Quantitative Business Valuation: A Mathematical Approach for Today's Professionals

Quantitative Business Valuation A Mathematical Approach for Today's Professionals Essential reading for the serious business appraiser, Quantitative Business Valuation, Second Edition is the definitive guide to quantitative measurements in the valuation process. No other book written on business valuation is as well researched, innovative, and bottom-line beneficial to you as a practitioner. Written by leading valuation and litigation economist Jay B. Abrams, this text is a rigorous and eye-opening treatment filled with applications for a wide variety of scenarios in the valuation of your privately held business. Substantially revised for greater clarity and logical flow, the Second Edition includes new coverage of: Converting forecast net income to forecast cash flow Damages in manufacturing firms Regressing scaled y-variables as a way to control for heteroscedasticity Mathematical derivation of the Price-to-Sales (PS) ratio Monte Carlo Simulation (MCS) and Real Options (RO) Analysis Venture capital and angel investor rates of return Lost inventory and lost profits damage formulas in litigation Organized into seven sections, the first three parts of this book follow the chronological sequence of performing a discounted cash flow. The fourth part puts it all together, covering empirical testing of Abrams' valuation theory and measuring valuation uncertainty and error. Parts five to seven round it all out with discussion of litigation, valuing ESOPs and partnership buyouts, and probabilistic methods including valuing start-ups. The resulting work, solidly grounded in economic theory and including all necessary mathematics, integrates existing science into the valuation profession—and develops valuation formulas and models that you will find useful on a daily basis.

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

About the Author :
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.