Prior posts in our “Valuation Basics” series have examined the various components of the cost of equity capital under the Capital Asset Pricing Model (“CAPM”). In this post we continue our discussion of those components, focusing on the equity risk premium and its modifying coefficient, the beta.

The CAPM has become the Delaware Court of Chancery’s preferred method for calculating a company’s cost of equity (*i.e.*, the rate of return an investor would demand in order to purchase the company’s stock). A company’s cost of equity under the CAPM is generally the sum of (1) a risk-free rate, plus (2) the equity risk premium adjusted by a beta, plus (3) a size risk premium.

The “equity risk premium” is the difference between the risk-free rate and the expected return from the market. That is, the equity risk premium predicts how a stock index will perform compared to a risk-free investment, such as a treasury bond. Because not all stocks listed on a particular index perform alike, an appraiser valuing a specific company typically adjusts the equity risk premium by a volatility metric called a “beta.” A company with a beta of 1.0 will have an equity risk premium in line with the market. A company with a beta higher than 1.0 will be more volatile than the market, and a company with a beta of less than 1.0 will be less volatile than the market.

Calculating the Equity Risk Premium

The *Ibbotson SBBI Valuation Yearbook* provides two methods for calculating the equity risk premium: historic and supply-side. The historic equity risk premium looks at stock market returns against risk-free returns dating back to 1926. The supply-side equity risk premium modifies the historic equity risk premium by adjusting the historic equity risk premium for any inflation included in the price-to-earnings ratio. The supply-side method thus produces a slightly lower equity risk premium than the historic method.

Although the historic equity risk premium is the more traditional method, in its recent appraisal opinions the Delaware Court of Chancery has embraced the supply-side equity risk premium as the prevailing methodology. *In Global GT LP v. Golden Telecom, Inc.*, for example, the court adopted the supply-side method over the historic method because the weight of authority supported a rate of return that was closer to the supply-side equity risk premium.

Calculating Beta

Small variances in beta can lead to large discrepancies in the overall valuation of a company. For example, suppose an appraiser determines that, as of the merger date, the equity risk premium for Company X was 6%. A beta of 1.5 would increase that number to 9%. A beta of 0.5 would decrease that number to 3%. Assuming Company X had very little debt, this could lead to an almost 6% swing in the weighted average cost of capital. Not surprisingly, therefore, beta calculations are frequently contested in appraisal actions.

Although the historical market beta of a publicly traded company can be calculated by examining the covariance between the stock’s historical performance and that of the S&P 500, this method is often unreliable when calculating the beta of smaller public companies, where the stock may not trade in an efficient market. An alternative method for calculating beta is to use the published betas of guideline companies to select a beta for the subject company. Because the guideline companies have their own unique capital structures, however, the appraiser must “unlever” the guideline betas to remove the impact that the guideline company’s debt has on its beta. An unlevered beta is calculated using the following equation:

where LB is the levered beta of the guideline company; T is the tax rate of the guideline company; D is the percentage of the guideline company’s capital structure that is debt; and E is the percentage of the guideline company’s capital structure that is equity.

After selecting an appropriate unlevered beta for the subject company based on the unlevered betas of the guideline companies, the appraiser must “relever” the selected beta based on the capital structure of the subject company, using the following equation:

UB*[1 + (1 – T)*(D/E)]

where UB is the selected unlevered beta for the subject company; T is the tax rate of the subject company; D is the percentage of the subject company’s capital structure that is debt; and E is the percentage of the subject company’s capital structure that is equity. This levered beta is then applied to the equity risk premium as part of the calculation of the subject company’s cost of equity capital. This is a generally accepted method for calculating beta under the CAPM, although it is not the only method.