## S150 S100 S100

Cash next year - Cash now Cash now

This is a bit cumbersome. To make it easier to read, we abbreviate cash flows and we use subscripts to indicate time. For example, name your two inputs Co for cash flow right now (at time 0), and Ci for cash flow next year (at time 1). Call your result a rate of return and name it

Now you can ask much more interesting and complex questions, such as what you would end up with if you started with S200 and earned 50% rate of return two years in a row, what the effect of inflation and investor competition would be on your rate of return, and so on. There will be dozens of other complications to this formula in this book. But we are getting ahead of ourselves. Trust me: This book will cover a lot of theory—but the theory is not difficult when properly defanged. Most of it is just common sense translated into formulas.

One can think of many complications easily.

### Other Readings

This book cannot do it all. It is important for you to keep up with current financial developments. Frequent reading of the financial section of a major newspaper (such as the New York Times [N.Y.T.]), the Wall Street Journal [W.S.J.], or the Financial Times [F.T.] can help, as can regular consumption of good business magazines, such as The Economist or Business Week. (See the website at http://welch.econ.brown.edu/book for more useful resource links.) I bet there will not be a single day on which you cannot find something that you just covered from this textbook in these publications. Although this is not a book on "how to read and understand the newspaper," you should be able to understand most of the contents of the financial pages after consuming this textbook. You should also know how to cruise the web—sites such as Yahoo!Finance contain a wealth of useful financial information. Yahoo!Finance is also used extensively in this book.

Advice: Follow current coverage of financial topics elsewhere!

Contents

Chapter 1 Introduction l

1 ■ 1 The Goal of Finance: Relative Valuation 2

The Law of One Price, 2;

1 ■ 2 Investments, Projects, and Firms 3

I Value and Capital Budgeting

(in a Perfect Market under Risk-Neutrality) 9

Chapter 2 The Time Value of Money and Net Present Value 13

2 ■ 1 Our Basic Scenario: Perfect Markets, Certainty, Constant Interest Rates 14

2-2 Loans and Bonds 14

2-3 Returns, Net Returns, and Rates of Return 15

2 -4 The Time Value of Money, Future Value, and Compounding 17

The Future Value of Money, 17; • Compounding and Future Value, 18; • How Banks Quote Interest Rates, 22;

2 ■ 5 Present Values, Discounting, and Capital Budgeting 23

2-6 Net Present Value 27

Application: Are Faster Growing Firms Better Bargains?, 30;

2-7 Summary 32

Chapter 3 Stock and Bond Valuation: Annuities and Perpetuities 37

31 Perpetuities 38

The Simple Perpetuity Formula, 38; • The Growing Perpetuity Formula, 39;

• Perpetuity Application: Stock Valuation with A Gordon Growth Model, 41;

3-2 Annuities 43

Annuity Application: Fixed-Rate Mortgage Payments, 44; • Annuity Application: A Level-Coupon Bond, 44;

3-3 The Four Formulas Summarized 47

3-4 Summary 49

A Advanced Material 50

Projects With Different Lives and Rental Equivalents, 50; • Perpetuity and Annuity Derivations, 53;

Chapter 4 A First Encounter With Capital Budgeting Rules 59

Separating Investment Decisions and Consumption Choices: Does Project Value Depend on When You Need Cash?, 60;

4-2 The Internal Rate of Return (IRR) 63

Projects with Multiple or No IRRs, 66; • IRR as a Capital Budgeting Rule, 68;

• Problems with IRR as a Capital Budgeting Rule, 69;

4-3 The Profitability Index 70

4-4 The Payback Capital Budgeting Rule 72

4 ■ 5 How do Chief Financial Officers (CFOs) Decide? 73

Chapter 5 Time-Varying Rates of Return and the Yield Curve 79

5 ■ 1 Working With Time-Varying Rates of Return 80

Compounding Different Rates of Return, 80; • Annualized Rates of Return ,81;

