A First Course in Finance

I. Investments and Returns Chapter 1: A Short Introduction 1•1 The Goal of Finance: Relative Valuation 1•2 How do CFOs do It? 1•3 Learning How to Approach New Problems 1•4 The Main Parts of This Book Chapter 2: The Time Value of Money 2•1 Basic Definitions 2•1.A. Investments, Projects, and Firms 2•1.B. Loans and Bonds 2•1.C. U.S. Treasuries 2•2 Returns, Net Returns, and Rates of Return 2•3 The Time Value of Money 2•3.A. The Future Value of Money 2•3.B. Compounding 2•3.C. Confusion: Interest Rates vs. Interest Quotes 2•4 Capital Budgeting 2•4.A. Discount Factor and Present Value (PV) 2•4.B. Net Present Value (NPV) 2•5 Summary Chapter 3: More Time Value of Money 3•1 Separating Investment Decisions and Present Values From Other Considerations 3•1.A. Does It Matter When You Need Cash? 3•1.B. Corporate Valuation: Growth as Investment Criteria? 3•1.C. The Value Today is just “All Inflows” or just “All Outflows” 3•2 Perpetuities 3•2.A. The Simple Perpetuity Formula 3•2.B. The Growing Perpetuity Formula 3•2.C. A Growing Perpetuity Application: Individual Stock Valuation with Gordon Growth Models 3•3 The Annuity Formula 3•3.A. An Annuity Application: Fixed-Rate Mortgage Payments 3•3.B. An Annuity Example: A Level-Coupon Bond 3•3.C. The Special Cash Flow Streams Summarized 3•4 Summary a Advanced Appendix: Proofs of Perpetuity and Annuity Formulas Chapter 4: Investment Horizon, The Yield Curve, and (Treasury) Bonds 4•1 Time-Varying Rates of Return 4•2 Annualized Rates of Return 4•3 The Yield Curve 4•3.A. An Example: The Yield Curve in May 2002 4•3.B. Compounding With The Yield Curve 4•3.C. Yield Curve Shapes 4•4 Present Values With Time-Varying Interest Rates 4•4.A. Valuing A Coupon Bond With A Particular Yield Curve 4•5 Why is the Yield Curve not Flat? 4•5.A. The Effect of Interest Rate Changes on Short-Term and Long-Term Treasury Bond Values 4•6 The Yield To Maturity (YTM) 4•7 Optional Bond Topics 4•7.A. Extracting Forward Interest Rates 4•7.B. Shorting and Locking in Forward Interest Rates 4•7.C. Bond Duration 4•7.D. Continuous Compounding 4•8 Summary Chapter 5: Uncertainty, Default, and Risk 83 5•1 An Introduction to Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5•1.A. Random Variables and Expected Values 84 5•1.B. Risk Neutrality (and Risk Aversion Preview) 87 5•2 Interest Rates and Credit Risk (Default Risk) . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5•2.A. Risk-Neutral Investors Demand Higher Promised Rates 88 5•2.B. A More Elaborate Example With Probability Ranges 89 5•2.C. Preview: Risk-Averse Investors Have Demanded Higher Expected Rates 91 5•3 Uncertainty in Capital Budgeting, Debt, and Equity . . . . . . . . . . . . . . . . . . . . . . . 93 5•3.A. Present Value With State-Contingent Payoff Tables 93 5•3.B. Splitting Project Payoffs into Debt and Equity 96 5•4 Robustness: How Bad are Your Mistakes? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5•4.A. Short-Term Projects 104 5•4.B. Long-Term Projects 104 5•4.C. Two Wrongs Do Not Make One Right 105 5•5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Chapter 6: Dealing With Imperfect Markets 111 6•1 Causes and Consequences of Imperfect Markets . . . . . . . . . . . . . . . . . . . . . . . . . 112 6•1.A. Perfect Market Assumptions 112 6•1.B. Value in Imperfect Markets 113 6•1.C. Perfect, Competitive, and Efficient Markets 113 6•2 The Effect of Disagreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6•2.A. Expected Return Differences vs. Promised Return Differences 117 6•2.B. Corporate Finance vs. Entrepreneurial or Personal Finance? 118 6•2.C. Covenants, Collateral, and Credit Rating Agencies 119 6•3 Market Depth and Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6•3.A. Typical Costs When Trading Real Goods—Houses 123 6•3.B. Typical Costs When Trading Financial Goods—Stocks 124 6•3.C. Transaction Costs in Returns and Net Present Values 126 6•3.D. Liquidity 127 6•4 An Introduction to The Tax Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6•4.A. The Basics of (Federal) Income Taxes 128 6•4.B. Before-Tax vs. After-Tax Expenses 130 6•4.C. Average and Marginal Tax Rates 131 6•4.D. Dividend and Capital Gains Taxes 131 6•4.E. Other Taxes 132 6•4.F. What You Need To Know About Tax Principles In Our Book 133 6•5 Working With Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6•5.A. Taxes in Rates of Returns 134 6•5.B. Tax-Exempt Bonds and the Marginal Investor 134 6•5.C. Taxes in NPV 135 6•5.D. Tax Timing 137 6•6 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6•6.A. Defining the Inflation Rate 138 6•6.B. Real and Nominal Interest Rates 139 6•6.C. Handling Inflation in Net Present Value 141 6•6.D. Interest Rates and Inflation Expectations 142 6•7 Multiple Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6•7.A. How to Work Problems You Have Not Encountered 144 6•7.B. Taxes on Nominal Returns? 