Gordon Growth Model and the Price-to-Earnings Ratio

Since you're here, reading this text at this moment, you probably already know that P/E means the price-to-earnings ratio. This is a pretty popular metric in stock valuation, as it's important to know how much you're paying for a unit of earnings. You'll only pay more if there's some expected growth that goes along with it.

The P/E can be based on trailing earnings (trailing P/E) or expected next period earnings (forward P/E). If earnings are expected to grow at all, which one do you think is bigger?

Right.

No. The trailing P/E will be bigger in this case.

Higher future earnings, lower forward P/E, since "E" is on the bottom. That's the logic there. The P/E based on fundamentals is a __justified P/E__. Plug in reasonable inputs, and that's what you should get. Then compare to the market. But another way to use this ratio is to start with the market P/E and extract the assumed growth rate. Then compare that growth rate to what seems reasonable. Sounds like a growth model is needed.

So back to the Gordon growth model again. It suggests that the stock price is just the geometric series of discounted future dividends growing at a constant rate. $$\displaystyle P_0 = \frac{D_1}{r - g} $$ If you want to get the forward P/E from this, just divide both sides by forward earnings per share. $$\displaystyle \frac{P_0}{E_1} =\frac{ \frac{D_1}{r - g}}{E_1} =\frac{ \frac{D_1}{E_1}}{r - g}$$ What is another way you could refer to that new numerator of D/E?

Absolutely! This is the ratio of what is paid out to what was earned. This is usually denoted as 1 - _b_, since _b_ is the retention ratio, or the proportion which _isn't_ paid out. So fine. The forward P/E can be that as well. $$\displaystyle \frac{P_0}{E_1} = \frac{\frac{D_1}{E_1}}{r - g} = \frac{1 - b}{r - g} $$

Not quite. The retention rate is the proportion which is reinvested, which is equal to one minus the rate shown here.

Right letters, but wrong values. This is dividends and earnings, not debt and equity.

For the trailing P/E, just use the trailing figures—current dividend and past earnings. $$\displaystyle \frac{P_0}{E_0} = \frac{\frac{D_0(1 + g)}{E_0}}{r - g} = \frac{(1 - b)(1 + g)}{r - g} $$ Again, bigger. It has to be, given the basis on older, lower earnings. But what do you think would happen to the P/E ratio if the retention ratio increased?

No. Consider that a higher retention ratio should mean a higher growth rate.

No. Notice that the numerator of the equation is the payout ratio. So if that gets smaller, a higher P/E can't be guaranteed.

Yes! There are competing effects here. The numerator of 1 - _b_ will be smaller for sure, since that's the payout ratio. Higher retention ratio, lower payout ratio, and downward pressure on the price and the P/E. But the whole point of earnings retention and reinvestment is to grow earnings faster, so there would likely be a higher growth rate. Depending on the quality of those investment opportunities, the P/E could go either way.

To summarize: [[summary]]

Trailing P/E

Forward P/E

The payout ratio

The retention rate

Debt to equity ratio

It must be lower

It must be higher

It could be higher or lower

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