We just learnt from the previous page that firm foundation theory suggests that the intrinsic value of stock is the present value of all its future dividends. And this is the exact model I will introduce here.
The idea of dividend discount model is pretty straightforward: find all the present value of all the future dividends and add them up. Suppose the stock pays dividends on annual basis, so we are standing at the beginning of year 1 and the dividend for the first year, D1, will be paid by the end of the 1st year. The dividend for the second year, D2, will be paid by the end of the 2nd year. So on so forth for year 3, 4, 5, ... until infinity. The annual interest rate is fixed, r. Then the intrinsic value of the stock (V0) should be:
As you might already recognized that, in the equation above, each term on the right hand side is the present value of a future dividend given a specific year. For example, the second term, D2/(1+r)^2, is the present value of 2nd year's dividend.
You might ask now, how can we figure out the exact value all these future dividends? Well, the truth is, we don't know. An educated answer would be, we just guess what's the value of these D's (in academia people call it "estimation"). I know that may sound absurd at the first — how can you be so sure about the future dividends given we know so little of the future, and perhaps that is why there is a lot of criticism about this fundamental value approach. However, long shot as it sounds, it can still provide guidance as long as we are fully aware what is the assumption we make when we estimate these future dividends.
The simplest assumption of what future dividend may be like is that these dividends have the same value. In this case, the above equation become:
What does this formula remind you now? Exactly! It is a perpetuity. Remember, a perpetuity is annuity that goes forever (with the same payment every period).
Here comes our example:
Suppose a stock pays $1 as dividend per year forever, and the required rate of return (it is just another way to say "discounted rate" in this context) is 15% per year, what should the stock be selling for?
Applying the perpetuity formula, we got the answer equal to $6.67.