• Present Values With Time-Varying Interest Rates, 84;

5-2 Inflation 85

Defining the Inflation Rate, 85; • Real and Nominal Interest Rates, 87; • Inflation in Net Present Values, 88;

5 ■ 3 Time-Varying Interest Rates in Bonds: U.S. Treasuries and The Yield Curve 90

Yield Curve Shapes, 90; • An Example: The Yield Curve on December 31, 2004, 92;

• Bond Payoffs and Your Investment Horizon, 94; • The Effect of Interest Rate Changes on Short-Term and Long-Term Bonds, 94;

5 ■ 4 Why is the (Nominal) Yield Curve Usually Upward-Sloping? 98

Does It Predict Higher Future Inflation?, 98; • Does It Predict Higher Future Interest Rates?, 99; • Does It Mean Bargains on the Long End?, 100; • Does It Compensate Investors For Risk?, 100; • Corporate Insights About Time-Varying Costs of Capital From the Yield Curve, 100;

5-5 Summary 101

### A The Finer Points of Bonds 104

Extracting Forward Interest Rates, 104; • Shorting and Locking in Forward Interest Rates, 106; • Bond Duration, 108; • Duration Similarity, 109; • Duration Hedging, 110; • Continuous Compounding, 111; • Some Institutional Knowledge: Price Quotes and STRIPS, 112; • Appendix Summary, 113;

Chapter 6 Uncertainty, Default, and Risk 117

6 ■ 1 An Introduction to Statistics 118

Random Variables and Expected Values, 118; • Variance, and Standard Deviation, 120; • Risk-Neutrality (and Risk-Aversion Preview), 121;

6-2 Interest Rates and Credit Risk (Default Risk) 122

Risk-Neutral Investors Demand Higher Promised Rates, 122; • A More Elaborate Example With Probability Ranges, 124; • Deconstructing Quoted Rates of Return — Time and Default Premiums, 125; • Credit Ratings and Default Rates, 126;

• Differences in Quoted Bond Returns in 2002, 128; • Credit Default Swaps, 129;

6 ■ 3 Uncertainty in Capital Budgeting 130

Present Value With State-Contingent Payoff Tables, 130;

6-4 Splitting Uncertain Project Payoffs into Debt and Equity 133

The Loan, 133; • The Levered Equity, 134; • Reflections On The Example: Payoff Tables, 135; • Reflections On The Example: Debt and Equity Risk, 136; • What "Leverage" Really Means — Financial and Operational Leverage, 137; • Working More Than Two Possible Outcomes, 138;

6-5 Summary 141

II Investments: Risk Vs. Expected Returns

(in a Perfect Market under Risk-Aversion) 147

Chapter 7 A First Look at Investments 151

7-1 Stocks, Bonds, and Cash, 1970-2004 152

Graphical Representations of Historical Returns, 152; • Historical Investment Performance, 155; • Comovement, Market-Beta, and Correlation, 159; • The Big Picture Take-aways, 161; • Will History Repeat Itself?, 162;

7-2 A Brief Overview of Equities Market Institutions and Vehicles 164

Brokers, 164; • Exchanges and Non-Exchanges, 164; • Investment Companies (ADRs and Funds), 166; • How Securities Appear and Disappear, 166; 7-3 Summary 168

Chapter 8 Investor Choice: Risk and Reward 171

8-1 Measuring Risk and Reward 172

Measuring Reward: The Expected Rate of Return, 174; • Measuring Risk: The Standard Deviation of the Rate of Return, 174;

8-2 Portfolios, Diversification, and Investor Preferences 175

Assume Investors Care Only About Risk and Reward, 178; 8-3 How To Measure Risk Contribution 179

An Asset's own Risk is not a Good Measure for Risk Contribution To a Portfolio, 179; • Beta Is a Good Measure for Risk Contribution to a Portfolio, 181; • Why not Correlation or Covariance?, 186; • Interpreting Typical Stock Market Betas, 186; 8-4 Expected Rates of Return and Market-Betas For (Weighted) Portfolios and Firms 188

