, 443 vs. dividends, 441–444

Capital gain or loss, 70 Capital gains yield, 276 Capital intensity ratio, 517 Capital market, 30

international money and, 551–554 Capital rationing, 385 Capital structure,

auto companies, 438 determining optimal, 413–419 effect of bankruptcy, 421 effect of taxes, 420 global, 428 international, 558–559 optimal, 416 signaling theory, 423 target, 401–402 trade-off theory, 422 variations in, 427–429

Capital structure and leverage, 400

debt and, 400 Capital structure changes, WACC

and, 414 Capital structure decisions,

checklist for, 425–427 Capital structure theory, 419–425 CAPM, 240–249

and Beta, concerns about, 257 approach, 314

Captive fi nance companies, 492 Carolina Power & Light

(CP&L), 28, 31 Cash,

and marketable securities, 485–488

currency, 486 demand deposits, 486

Cash budget, 482–485 Cash conversion cycle (CCC),

479–481 Cash fl ow,

incremental, 366 timing of, 366 earnings, and dividends, 451 normal and nonnormal, 344

Cash fl ow (CF1), 143 Cash fl ow estimation,

and risk analysis, 364 concepts in, 364–368 Home Depot growth, 364

Cash fl ow statement, 63–67 massaging, 66

Cash fl ow vs. accounting income, 365

CCC, calculating the targeted,

479, 480 see also cash conversion cycle

Changing ratios, analyzing effects of, 524–525

Chevron Corporation, 271, 451, 452, 453, 459

Chrysler, 492 Circuit City, 270 Cisco Systems, 45 Citi Smith Barney, 34, 316 Citibank, 34 Citigroup, 16, 29, 36, 37, 47, 54,

229, 273, 499, 534 Citrus Products Inc., 563 Class life, 397 Classifi ed stock, 272 Clientele effect, 445 Clienteles, 445 Closely held corporation, 40 Coca-Cola, 14, 19, 178, 179, 198,

460, 534 Coeffi cient of variation (CV), 238 Coleman Technologies, 333 Colgate-Palmolive, 534 Collection fl oat, 487 Collection policy, 490 Commercial bank, 34 Commercial paper, 499 Common size analysis, 87 Common stock,

cost of new, 318–320 external equity, 320 fl otation costs, 318 increased cost of capital, 318 market for, 40–43 types of, 272–273 valuing, 290

Compensating balance, 495 Compound interest, 126 Compounding process, graphic

view, 130 Compounding, 125 Conservative approach, 478 Consol, 141 Constant growth (Gordon)

model, 278 Constant growth model, conditions

for, 282 Constant growth stocks, 278–283

illustration, 279 Constraints, dividend, 456 Convertible bond, 199 Corporate (within-fi rm) risk, 375

Corporate bonds, 196 types of, 215

Corporate governance, 15 Corporate objectives, statement

of, 511 Corporate raider, 19 Corporate scope, 511 Corporate strategies, 511 Corporate taxes, 72 Corporate valuation model,

286–291 Corporate valuation vs. discounted

dividend models, 290 Corporation, 7

closely held, 40 global, 535–538 multinational, 535–538 publicly owned, 41 valuing the entire, 286–291

Correlation, 243 Correlation coeffi cient (!), 243 Cost of capital, 306

adjusting for risk, 323 After-tax cost of debt,

rd(1 – T), 311 creating value at GE, 306 global variations in, 322 problems with estimates, 325 risk-adjusted, 375

Cost of debt, rd(1 – T), 310–312 money, 163–164 new common stock (re), 313 preferred stock (rp), 312 retained earnings (rs), 313

Costly trade credit, 495 Country risk, 554

measuring, 555 Coupon interest rate, 197 Coupon payment, 197 Coupons, semiannual, bonds

with, 209–210 Credit period, 490 Credit policy, 490 Credit policy, setting and

implementing, 491 Credit score, 491 Credit standards, 490 Credit terms, 491 Cross rate, 542 Crossover rate, 350 Cumulative voting, 271 Currency board

arrangement, 541 Currency, 486 Current asset

fi nancing policies, 475–478 fi nancing policy, 476 investment policies, 474–475

I-2

I-3Index

Current ratio, 88 Current yield, 205

D D’Leon Inc., 81, 118 Days sales outstanding (DSO), 90 Dealer market, 40 Debenture, 215 Debt, 400 Debt fi nancing, used to constrain

managers, 424 Debt management ratios, 92–95 Debt ratio, 94 Decision tree, 383 Declaration date, 453 Default risk, 214–220 Default risk premium (DRP), 172 Dell, 287, 368, 460 Delta Airlines, 173, 241 Demand deposits, 486 Depreciation of currency, 541, 550 Depreciation rates, effect of

different, 371 Depreciation, 63 Derivative, 33 Determinants of market interest

rates, 168–174 Deutsche Bank, 47 Devaluation of currency, 540 Direct investments, 551 Direct quotations, 544 Discount bond, 202 Discount on forward rate, 545 Discounted cash fl ow (DCF)

approach, 315 Discounted dividend model,

275–278 vs. corporate valuation, 290

Discounted payback, 354 Discounting, 131 Discounting process, graphic

view, 132 Discounts, 490 Diversifi able risk, 243 Diversifying overseas, benefi ts

of, 250 Dividend distribution, 440 Dividend irrelevance theory, 442 Dividend policy,

alternative capital, 456 constraints on, 456 effects of, 457 factors infl uencing, 455–457 in practice, establishing, 446–454 investment opportunities, 456 issues in, 444–445

