Proving that the P/E Ratio is Just a Limiting Case of the Potential Payback Period (PPP) When Earnings Growth and Interest Rate are Ignored.

Abstract

The Potential Payback Period (PPP) extends the traditional Price-to-Earnings (P/E) ratio by incorporating earnings growth, discount rate, and risk. This article provides a mathematical demonstration that when both the earnings growth rate and the discount rate are zero (i.e., g = r = 0), the PPP simplifies to the P/E ratio. A similar result holds when g equals r and both are nonzero. These findings confirm the PPP's consistency with the P/E ratio under simplified conditions, and reveal far-reaching implications for how stocks can and should be valued across varying economic environments.

Keywords: Potential Payback Period, P/E ratio, L'Hôpital's Rule, growth rate, discount rate, stock valuation