Mathematics of Stock Valuation: Why the Potential Payback Period (PPP) Outperforms the P / E and PEG Ratios

Abstract

This article introduces the Potential Payback Period (PPP), a valuation model initiated by the author, as a mathematically rigorous and conceptually richer alternative to traditional ratios. While the Price-to-Earnings ( P / E ) and PEG ratios have long been used to assess stock value, they suffer from critical limitations: the P / E ignores growth and discounting, while the PEG applies a simplistic linear adjustment and neglects risk. The PPP corrects these shortcomings by incorporating earnings growth, interest rates, and risk (via CAPM-based discounting) into a unified logarithmic structure. Using tools such as the Gordon Growth Model, Taylor expansion, and L’Hospital’s Rule, the paper shows that the P / E and PEG ratios are special cases of the PPP [1] - [3] . As a result, the PPP offers a more consistent, interpretable, and forward-looking metric that aligns with modern financial theory and investor needs.