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Investment decisions under risk and the Modigliani and Miller Hypothesis Gilley, Donald Robin

Abstract

Although we live in a world of considerable uncertainty and chance, most capital investment decisions consider the element of risk only qualitatively, if at all. The believed risk should be an explicit and quantitative part of the normal excess present value or excess rate of return method of investment analysis. These risks are described by the subjective probability distribution of possible investment outcomes and the coefficient of variation of this distribution is a measure of the relative risk. At the same time, only incremental risk is relevant which depends upon the existing earnings risk as well as the project earnings risk and the coefficient of association between these streams. Risk bears on the investment valuation through the investor's attitude which is conditioned by his sense of economic wealth and his psychological reaction to the risk phenomenon. This felt risk can be quantified through the investor's trade-off between income and risk, or his utility of money function. This is then used to modify the uncertain expected income to an equivalent certain income which is then evaluated in the normal way. However, this is only feasible for individual investors or small groups of co-investors. For corporate investment decisions it is preferable to relate the risk to a variable rate of required return or market discount. This rate then enables the uncertain expected income to be evaluated directly In the usual manner. This method is applicable on any entity basis including the individual project which is the unit of investment decision. Here the venture has a unique risk with an appropriate capital structure and cost of capital funds. In fact, this method of evaluation depends upon the existence of a valuation function expressing the cost of corporate capital under risk. The cost of capital has been a difficult concept to define and measure while the aspect of risk has received little attention. Thus the rigorous Modigliani and Miller statement of the valuation of earnings under risk is highly significant. Here earnings risk is classified on the basis of equal coefficient of variation and perfect correlation. The use of debt capital creates financial risk but displays cost advantages under tax. However, leverage is restrained by an interest rate function which is related to financial risk and the uncertainty of creditor payments. Implicit in the formulation of this hypothesis is an investor loss aversion attitude which might be broadened into a risk aversion basis of valuation. The comprehensive hypothesis, with a point of minimum cost of capital, provides a strong theoretical position but is difficult to empirically validate. The valuation of after-tax earnings under variable risk can be inferred from the Modigliani and Miller hypothesis. From this can be derived a general expression for the marginal value of an investment under risk. This includes the special case, usually assumed, where the investment income is of equivalent risk and perfectly correlated to the existing corporate income. The method may be used to evaluate alternative financing arrangements and mutually exclusive projects as well as insurance proposals. This variable rate of discount or return concept provides a direct and intuitively appealing means of adding another dimension to the analysis of investment opportunities. Although there is need for theoretical development, empirical verification and organizational acceptance of this approach, it is perhaps a basis for improved corporate investment decisions under risk.

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