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A critical evaluation of the role of the cost of capital as a risk-adjusted discount rate in the economic analysis of capital investments Holloway, James Benjamin

Abstract

This study consists of a critical evaluation of the role of the cost of capital as a "risk-adjusted" discount rate in the economic analysis of capital investments. In conventional theory, the cost of capital is formulated as a discount rate which serves as a financial standard, in accordance with one variation or another of the following definition: The cost of capital is the minimum acceptable rate of return that a proposed investment in real assets must offer in order to be worthwhile undertaking from the stand-point of the current owners of the firm. Unfortunately, theorists have found it difficult to incorporate a proper measure of risk into the specification of the cost of capital as a single-valued rate of discount. Ezra Solomon, among others, has avoided much of the difficulty by assuming that all projects to be evaluated are of a quality, in respect to uncertainty of future earnings, which is "homogeneous" with the quality of earnings attributed to existing operations. The problem of dealing with investments of a quality significantly different from earnings from existing assets is largely unresolved. This study consists of an analysis of the relationship which should exist between a project's risk and the cost of capital appropriate to its evaluation. The analysis rests upon several simplifying assumptions regarding the behavior of investors and capital markets; and employs for its investigation two models of risk and valuation: The classical certainty-equivalence model and John Lintner's recently derived risk asset valuation and portfolio selection model. In recognition of certain weaknesses in the conventional discounted cash flow approaches to capital project evaluation, several theorists including David B. Hertz and Frederick S. Hillier, have proposed that Monte Carlo Simulation and analytical-statistics methods be employed to account for risk by generating stochastic expressions for valuation indices. To the extent that the expression of probabilistic valuation indices depends upon a "risk-adjusted" cost of capital discount rate, there exists the inconsistency of "double accounting for risk;" once in the cost of capital, and once again in the stochastic expression of the indices themselves. This study assesses the relevance of the cost of capital as a discount rate in the generation of stochastic discounted cash flow indices. The investigation disclosed that: (1) the cost of capital is a derived variable consisting of a complex function of the risk-free rate of interest, and the expected values and risk parameters of earnings expectations of the firm, the project concerned, and securities comprising the market as a whole; that (2) the cost of capital is essentially inefficient as a means of accounting for risk because its correct derivation depends upon the employment of a valuation model which is of itself both sufficient and more direct as a means of evaluation; and (3) that the cost of capital, as a "risk-adjusted" rate of discount is both inappropriate and irrelevant for employment in the generation of stochastic expressions of valuation indices.

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