The Dividend Discount Model

At its simplest, the dividend discount model just discounts dividends. That's about it. So the price of a stock is the sum of these discounted dividends going out to infinity. $$\displaystyle V_0 = \sum\limits_{t=1}^{\infty} \frac{D_t}{(1 + r)^t} $$ Voila. But you've probably already seen that.

The thing is, not only do analysts not know the value of dividends into infinity (nor the appropriate discount rate, for that matter), but it's hardly even worth estimating beyond a certain point. Pro-forma statements can be estimated for a few years, but that's about all. At the end of those statements, what do you think the stock will have to be worth?

No, Stocks can go up or down in value.

No. It's possible to be worth the same as it is today, but it's unlikely. The dividend discount model would have some specific requirements to make that be true.

Right! It's still just worth future dividends. That doesn't change. So if you can only estimate what will happen in the next year, maybe you just estimate that dividend, and then a future price in Year 1. $$\displaystyle V_0 = \frac{D_1}{(1 + r)^1} + \frac{P_1}{(1 + r)^1} = \frac{D_1 + P_1}{(1 + r)^1} $$

If you're comfortable estimating several years, go ahead and do that. Just add more dividends, and then push back the estimated terminal price. $$\displaystyle V_0 = \sum\limits_{t=1}^n \frac{D_t}{(1 + r)^t} + \frac{P_n}{(1 + r)^n} $$ Notice that in each case, the terminal price is estimated in the same time period as the last forecast dividend. How would you relate this to the initial formula of simply adding up all of the discounted dividends?

No. There's no inconsistency. Consider taking some simple assumptions and just moving the terminal price back further and further.

No. There's no reason to assume that this is the case. The price of a stock could remain constant in each period.

Exactly! The stock price could remain the same or even increase in each period, and the power of discounting would still bring this value to zero once it is far enough in the future. Without a termination, there's no real terminal price. But even if you thought of it being there at "time infinity," it would be worth nothing today, since you'll never get there.

To summarize: [[summary]]

Less

The same that it is today

The dividends beyond that point discounted to that time

It is inconsistent

The price is assumed to decline, getting closer to zero in each period

The terminal price is discounted an infinite number of periods, so it's essentially zero today.

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