Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration

Y. Gerchak, T. B. ASTEBRO

Engineering and Process Economics

2000, vol. 45, n°4, pp.339-349

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

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.