Abstract
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 two limit theorems that also apply in a more general context (i.e., that also apply for projects where stages are not necessarily executed in sequence). Our work has direct applications in the fields of project selection, project portfolio management, and project valuation. In addition, our work is closely related to the work of CPM/PERT, however, whereas CPM/PERT deals with project completion time, we focus on project NPV.
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