Dividend reinvestment plan (DRIP), 454–455

Dividend yield, 276 Dividend yields around the

world, 449 Dividends,

earnings, and cash fl ows, 451 reasons preferred, 442 vs. capital gains, 441–444 vs. growth, 280–282

Dividend-yield-plus-growth-rate approach, 315

Domestic vs. multinational fi nancial management, 538–539

Dow Chemical, 534 Dow Jones Industrial Average, 45 DuPont equation, 101–102 Duration, 211 Dutch auction, 43

E Eagle, 81 Earnings, cash fl ows, and

dividends, 451 EBITDA, 63 Economic value added (EVA) vs.

net income, 108 Effective (equivalent) annual rate

(EFF% or EAR), 149 Effi cient markets hypothesis

(EMH), 47, 49 semi-strong form, 47 strong form, 47 weak form, 47

Electronic communications networks (ECNs), 38

Enron, 11, 14, 17, 15, 16, 106, 219 Equilibrium stock prices, changes

in, 302–303 Equilibrium, 12, 302 Eurobond, 552 Eurocredits, 551 Eurodollar, 551 European terms, 543 EVA approach, 290 Excess capacity adjustments, 517 Exchange rate, 540, 550–551 Exchange rate risk, 554 Exchange traded funds, 35 Ex-dividend date, 453 Executive compensation, intrinsic

values, stock prices, and, 10–13 Expansion project, analysis of,

369–372 Expected dividends, basis for

stock value, 277 Expected infl ation, impact of, 253 Expected rate of return, r̂, 234, 276 Expected return on a portfolio,

(r̂p), 241

Expected risk premium, 315 Expected total return, 276 External capital, cost of raising, 319 External equity, when to use, 320 Externality, 367

environmental, 368 negative within-fi rm, 367 positive within-fi rm, 368

ExxonMobil, 14, 215, 299

F Fannie Mae, 19 Federal budget defi cits or

surpluses, 184 Federal reserve policy, 183 Finance,

capital markets, 5 corporate, 5 defi ned, 4–6 investments, 5 jobs in, 6 vs. economics and accounting, 4 within an organization, 4

Finance theory, behavioral, 49 Financial analysis on the Internet, 68 Financial calculators, 127, 128 Financial fl exibility, 402, 426 Financial institutions, 34–38 Financial leverage, 409 Financial management,

multinational, 534 multinational vs. domestic,

538–539 overview, 2 striking the right balance, 2

Financial markets, 30–34 and institutions, 26 recent trends, 31 types of, 30–31

Financial plan, 512 Financial planning and

forecasting, 509 strategic, 511–512

Financial report, balance sheet, 57–61

Financial risk, 403–407, 408–413 defi ned, 408

Financial services corporation, 34 Financial statement analysis, 85

analyzing stocks, 85 Financial statements

and reports, 55–56 cash fl ow, and taxes, 54 forecasted, 518–522 quality of, 54 warning signs, 106

Financing policies, current asset, 475–478

I-4 Index

Financing, short-term, 500–501 Fixed assets turnover ratio, 91 Fixed exchange rate, 540 Fixed-peg arrangement, 542 Fixed-rate bond, 197 Float, 487 Floating exchange rate, 540 Floating-rate bond, 197 Flotation cost, F, 319

added to project cost, 318 Flotation cost adjustment, 319 Ford Motor Company, 43, 122,

241, 451, 492 Forecasted balance sheet, 519 Forecasted fi nancial statements,

518–522 inputs, 518 ratios and EPS, 520 used for operations, 520

Forecasted income statement, 519 Foreign bond, 196, 552 Foreign exchange rate quotations,

542–544 Foreign trade defi cit, 184 Formula approach, 127 Forward exchange rate, 540, 545 Founders’ shares, 273 Fractional time periods, 150 Free cash fl ow, 68

and small businesses, 69 Free trade credit, 495 Freely-fl oating regime, 541 Frito-Lay, 81 Funds, spontaneously

generated, 514 Future value (FVN), 125–130 Futures market, 30 FVAN, 135

G General Electric, 2–3, 9, 12, 14,

215, 231, 232, 306, 355, 492, 509–512

creating value at, 306 General Motors, 19, 231, 232, 273,

451, 492 General Motors Acceptance

Corporation (GMAC), 491 Georgia-Pacifi c Corporation, 417 Global accounting standards, 97 Global corporations, 535–538 Global perspectives boxes, 14, 38,

