Quantitative Business Valuation

JAY B. ABRAMS is a leading valuation and litigation economist. He is the principal in Abrams Valuation Group, Inc. and is credited with numerous inventions, including the Abrams Log Size Model for calculating discount rates. He is also a popular finance lecturer and the author of numerous journal articles.

• List of Tables and Figures xiiiIntroduction xxiAcknowledgments xxviiPart I Forecasting Cash Flow 1Chapter 1 Cash Flow: A Mathematical Derivation 5Introduction 7The Mathematical Model 11Analysis of the Mathematical Model 25Summary 27References 27Chapter 2 Forecasting Cash Flow: Mathematics of the Payout Ratio 29Introduction 31The Mathematics 32Forecasting Gross Cash Flow Is Incorrect 43Conclusion 44References 44Chapter 3 Using Regression Analysis 45Introduction 47Forecasting Costs and Expenses 48Performing Regression Analysis 51Use of Regression Statistics to Test the Robustness of the Relationship 52Problems with Regression Analysis for Forecasting Costs 63Using Regression Analysis to Forecast Sales 64Autocorrelation in Time Series Analysis 69Application of Regression Analysis to the Guideline Company (GC) Methods 69Summary 73References 74Appendix 3A The ANOVA Table (Table A3.1, Rows 28–32) 75Chapter 4 Annuity Discount Factors and the Gordon Model 79Introduction 81ADF with End-of-Year Cash Flows 83Midyear Cash Flows 91Starting Periods Other Than Year 1 93Periodic Perpetuity Factors (PPFs): Perpetuities for Periodic Cash Flows 101ADFs in Loan Mathematics 107Relationship of the Gordon Model to the Price/Earnings and Price/Sales Ratios 110The Bias in Annual (versus Monthly) Discounting Is Immaterial 113Conclusions 119References 121Appendix 4A Mathematical Appendix 123Appendix 4B Mathematical Appendix: Monthly ADFs 141Part II Calculating Discount Rates 145Chapter 5 Discount Rates as a Function of Log Size 149Research Included in the First Edition 151Table 5.1: Analysis of Historical Stock Returns 152Application of the Log Size Model 167Discussion of Models and Size Effects 181Industry Effects 191The Wedge between Public and Private Firm Valuations 192Satisfying Revenue Ruling 59-60 196Summary and Conclusions 198References 199Appendix 5A Automating Iteration Using Newton’s Method 203Appendix 5B Mathematical Appendix 207Appendix 5C Abbreviated Review and Use 211Chapter 6 Arithmetic versus Geometric Means: Empirical Evidence and Theoretical Issues 223Introduction 225Theoretical Superiority of the Arithmetic Mean 226Empirical Evidence of the Superiority of the Arithmetic Mean 227Indro and Lee Article 232References 233Chapter 7 An Iterative Valuation Approach 235Introduction 237Equity Valuation Method 237Invested Capital Approach 243Log Size 245Summary 245References 247Part III Adjusting for Control and Marketability 249Chapter 8 Adjusting for Levels of Control and Marketability 253Introduction 257The Value of Control and Adjusting for Level of Control 257Discount for Lack of Marketability (DLOM) 301Conclusion 358References 359Appendix 8A Mathematical Appendix 365Part IV Putting It All Together 375Chapter 9 Empirical Testing of Abrams’s Valuation Theory 377Introduction 379Table 9.1: Log Size for 1938–1986 380Table 9.2: Reconciliation to the IBA Database 382Calculation of DLOM 387Interpretation of the Error 400Conclusion 401References 401Chapter 10 Measuring Valuation Uncertainty and Error 403Introduction 405Measuring Valuation Uncertainty 406Measuring the Effects of Valuation Error 410Summary and Conclusions 422Reference 423Part V Litigation 425Chapter 11 Demonstrating Expert Bias 427Introduction 429Market Methods 429A Balanced DCF Valuation 432Summary 434Chapter 12 Lost Inventory and Lost Profits Damage Formulas in Litigation 435Introduction 437Commentary to Table 12.1: Sample Damage Calculations with VM = $95 438Table 12.1B: Lost Profits Formulas Based on EBITDA for Lost Sales on Inventory Never Produced 445When Reality May Vary with Our Assumptions 446Modification of Formulas for Wholesale and Retail Businesses 447Legal Treatment 447Summary 448Reference 448Part VI Valuing Esops and Buyouts of Partners and Shareholders 449Chapter 13 ESOPs: Measuring and Apportioning Dilution 451Introduction 453Definitions of Dilution 454Table 13.1: Calculation of Lifetime ESOP Costs 456The Direct Approach 457The Iterative Approach 466Summary 469References 474Appendix 13A Mathematical Appendix 475Chapter 14 The Trade-off in Selling to an ESOP versus an Outside Buyer 477Section 1: Introduction 479Section 2: Advantages and Disadvantages of Selling to an ESOP versus a Third Party 480Section 3: The Mathematics 481Section 4: Sample Calculations in the Tables 486Section 5: Conclusion 494References 494Chapter 15 Buyouts of Partners and Shareholders 497Introduction 499Table 15.1: Pre- and Post-Transaction Valuations 499Table 15.2: Dilution in FMV as a Result of the Partner Buyout 501Sharing the Dilution 503Conclusion 506Part VII Probabilistic Methods 507Chapter 16 Valuing Start-Ups 511Issues Unique to Start-Ups 513Organization of the Chapter 513Part 1: First Chicago Approach 514Venture Capital Valuation Approach 520Part 2: Debt Restructuring Study 521Part 3: Exponentially Declining Sales Growth Model 534References 536Chapter 17 Monte Carlo Risk Simulation, by Dr. Johnathan Mun 539What Is Monte Carlo Risk Simulation? 541Comparing Simulation with Traditional Analyses 543Running a Monte Carlo Simulation Using Risk Simulator 543Using Forecast Charts and Confidence Intervals 554Tornado and Sensitivity Tools in Simulation 556Sensitivity Analysis 563Distributional Fitting: Single Variable and Multiple Variables 567Getting the Risk Simulator Software 571Chapter 18 Real Options, by Dr. Johnathan Mun 573Part 1: Introduction to Real Options 575Part 2: Traditional Valuation Approaches 585Part 3: Application: Real Options SLS Software 597Glossary 617About the Author 621Index 623