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

The Price/Earnings (P/E) ratio and its derivative, the PEG ratio, have long served as simple heuristics in stock valuation. However, both metrics suffer from inherent limitations: the P/E ratio ignores growth, discounting, and risk, while the PEG ratio relies on a linear treatment of earnings growth and neglects the time value of money. This paper introduces the Potential Payback Period (PPP) as a more robust and mathematically grounded alternative. Through the use of Taylor expansion, the Gordon Growth Model, and L’Hospital’s Rule, we show how the PPP generalizes and extends the logic behind the P/E and PEG ratios. By incorporating earnings growth, interest rates, and risk into a logarithmic structure, the PPP provides a dynamic and interpretable measure of a stock's earning power. The result is a valuation metric that aligns more closely with financial theory and offers practical advantages in a range of investment contexts.