A Note on Formulating and Corroborating Discount Rates for Small Firms
Trevino, Gene A., Journal of Legal Economics
Economists are frequently called upon to assess the value of' lost profits in personal injury cases involving self-employed individuals and corporate litigation. The vast majority of lost profits cases, as a result of injury to a business owner or the entity, will involve a small business. An important part of this analysis entails the formulation of an appropriate discount rate. The discount rate should represent the risks and rewards inherent in the subject business (Margulis 1992). This paper is oriented towards small firms such as sole proprietorships. For the purpose of this paper, small businesses are defined as firms with less than $1,000,000 dollars in sales. These firms represent a challenge to economists because there is little or no comparable market information available from which to derive an appropriate discount rate. This paper is divided into three sections. The first section reviews the more common approaches to formulating discount rates for small firms. The second section explains how one can corroborate formulated discount rates via various market based methods. In the third section, an illustrative example is presented.
The formulation of a discount rate is necessary when discounting lost profits for an enterprise because the cash flows are subject to both systematic and nonsystematic risks. If the cash flows can be predicted with certainty or have been adjusted for these risks, a riskfree rate can be used. In the majority of lost profits cases, the cash flows cannot be predicted with certainty; hence, the economist must use a risk adjusted discount rate. There are three commonly used methodologies for the formulation of risk adjusted discount rates. These three methodologies are as follows: the market based rate method, the capital asset pricing model, and the build-up method.
The market approach uses the price-to-earnings ratios for publicly traded companies to derive a capitalization rate (Pratt, Reilly, and Schweihs 1996). This is done by dividing the price-to-earnings ratio into 1. For example, if the price-to-earnings ratio for a comparable public company is 6, the implied capitalization rate would be 16.67% [(1/6) X 100]. The expected growth rate for the subject company is then added to the implied capitalization rate in order to calculate a discount rate. Proceeding with our example, if the expected longterm growth rate for the subject company is 4.5%, then the discount rate would be 21.17% (16.67% + 4.5%)1. While theoretically sound, this methodology is not appropriate for small firms, since there are many egregious differences which make them not comparable with publicly traded companies. The publicly traded firms are generally larger and enjoy advantages such as economies of scale. Moreover, publicly traded firms are subject to general market fluctuations, which may cause them to deviate from their economic value.
The capital asset pricing model, referred to as CAPM, is a concept taken from modern portfolio theory and is used to model how markets measure risk (Pratt, Reilly, and Schweihs 1996). The formula for the CAPM model is depicted below.
DR = Rf + b(Rm - Rf) DR = Cash Flow Discount Rate Rf = Risk Free Rate b =Beta Rm = Equity Market Returns
Conceptually, this model uses the risk-free rate of return as a starting point for assessing risk. It next considers an equity premium by taking the differential between equity returns and the risk-free return. This equity premium is then multiplied by a beta factor. A beta factor is a measure of relative volatility which measures a stock's volatility relative to the market as a whole. This approach to formulating a discount rate may also not be appropriate for small firms because it is difficult, if not impossible, to locate comparable betas. In order to make the discount rate formulated with the CAPM more applicable to small firms, an additional risk premium can be added. While this additional risk premium may account for size differences, the discount rate still has the shortcoming of having been calculated with a less than perfect beta proxy. …