97, 250, 322, 380, 428, 449, 555 Global variations in the cost of

capital, 322 Going public, 41 Goldman Sachs, 47 Goodyear, 460

Google Inc., 3, 43, 45, 283, 287 Gordon-Lintner’s theory, 443 Greenmail, 460 Growth rate, g, 276 Growth vs. dividends, 280–282 Gulf Oil, 271

H Half-year convention, 397 Hamada equation, 415 Hedge funds, 35 Herman Miller, Inc., 489 Hewlett-Packard, 7, 368, 459, 534 Historical risk premium, 315 Holder-of-record date, 453 Home Depot Inc., 14, 364, 366, 367,

460, 475, 488 Horizon (terminal) value, 284 Hostile takeover, 19 Hughes Aircraft, 273 Humped yield curve, 176 Hypothesis, 444

I IBM, 14, 19, 33, 368, 460, 492, 534 Incentive signaling, 444 Income bond, 200 Income statement, 61–63

forecasted, 519 Income taxes, 70–75 Incremental cash fl ow, 366 Indenture, 215 Independent projects, 340, 352 Indexed (purchasing power)

bond, 200 Indirect quotations, 544 Infl ation, 163

and interest rates, link between, 178

impact of expected, 253 interest rates and exchange

rates, 550–551 Infl ation premium (IP), 170 Information content (signaling), 444 Initial public offering (IPO)

market, 41 Inputs, changes to, 372 Intel, 45, 368 Interbank foreign currency

quotations, 543 Interest, simple vs. compound, 126 Interest charges, calculating, 497, 498 Interest rate, I, fi nding, 133–134, 140 Interest rate(s), 162, 550–551

and business decisions, 185–187 and infl ation, link between, 178 comparing, 148–150

Effective (equivalent) annual rate (EFF% or EAR), 149

term structure of, 175–176 yield curve used to estimate

future, 180–182 Interest rate (price) risk, 210 Interest rate levels, 165–168

macroeconomic factors infl uence, 183–185

Interest rate parity, 546–547 Interest rate risk, 173 Internal rate of return (IRR),

341–344 International capital budgeting,

556–558 International capital structures,

558–559 International credit markets, 551 International factors, 184 International money and capital

markets, 551–554 International monetary system,

540–542 International money

terminology, 540 International stock markets,

552, 553 International stocks, investing in,

555–556 Internet, fi nancial analysis on

the, 68 Intrinsic value vs. stock price,

273–275 Intrinsic value, 11, 274

investor concerns, 274 stock prices, and executive

compensation, 10–13 Inventories, 488–489

modifying, 524 Inventory conversion period, 479 Inventory turnover ratio, 90 Inverted (abnormal) yield

curve, 176 Investing overseas, 554 Investment, vertically

integrated, 536 Investment bank, 34 Investment horizon, 213 Investment opportunities, 456 Investment policies, current asset,

474–475 Investment-grade bond, 216 Investor, marginal, 12 IRR compared to NPV, 343

J JPMorgan Chase, 34 Junk bond, 216

I-5Index

K Keebler Foods Co., 400 Kellogg Co., 400

L Law of one price, 547 Leverage, capital structure and, 400 LIBOR, 551 Limited liability company

(LLC), 7 Limited liability partnership

(LLP), 7 Line of credit, 496 Liquid asset, 88 Liquidity premium (LP), 172 Liquidity ratios, 88, 88–89 Lockbox, 486 Low-regular-dividend-plus-

extras, 451

M Macroeconomic factors, and

interest rate levels, 183–185 Managed-fl oat regime, 541 Managerial conservatism/

aggressiveness, 402 Managers, stockholders, and

bondholders, confl icts between, 18–21

Managers vs. stockholders, 18 Marginal investor, 12, 275 Marginal tax rate, 70 Market, measuring the, 45 Market (beta) risk, 375 Market effi ciency, conclusions

about, 50 Market for common stock, 40–43 Market instruments, summary of, 32 Market interest rates,

determinants of, 168–174 Market portfolio, 244 Market price (P0), 11, 276 Market risk premium, 251

estimating, 252 Market risk, 243 Market value ratios, 99 Market, initial public offering

(IPO), 41 Market/book (M/B) ratio, 100 Marketable securities, 487

cash and, 485–488 Markets,

fi nancial, 30–34 tale of three, 229

Maturity date, 197 Maturity matching approach, 476

Maturity risk premium (MRP), 173

McDonald’s, 534 global Big Mac prices, 548–549

Merrill Lynch, 16, 29, 47, 229, 273, 316, 499

Microsoft, 3, 7, 14, 28, 45, 271, 283, 368, 440, 459, 460, 469, 485, 487

Mission statement, 511 Moderate current asset policy, 475 Modifi ed IRR (MIRR), 347–349 Modigliani-Miller theory, 419 Monetary arrangements,

current, 541 Money market, 30 Money market funds, 35 Monte Carlo simulation, 379 Mortgage bond, 215 Multinational corporations,

535–538 Multinational fi nancial

management, 534 U.S. fi rms, 534 vs. domestic, 538–539

Multiple IRRs, 344, 344–345 Municipal bonds, 196 Mutual funds, 35 Mutual of Chicago Insurance

