Cost of Capital and Valuation with Imperfect Diversification and Unsystematic Risks

Abstract

Especially with the evaluation of non-listed (medium-sized) companies, the following problems and significant restrictions pertaining to the applicability of the CAPM must be taken into account when determining cost of capital. 1. Homogeneity of expectations and planning consistency. Given the reality that information is distributed asymmetrically, how should the individual state of information be taken into account when determining (subjective) decision values? And how should capital cost be kept consistent with the risks that are explicitly or implicitly taken into account when revenues (cash flows) are being planned? 2. Diversification. How should non-diversified (idiosyncratic) risks in capital cost and valuation be taken into account when the evaluator does not have a perfectly diversified portfolio (and also cannot obtain one)? 3. Risk measures. When determining cost of capital and company value, what are the consequences of applying measures of risk other than the beta factor and standard deviations of the CAPM because in an imperfect capital market (a) creditors are subject to financing restrictions and/or (b) the evaluator is applying a safety first approach and thus wants to limit the extent of downside risks such as the probability of insolvency?

This paper deals with all of these aspects, whereby, for the sake of simplicity, only a 1-periodmodel (without taxes) is examined. Chapter II shows how the expected values of returns and the risk measure are derived consistent to planning from the company’s (i.e. the evaluator’s) information regarding the uncertain returns to be evaluated. Chapter III then shows how a replication model can be used to take imperfect diversification into account. The equity capital cost rate is calculated for an arbitrary degree of diversification and it is shown how a company’s capital cost can be derived from the probability distribution of its uncertain returns (earnings), rather than from its returns expressed as a relative change in value. It is then shown how this approach can be generalised by utilizing risk measures other than standard deviations and the beta factor based on them. Such risk measures are helpful with non-normal distributions of returns.

Keywords: Capital-Asset-Pricing-Model, CAPM, cost of capital, risks

JEL Classification: G12, G14, G31