A Simple Approach to the Valuation of Risky Streams

Abstract

The optimal investment decision or the capital budgeting problem in a competitive environment are equivalent to the problem of valuing a stream of returns. If the returns from a project can be valued, then the criterion for acceptance is simply whether value exceeds cost. More generally, if returns are net of costs then the criterion for acceptance is whether the value of the net stream is positive.' There are a number of methodologies currently available for determining the value of a stream of returns. If the returns are certain, then there is widespread agreement that value is determined as present discounted value. If returns are uncertain, matters become more complex. The classical method of simply substituting expected returns-or, in its refined version, certainty equivalents-and discounting at some riskadjusted rate has passed from fashion, at least in academic circles if not in business practice. The current view is that the valuation problem calls for the use of dynamic programming techniques coupled with capital asset pricing models. At each stage a capital asset pricing model is In an asset market where there are no unexploited arbitrage opportunities, there will exist a linear valuation operator that can unambiguously price return streams with perfect market substitutes or bound values for streams bounded by market combinations. This is possible, without further assumptions, only if the project retums can be duplicated (or bounded) by a deterministic intertemporal program of purchasing a portfolio of marketed assets. These results are proven and used to simplify and unify a number of topics in financial economics, including project valuation, Modigliani-Miller theory, forward pricing, the closed-end mutual fund paradox, and efficient market theories. * The author is grateful to NSF grant # SOC77-22301 for financial support and to the participants in the seminar at Stanford University and the June 1977 ESSEC Conference in Cergy, France, for helpful comments. 1. This is true under capital budgeting constraints as well; value then includes the shadow prices of rationed resources, but then the statement is simply true as a tautology at this level of generality.