Growth Rates and Share Repurchases
The Gordon growth model is a nice, simple tool for equating constantly growing dividends and a present value, or price. Now consider what happens over time.
Sure, dividends may grow at some rate, like 5%. Suppose you have a stock valued at 21, based on the following:
$$\displaystyle V_0 = \frac{D_0(1 + g)}{r - g} = \frac{1.00(1 + 0.05)}{0.10 - 0.05} = 21 $$.
Think about what happens to the value of the stock in one year. The only thing that changes is the next year dividend, which advances another 5%. What effect do you think that will have on the Year 1 value of the stock?
Absolutely.
No. It will grow at 5% as well.
Both sides of the equation are multiplied by 1 + _g_ for this result. Over time, price grows at the same rate as dividends.
| Earnings | Shares | EPS | Dividends | Price | Dividend Yield | Price Yield |
|---|---|---|---|---|---|---|
| 1,000.00 | 1,000 | 1.00 | 1.00 | 21.00 | $$ \, $$ | $$ \, $$ |
| 1,050.00 | 1,000 | 1.05 | 1.05 | 22.05 | 5.00% | 5.00% |
| 1,102.50 | 1,000 | 1.10 | 1.10 | 23.15 | 5.00% | 5.00% |
| 1,157.63 | 1,000 | 1.16 | 1.16 | 24.31 | 5.00% | 5.00% |
| 1,215.51 | 1,000 | 1.22 | 1.22 | 25.53 | 5.00% | 5.00% |
For simplicity, notice that all earnings are paid to shareholders in a cash dividend. The dividends and price appreciation are both 5%, providing investors with their 10% required return. This would work for any constant payout ratio.
Now think about what would happen if a share repurchase was performed each year with half of the earnings, with the other half paid in a cash dividend. Knowing that these should be equivalent for shareholder value, which metric do you expect will be higher in this case?
No. The equivalence refers specifically to total return. It should still be 10%.
No. The dividends would be cut in half, so this would fall.
That's right!
Dividend yield falls and price appreciation (or price yield) rises, leaving stockholders with the same 10% total return.
| Earnings | Shares | EPS | Dividends | Price | Dividend Yield | Price Yield |
|---|---|---|---|---|---|---|
| $$ \, $$ | 1,000 | $$ \, $$ | $$ \, $$ | 21.00 | $$ \, $$ | $$ \, $$ |
| 1,000.00 | 976 | 1.02 | 0.51 | 22.59 | $$ \, $$ | $$ \, $$ |
| 1,050.00 | 953 | 1.10 | 0.55 | 24.30 | 2.44% | 7.56% |
| 1,102.50 | 930 | 1.19 | 0.59 | 26.13 | 2.44% | 7.56% |
| 1,157.63 | 908 | 1.27 | 0.64 | 28.11 | 2.44% | 7.56% |
| 1,215.51 | 886 | 1.37 | 0.74 | 30.23 | 2.44% | 7.56% |
There are two different choices of how to pay dividends, with the same return and same starting price. What does this tell you about use of the Gordon growth model (GGM)?
No. It can. The GGM was used for all prices in these examples.
No. This would combine half of the dividends with the same growth rate as in the first case. That would result in a price that is far too low.
Exactly!
The logic works in a couple of ways here. First, no matter what the company does with the money, it belongs to shareholders, and so they should get the same return. Also, the GGM uses the required rate of return with a dividend and a growth rate. So if dividends are cut in half, the growth rate of those dividends must be larger.
What is it specifically that makes the growth of dividends larger in the second case?
No, that's not it. It's due to the greater price appreciation from fewer shares outstanding.
You got it!
That's an important point here. The payout ratio is still 100%, so there's no reinvestment; it's just going to purchase some shares rather than to pay a dividend. Shareholders can re-create the first scenario by selling shares if they want.
Share repurchases (or "buybacks") are common. They are less predictable, and managers tend to choose advantageous timing for buybacks while keeping dividends steady—probably because investors like to see that. So buybacks are harder to predict, but they are _vital_ to include in forecasts like this. Without considering buybacks in this simple example, the estimated price would be about half of what it really is.
Another use of the GGM is to calculate an implied growth rate. It's fine to use it for calculating price. Keep the same numbers as before.
$$\displaystyle V_0 = \frac{D_0(1 + g)}{r - g} = \frac{1.00(1 + 0.05)}{0.10 - 0.05} = 21 $$
If the market price was 18, then you'd say that the stock is undervalued. But of course that value of 21 assumes that your growth rate is correct. Maybe the market is assigning a different growth rate of dividends to this stock. Do you think this growth rate implied by the market would be higher or lower?
Yes!
No. It would have to be lower. Lower growth of dividends relates directly to a lower valued security.
A lower price implies a lower growth rate, and a 5% growth rate is pretty high. Finding it just takes a little algebra.
$$\displaystyle V_0 = 18 = \frac{1.00(1 + g)}{0.10 - g} $$
$$\displaystyle 18(0.10) - 18g = 1 + g $$
$$\displaystyle g = \frac{1.8 - 1}{19} = 0.0421 = 4.21 \% $$
That's not a huge difference, so maybe a price of 18 isn't such a bargain. Even a 4.21% growth rate might be an optimistic assumption.
To summarize:
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No change
5% growth as well
Total return
Dividend yield
Price appreciation
The GGM can't be used if share repurchases are performed
The GGM is fine for companies that perform share repurchases, as long as price growth is incorporated in the assumed growth rate
The GGM is fine for companies that perform share repurchases, as long as dividends are assumed to grow at the same rate as earnings
Greater earnings from reinvestment
Greater price appreciation from fewer shares outstanding
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