Quarterly earnings announcements consistently generate large market reactions [1] [2] . Firms missing or beating analyst expectations by just a few cents often experience multi-percent price swings, despite the seemingly trivial magnitude of the surprises. Explaining these disproportionate responses is a longstanding challenge in finance [3] .

Traditional valuation tools—P/E, PEG, Gordon Growth Model (GGM), and DCF—cannot account for the amplification. P/E is static, PEG is linear (which distorts financial realities that follow compounding dynamics), and both GGM and DCF depend on restrictive assumptions (e.g., g < r) that do not hold in modern markets.

The Potential Payback Period (PPP) framework clarifies this puzzle by embedding earnings growth (g) and discount rates (r) logarithmically, showing how small quarterly earnings revisions propagate across a multi-year horizon, leading to large valuation shifts.

The valuation of equities has evolved through several frameworks:

These models proved useful in more stable markets of past decades, when growth rates (g) typically remained below discount rates (r). In today’s environment, with many firms sustaining growth above risk-free rates and interest rates fluctuating daily, they appear less reliable.

The PPP extends this trajectory [7] . It subsumes P/E as a special case (when g = 0 and r = 0) while addressing the weaknesses of PEG, GGM, and DCF. By combining growth and discounting in one dynamic metric, it better reflects modern market realities [8] - [10] .

Recent studies (e.g., Haboub, Kartsaklas & Sarafidis, 2025; Xu, 2024) show that residual-income and abnormal-earnings models predict stock returns more accurately than traditional P/E-based approaches but remain sensitive to parameter instability. PPP aligns closely with these models’ theoretical foundations while offering a simpler yet equally powerful framework: it collapses the valuation logic into a single dynamic horizon, which may explain its superior predictive power for earnings-surprise-driven price changes.

The PPP generalizes the static P/E ratio by asking not how many years of current earnings, but how many years of future growing and discounted earnings are needed to match today’s price [7] :

PPP Formula:

$PPP=\frac{\log \left(\frac{P/E\times \left(g-r\right)}{1+r}+1\right)}{\log \left(\frac{1+g}{1+r}\right)}$

where:

Special Case: When g = 0 and r = 0, PPP collapses to the traditional $P/E$ ratio. This result follows from taking the mathematical limits as both g and r approach zero, which resolves the apparent indeterminate form of the PPP equation and shows that P/E is a limiting case of PPP.

Determining r: The discount rate r is estimated using the Capital Asset Pricing Model (CAPM):

$r=r_f+\beta \times \left(r_m-r_f\right)$

where $r_f$ is the risk-free rate (e.g. 10-year Treasury yield), $\beta$ is the stock’s beta, and $r_m$ is the expected market return.

The logarithmic form captures compounding, making PPP highly sensitive to small changes in g or r. This sensitivity explains the amplification of earnings surprises and interest rate shifts [5] [6] .

The Potential Payback Period (PPP) expresses valuation in years, while investors typically compare opportunities in rates of return. The bridge is the Stock Internal Rate of Return (SIRR), defined from PPP as [7] :

$SIRR=2^{1/PPP}-1$

Intuition: PPP is the horizon at which the investment “pays back” in discounted earnings. The compounding rate that doubles capital over exactly PPP years is $2^{1/PPP}-1$; that rate is SIRR. Thus, shorter PPP implies higher SIRR, and vice versa.

This translation allows earnings-driven valuation changes to be expressed directly in return space, making PPP outcomes interpretable as SIRR values that can be positioned alongside bond yields when comparing cross-asset opportunities.

Earnings growth (g) can be viewed as the first derivative of corporate performance, representing the speed at which earnings expand. Quarterly earnings surprises, even when numerically small, are interpreted by markets as inflexions in this growth trajectory—accelerations or decelerations measured as second derivatives of earnings growth.

This distinction matters. A firm that slightly beats expectations signals not just higher earnings for one quarter, but a potential upward adjustment in the slope of growth. Conversely, a small miss suggests a deceleration, prompting downward revisions.

Because the Potential Payback Period (PPP) compounds growth logarithmically across a multi-year horizon, such second-derivative signals propagate forward, producing disproportionately large valuation shifts. In this sense, earnings surprises act as catalysts: they trigger revisions in projected growth, which then translate into amplified changes in PPP.

Observation: Following earnings revisions, mature companies tend to show larger shifts in PPP than growth companies. This confirms why minor earnings surprises often trigger sharper corrections in mature firms than in high-growth firms.

Quarterly earnings surprises are interpreted as revisions in forward-looking growth trajectories. In PPP terms, these revisions lengthen or shorten the payback horizon. In rate-of-return terms, they raise or lower the internal rate of return (SIRR) implied by today’s price.

To illustrate, we present the following practical example:

Baseline:

Baseline PPP: ≈ 12.57 years

Baseline SIRR: ≈ 5.67%

What appears as ‘irrational overreaction’ is rational under PPP. A ±1pp change in growth expectations, though trivial in quarterly terms, alters intrinsic value—as reflected in the period of time required to recoup the initial investment—by several months across a multi-year horizon. Investors immediately price this adjustment, producing sharp stock price moves.

Traditional metrics cannot account for this dynamic. The P/E ratio is static, while the PEG ratio is simplistically and misleadingly linear. By embedding compounding effects through a logarithmic structure, the PPP aligns valuation more closely with observed market behavior.

Sensitivity: Because of its logarithmic structure, PPP is highly sensitive to small forecast errors in g and r. A ±1pp error in g can shift PPP by several months, while the same error in r shifts it by a comparable magnitude. This strong sensitivity explains why valuation responses appear disproportionate, but it also represents a limitation of the model, since inaccurate inputs may amplify estimation errors in practice. For this reason, conducting sensitivity analysis on g and r is crucial in any prevision based on PPP, as it helps investors assess the robustness of valuation outcomes under different scenarios.

Quarterly earnings surprises may appear small in absolute terms but, when reframed through PPP and translated into SIRR, they represent significant valuation adjustments. PPP helps clarify why the market’s reaction is not irrational: minor earnings revisions alter intrinsic value not just by pennies, but by percentage points of expected return and multi-year payback horizons.

By integrating growth and discounting logarithmically, PPP explains how minor revisions compound over time, producing amplified and measurable valuation shifts. It subsumes P/E as a special case (when g = 0 and r = 0), corrects PEG’s linearity, and avoids GGM/DCF instability when g ≥ r.

The conclusion is clear: PPP resolves the puzzle of why earnings surprises move stock prices so sharply. What looks like overreaction is, in fact, consistent with rational valuation dynamics.