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

by Jay B. Abrams

Overview

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.

Product Details

ISBN-13:	9780470594513
Publisher:	Wiley
Publication date:	02/25/2010
Sold by:	JOHN WILEY & SONS
Format:	eBook
Pages:	672
File size:	15 MB
Note:	This product may take a few minutes to download.

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.

Table of Contents

List of Tables and Figures.

Introduction.

Acknowledgments.

PART I FORECASTING CASH FLOW.

CHAPTER 1 Cash Flow: A Mathematical Derivation.

Introduction.

The Mathematical Model.

Analysis of the Mathematical Model.

Summary.

References.

CHAPTER 2 Forecasting Cash Flow: Mathematics of the Payout Ratio.

Introduction.

The Mathematics.

Forecasting Gross Cash Flow Is Incorrect.

Conclusion.

References.

CHAPTER 3 Using Regression Analysis.

Introduction.

Forecasting Costs and Expenses.

Performing Regression Analysis.

Use of Regression Statistics to Test the Robustness of the Relationship.

Problems with Regression Analysis for Forecasting Costs.

Using Regression Analysis to Forecast Sales.

Autocorrelation in Time Series Analysis.

Application of Regression Analysis to the Guideline Company (GC) Methods.

Summary.

References.

APPENDIX 3A The ANOVA Table (Table A3.1, Rows 28–32).

CHAPTER 4 Annuity Discount Factors and the Gordon Model.

Introduction.

ADF with End-of-Year Cash Flows.

Midyear Cash Flows.

Starting Periods Other Than Year 1.

Periodic Perpetuity Factors (PPFs): Perpetuities for Periodic Cash Flows.

ADFs in Loan Mathematics.

Relationship of the Gordon Model to the Price/Earnings and Price/Sales Ratios.

The Bias in Annual (versus Monthly) Discounting Is Immaterial.

Conclusions.

References.

APPENDIX 4A Mathematical Appendix.

APPENDIX 4B Mathematical Appendix: Monthly ADFs.

PART II CALCULATING DISCOUNT RATES.

CHAPTER 5 Discount Rates as a Function of Log Size.

Research Included in the First Edition.

Table 5.1: Analysis of Historical Stock Returns.

Application of the Log Size Model.

Discussion of Models and Size Effects.

Industry Effects.

The Wedge between Public and Private Firm Valuations.

Satisfying Revenue Ruling 59-60.

Summary and Conclusions.

References.

APPENDIX 5A Automating Iteration Using Newton’s Method.

APPENDIX 5B Mathematical Appendix.

APPENDIX 5C Abbreviated Review and Use.

CHAPTER 6 Arithmetic versus Geometric Means: Empirical Evidence and Theoretical Issues.

Introduction.

Theoretical Superiority of the Arithmetic Mean.

Empirical Evidence of the Superiority of the Arithmetic Mean.

Indro and Lee Article.

References.

CHAPTER 7 An Iterative Valuation Approach.

Introduction.

Equity Valuation Method.

Invested Capital Approach.

Log Size.

Summary.

References.

PART III ADJUSTING FOR CONTROL AND MARKETABILITY.

CHAPTER 8 Adjusting for Levels of Control and Marketability.

Introduction.

The Value of Control and Adjusting for Level of Control.

Discount for Lack of Marketability (DLOM).

Conclusion.

References.

APPENDIX 8A Mathematical Appendix.

PART IV PUTTING IT ALL TOGETHER.

CHAPTER 9 Empirical Testing of Abrams’s Valuation Theory.

Introduction.

Table 9.1: Log Size for 1938–1986.

Table 9.2: Reconciliation to the IBA Database.

Calculation of DLOM.

Interpretation of the Error.

Conclusion.

References.

CHAPTER 10 Measuring Valuation Uncertainty and Error.

Introduction.

Measuring Valuation Uncertainty.

Measuring the Effects of Valuation Error.

Summary and Conclusions.

Reference.

PART V LITIGATION.

CHAPTER 11 Demonstrating Expert Bias.

Introduction.

Market Methods.

A Balanced DCF Valuation.

Summary.

CHAPTER 12 Lost Inventory and Lost Profits Damage Formulas in Litigation.

Introduction.

Commentary to Table 12.1: Sample Damage Calculations with VM = $95.

Table 12.1B: Lost Profits Formulas Based on EBITDA for Lost Sales on Inventory Never Produced.

When Reality May Vary with Our Assumptions.

Modification of Formulas for Wholesale and Retail Businesses.

Legal Treatment.

Summary.

Reference.

PART VI VALUING ESOPs AND BUYOUTS OF PARTNERS AND SHAREHOLDERS.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution.

Introduction.

Definitions of Dilution.

Table 13.1: Calculation of Lifetime ESOP Costs.

The Direct Approach.

The Iterative Approach.

Summary.

References.

APPENDIX 13A Mathematical Appendix.

CHAPTER 14 The Trade-off in Selling to an ESOP versus an Outside Buyer.

Section 1: Introduction.

Section 2: Advantages and Disadvantages of Selling to an ESOP versus a Third Party.

Section 3: The Mathematics.

Section 4: Sample Calculations in the Tables.

Section 5: Conclusion.

References.

CHAPTER 15 Buyouts of Partners and Shareholders.

Introduction.

Table 15.1: Pre- and Post-Transaction Valuations.

Table 15.2: Dilution in FMV as a Result of the Partner Buyout.

Sharing the Dilution.

Conclusion.

PART VII PROBABILISTIC METHODS.

CHAPTER 16 Valuing Start-Ups.

Issues Unique to Start-Ups.

Organization of the Chapter.

Part 1: First Chicago Approach.

Venture Capital Valuation Approach.

Part 2: Debt Restructuring Study.

Part 3: Exponentially Declining Sales Growth Model.

References.

CHAPTER 17 Monte Carlo Risk Simulation, by Dr. Johnathan Mun.

What Is Monte Carlo Risk Simulation?.

Comparing Simulation with Traditional Analyses.

Running a Monte Carlo Simulation Using Risk Simulator.

Using Forecast Charts and Confidence Intervals.

Tornado and Sensitivity Tools in Simulation.

Sensitivity Analysis.

Distributional Fitting: Single Variable and Multiple Variables.

Getting the Risk Simulator Software.

CHAPTER 18 Real Options, by Dr. Johnathan Mun.

Part 1: Introduction to Real Options.

Part 2: Traditional Valuation Approaches.

Part 3: Application: Real Options SLS Software.

Glossary.

About the Author.

Index.