Valuing Constant-Growth Perpetuities with Finance Intuition (Instead of Infinite Series)

Abstract

The formula for calculating the present value of a finite level annuity is one of the simplest equations in corporate finance. It is PV = PMT/r, where PV is the present value, PMT is the payment, and r is the periodic interest rate. However, corporate finance instructors and textbooks rarely discuss the derivation of this equation. This is because the typical derivation requires a knowledge of calculus beyond that of most business majors. In this paper, I demonstrate that it is possible to use basic ideas from finance – how competitive markets set the price of an asset equal to the asset’s market value – at the same place in the derivation that usually requires taking limits.