Estimating a Required Return Using the Gordon Growth Model
Time for a little algebra.
The Gordon growth model equates the current price of a stock to the summation of a geometric series of discounted future dividend payments, assumed to grow at a constant rate.
$$\displaystyle P_0 = \frac{D_1}{r - g} $$
To solve for _r_, complete the following:
$$\displaystyle r - g = \frac{D_1}{P_0} $$
leading to
$$\displaystyle r = \frac{D_1}{P_0} + g $$.
How would you interpret this formulation of the required rate of return, _r_?
No. The first expression here is the next period dividend divided by price, which is the dividend yield.
No. Consider that _g_ is the growth rate, which is the rate at which price grows as well.
That's right!
The first part is the next period dividend divided by price, which is the dividend yield. The second part is _g_, which is the growth rate of dividends. Recall that looking forward an extra period requires just multiplying both sides of the original GGM by 1 + _g_, so this is the rate at which price grows as well, making it the capital gains yield.
Considering how the Gordon growth model works, as a dividend discount model, what is another way of considering the required rate of return, _r_?
Not quite. A risk premium is just part of a total return. But _r_ in this case is a total required rate of return.
Exactly!
The price of a stock is equated to future expected cash flows through this mechanism, making it an internal rate of return as well. And now, that IRR can be decomposed to a dividend yield and an assumed growth rate.
No. Debt isn't an issue here.
Suppose you have an equity index that you want to evaluate. You can use the total dividends, the price of the index, and a required rate of return as inputs to the Gordon growth model. If you do that, what would indicate that the index is fairly valued?
No. The price of an index doesn't have a lot of information in it by itself. It has to be compared to something. Also, this is used as an input to the GGM, so consider what the output would be.
No. A required rate of return just addresses fair compensation for risk, but it wouldn't tell you anything about relative value.
Yes!
If all of these things were input into the GGM, the output would be the growth rate, _g_. Recall that this is the assumed growth rate of dividends forever, so it should be a reasonable level, like a macroeconomic growth rate. If it's above this, then the market is pricing in a growth rate that is too high, indicating that the market might be overvalued.
This is just a simple one-stage model, but breaking down the components this way can be interesting, since history has taught that many growth rates have proven unsustainable in the past. The future will probably have similar lessons to share.
To summarize:
[[summary]]
The dividend yield plus payout ratio
The payout ratio plus capital gains yield
The dividend yield plus capital gains yield
A risk premium
An internal rate of return
A sum of debt and equity returns
A reasonable price
A reasonable required rate of return
A reasonable growth rate of dividends
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