8-5 Spreadsheet Calculations For Risk and Reward 191

Statistical Nuances, 191;

8-6 Summary 193

A An Investor's Specific Trade-Off of Risk vs Reward 196

A Short-Cut Formula For the Risk of a Portfolio, 198; • Graphing the Mean-Variance Efficient Frontier, 200; • Adding a Risk-Free Rate, 203;

Chapter 9 The Capital Asset Pricing Model 213

9 ■ 1 What You Already Know And What You Want To Know 214

9-2 The Capital-Asset Pricing Model (CAPM) — A Cookbook Recipe Approach 215

The Security Market Line (SML), 216;

9 ■ 3 The CAPM Cost of Capital in the Present Value Formula 219

Deconstructing Quoted Rates of Return — Risk Premiums, 219;

9-4 Estimating the CAPM Inputs 221

The Equity Premium, 221; • The Risk-Free Rate and Multi-Year Considerations, 225;

• Investment Projects' Market Betas, 226;

9-5 Empirical Reality 232

The Relationship Between Beta and Expected Rates of Return If the CAPM Does Not Work, 232; . Does the CAPM Work?, 234;

9-6 Summary 240

A Application: Certainty Equivalence 243

Valuing Goods Not Priced at Fair Value, 243; • Application: The CAPM Hurdle Rate For a Project With Cash Flow History Only, 246;

B Theory: CAPM Background 248

Portfolio Separation, 248; • The Mean-Variance Efficient Frontier and CAPM-type Formulas, 248; . CAPM Logic Recap, 250;

C Theory: CAPM Alternatives!? 251

The Arbitrage Pricing Theory (APT) and Intertemporal CAPM (ICAPM), 251; • The Fama-French-Momentum (-And-More) Model ,253;

III Value and Market Efficiency in an Imperfect Market 259

Chapter 10 Market Imperfections 263

10-1 Causes and Consequences of Imperfect Markets 264

Perfect Market Assumptions and Violations, 264; • Application: How Perfect is the Market for PepsiCo Shares?, 265; • Ambiguous Value in Imperfect Markets, 266;

• Some Imperfect Market Examples, 267; • Do You Always Get What You Pay For?, 267; • Social Value and Surplus, 268;

### 10-2 The Effects of Disagreements 269

Expected Return Differences vs. Promised Return Differences, 269; • Corporate Finance vs. Entrepreneurial Finance: The Firm's Credit Quality, 270; • Covenants, Collateral, and Credit Rating Agencies, 271;

### 10-3 Market Depth and Transaction Costs 272

Typical Costs When Trading Real Goods—Real Estate, 272; • Typical Costs When Trading Financial Goods—Stocks, 273; • Transaction Costs in Returns and Net Present Values, 275; • The Value of Liquidity, 276;

10-4 An Introduction to The Tax Code 277

The Basics of (Federal) Income Taxes, 277;

10-5 Working With Taxes 279

Taxes in Rates of Returns, 279; • Tax-Exempt Bonds and the Marginal Investor, 279;

• Taxes in Net Present Values, 280; • Tax Timing, 282;

10-6 Stated Yields and Premiums in Imperfect Markets 283

Deconstructing Quoted Rates of Return — Liquidity and Tax Premiums, 284;

10-7 Multiple Effects: How to Work Problems You Have Not Yet Encountered 286

Solving a Problem With Inflation and Taxes, 286; • Taxes on Nominal Returns?, 287;

10-8 Summary 288

Chapter 11 Efficient Markets, Classical Finance, and Behavioral Finance 295

11-1 Arbitrage and Great Bets 296

11-2 Market Efficiency 298

Short-Term vs. Long-Term Market Efficiency, 299; • Relation to Perfect Market, 300;

• Market Efficiency in Modern Financial Markets, 301;

