The Mathematical Foundations of the Potential Payback Period (PPP)

This paper presents the mathematical foundations of the Potential Payback Period (PPP) as a unified framework for asset valuation and return determination. The PPP integrates earnings growth, discounting, and risk into a single dynamic metric derived from exponential growth and present value theory. Using limit analysis (L’Hôpital’s rule and Taylor expansions), we show that the Price-to-Earnings (P/E) ratio emerges as a limiting case of the PPP. The framework further defines a closed-loop system in which terminal valuation and return are endogenously determined, enabling the construction of return measures comparable to bond yields.