Corporate valuation using imprecise cost of capital
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Corporate valuation using imprecise cost of capital Simon Elsner • Hans-Christian Krumholz
Published online: 14 August 2013 Springer-Verlag Berlin Heidelberg 2013
Abstract If the estimated cost of capital bears a standard error, the estimation remains imprecise and firm values are biased on average, even though the estimator of the cost of capital is unbiased. Literature contributes approaches using adjusted discount factors to correct for such biases. This paper examines the theoretical and practical problems arising from the use of these approaches which are most likely to occur in the context of terminal value estimation. The adjusted discount factors imply time-dependent discount rates. Therefore, the commonly used valuation formula for perpetuities (Gordon formula) is no longer suitable to estimate unbiased terminal values. To continue application of this formula, this paper derives a new formula to directly adjust the cost of capital for estimation errors which yields unbiased terminal values. Keywords Corporate valuation Cost of capital Discount factors Estimation bias Parameter uncertainty JEL Classification
C13 G30
1 Introduction The cost of capital is one key input parameter to estimate the value of a firm when discounted cash flow or residual income models are applied. From an economic Both authors are post-graduates of the Institute of Strategic Management and Finance, Werner Kress endowed chair, Prof. Dr. Frank Richter, Ulm University, Ulm, Germany. S. Elsner H.-C. Krumholz (&) Ulm University, Ulm, Germany e-mail: [email protected] S. Elsner e-mail: [email protected]
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perspective, all cash flows that a firm is expected to generate in the future need to be discounted by an appropriate rate that takes into account the timing and risk of these cash flows. Under certain conditions, the cost of capital to discount the expected cash flows corresponds to the expected rate of return of the firm (see Fama 1996). From an economical and econometrical point of view, the estimated firm value should be unbiased in order to avoid under- or overstated firm values. If this condition is fulfilled, the estimated firm value corresponds at least on average to the unknown firm value being estimated. Under specific conditions, an unbiased estimator of the expected rate of return is the arithmetic mean of realized rates of return. Alternatively, the cost of capital can be estimated using an asset pricing model that describes the relation of the expected pay offs and their risk with the expected rate of return. The key ingredient to the capital asset pricing model (CAPM) is the expected market risk premium. Moreover, an estimator of the expected market risk premium is based on the arithmetic mean of realised market rates of return in this setup. Econometricians showed that such estimates from realisations are prone to estimation errors, indicating there is uncertainty about the true expected rate of return, as theoretically shown by Gold
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