Overview
The dividend discount model is a model used to calculate a valuation for a firm using present value calculations.
Present value takes a series of future cash flows and calculates a single present value of those cash flows. In the case of company valuation, the shareholders receive cash flows in the form of dividends. As such, given a series of future dividends {% D_1,D_2, ... D_n %}, the present value of those dividends can be seen to be
{% Value = \sum_{i=1}^n \frac{D_i}{(1+r)^i} %}
where {% r %} is the discount rate appropriate to dividends.
Gordon Growth Model and Dividend Growth
One of the challenges of applying the dividend discount model is estimating the future dividends. A simple model that accomplishes this is the Gordon Growth Model, which assumes that the expected dividend growth rate is a constant over time. That is, it is assumed that the following
{% D_{i+1} = D_i(1+g) %}
When this assumption is applied, the present value of the dividends is given by
{% V= \frac{D_0(1+g)}{(1+r)} + \frac{D_0(1+g)^2}{(1+r)^2} + ... + \frac{D_0(1+g)^n}{(1+r)^n} + ... %}
which can be further reduced to
{% V = \frac{D(1+g)}{r-g} %}
Terminal Value
A justification for the dividend discount model and the foundation of a practical approach to valuation is the terminal value model. In this model, we allow shareholders to hold the stock for a period of time and then to be able to sell the stock. In the single period model (where the shareholder holds the stock for a single period and then sells it), the present value of the shareholder's stock is the dividend she receives in the next period and the price of the stock sold at the end of that period, both discounted back.
{% V = \frac{D_1 + P_1}{(1+r)} %}
Likewise, if the shareholder holds the stock for two periods and then sells, the present value to her in that case is
{% V = \frac{D_1}{(1+r)} + \frac{D_2 + P_2}{(1+r)^2} %}
Taking the limit as the shareholder extends the holding period out to infinity, the dividend discount model given above
is recovered. In addition, the terminal value approach provides a practical method of applying the dividend discount model.
That is, the analyst does not have to make assumptions about the growth of the dividend out to infinity, rather, if she can
formulate a forecast of dividend policy for a certain number of periods and can make an estimate of the share price at the end
of that period, she can still apply the dividend discount approach using the terminal value formula given here.