Company, 298 Mutually exclusive projects,

340, 352

N Nasdaq, 38, 45 Negative working capital,

operating with, 481 Net income vs. economic value

added (EVA), 108 Net present value (NPV), 338–341 Net present value profi le, 349 Net working capital, 60, 339, 473 New World Chemicals Inc., 531 New York Stock Exchange, 38 Nominal (quoted) risk-free rate,

rRF , 170 Nominal (quoted, or stated)

interest rate, INOM, 148 Nonconstant growth stocks,

valuing, 283–286 Nonnormal cash fl ows, 344 Normal cash fl ows, 344 Normal yield curve, 176 Northwest Milling Company, 198 NPV compared to IRR, 343 NPV profi les, 349–353 Number of periods (N),

fi nding, 139 Number of years, N, fi nding, 134

O Operating breakeven, 405 Operating income, 61 Operating leverage, 405 Operating margin, 96 Operating plan, 512 Opportunity cost, 131, 367, 371

and assets, 367 Optimal capital budget, 385 Optimal capital structure, 401, 416

determining, 413–419 Optimal dividend policy, 442 Option value, 383 Ordinary (deferred) annuity, 135 Original issue discount (OID)

bond, 197 Original maturity, 198 Over-the-counter (OTC) market, 39 Oversubscribed, 41

P P/E multiple approach, 290 Pacifi c Timber Company, 198 Par value, 197 Partnership, 7 Payables deferral period, 479 Payback period, 353–355 Payment (PMT), 143 Payment date, 454 Payment fl oat, 487 Payment procedures, 453 Permanent current assets, 476 Payout ratio, 446 Perpetuity, 141–142 Phillips Petroleum, 460 Physical location exchanges, 39 Political risk, 557 Porter Electronic Controls Inc., 457 Portfolio context, risk in, 240–249 Portfolio investments, 551 Portfolio risk, 242, 245 Post-audit, 386 Preemptive right, 272 Preferred stock, 291–292 Premium bond, 203 Premium on forward rate, 545 Present value (PV), 125, 131–133

of an ordinary annuity, 138–139 Price/earnings (P/E) ratio, 99 PricewaterhouseCoopers (PWC), 14 Primary market, 30 Prime rate, 497 Private equity companies, 36 Private market, 31 Probability distribution, 233 Procter & Gamble, 33, 283, 460 Production opportunities, 163 Profi t margin, 96

I-6 Index

Profi tability ratios, 96–98 Progressive tax, 70 Promissory note, 495 Proprietorship, 6 Proxy fi ght, 271 Proxy, 271 Public market, 31 Publicly owned corporation, 41 Purchasing power parity (PPP),

547–550 Pure expectations theory, 180 Putable bond, 200 PVAN, 138

Q Quick (acid test) ratio, 89

R Raider, corporate, 19 Rates of return, risk and, 229 Ratio analysis, 87 Ratios,

analyzing effects of changing, 524–525

and EPS, 520 in different industries, 103 uses and limitations of, 106–108

Real option, 382–384 types of, 382

Real risk-free rate of interest (r*), 169

Realized rate of return (r̄), 241 Regression, used to improve

forecasts, 523–524 Regression analysis, 523 Regular interest, 498 Reinvestment rate assumptions,

346–347 Reinvestment rate risk, 174, 213 Relaxed current asset policy, 475 Relevant risk, 245 Reorganization, bankruptcy

and, 219 Repatriation of earnings, 557 Replacement analysis, 372–374 Replacement projects, 366 Reports, fi nancial, 55–56 Required rate of return (rs), 276 Required returns, 238 Reserve borrowing capacity, 424 Residual dividend model, 446, 447 Restricted current asset

policy, 475 Retained earnings

breakpoint, 320 Retention ratio, 514 Retirement concerns, 123

Return on common equity (ROE), 98

Return on total assets (ROA), 97 Returns, stock markets and, 43–46 Revaluation of currency, 540 Reverse splits, 458 Revolving credit agreement, 497 Risk, 163, 232

business, 402, 403–413 fi nancial, 403–407, 408–413 interest rate, 173 measuring with historical

data, 237 reinvestment rate, 174, 213

Risk analysis and cash fl ow estimation, 364 Home Depot growth, 364 in capital budgeting, 374–375

Risk and rates of return, 229 relationship, 251–257

Risk and return, trade-off between, 239

Risk aversion, 238–239 changes in, 255

Risk premium (RP), 239, 315 Risk-adjusted cost of capital, 375 RJR Nabisco, 271 ROE, potential misuses of, 108–109 ROE, see also return on common

equity rRF , 169

S S corporation, 7, 75 Sales forecast, 512–513 Salomon Smith Barney, 37 Sarbanes-Oxley Act, 5 Scenario analysis, 378 Sears, 492 Seasoned issue, 206 Secondary market, 30 Secured fi nancing, 500 Secured loan, 500 Security in short-term fi nancing,

