Demystifying the Use of Beta in the Determination of the Cost of Capital and an Illustration of its Use in Lazard's Valuation of Conrail
Samuel C. Thompson, Jr.
Penn State Dickinson School of Law
Journal of Corporation Law, Vol. 25, No. 2, Pp. 241-306, 2000
The discounted cash flow (DCF) method is commonly utilized by firms in determining whether to make an investment in a capital project, and involves calculating the valuation of a target firm in a merger or acquisition transaction. The determination of the appropriate cost of capital is a necessary element in the DCF method. One of the principal ways of determining the cost of equity capital is the capital asset pricing model (CAPM). CAPM posits that the cost of equity capital for a target firm is equal to the sum of (1) the risk-free rate of return and (2) the beta for the investment multiplied by the market risk premium. While the risk-free rate of return and the market risk premium are determined by observing market factors, the beta is specific to the target firm. The beta is an essential element in CAPM and therefore is often an essential element in the DCF method.
The beta measures the sensitivity of the returns for a particular stock to the returns on the market. The concepts of covariance and variance and the use of regression analysis, including Excel's linear regression function, can be utilized to derive the beta. The beta for a target firm can be expressed as either levered or unlevered and, depending on the circumstances, the beta may sometimes be necessary to move from a levered to an unlevered beta, or vice versa.
The Article first discusses the derivation of the beta and then illustrates how the beta and the CAPM were used by the investment banking firm of Lazard Freres & Co., LLC, in determining the cost of capital for Conrail and in valuing Conrail's free cash flows. Conrail was the target of competing bids in an acquisition by CSX and Norfolk Southern. The Article examines the formula for moving between unlevered and levered betas and elaborates on the use of the beta in the CAPM. The Article specifically analyzes Lazard's use of the CAPM and the beta in computing Conrail's weighted average cost of capital (WACC), as well as Lazard's use of this cost of capital in calculating the value of Conrail's cash flows. The analysis provided in this Article illustrates the computation of levered and unlevered betas and their use in a DCF model in a real life acquisition context.
Number of Pages in PDF File: 66
JEL Classification: G31, G32Accepted Paper Series
Date posted: May 29, 2000
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