Abrams Valuation Group, Inc.
Uniquely Applying Original Valuation Theory

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— Daniel H. O'Connell, O'Connell & Bouman

Book Review

by Rand M. Curtiss, ASA, ASA, FIBA, MCBA

Quantivative Business Valuation
A Mathematical Aproach for Today's Professionals

By Jay B. Abrams, ASA, CPA, MBA
(McGraw Hill, 2000)

Jay Abrams has made a major contribution to the business valuation profession with the publication of Quantitative Business Valuation. Jay's book integrates sound valuation theory and practice with rigorous statistical analysis in an intellectually honest and explicit presentation. It is an exploration deep into the unknown of many of the major topics in the field.

Those of us of a certain age learned corporate finance and statistics in the era of slide rules, pencil, paper and ledger paper. We had no calculators or personal computers. Data sources were extremely limited, if they existed at all, and numbers had to be manually entered if we were to perform statistical calculations such as regression analysis. These fundamental constraints forced us, sometimes inadvertently, to take many shortcuts to get our appraisal jobs done. Moreover, some concepts, which we take for granted today, such as discounts for lack of control and lack of marketability, were not developed until relatively recently. (Revenue Ruling 59-60 is silent on fractional interest discounts.) In the old days, it was all we could do to calculate point estimates of value. It took hours to hand-crank a multi-period financial projection (income statement and balance sheet, let alone cash flow statement and related ratios).

The truth, however, is that business values are more properly conceived of as probability distributions with a range of values and weights. Jay Abrams shows us how to move from the point-estimate world to the probabilistic world in a detailed, quantitative and rigorous manner using modern concepts, data and tools. He describes how objective data can be used to quantify many aspects of valuations which are normally either subjective or not addressed at all by many practitioners. Chapter 2 of the book serves as an excellent review of regression and statistical analysis, and provides examples dealing with forecasting sales and expenses as well as using regression analysis in a public company guideline analysis.

Chapter 3 presents original work which generalizes the traditional annuity model (constant cash flows over time) to include growth. Abrams shows how the classic Gordon growth model is a special case of the generalized model. Original extensions of this work by the author cover periodic cash flows (which occur at regular intervals or cycles, not every year), which can be extremely helpful shortcuts when dealing with items such as moving expenses or major capital expenditures.

Chapter 11, which describes the difference between valuation uncertainty and valuation error, is by itself worth the price of the book. Uncertainty stems from the fact that variables such as the true cost of equity capital cannot be observed, only estimated with a certain degree of statistical confidence, which itself can be quantified. Errors occur when appraisers make mistakes in forecasting variables such as cash flow, growth and discount rates. Abrams shows that errors in estimating the last two cause much greater distortions than errors in cash flow forecasts, a conclusion which some may find incredibly unsettling. This means that we should spend more time working on the latter, than the former, in developing our opinions!

Chapter 7, which addresses adjustments for levels of control and marketability, provides a thorough review of the professional literature as well as less well-known academic studies. Not only does it thoroughly analyze the controversy, but it also includes application of the Black-Scholes model and original empirical work by Abrams that culminates in a presentation of a regression-based factor model of the discount for lack of marketability. Examples of the model appear as sample reports in Chapters 8 and 9.

Chapter 12 provides a rigorous mathematical approach to the valuation of startups, and compares it to scenario analysis and venture capital pricing methods. Chapter 13 is a definitive treatise on measuring dilution that occurs in sales of stock to ESOPs. Abrams' mathematical analysis removes all of the mystery from that phenomenon and allows the appraiser to provide specific, quantified recommendations to clients that will enable them to achieve their goals.

Abrams' introduction to the book clearly states that it is an advanced treatment and that it is not easy reading. Familiarity with statistics, particularly regression analysis, is essential.

The beauty of the book is that it explicitly addresses many of the issues appraisers must consider, such as the Mandelbaum factors for the discount for lack of marketability and Chris Mercer's Quantitative Marketability Discount Model. The author has some constructive disagreements, and considerately provides Mercer with space for a counter-argument, which is extremely informative.


Aside from the analytical rigor, which some will find difficult, there are some minor errors in the book, most of which concern detail entries in exhibits, a minor annoyance. The errata do not detract from understanding of the author's premises, logic and conclusions. Click here to view the Errata.

The business appraisal profession is becoming ever more sophisticated as highly skilled individuals migrate to the field and devote analytical energy to addressing complex valuation issues. Jay Abrams' book provides a clear road map for rigorously upgrading our own analyses. ASA BV practitioners are strongly commended to read and study it.

Rand M. Curtiss is President of Loveman-Curtiss, Inc., a Cleveland-based appraisal firm, and Chairman of the American Business Appraisers National Network of independent business appraisal firms.