Probability Distribution Function of the Internal Rate of Return for Short-Term Projects with Some Random Cash Flows and Extensions

Abstract

This article reports closed-form probability density function and related expressions of the internal rate of return for one- and two-period pure and simple probabilistic engineering economy problems. The random cash flows are either uniform or exponential variables. In addition, there is no correlation between the cash flows. The probability density function of the internal rate of return is an important tool that helps decision makers estimate the probability of the internal rate of return exceeding the minimum attractive rate of return. Hillier's method (1963) using normal cash flows is also evaluated when the cash flows are uniformly distributed.