Probability Distribution of the Project Payback Period Using the Equivalent Cash Flow Decomposition

Abstract

For stochastic cash flows, probabilistic approaches to determine a complete distribution of payback period are very limited. The payback analysis based on the net present value (NPV) has several advantages. For annual cash flows, however, the NPV-based method does not provide a complete payback distribution. This article proposes a new technique, the equivalent cash flow decomposition (ECFD), which converts an annual cash flow into an equivalent subannual cash flow at a desired level of precision. The ECFD technique can be used in conjunction with any probabilistic cash flow technique. This article demonstrates that the ECFD technique overcomes the discontinuity limitation of the conventional NPV-based payback period method and generates a complete distribution of the payback period of annual cash flows. Examples indicate that the proposed method is robust with the accuracy comparable to Monte Carlo simulation.