This paper has provided a systematic technique, the evaluation of the distribution with the NPV ana the derivation of the IRR in the investment alternatives, for the cost estimating analysts. The proposals of investment alternatives are included the venture capital under risk and probabilities at each events, within the cash inflows are occuring at random timing. Therefore. we have considered the followings : 1) the first cash outflow is deterministic. 2) the cash inflows are random variables with known distributions. 3) the lengths of the time intervals between the cash inflows are independently distributed and independent of the cash inflows. In this paper. the first two moments of the distribution, the Laplace Transforms and the convolutions are computed for both independent cash inflows and mutually exclusive alternatives as in the case of quite correlated cash inflows.