500–501 Security market line (SML)

equation, 253 Self-liquidating approach, 476 Semiannual compounding,

146–148 Semiannual coupons, bonds with,

209–210 Sensitivity analysis, 376 Share repurchases, 440 Shareholder

distributions, dividends and share repurchases, 440

value, stock prices and, 8–10

wealth maximization, 9, 14 Short-term fi nancing, use of

security in, 500–501 Signal, 424, 444 Signaling theory, 423 Simple interest, 126, 498 Sinking fund provision, 199 Sinking funds, 199 Ski Equipment Inc., 506 Southeastern Steel Company, 468 Special studies, 525 Spontaneous funds, 500 Spontaneously generated

funds, 514 Spot market, 30 Spot rate, 540, 545 Spreadsheets, 128 Stand-alone risk, 232, 233–240, 375

measuring, 236, 376–381 statistical measures of, 233

Standard deviation (sigma), 236, 237

Starbucks, 84, 270 Statement of cash fl ows, 63, 63–67 Statement of corporate

objectives, 511 Statement of stockholders’

equity, 67 Stock,

and valuation, 269 that doesn’t pay dividends,

evaluating, 287 types of common, 272–273 valuation, searching for the

right stock, 269 Stock dividends, 458

and stock splits, 457–459 Stock market, 38–40

and returns, 43–46 global indices, 552 OTC and Nasdaq, 39 physical location, 39

Stock market effi ciency, 46–50 Stock market equilibrium, 301–303 Stock market reporting, 43 Stock market returns, 46 Stock market transactions, types

of, 41 Stock prices,

and shareholder value, 8–10 effect of split, 458 intrinsic values, and executive

compensation, 10–13 recent trends, 231–232 vs. intrinsic value, 273–275

Stock repurchases, 460, 459–463 advantages of, 461 conclusions on, 462 disadvantages of, 462 effects of, 460

I-7Index

Stock splits, 457 effect on stock prices, 458

Stock value, expected dividends as basis for, 277

Stockholder rights, control of the fi rm, 271 preemptive right, 272

Stockholder wealth maximization, 9

Stockholders, legal rights and privileges,

270–272 vs. bondholders, 20 vs. managers, 18

Strategic business plan, 337 Stretching accounts payable, 495 Strategic planning, 511–512 Subordinated debenture, 215 Sunk cost, 366–367, 371 Supernormal (nonconstant)

growth, 283 Supply chain management, 489 Survivor bias, 100 Survivorship bias, 252 Sustainable growth rate, 515 Symmetric information, 423 Synergy, 511

T Takeover, 271

hostile, 19 Target capital structure, 401,

401–402 Target cash balance, 483 Target payout ratio, 441 Target payout ratio, 446 Tax depreciation, 397–398 Tax loss carry-back or carry-

forward, 74 Taxes,

corporate, 72 effect on capital structure, 420 income, 70–75 individual, 70

Teledyne, 460 Temporary current assets, 476 Tender offer, 460

Term structure of interest rates, 175–176

Terminal (horizon) date, 284 Texas Instruments, 460 3M’s cost of capital, 334 Time line, 124–125 Time preferences for

consumption, 163 Time value of money, 123 Times-interest-earned (TIE)

ratio, 95 Total assets, total debt to, 94 Total assets turnover ratio, 92 Total debt to total assets, 94 Total return, 207 Trade credit, 493 Trade-off theory, 422 Trading in foreign exchange,

544–546 Treasury bonds, 196

almost riskless, 171 Trend analysis, 100 Tyco, 18

U Unethical behavior,

and employees, 17 consequences of, 16

Uneven (nonconstant) cash fl ows, 143–144

Uneven cash fl ow stream, future value of, 144–145

Uneven cash fl ows, solving for I, 145–146

Unlevered beta, 416

V Vertically integrated

investment, 536

W WACC,

and capital structure changes, 414 factors affecting, 321

factors fi rm can control, 322 factors fi rm cannot control, 321 see also weighted average cost

of capital Wachovia, 34 Wal-Mart, 9, 10, 14, 340, 475, 488 Walt Disney Company, 18, 19, 198 Warrant, 199 Weighted average cost of capital

(WACC), 310, 321 overview, 307–309

Wells Fargo, 34 Western Money Management

Inc., 228 Whistle-blowers, protection for, 17 Window dressing techniques, 107 Within-fi rm and beta risk, 381–382 Working capital management, 472

Best Buy, 472 Working capital, 59, 473

background, 473–474 operating with negative, 481

WorldCom, 14, 16, 17, 54 Worst-case scenario, 378

X Xerox, 19, 459, 460, 535

Y Yahoo!, 68 Yield curve, 175

shape determined, 176–180 used to estimate future interest

rates, 180–182 Yield spread, 217 Yield to call (YTC), 204 Yield to maturity (YTM), 203 Yogi Berra, 420

