Earlier this month, Richard Fox of Fox Business Appraisels, LLC, delivered the IBA’s 2010 Stanton Memorial lecture presentation entitled, “Regression Analysis as a Tool for Validating Valuation Methodology”, in the IBA Symposium track during the 2010 NACVA/IBA Annual Consultants’ Conference.
Mr. Fox’s presentation focuses on the technical use of regression analysis to determine the validity of various valuation methods. With his classic New Orleans sense of humor, Mr. Fox began the talk with the following quote:
“Statistics show that teen pregnancy drops off significantly after age 25.”
-Colorado Springs State Senator MaryAnne Tebedo
Mr. Fox’s goal of showing the quote from MaryAnne Tebedo most likely was to impress upon the audience the need for business appraisers to understand the validity of their conclusions. For example, if an appraiser relies upon the direct market data method to value a company, the market data sample should be analyzed to determine if any conclusions can be drawn from the market multiples. To perform a regression analysis, certain assumptions must be made, such as that the relationship between the independent variable, “x”, and the dependent variable, “y”, is linear in nature. The assumptions vary based on the type of regression performed.
When using the ordinary least squares method of regression, the independent (x) and dependent (y) variables are plotted on a traditional graph. A line is drawn on the graph that minimizes the differences between the observations (i.e., the plot of the x and y coordinates) and the corresponding points on the regression line (i.e., predicted values). The “differences” between the line and the observations are often called residuals.
One of the key assumptions of a valid regression analysis is that the residuals are independent of each other. If the residuals are related in some manner, then autocorrelation may be an issue. Autocorrelation can cause the results of the regression to seem more reliable than they actually are. Another tongue-twister of a statistical word was that for linear regression analysis to be valid the residuals must be homoskedastic. Homoskedasticity means that the actual y values (dependent variables) have the same probability of occurring, regardless of the x values. Mr. Fox provided real-world examples of how these issues arise in the course of a business appraisal.
Mr. Fox downloaded market data from the IBA Market Database on Standard Industrial Classification code 5962 (automatic merchandising machine operators). He began his analysis by observing the data and ensuring that there are no nonsensical data points (e.g., price or sales are negative numbers). He used Microsoft Excel’s regression analysis add-in to regress a scatter plot of sales (x variable) and the corresponding prices (y variable). The R Square statistic from his presentation slides was 64%, which indicated that sales may be a good predictor of the price paid for a company. However, the standard error of the estimate was large, which could be an issue for an expert witness if a Daubert motion is raised by opposing counsel. Mr. Fox further analyzed the regression analysis with various other tests, such as the Durbin-Watson statistic, F-test, and T-Test. The intricacies of these tests should be understood by the appraiser to determine if his or her conclusions are valid.
In addition to performing a regression analysis on the IBA market data, Mr. Fox also presented examples of how a regression analysis can be used to forecast sales or earnings, determine the cost of capital, and to determine non-controlling interest discounts. His primary assertion throughout the presentation was that a business appraiser must understand not only the assumptions and complexities of a regression analysis, but how a regression analysis can be challenged by an opposing professional. In some cases, regression analysis creates a perception of high analytical rigor, when in reality a ruler would have sufficed. Richard Fox is president of Fox Business Appraisals, LLC, deals primarily in business valuations for estate planning, marital dissolution, mergers& acquisitions, and litigation support. He is an active Lifetime member of the Institute of Business Appraisers, holding the designations of Certified Business Appraiser (CBA) and Business Valuator Accredited for Litigation (BVAL). He is a member of the CFA Institute and the CFA Society of Louisiana. Mr. Fox is a qualified expert witness for the U.S. Bankruptcy Court, Eastern District, and his work has been submitted to the IRS, US Bankruptcy Courts, and local courts. Mr. Fox holds a B.S. in Mathematics and an M.B.A. in Finance from Tulane University, and currently teaches Finance at the Southeastern Louisiana University School of
Business.