Dividend Growth Model

In this section, we introduce a new model for stock valuation — the dividend growth model. Different from the constant dividend model (in which the stock value equals to a stream of constant dividends paid forever) introduced in last section, this dividend growth model assumes dividends grow at a constant rate with infinite payments.

The interactive chart below shows what's a stream of growing dividends like. The first dividend at the end of year 1 is $10. Let's denote their constant growth rate by "g". What does it mean is, for example, the second year's dividend is $10×(1+g), and the third year's is $10×(1+g)×(1+g), so on so forth.

You can play with the value of g by dragging the dot and see what will happen to the dividends when the growth rate g changes between 0 and 20%.

As you can tell, the higher the growth rate of the dividends, the higher value of the later dividends, and it can make a huge difference. To avoiding the explosion of the present value of all the dividends, this model thus assumes that the different growth rate should be no bigger than the discount rate period, r. Thus, when we apply this dividend growth model, we should always check if g<r. If this prerequisite is not met, then the present value of the stock is +∞ (positive infinite). That can't be real.

Knowing what's a stream of infinite growing dividends like, then it's time to figure out its present value. Since these growing dividends are essentially a growing perpetuity, we can directly apply the formula below:

Here, D is the first dividend payment by the end of the first year (one year from now). r is the discounted rate (or interest rate, or require rate of stock return), g is the dividend growth rate.