11-3 Classifications Of Market Efficiency Beliefs and Behavioral Finance 302

The Traditional Classification, 303; • The Fundamentals-Based Classification and Behavioral Finance, 304;

11-4 The Random Walk and The Signal-To-Noise Ratio 305

The Signal, 306; • The Noise, 308; • Detecting an Abnormal Signal in the Noise, 308;

• Technical Analysis, 309; • Investment Manager Performance Evaluation, 312;

### 11-5 Corporate Consequences 315

If the Financial Markets are (Close To) Perfect, 315; • If the Market is not Perfect but at least Efficient, 316; »If the Finance Market is Not Even Efficient, 317;

• Comparison and Summary, 318;

11-6 Event Studies Can Measure Instant Value Impacts 319

An Example: The Congressional Mid-Term Election of 2006, 319; • Important Event Study Limitations, 322; • Some Other Event Study Results, 323; 11-7 Summary 324

IV Financial Analysis and Applied Valuation 329

Chapter 12 Capital Budgeting Applications and Pitfalls 333

12-1 So Many Returns: The Internal Rate of Return, the Cost of Capital, the Hurdle Rate, and the Expected Rate of Return 334

12-2 Promised vs. Expected Returns and Cash Flows 335

Expected, Typical, and Most Likely Scenarios, 335;

### 12-3 Badly Blended Costs of Capital 337

Does Risk-Reducing Corporate Diversification Create Value?, 337; • How To Misuse the CAPM, 339; • Differential Costs of Capital — Theory and Practice, 341;

12-4 The Economics of Project Interactions 343

The Ultimate Project Selection Rule, 344; • Project Pairs, 344; • One More Project: Incremental Rather Than Average Contribution, 347;

12-5 Future Contingencies and Real Options 354

A Specific Example, 354; • Valuing Real Options — Importance and Difficulty, 356; • Embedded Real Options, 357;

12-6 Behavioral Biases 358

12-7 Incentive (Agency) Biases 359

12 -8 An NPV Checklist 363

12-9 Summary 365

A Valuing Some More Real Options 367

Decision Trees: One Set of Parameters, 367; • Projects With Different Parameters, 373;

Chapter 13 From Financial Statements To Economic Cash Flows 379

13 1 Financial Statements 380

The Contents of Financials, 381; • PepsiCo's Financials, 387; • Why Financiers and Accountants Think Differently, 388;

13-2 A Bottom-Up Example — Long-Term Accruals (Depreciation) 390

Doing Accounting, 391; • Doing Finance, 392; • Reverse-Engineering Accounting into Finance, 394; • Depreciation Nuances, 396;

13-3 A Bottom-Up Example — Deferred Taxes 398

Reverse-Engineering Accounting into Finance, 399;

13 -4 A Bottom-Up Example — Short-Term Accruals 400

(Net) Working Capital, 400;

13-5 Earnings Management 403

13-6 Extracting Present Value Cash Flows from PepsiCo's Financials 404

13-7 Summary 409

A Supplementary Financials - Coca Cola 410

Coca Cola's Financials From EdgarScan, Restated, 410; • Coca Cola's Financials From YahoolFinance, Not Restated, 410;

Chapter 14 Valuation From Comparables and Some Financial Ratios 419

14-1 Comparables and Net Present Value 420

The Law of One Price, 420;

14-2 The Price-Earnings (P/E) Ratio 423

Definition, 424; • Why P/E Ratios differ, 425; • Empirical Evidence, 427;

### 14-3 Problems With Price-Earnings Ratios 433

Selection of Comparison Firms, 435; • (Non-) Aggregation of Comparables, 436; • Trailing Twelve Month (TTM) Figures and Other Adjustments, 440; • Debt Adjustments For P/E Ratios, 441;

14-4 Other Financial Ratios 443

Valuation Ratios, 443; • Non-Valuation Diagnostic Financial Ratios, 446;