Z Zero coupon bond, 197 Zero growth stock, 282

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FREQUENTLY USED SYMBOLS/ABBREVIATIONS ACP Average collection period ADR American depository receipt APR Annual percentage rate A/R Accounts receivable b Beta coeffi cient, a measure of an asset’s riskiness bL Levered beta bU Unlevered beta BEP Basic earning power BVPS Book value per share CAPM Capital Asset Pricing Model CCC Cash conversion cycle CF Cash fl ow; CFt is the cash fl ow in Period t CFPS Cash fl ow per share CV Coeffi cient of variation Dp Dividend of preferred stock Dt Dividend in Period t DCF Discounted cash fl ow D/E Debt-to-equity ratio DPS Dividends per share DRIP Dividend reinvestment plan DRP Default risk premium DSO Days sales outstanding EAR Effective annual rate, EFF% EBIT Earnings before interest and taxes; operating income EBITDA Earnings before interest, taxes, depreciation, and amortization EPS Earnings per share EVA Economic value added F (1) Fixed operating costs (2) Flotation cost FCF Free cash fl ow FVN Future value for Year N FVAN Future value of an annuity for N years g Growth rate in earnings, dividends, and stock prices I Interest rate; also referred to as r I/YR Interest rate key on some calculators INT Interest payment in dollars IP Infl ation premium IPO Initial public offering IRR Internal rate of return LP Liquidity premium M Maturity value of a bond M/B Market-to-book ratio MIRR Modifi ed internal rate of return MRP Maturity risk premium MVA Market value added N Calculator key denoting number of periods NWC Net working capital NPV Net present value P (1) Price of a share of stock in Period t; P0 ! price of the stock today (2) Sales price per unit of product sold Pf Price of good in foreign country Ph Price of good in home country

P/E Price/earnings ratio PMT Payment of an annuity PPP Purchasing power parity PV Present value PVAN Present value of an annuity for N years Q Quantity produced or sold QBE Break-even quantity r (1) A percentage discount rate, or cost of capital; also referred to as I (2) Nominal risk-adjusted required rate of return r̄ “r bar,” historic, or realized, rate of return r̂ “r hat,” an expected rate of return r* Real risk-free rate of return rd Before-tax cost of debt re Cost of new common stock (outside equity) rf Interest rate in foreign country rh Interest rate in home country ri Required return for an individual fi rm or security rM Return for “the market,” or an “average” stock rNOM Nominal rate of interest; also referred to as INOM rp (1) Cost of preferred stock (2) Portfolio’s return rPER Periodic rate of return rRF Rate of return on a risk-free security rs (1) Cost of retained earnings (2) Required return on common stock " Correlation coeffi cient; also denoted as R when using historical data ROA Return on assets ROE Return on equity RP Risk premium RPM Market risk premium RR Retention rate S (1) Sales (2) Estimated standard deviation for sample data SML Security Market Line # Summation sign $ Standard deviation t Time period T Marginal income tax rate TVN A stock’s horizon, or terminal, value at t ! N TIE Times interest earned V Variable cost per unit VB Bond value Vp Value of preferred stock VC Total variable costs WACC Weighted averaged cost of capital YTC Yield to call YTM Yield to maturity

Front Cover
Title Page
Copyright
CONTENTS
PREFACE
PART 1 Introduction to Financial Management

CHAPTER 1 An Overview of Financial Management

Striking the Right Balance
PUTTING THINGS IN PERSPECTIVE
1-1 What Is Finance
1-2 Jobs in Finance
1-3 Forms of Business Organization
1-4 Stock Prices and Shareholder Value
1-5 Intrinsic Values, Stock Prices, and Executive Compensation
1-6 Important Business Trends
1-7 Business Ethics
1-8 Conflicts Between Managers, Stockholders, and Bondholders
TYING IT ALL TOGETHER

PART 2 Fundamental Concepts in Financial Management

CHAPTER 2 Financial Markets and Institutions

Efficient Financial Markets Are Necessary for a Growing Economy
PUTTING THINGS IN PERSPECTIVE
2-1 The Capital Allocation Process
2-2 Financial Markets
2-3 Financial Institutions
2-4 The Stock Market
2-5 The Market for Common Stock
2-6 Stock Markets and Returns
2-7 Stock Market Efficiency
TYING IT ALL TOGETHER
INTEGRATED CASE: Smyth Barry & Company

CHAPTER 3 Financial Statements, Cash Flow, and Taxes

The "Quality" of Financial Statements
PUTTING THINGS IN PERSPECTIVE
3-1 Financial Statements and Reports
3-2 The Balance Sheet
3-3 The Income Statement
3-4 Statement of Cash Flows
3-5 Statement of Stockholders' Equity
3-6 Free Cash Flow
3-7 Income Taxes
TYING IT ALL TOGETHER
INTEGRATED CASE: D'Leon Inc., Part I
THOMSON ONE: BUSINESS SCHOOL EDITION: Exploring Starbucks' Financial Statements

CHAPTER 4 Analysis of Financial Statements

Can You Make Money Analyzing Stocks?
PUTTING THINGS IN PERSPECTIVE
4-1 Ratio Analysis
4-2 Liquidity Ratios
4-3 Asset Management Ratios
4-4 Debt Management Ratios
4-5 Profitability Ratios
4-6 Market Value Ratios
4-7 Trend Analysis
4-8 The DuPont Equation
4-9 Ratios in Different Industries
4-10 Summary of Allied's Ratios
4-11 Benchmarking
4-12 Uses and Limitations of Ratios
4-13 Potential Misuses of ROE
4-14 Looking Beyond the Numbers
TYING IT ALL TOGETHER
INTEGRATED CASE: D'Leon Inc., Part II
THOMSON ONE: BUSINESS SCHOOL EDITION: Conducting a Financial Ratio Analysis on Ford Motor Company

