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The Mathematical Foundations of the Potential Payback Period (PPP)

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  • Sam, Rainsy

Abstract

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.

Suggested Citation

  • Sam, Rainsy, 2026. "The Mathematical Foundations of the Potential Payback Period (PPP)," MPRA Paper 128772, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:128772
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    File URL: https://mpra.ub.uni-muenchen.de/128772/1/MPRA_paper_128772.docx
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    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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