14-5 Summary 453

V Capital Structure and Payout Policy 457

Chapter 15 Corporate Claims 461

15-1 The Basic Building Blocks 462

Cash Flow Rights as Payoff Diagrams, 463;

15-2 Liabilities 465

Financial Claims (Debt), 465; • Non-Financial Liabilities, 470;

15-3 Ordinary Equity (Common Stock) 471

Preferred Equity and Warrants, 472; 15-4 Tracking IBM's Capital Structure From 2001 to 2003 473

IBM's Liabilities, 4/3; • IBM's Equity, 4/9; • Observations on the Evolution of IBM's Capital Structure, 481;

### 15-5 Measuring Leverage 482

Total Leverage: The Total-Liabilities-To-Total-Assets Ratio, 482; • Financial Leverage: The Financial Debt-To-Financial Capital Ratio, 483; • Comparing Total and Financial Leverage Ratios, 484; • A Flow-Based Approach: The Interest-Coverage Ratio, 486;

15-6 Summary 486

Chapter 16 Capital Structure and Capital Budgeting in a Perfect Market 491

16-1 Conceptual Basics 492

Maximization of Equity Value or Firm Value?, 492;

16-2 Modigliani and Miller, The Informal Way 494

16-3 Modigliani and Miller, The Formal Way 496

16-4 The Weighted Average Cost of Capital (WACC) 500

An Example In a Risk-Averse World In Which Riskier Securities Must Offer Higher Expected Rates of Return , 500; • The WACC Formula (Without Taxes), 503; • The CAPM and WACC in the NPV Formula — A Seamless Magical Fit, 505; • How the Cost of Capital Varies With Leverage, 507; • The Effect of Debt on Earnings-Per-Share and Price-Earnings Ratios, 511; 16-5 The Big Picture: How to Think of Debt and Equity 513

16-6 M&M For Operations and For Non-Financial Liabilities 514

Value Irrelevance, 514; • The Weighted Average Cost of Capital, 515;

16 -7 Summary 516

Chapter 17 The Weighted Cost of Capital and Adjusted Present Value in an Imperfect Market With Taxes 521

17-1 Relative Taxation of Debt and Equity 522

Hypothetical Equal Taxation and Capital Budgeting, 522; • Realistic Differential Taxation of Debt and Equity, 523;

17-2 Firm Value Under Different Capital Structures 524

Future Corporate Income Taxes and Owner Returns, 524;

17-3 Formulaic Valuation Methods: APV and WACC 526

Adjusted Present Value (APV): Theory, 526; • Tax-Adjusted Weighted Average Cost of Capital (WACC) Valuation: Theory, 529;

17-4 A Sample Application of Tax-Adjusted Valuation Techniques 533

The Flow-To-Equity Direct Valuation from the Pro Forma Financials, 533; • APV, 535; . WACC, 536;

17-5 The Tax Subsidy on PepsiCo's Financial Statement 538

### 17-6 Contemplating Corporate Taxes 539

Which Tax-Adjusted Valuation Method is Best?, 539; • A Quick-and-Dirty Heuristic Tax-Savings Rule, 540; • Can Investment and Financing Decisions Be Separate?, 541; • Some Other Corporate Tax Avoidance Schemes, 541;

17-7 Summary 543

A The Discount Factor on Tax Obligations and Tax Shelters 546

Chapter 18 More Market Imperfections Influencing Capital Structure 555

18-1 What Matters? 556

18-2 The Role of Personal Income Taxes and Clientele Effects 557

Background: The Tax Code For Security Owners, 557; • The Principle Should Be "Joint Tax Avoidance", 558; • Tax Clienteles, 559; • How to Think About Different (International) Tax Codes, 566;

18-3 Operating Policy: Behavior in Bad Times (Financial Distress) 569

The Tradeoff in the Presence of Financial Distress Costs, 569; • Direct Losses of Firm Value, 570; • Operational Distortions of Incentives, 574; • Strategic Considerations, 576;

