The Dividend Discount Model (DDM)

This infinite cash flow stream can be condensed as something called a geometric series to: $$\displaystyle P_0 = \frac{D_1}{r_e-g} $$ Price, dividends, and the return on equity are still identifiable. But this new expression introduces _g_, which is the __sustainable growth rate__ of dividends. This variable _g_ now takes center stage. How would you describe the relationship between the growth rate _g_ and the price of a stock, leaving everything else unchanged?

No, just the opposite actually. A higher _g_ would mean a higher price.

Absolutely!

Mathematically, this makes sense because a higher _g_ means that the difference in the denominator must be smaller. This will make the whole fraction, and therefore the price it equals, larger. Logically, it makes sense as well. A stock with a larger growth rate must mean higher future earnings, making the company more valuable.

With a little algebra, this expression can be used to solve explicitly for the return of equity: $$\displaystyle r_e = \frac{D_1}{P_0} + g $$ The fraction of dividends divided by price is called the _dividend yield_, and the return of equity can be stated as simply being the sum of the dividend yield and the sustainable growth rate. So if investors require a 9% return on a stock of a firm which is growing at 3.5% annually, what would you expect the dividend yield to be?

Yes! That's right. The 9% expected return should be the sum of a 5.5% dividend yield and the 3.5% estimated growth rate. Price will adjust up or down so that the dividend yield would be 5.5%, meeting investors' requirement for a 9% return.

No, you might have made a little calculation error.

No, it looks like you might have just added the two, but look carefully at the variables being given.

Price and current dividends are easily observable for any stock, but the estimation of the sustainable growth rate is the real challenge. One method for estimating this is to take published estimates of others on expected growth of the firm, but you can also calculate your own estimate using some earnings data. Consider the earnings of a firm. They have to do something with that money. Some of these earnings are paid out to the owners of the firm (dividends). What do you think happens to the rest?

No, bondholders are paid their interest, and that is an expense which is accounted for before the earnings figure is obtained.

No, hopefully not! The CEO's compensation package is predefined. It might include some stock options or incentives, but not all of the earnings unpaid to stockholders.

More specifically, the portion of earnings paid to stockholders in the form of dividends is called the _payout ratio_, and so the proportion reinvested is one minus the payout ratio, which is also referred to as the _retention rate_. So mathematically, you have: $$\displaystyle g = \left(1 - \frac{D}{EPS} \right) ROE $$ which says that the growth rate is equal to one minus the payout ratio (dividends as a proportion of earnings per share) times the return on equity, or ROE.

To summarize this discussion: [[summary]]

Why would you purchase a stock? For return, of course. The standard answer is always "dividends and capital gains." But capital gains are relatively short-term price fluctuations that shift some value from one investor to another. The only real value from holding a stock is found in future dividends, or the company earnings which are then paid out to the owners. So the __dividend discount model (DDM)__ is that same answer given mathematically, showing the price of the stock today as the sum of all discounted future dividends: $$\displaystyle P_0 = \frac{D_1}{1+r_e} + \frac{D_2}{(1+r_e)^2} + ... + \frac{D_n}{(1+r_e)^n} $$

That's right! Those remaining earnings are simply reinvested back into the firm implicitly, and this allows the firm to grow. So the growth rate would be whatever portion of the earnings are reinvested multiplied by the return.

A higher _g_ would mean a lower price

A higher _g_ would mean a higher price

5.5%

6.5%

12.5%

The rest goes to bondholders

The rest is paid to the CEO

The rest stays with the firm for things like reinvestment or an added liquidity cushion

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