#### Introduction

Regression analysis is a statistical technique to measure the mathematical relationship between a dependent variable and one or more independent variables. In the context of the Market Approach in business valuation, the dependent variable is usually some variation of Fair Market Value (FMV), i.e., market capitalization in the Guideline Public Company method, selling price (IBA), or MVIC (Market Value of Invested Capital, Pratt's Stats). We can use the dependent variable in dollars or as a scaled variable, i.e., divided by sales, earnings, EBIT, etc.

#### Confessions of a Reformed Quant

I have used regression analysis in valuation ever since I started in the valuation profession in 1983. I used it on my very first valuation-of a major motion picture producer-to forecast syndication revenues as a function of either theatrical revenues or television revenues. (It turned out that the latter was statistically significant, not the former.)

Regressions are enjoyable to perform, and they can be very powerful. It is much harder to argue with a well-done regression than with mean or median multiples with subjective adjustments. One of the great benefits of regression is its objectivity and rich statistical feedback to provide information on its own reliability.

As regression textbooks tend to be very general, they do not address many issues that are specific to business valuation. The textbooks give us the basic tools. They tell us how to use the tools, but not where to use them. Much of what I have learned about using regression analysis has been from experience-a combination of trial-and-error, seeing what works and what does not, and thinking about how to do it better.

In my early years I enjoyed regression so much that I was willing to do "the shotgun approach"-regressing the dependent variable(s) against 100+ independent variables. Even for a quant like me, eventually this became tiring and is very unprofitable on fixed fee assignments. There had to be a better way.

Eventually I realized the need to develop a theoretical model as a guide to tell me where to look for independent variables and-equally as important-where not to look.

#### Theoretical Relationships between FMV and Valuation Drivers

In this article we develop the theoretical relationship that should exist between FMV and the valuation drivers, i.e., the independent variables that affect value, e.g., income, cash flow, risk, growth, etc. The importance of doing so is:

1. To reduce the risk of data mining, which is finding apparently statistically significant relationships that are in reality the result of chance through brute force regression analysis of many dozens of variables.
2. To save time by not having to test independent variables that should have no theoretical relationship to FMV.

The Gordon model multiple is the logical place to start, as it is the value equation of a mature firm. Before diving into it, let's begin with some algebraic definitions.

#### Definitions

Jay Abrams, ASA, CPA, MBA, founder and head of Abrams Valuation Group (AVG), is one of those rare individuals who integrates theory and practice. He has valued businesses and consulted on mergers and acquisitions in a wide range of industries, provided valuations and discounts for fractional interests and restricted stock, and conducted independent statistical and mathematical research regarding problems facing businesses. During his 25 years of accounting and valuation experience, he has made, and continues to make, significant contributions to the science of valuing businesses. Mr. Abrams' book, Quantitative Business Valuation: A Mathematical Approach For Today's Professionals (McGraw-Hill, 2001) shows how to integrate advanced scientific methods into real-world valuation analysis.