Midyear or End of Year Present Value Factors? Clues from Valuation in Discrete and Continuous Time

This article addresses whether appraisers should be using midyear or end-of-year present value factors. Although this is a topic that other authors and I have addressed, this article has some unique and novel approaches to the topic. The mathematics in this article accounts for cash flow growth within and between years rather than between years only, as others have modeled. We model in both discrete and continuous time, with discrete time in multiple time frames, almost continuous, daily, monthly, quarterly, and annual cash flows. Our continuous time results are very surprising. We conclude that, absent strong seasonality, midyear annual cash flows are very accurate and very little difference is seen in valuation results between quarterly, monthly, daily, and continuous cash flows. They are all close to midyear Gordon model multiple results.