18-4 Operating Policy: Behavior in Good Times 577

Agency Issues, 577;

18-5 Bondholder Expropriation 579

Project Risk Changes, 579; • Issuance of Bonds of Similar Priority, 580; • Counteracting Forces Against Expropriation, 581;

18-6 Inside Information and Adverse Selection 584

18-7 Transaction Costs and Behavioral Issues 586

18-8 Static Capital Structure Summary 588

The Cost of Capital, 588;

18-9 Valuation Formulas With Many Market Imperfections 590

Do You Need Other Valuation (APV or WACC) Formulas?, 592; • Lesser Evils: Combining WACC with the CAPM, 593; 18-10Capital Structure Dynamics 594

18-llSummar y 596

Chapter 19 Equity Payouts: Dividends and Share Repurchases 601

19 1 Background 602

Dividend Mechanics, 602; • Share Repurchase Mechanics, 603;

19-2 Perfect Market Irrelevance 604

19-3 Dividends and Share Repurchases 606

Personal Income Tax Differences and Investor Clienteles, 607; • Non-Tax Differences, 610;

19-4 Empirical Evidence 611

Historical Payout Patterns, 611; • Market Reactions, 613; 19-5 Survey Evidence 619

19-6 Summary 620

VI Pro Forma Financial Statements 625

Chapter 20 Pro Forma Financial Statements 627

20 1 The Goal and Logic 628

An External Analyst's View Versus an Entrepreneur's View, 629;

20-2 The Template 630

20-3 The Length of the Detailed Projection Period 632

### 20-4 The Detailed Projection Phase 634

Faking It: Direct Extrapolation of Historical Cash Flows, 635; • The Real Thing: Detailed Financial Pro Forma Projections, 637; • Ratio Calculations and Policy with Pro Formas, 641;

20-5 The Terminal Value 643

The Cost of Capital, 643; • The Cost of Capital Minus the Growth Rate of Cash Flows, 645;

20-6 Some Pro Formas 648

An Unbiased Pro Forma, 648; • A Calibrated Pro Forma, 648;

20-7 Alternative Assumptions and Sensitivity Analysis 652

Fiddling with Individual Items, 652; • Do Not Forget Failure, 653; • Assessing the Quality of a Pro Forma, 654;

20-8 Proposing Capital Structure Change 655

20-9 Our Pro Forma in Hindsight 657

20- lOCaution—The Emperor's New Clothes 659

20-llSummary 660

A In-a-Pinch Advice: Fixed vs. Variable Components 662

VII Appendices 669

Chapter A Epilogue 671

A -1 Thoughts on Business and Finance Education 672

Common Student Misconceptions, 672; • Common Faculty Misconceptions, 673; • Business School vs. Practice, 674; • The Rankings, 675;

A-2 Finance As A Discipline 676

Art or Science?, 676; • Will We Ever Fully Understand Finance?, 677; A-3 Finance Research 677

Accomplishments of Finance, 677; • Interesting Current Academic Research, 678;

• Getting Involved in Academic Research, 678; • Finance Degrees, 678;

• Academic Careers in Finance and Economics: A Ph.D.?, 678; • Being a Professor A Dream Job for the Lazy?, 679; • The Best Finance Journals, 681;

A-4 Bon Voyage 681

Chapter B More Resources 683

2 ■ 1 Prominently Used Data Websites 684

2-2 Necessary Algebraic Background 685

2 ■ 3 Laws of Probability, Portfolios, and Expectations 686

Single Random Variables, 686; • Portfolios, 689;

2-4 Cumulative Normal Distribution Table 691

2-5 A Short Glossary of Some Bonds and Rates 692

Chapter A Index 697

"Special Topics" chapters omitted in Essentials version, but in the full Corporate Finance version:

>■ Capital Structure Change, Issuing Securities, Investment Banking, and M&A.

> Capital Structure Patterns in the United States.

>- International Finance.

>- Corporate Governance.

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