145 6•8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Chapter 7: Capital Budgeting (NPV) Applications and Advice 153 7•1 The Economics of Project Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7•1.A. The Ultimate Project Selection Rule 154 7•1.B. Project Pairs and Externalities 155 7•1.C. One More Project: Marginal Rather Than Average Contribution 157 7•2 Comparing Projects With Different Lives and Rental Equivalents . . . . . . . . . . . . . . . 162 7•3 Expected, Typical, and Most Likely Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7•4 Future Contingencies and Real Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 7•4.A. A Basic Introduction 165 7•4.B. More Complex Option Valuation in a Risk-Neutral World 166 7•4.C. Decision Trees: One Set of Parameters 166 7•4.D. Decision Trees: One Set of Parameters 171 7•4.E. Summary 173 7•5 Mental Biases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7•6 Incentive (Agency) Biases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 7•7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Chapter 8: Other Important Capital Budgeting Topics 183 8•1 Profitability Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 8•2 The Internal Rate of Return (IRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8•2.A. Definition 185 8•2.B. Problems with IRR 187 8•3 So Many Returns: The Internal Rate of Return, the Cost of Capital, the Hurdle Rate, and the Expected Rate of Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 8•4 Other Capital Budgeting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 8•4.A. The Problems of Payback 189 8•4.B. More Rules 190 8•5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 II. Corporate Financials 193 Chapter 9: Understanding Financial Statements 197 9•1 Financial Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 9•1.A. The Contents of Financials 199 9•1.B. PepsiCo’s 2001 Financials 205 9•1.C. Why Finance and Accounting Think Differently 206 9•2 The Bottom-Up Example — Long-Term Accruals (Depreciation) . . . . . . . . . . . . . . . 208 9•2.A. Doing Accounting 208 9•2.B. Doing Finance 211 9•2.C. Translating Accounting into Finance 212 9•3 The Hypothetical Bottom-Up Example — Short-Term Accruals . . . . . . . . . . . . . . . . 215 9•3.A. Working Capital 215 9•3.B. Earnings Management 218 9•4 Completing the Picture: PepsiCo’s Financials . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 9•5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 A Appendix: Supplementary Financials — Coca Cola . . . . . . . . . . . . . . . . . . . . . . . 225 a. Coca Cola’s Financials From EdgarScan 226 b. Coca Cola’s Financials From Yahoo!Finance 227 B Appendix: Abbreviated PepsiCo Income Statement and Cash Flow Statement . . . . . . . 228 Chapter 10: Valuation From Comparables 233 10•1 Comparables vs. NPV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 10•2 The Price-Earnings (PE) Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10•2.A. Definition 235 10•2.B. Why P/E Ratios differ 236 10•2.C. P/E Ratio Application Example: Valuing Beverage Companies 244 10•3 Problems With P/E Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 10•3.A. Selection of Comparison Firms 246 10•3.B. (Non-) Aggregation of Comparables 247 10•3.C. A Major Blunder: Never Average P/E ratios 248 10•3.D. Computing Trailing Twelve Month (TTM) Figures 250 10•3.E. Leverage Adjustments For P/E Ratios 251 10•4 Other Financial Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 10•4.A. Value-Based Ratios 255 10•4.B. Non-Value-Based Ratios Used in Corporate Analyses 257 10•5 Closing Thoughts: Comparables or NPV? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 10•6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 A Advanced Appendix: A Formula For Unlevering P/E ratios . . . . . . . . . . . . . . . . . . . 263III. Risk and Investments 267 Chapter 11: A First Look at Investments 271 11•1 Stocks, Bonds, and Cash, 1970–2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 11•1.A. Graphical Representation of Historical Stock Market Returns 272 11•1.B. Comparative Investment Performance 276 11•1.C. Comovement, Beta, and Correlation 280 11•2 Visible and General Historical Stock Regularities . . . . . . . . . . . . . . . . . . . . . . . . 282 11•3 History or Opportunities? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 11•4 Eggs and Baskets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 11•4.A. The Overall Basket 284 11•4.B. The Marginal Risk Contribution 285 11•4.C. The Market Equilibrium 285 11•5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Chapter 12: Securities and Portfolios 287 12•1 Some Background Information About Equities Market Microstructure . . . . . . . . . . . 