The Dividend Discount Model

If you own a share forever, the only cash you actually ever receive from it — not on paper, but into your bank account — is its dividends. Everything else, the price you could sell it for, is just other people's opinion of the dividends still to come. The dividend discount model (DDM) takes that idea literally: a stock is worth the present value of every future dividend, nothing more.

$$P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1+r_e)^t}$$

In words: add up each future dividend $D_t$, shrunk by discounting it back at the cost of equity $r_e$ for however many years, $t$, away it is. That infinite sum is unusable directly, so the standard simplification — the Gordon growth model — assumes dividends grow at a constant rate $g$ forever:

$$P_0 = \frac{D_1}{r_e - g}$$

$D_1$ is next year's expected dividend, not this year's just-paid one. The formula only makes sense when $r_e > g$; if a company could grow its dividend faster than its own cost of equity forever, the sum never converges — a useful sanity check when a number comes out negative or absurd.

A worked example

A utility stock just paid a $2.00 dividend, expected to grow 3% a year forever. Cost of equity is 8%. Next year's dividend is $D_1 = 2.00 \times 1.03 = 2.06$, i.e. $2.06.

$$P_0 = \frac{2.06}{0.08 - 0.03} = \frac{2.06}{0.05} = 41.20$$

That is, $41.20 per share.

If the stock trades at $35, DDM says it is undervalued relative to its dividend stream at these assumptions; at $50, overvalued. Either way, the answer is only as good as the constant-growth assumption behind it.

A two-stage version handles companies growing fast now and slowing later: forecast dividends explicitly for, say, five years, then apply Gordon growth from year six onward as the terminal value — the same forecast-then-perpetuity structure a full DCF uses.