Harmonic Mean as an Approximation for Discounting Intraperiod Cash Flows

Abstract

We examine the possible errors of various present value approximations that center on the widely used end-of-period convention in cases of intraperiod cash flows. We suggest a new formula for adjusting the end-of-period present value based on the harmonic mean of the end-of-period and beginning-of-period present values. This approximation minimizes the maximum possible error in general. We give useful nomograms for several cash flow patterns to assess and correct for the errors of the different approximation methods. We find that the harmonic approximation has acceptable errors for most of these patterns. The findings are illustrated in a realistic example.

Acknowledgments

We thank Joseph C. Hartman (the editor) and two anonymous reviewers for their helpful comments. The work reported in the article has been developed in the framework of the project “Talent Care and Cultivation in the Scientific Workshops of BME.” This project was supported by the grant TÁMOP-4.2.2.B-10/1-2010-0009.