288 12•1.A. Brokers 288 12•1.B. Exchanges and Non-Exchanges 288 12•1.C. How Securities Appear and Disappear 289 12•2 Equities Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 12•2.A. Going Long 291 12•2.B. Going Short: The Academic Fiction 291 12•2.C. Going Short: The Real World 292 12•3 Portfolios and Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 12•3.A. Portfolio Returns 294 12•3.B. Funds and Net Holdings 296 12•3.C. Some Common Indexes 297 12•3.D. Equal-Weighted and Value-Weighted Portfolios 298 12•3.E. Quo Vadis? Random Returns on Portfolios 301 12•4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Chapter 13: Statistics 305 13•1 Historical and Future Rates of Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 13•2 The Data: Twelve Annual Rates of Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 13•3 Univariate Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 13•3.A. The Mean 308 13•3.B. The Variance and Standard Deviation 308 13•4 Bivariate Statistics: Covariation Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 13•4.A. Intuitive Covariation 311 13•4.B. Covariation: Covariance, Correlation, and Beta 312 13•4.C. Computing Covariation Statistics For The Annual Returns Data 320 13•5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 13•6 Advanced Appendix: More Statistical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 13•6.A. Historical and Future Statistics 324 13•6.B. Improving Future Estimates From Historical Estimates 324 13•6.C. Other Measures of Spread 326 13•6.D. Translating Mean and Variance Statistics Into Probabilities 326 13•6.E. Correlation and Causation 327 Chapter 14: Statistics of Portfolios 329 14•1 Two Investment Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 14•1.A. Expected Rates of Returns 331 14•1.B. Covariance 332 14•1.C. Beta 333 14•1.D. Variance 334 14•2 Three and More Investment Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 14•2.A. Expected Returns, Covariance, Beta 336 14•2.B. Variance 338 14•2.C. Advanced Nerd Section: Variance with N Securities and Double Summations 340 14•2.D. Another Variance Example: PepsiCo, CocaCola, and Cadbury 342 14•3 Historical Statistics For Some Asset-Class Index Portfolios . . . . . . . . . . . . . . . . . . 345 14•4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 A Appendix: More Historical Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 a. Country Fund Rates of Return 352 b. Dow-Jones Constituents 353 Chapter 15: The Principle of Diversification 357 15•1 What Should You Care About? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 15•2 Diversification: The Informal Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 15•3 Diversification: The Formal Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 15•3.A. Uncorrelated Securities 360 15•3.B. Correlated Securities 363 15•3.C. Measures of Contribution Diversification: Covariance, Correlation, or Beta? 363 15•4 Does Diversification Work in the Real World? . . . . . . . . . . . . . . . . . . . . . . . . . . 368 15•4.A. Diversification Among The Dow-Jones 30 Stocks 368 15•4.B. Mutual Funds 370 15•4.C. Alternative Assets 370 15•5 Diversification Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 15•6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 Chapter 16: The Efficient Frontier—Optimally Diversified Portfolios 381 16•1 The Mean-Variance Efficient Frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 16•1.A. The Mean-Variance Efficient Frontier With Two Risky Securities 382 16•1.B. Different Covariance Scenarios 385 16•1.C. The Mean-Variance Efficient Frontier With Many Risky Securities 386 16•2 Real-World Mean-Variance Efficient Frontier Implementation Problems . . . . . . . . . . . 392 16•3 Combinations of Portfolios on The Efficient Frontier . . . . . . . . . . . . . . . . . . . . . . 394 16•4 The Mean-Variance Efficient Frontier With A Risk-Free Security . . . . . . . . . . . . . . . 397 16•4.A. Risk-Reward Combinations of Any Portfolio Plus the Risk-Free Asset 397 16•4.B. The Best Risk-Reward Combinations With A Risk-Free Asset 399 16•4.C. The Formula to Determine the Tangency Portfolio 400 16•4.D. Combining The Risk-Free Security And the Tangency Portfolio 402 16•5 What does a Security need to offer to be in an Efficient Frontier Portfolio? . . . . . . . . 403 16•5.A. What if the Risk-Reward Relationship is Non-Linear? 403 16•5.B. What if the Risk-Reward Relationships is Linear? 404 16•5.C. The Line Parameters 406 16•6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 A Advanced Appendix: Excessive Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 a. The Optimal Portfolio Weights Formula 411 b. The Combination of MVE Portfolios is MVE — With Risk-Free Security. 412 c. The Combination of Mean-Variance Efficient Portfolios is Mean-Variance Efficient — Without Risk-Free Security. 413 d. Proof of the Linear Beta vs. Expected Rate of Return Relationship for MVE Frontier Portfolios 413 Chapter 17: The CAPM: A Cookbook Recipe Approach 421 17•1 The Opportunity Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 17•2 The CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 17•2.A. The Premise and Formula 423 17•2.B. The Security Ma