On Risky Investments with Random Timing of Cash Returns and Fixed Planning Horizon

This paper provides a computational technique for the evaluation of the net present value (NPV) of an investment, in which the cash inflows occur at random time points and which terminates after a fixed time interval. The initial cash outlay is deterministic and the magnitudes of the cash inflows are nonnegative random variables with known distributions.

The lengths of the intervals between successive cash inflows are independently distributed and independent of the magnitude of the inflows. The Laplace transform of the distribution of the NPV is computed for both cases of mutual independence and perfect correlation of the inflows.

It is argued that these distributions are indispensable in determining the accuracy of the manager's estimates and in evaluating actual versus expected performance of a project.