## The Dividend Discount Model

DIVIDEND DISCOUNT MODEL Discounted cashflow model of today's stock price which states that share value equals the present value of all expected future dividends.

We have managed to explain today's stock price P0 in terms of the dividend DIV1 and the expected stock price next year P1. But future stock prices are not easy to forecast directly, though you may encounter individuals who claim to be able to do so. A formula that requires tomorrow's stock price to explain today's stock price is not generally helpful.

As it turns out, we can express a stock's value as the present value of all the forecast future dividends paid by the company to its shareholders without referring to the future stock price. This is the dividend discount model:

P0 = present value of (DIV1, DIV2, DIV3

DIV, DIV2

DIV3

How far out in the future could we look? In principle, 40, 60, or 100 years or moreâ€” corporations are potentially immortal. However, far-distant dividends will not have significant present values. For example, the present value of $1 received in 30 years using a 10 percent discount rate is only $.057. Most of the value of established companies comes from dividends to be paid within a person's working lifetime.

How do we get from the one-period formula P0 = (DIVj + Pj)/(1 + r) to the dividend discount model? We look at increasingly long investment horizons.

Let's consider investors with different investment horizons. Each investor will value the share of stock as the present value of the dividends that she expects to receive plus the present value of the price at which the stock is eventually sold. Unlike bonds, however, the final horizon date for stocks is not specifiedâ€”stocks do not "mature." More-

over, both dividends and final sales price can only be estimated. But the general valuation approach is the same. For a one-period investor, the valuation formula looks like this:

P DIV1+ Pi

A 2-year investor would value the stock as p _ DIV, DIV, + P,

1 + r (1 + r)2 and a 3-year investor would use the formula p _ D1V| DIV2 , DIV3+ P3

In fact we can look as far out into the future as we like. Suppose we call our horizon date H. Then the stock valuation formula would be

DIV1 + DIV2 + . DIVg + PH Po 1 + r (1 + r)2 (1 + r)H

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