CALCULATING THE EXPECTATION AND VARIANCE OF THE PRESENT VALUE FOR A RANDOM PROFIT STREAM OF UNCERTAIN DURATION

Abstract

We derive the mean and variance of the random discounted sum when Nis uncertain, as are the Xn's. This quantity arises in applications involving random cash-flows over an uncertain number of years. One such application is R&D projects, where both the magnitude and duration of cash-flows are uncertain at the time of investment decision. Previous models have assumed cash-flow duration to be certain. We relax this assumption. We then specialize these results to geometric, mixed-geometric and Poisson distributions of the cash-flow duration.