Moments and distribution of the net present value of a serial project

We study the Net Present Value (NPV) of a project with multiple stages that are executed in sequence. A cash flow (positive or negative) may be incurred at the start of each stage, and a payoff is obtained at the end of the project. The duration of a stage is a random variable with a general distribution function. For such projects, we obtain exact, closed-form expressions for the moments of the NPV, and develop a highly accurate closed-form approximation of the NPV distribution itself. In addition, we show that the optimal sequence of stages (that maximizes the expected NPV) can be obtained efficiently, and demonstrate that the problem of finding this optimal sequence is equivalent to the least cost fault detection problem. We also illustrate how our results can be applied to a general project scheduling problem where stages are not necessarily executed in series. Lastly, we prove two limit theorems that allow to approximate the NPV distribution. Our work has direct applications in the fields of project selection, project portfolio management, and project valuation.