A Mathematical Approach for Today′s Professionals
"Jay Abrams′ book is close to the equivalent of several graduate dissertations rolled into one book. For each topic (covered), he presents a scholarly summary of past research, new empirical research of his own, and his conclusions. It is a well–documented contribution to in–depth understanding of important business valuation issues, and should not be overlooked by the serious practitioner."
Shannon Pratt, DBAManaging Director, Willamette Management AssociatesCoauthor, Valuing a Business
"A must–read for the serious business appraiser."
Jay E. Fishman, ASA, CBAPresident, Financial Research, Inc.
"The problem of simplified valuation procedures and coherent theory still remains complex and is ever evolving. Jay Abrams deals very effectively with this complexity through the use of mathematical formulas. Input to his models is explained with clarity and effectiveness, which adds to the overall value of this advanced text on business valuation."
Terry A. Isom, Chairman, National Association of Certified Valuation Analysts
"Jay Abrams′ book strives to provide mathematical modeling for what practitioners often do by reasoning alone. This book is a must–read for practitioners who are searching for additional techniques for dealing with some of business valuation′s imponderables."
David M. Bishop, FIBA, BVAL, ASA, MCBAPresident, American Business Appraisers, Inc.
"Jay Abrams′ book will not only challenge the top theoreticians in the field; his step–by–step explanations will make advanced quantitative techniques available to the many appraisers who are not capable of independently creating the underlying mathematical analysis."
Kent Osborne, ASAChairman, Editorial Review Board of the American Society of Appraisers
"While a proliferation of business valuation treatises and guides exists in the market, most are very general in nature and do nothing more than rehash fundamental concepts. I am unaware of any author who has stepped into the unknown as Jay Abrams has and compiled and developed a treatise of extremely useful analytical tools for the serious valuator."
Robert J. Grossman, CPA/ABV, ASA, CVAPartner, Grossman Yanak & Ford
"Jay Abrams develops unusual approaches which merit consideration when ′cookie cutter′ methodologies are inadequate. This manuscript contributes to the dialogue among practitioners and strengthens the theoretical foundations of business valuation."
Herbert T. SpiroPresident, American Valuation Group, Inc.
"There is no question about it, the use of rigorous quantitative methods is the cure for subjective valuation analysis. This book not only satisfies this need which has grown considerably in recent years but is chock–full of new tools that have been carefully developed."
Edward MurrayValuation Partner, Arthur Andersen, LLP
PART I FORECASTING CASH FLOW.
CHAPTER 1 Cash Flow: A Mathematical Derivation.
The Mathematical Model.
Analysis of the Mathematical Model.
CHAPTER 2 Forecasting Cash Flow: Mathematics of the Payout Ratio.
Forecasting Gross Cash Flow Is Incorrect.
CHAPTER 3 Using Regression Analysis.
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.
APPENDIX 3A The ANOVA Table (Table A3.1, Rows 28 32).
CHAPTER 4 Annuity Discount Factors and the Gordon Model.
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.
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.
The Wedge between Public and Private Firm Valuations.
Satisfying Revenue Ruling 59–60.
Summary and Conclusions.
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.
Theoretical Superiority of the Arithmetic Mean.
Empirical Evidence of the Superiority of the Arithmetic Mean.
Indro and Lee Article.
CHAPTER 7 An Iterative Valuation Approach.
Equity Valuation Method.
Invested Capital Approach.
PART III ADJUSTING FOR CONTROL AND MARKETABILITY.
CHAPTER 8 Adjusting for Levels of Control and Marketability.
The Value of Control and Adjusting for Level of Control.
Discount for Lack of Marketability (DLOM).
APPENDIX 8A Mathematical Appendix.
PART IV PUTTING IT ALL TOGETHER.
CHAPTER 9 Empirical Testing of Abrams s Valuation Theory.
Table 9.1: Log Size for 1938 1986.
Table 9.2: Reconciliation to the IBA Database.
Calculation of DLOM.
Interpretation of the Error.
CHAPTER 10 Measuring Valuation Uncertainty and Error.
Measuring Valuation Uncertainty.
Measuring the Effects of Valuation Error.
Summary and Conclusions.
PART V LITIGATION.
CHAPTER 11 Demonstrating Expert Bias.
A Balanced DCF Valuation.
CHAPTER 12 Lost Inventory and Lost Profits Damage Formulas in Litigation.
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.
PART VI VALUING ESOPs AND BUYOUTS OF PARTNERS AND SHAREHOLDERS.
CHAPTER 13 ESOPs: Measuring and Apportioning Dilution.
Definitions of Dilution.
Table 13.1: Calculation of Lifetime ESOP Costs.
The Direct Approach.
The Iterative Approach.
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.
CHAPTER 15 Buyouts of Partners and Shareholders.
Table 15.1: Pre– and Post–Transaction Valuations.
Table 15.2: Dilution in FMV as a Result of the Partner Buyout.
Sharing the Dilution.
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.
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.
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.
About the Author.