The structure of the distributions of cash flows and discount rates in multiperiod valuation problems

Abstract

In capital budgeting problems future cash flows are discounted using the expected one-period returns of the investment. In this paper we relate this approach to the assumption that markets are free of arbitrage. Our goal is to uncover implicit assumptions on the set of cash flow distributions that are suitable for the capital budgeting method. Our results are twofold. First we obtain that for deterministic cost of capital the set of admissible cash flow distributions is large in the sense that no particular structure of the evolution of the distributions is implied. We give stylized examples that demonstrate that even strong assumptions on the return distributions do not restrain the shape of the cash flow distributions. This shows that Fama’s assertion that the distributions of one-period single returns become more and more skewed cannot be generalized to multiperiod budgeting problems. Secondly, in a subsequent analysis we characterize the cash flow distributions under the additional assumption of a deterministic dividend yield. In this case a linear relationship between returns and cash flows obtains.