A Probabilistic Internal Rate of Return: Theory and Illustration

Abstract

The purpose of this paper is to provide a theoretical background on the internal rate of return (IRR), on theprobabilistic IRR, and to present an illustration based upon both a Taylor series expansion and a Monte Carlosimulation. It is shown that Monte Carlo simulation results in a more precise outcome as compared to thetheoretical expectations from a Taylor series expansion. This precision is more than twice in terms of thestandard deviations of the IRR, and around six times more in terms of the standard errors of the IRR. Second,the distributions of the internal rate of return follow approximately a normal distribution, and this allows asound basis for project appraisal and risk management. Third, the grand means of the internal rates of returns forall four cases considered are statistically insignificantly different from each other, as expected, and they arestatistically insignificantly different from the average internal rate of return, obtained by discounting the meanamounts of the cash flows. Fifth, the standard deviations and the standard errors of the IRR are directlyproportional to the assumed standard deviations of the cash flows.