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A Quantitative Revelation in Equity Valuation: The P/E Ratio is a Degenerate Case of the Potential Payback Period (PPP): Why Settle for the Limited when a Comprehensive Model Exists?

نُشر
الخادم
Preprints.org
DOI
10.20944/preprints202505.2166.v1

This article introduces the Potential Payback Period (PPP) as a generalized, risk- and growth-adjusted metric for equity valuation. In contrast to the traditional Price-to-Earnings (P/E) ratio, which assumes static earnings and neglects the time value of money, the PPP accounts for expected earnings growth and discount rates, thus providing a more dynamic and realistic measure of a stock’s investment appeal. By applying L’Hôpital’s Rule to the PPP formula, we demonstrate that the P/E ratio emerges as a limiting or degenerate case of PPP in two scenarios: (1) when the earnings growth rate converges to the discount rate, and (2) when both growth and discount rates are zero—an idealized static world. This theoretical result recontextualizes the P/E ratio within a broader, mathematically grounded framework and offers significant implications for valuation theory and portfolio management. PPP serves not merely as a substitute for P/E, but as its logical and quantitative extension.

يمكنك كتابة مراجعة PREreview لـ A Quantitative Revelation in Equity Valuation: The P/E Ratio is a Degenerate Case of the Potential Payback Period (PPP): Why Settle for the Limited when a Comprehensive Model Exists?. مراجعة PREreview هي مراجعة لمسودة بحثية أولية، ويمكن أن تتراوح بين بضع جمل وتقرير مطوّل، على غرار تقرير مراجعة الأقران الذي تنظمه المجلات العلمية.

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