# EXPLORING THE POTENTIAL PAYBACK PERIOD (PPP)

AS A BRIDGE BETWEEN STOCKS AND BONDS: AN EXAMPLE THROUGH

THE MATHEMATICAL RELATIONSHIP BETWEEN NASDAQ LEVELS

AND 10-YEAR U.S. TREASURY BOND YIELDS

If the available data (P/E ratio, projected earnings growth rate, risk-free interest rate, expected market
return, Beta) are consistent, the NASDAQ appears close to a correction based on the Potential Payback Period
(PPP), which synthesizes all these data.

The discount rate "r" is calculated using the Capital Asset Pricing Model (CAPM), which incorporates the
expected market return, a risk-free interest rate, and Beta (β) as a risk factor associated with any stock.
The formula for "r" is:

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The PPP concept can be further developed to make it a more concrete and practical evaluation tool for stocks
while keeping it closely related to corporate finance for the sake of rigor. This approach naturally led to
the "Internal Rate of Return" (IRR) applied to stocks.

From a stock’s PPP, we can deduce its IRR, recognizing that both PPP and IRR are common tools for selecting
investments in corporate finance. In corporate finance, the IRR is the discount rate that equates the
initial investment with the expected net cash flows from that investment over its lifetime. By applying this
concept to an investment in a stock and using the PPP as the investment's duration, we can derive a precise
Internal Rate of Return for each PPP value. In other words, the redefined IRR, as a tool for evaluating a
stock, is the discount rate that enables an investor to potentially double their investment through the
cumulative earnings per share over the calculated PPP period for that stock.

Expressed as a percentage, the IRR is more concrete and meaningful in conveying the attractiveness and
opportunity of an investment, whether for an industrial investment or an investment in a stock market.

In real life, the PPP varies within a relatively narrow range of 5 to 15 years, corresponding to an IRR that
moves in the opposite direction of the PPP, ranging from 15% to 5%. These PPP and IRR figures can be
considered significant, realistic, and credible due to their reasonable order of magnitude and relative
stability, reflecting the consistency, rationality and homogeneity of financial markets, as shown in the
graph below depicting the evolution of the IRR as a function of the PPP.

To evaluate the attractiveness of a stock, one must compare its IRR (Internal Rate of Return) with a
risk-free interest rate, such as the yield on a 10-year U.S. Treasury bond. The IRR of the stock should be
higher than the risk-free interest rate to reflect the risk premium associated with each stock.

Currently, using the most favorable underlying data provided today by ChatGPT, the IRR of the NASDAQ is very
close to the yield on the 10-year U.S. Treasury bond: 4.07% versus 3.92%. A correction seems likely.
However, this correction will primarily affect companies that have poorer growth prospects combined with a
relatively high P/E ratio, meaning a relatively high PPP.

Most Favorable Scenario

• P/E ratio: 24.60

• Earnings growth rate (g): 12%

• Discount rate (r): 3.92 + 1.2 (7.00 – 3.92) = 7.616%

• PPP: 17.39 years

• IRR: 4.07%

Less Favorable Scenario

• P/E ratio: 24.60

• Earnings growth rate (g): 10%

• Discount rate (r): 3.92 + 1.4 (8.00 – 3.92) = 9.632%

• PPP: 23.68 years

• IRR: 2.97%

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