CHAPTER 5 Time Value of Money

Will You Be Able to Retire?
PUTTING THINGS IN PERSPECTIVE
5-1 Time Lines
5-2 Future Values
5-3 Present Values
5-4 Finding the Interest Rate, I
5-5 Finding the Number of Years, N
5-6 Annuities
5-7 Future Value of an Ordinary Annuity
5-8 Future Value of an Annuity Due
5-9 Present Value of an Ordinary Annuity
5-10 Finding Annuity Payments, Periods, and Interest Rates
5-11 Perpetuities
5-12 Uneven Cash Flows
5-13 Future Value of an Uneven Cash Flow Stream
5-14 Solving for I with Uneven Cash Flows
5-15 Semiannual and Other Compounding Periods
5-16 Comparing Interest Rates
5-17 Fractional Time Periods
5-18 Amortized Loans
TYING IT ALL TOGETHER
INTEGRATED CASE: First National Bank

PART 3 Financial Assets

CHAPTER 6 Interest Rates

Low Interest Rates Encourage Investment and Stimulate Consumer Spending
PUTTING THINGS IN PERSPECTIVE
6-1 The Cost of Money
6-2 Interest Rate Levels
6-3 The Determinants of Market Interest Rates
6-4 The Term Structure of Interest Rates
6-5 What Determines the Shape of the Yield Curve?
6-6 Using the Yield Curve to Estimate Future Interest Rates
6-7 Macroeconomic Factors That Influence Interest Rate Levels
6-8 Interest Rates and Business Decisions
TYING IT ALL TOGETHER
INTEGRATED CASE: Morton Handley & Company

CHAPTER 7 Bonds and Their Valuation

Sizing Up Risk in the Bond Market
PUTTING THINGS IN PERSPECTIVE
7-1 Who Issues Bonds?
7-2 Key Characteristics of Bonds
7-3 Bond Valuation
7-4 Bond Yields
7-5 Changes in Bond Values Over Time
7-6 Bonds with Semiannual Coupons
7-7 Assessing a Bond’s Riskiness
7-8 Default Risk
7-9 Bond Markets
TYING IT ALL TOGETHER
INTEGRATED CASE: Western Money Management Inc.

CHAPTER 8 Risk and Rates of Return

A Tale of Three Markets—or Is It Four?
PUTTING THINGS IN PERSPECTIVE
8-1 Stock Prices Over the Last 20 Years
8-2 Stand-Alone Risk
8-3 Risk in a Portfolio Context: The CAPM
8-4 The Relationship between Risk and Rates of Return
8-5 Some Concerns about Beta and the CAPM
8-6 Some Concluding Thoughts: Implications for Corporate Managers and Investors
TYING IT ALL TOGETHER
INTEGRATED CASE: Merrill Finch Inc.
THOMSON ONE: BUSINESS SCHOOL EDITION: Using Past Information to Estimate Required Returns

CHAPTER 9 Stocks and Their Valuation

Searching for the Right Stock
PUTTING THINGS IN PERSPECTIVE
9-1 Legal Rights and Privileges of Common Stockholders
9-2 Types of Common Stock
9-3 Stock Price versus Intrinsic Value
9-4 The Discounted Dividend Model
9-5 Constant Growth Stocks
9-6 Valuing Nonconstant Growth Stocks
9-7 Valuing the Entire Corporation
9-8 Preferred Stock
TYING IT ALL TOGETHER
INTEGRATED CASE: Mutual of Chicago Insurance Company
THOMSON ONE: BUSINESS SCHOOL EDITION: Estimating ExxonMobil’s Intrinsic Stock Value
APPENDIX 9A: Stock Market Equilibrium

PART 4 Investing in Long-Term Assets: Capital Budgeting

CHAPTER 10 The Cost of Capital

Creating Value at GE
PUTTING THINGS IN PERSPECTIVE
10-1 An Overview of the Weighted Average Cost of Capital (WACC)
10-2 Basic Definitions
10-3 Cost of Debt, r[sub(d)](1 – T)
10-4 Cost of Preferred Stock, r[sub(p)]
10-5 The Cost of Retained Earnings, r[sub(s)]
10-6 Cost of New Common Stock, r[sub(e)]
10-7 Composite, or Weighted Average, Cost of Capital, WACC
10-8 Factors That Affect the WACC
10-9 Adjusting the Cost of Capital for Risk
10-10 Some Other Problems with Cost of Capital Estimates
TYING IT ALL TOGETHER
INTEGRATED CASE: Coleman Technologies Inc.
THOMSON ONE: BUSINESS SCHOOL EDITION: Calculating 3M’s Cost of Capital 334

