Capital Budgeting in Arbitrage-Free Markets

In capital budgeting problems future cash flows are discounted using the expected one period returns of the investment. In this paper we establish a theory that relates 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. As results we obtain that 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. In a subsequent analysis we characterize the cash flow distributions under the additional assumption of a deterministic dividend yield. In this case strong properties for the evolution of the distributions can be obtained.