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1. Let’s first start with the basic dividend growth model or what we know as the Gordon Constant Growth Model. We know that the PV of a stock is found by PV = D1/(r-g). We also know that D1 or dividends in year 1 is a function of the payout ratio on the EPS. Therefore, we could take D1 = EPS1*(1-payout ratio). We also know that EPS1 or D1 is a function of the growth rate. So, EPS1 = EPS0 * (1+g).

2. Based on the above we now can expand the numerator as PV = EPS0 * (1-payout ratio) * (1+g).

3. We know that the P/E ratio is just the price per share divided by the EPS. Therefore, if we multiply both sides of the equation by 1/EPS, we will get P/E = (1-payout ratio)*(1+g)/(r-g)

4. Now, to the denominator. We know that the required rate of return (r) can be estimated using the CAPM of Rf + Beta(Rm-Rf). The (Rm-Rf) is simply the market risk premium or the premium that can be made as a result of investing in the risky part of the market or non treasury securities. If we rewrite the equation now, we have P/E = (1-payout ratio)*(1+g)/(Rf + beta (MRP)) -g).

5. We could also expand g or growth. The sustainable growth rate can be estimated by the ROE * the retention rate. The retention rate is simply (1-payout ratio).

6. Therefore, now we have the main factors:

**growth:** Since growth appears in both the numerator and the denominator it is a major factor that affects the P/E ratio. Looking at the rewritten equation, we can see that the higher the growth rate, the higher the P/E ratio. Therefore, companies that have higher expected growth rates should have higher P/E ratios assuming other factors are the same.

**risk: ** In the denominator is the required rate of return or r. We estimated this by using the CAPM. Its major components are the Beta, which measures the risk of the company relative to the market. Therefore, the higher the risk (beta), then the higher the required rate of return. The higher the required rate of return, the lower the P/E ratio. Therefore, the higher the risk, all other factors being constant, the lower the P/E ratio.

We could continue to go on and breakdown the ROE using the DuPont equation (PM x AT x EM). As you dig deeper, you would see that the quality of those earnings (EPS) also affects the P/E ratio. Now, when you compare two companies or industries, you can dissect the P/E ratio and give both quantitative and qualitative reasons why the P/E ratio is higher or lower (justifying the P/E ratio)

Hope this helps…