CHAPTER 11 The Basics of Capital Budgeting

Competition in the Aircraft Industry: Airbus vs. Boeing
PUTTING THINGS IN PERSPECTIVE
11-1 An Overview of Capital Budgeting
11-2 Net Present Value (NPV)
11-3 Internal Rate of Return (IRR)
11-4 Multiple Internal Rates of Return
11-5 Reinvestment Rate Assumptions
11-6 Modified Internal Rate of Return (MIRR)
11-7 NPV Profiles
11-8 Payback Period
11-9 Conclusions on Capital Budgeting Methods
11-10 Decision Criteria Used in Practice
TYING IT ALL TOGETHER
INTEGRATED CASE: Allied Components Company

CHAPTER 12 Cash Flow Estimation and Risk Analysis

Home Depot Keeps Growing
PUTTING THINGS IN PERSPECTIVE
12-1 Conceptual Issues in Cash Flow Estimation
12-2 Analysis of an Expansion Project
12-3 Replacement Analysis
12-4 Risk Analysis in Capital Budgeting
12-5 Measuring Stand-Alone Risk
12-6 Within-Firm and Beta Risk
12-7 Real Options
12-8 The Optimal Capital Budget
12-9 The Post-Audit
TYING IT ALL TOGETHER
INTEGRATED CASE: Allied Food Products
APPENDIX 12A: Tax Depreciation

PART 5 Capital Structure and Dividend Policy

CHAPTER 13 Capital Structure and Leverage

Debt: Rocket Booster or Anchor?
PUTTING THINGS IN PERSPECTIVE
13-1 The Target Capital Structure
13-2 Business and Financial Risk
13-3 Determining the Optimal Capital Structure
13-4 Capital Structure Theory
13-5 Checklist for Capital Structure Decisions
13-6 Variations in Capital Structures
TYING IT ALL TOGETHER
INTEGRATED CASE: Campus Deli Inc.
THOMSON ONE: BUSINESS SCHOOL EDITION: Exploring the Capital Structures for Four of the World’s Leading Auto Companies

CHAPTER 14 Distributions to Shareholders: Dividends and Share Repurchases

Microsoft Shifts Gears and Begins to Unload Part of Its Vast Cash Hoard
PUTTING THINGS IN PERSPECTIVE
14-1 Dividends versus Capital Gains: What Do Investors Prefer?
14-2 Other Dividend Policy Issues
14-3 Establishing the Dividend Policy in Practice
14-4 Dividend Reinvestment Plans
14-5 Summary of Factors Influencing Dividend Policy
14-6 Stock Dividends and Stock Splits
14-7 Stock Repurchases
TYING IT ALL TOGETHER
INTEGRATED CASE: Southeastern Steel Company
THOMSON ONE: BUSINESS SCHOOL EDITION: Microsoft’s Dividend Policy

PART 6 Working Capital Management, Forecasting, and Multinational Financial Management

CHAPTER 15 Working Capital Management

Best Buy Manages Its Working Capital Well
PUTTING THINGS IN PERSPECTIVE
15-1 Background on Working Capital
15-2 Current Asset Investment Policies
15-3 Current Asset Financing Policies
15-4 The Cash Conversion Cycle
15-5 The Cash Budget
15-6 Cash and Marketable Securities
15-7 Inventories
15-8 Accounts Receivable
15-9 Accounts Payable (Trade Credit)
15-10 Bank Loans
15-11 Commercial Paper
15-12 Accruals (Accrued Liabilities)
15-13 Use of Security in Short-Term Financing
TYING IT ALL TOGETHER
INTEGRATED CASE: Ski Equipment Inc.

CHAPTER 16 Financial Planning and Forecasting

The Miss That Hit Like a Bombshell
PUTTING THINGS IN PERSPECTIVE
16-1 Strategic Planning
16-2 The Sales Forecast
16-3 The AFN Equation
16-4 Forecasted Financial Statements
16-5 Using Regression to Improve Forecasts
16-6 Analyzing the Effects of Changing Ratios
TYING IT ALL TOGETHER
INTEGRATED CASE: New World Chemicals Inc.
THOMSON ONE: BUSINESS SCHOOL EDITION: Forecasting the Future Performance of Abercrombie & Fitch

CHAPTER 17 Multinational Financial Management

U.S. Firms Look Overseas to Enhance Shareholder Value
PUTTING THINGS IN PERSPECTIVE
17-1 Multinational or Global Corporations
17-2 Multinational versus Domestic Financial Management
17-3 The International Monetary System
17-4 Foreign Exchange Rate Quotations
17-5 Trading in Foreign Exchange
17-6 Interest Rate Parity
17-7 Purchasing Power Parity
17-8 Inflation, Interest Rates, and Exchange Rates
17-9 International Money and Capital Markets
17-10 Investing Overseas
17-11 International Capital Budgeting
17-12 International Capital Structures
TYING IT ALL TOGETHER
INTEGRATED CASE: Citrus Products Inc.

APPENDIXES

Appendix A: Solutions to Self-Test Questions and Problems
Appendix B: Answers to Selected End-of-Chapter Problems
Appendix C: Selected Equations and Tables

INDEX