Dividend Discount Model

The model builds from the simplest case. For a one-year holding period, value equals the expected dividend plus the expected year-end price, both divided by one plus the required return on equity. Extending the horizon, the expected sale price is itself the present value of the dividends the next buyer expects, so substituting repeatedly makes the terminal price disappear and leaves an infinite stream of dividends discounted at the required return. This is the general dividend discount model: value equals the sum, over all future periods, of the expected dividend in each period divided by one plus the required return raised to that period's power.

The substitution matters conceptually. Price appears in the short-horizon version only as a stand-in for later dividends, which is why the model does not require the investor to hold the share forever. It requires only that some future holder eventually receives cash.

When dividends are assumed to grow at a constant rate forever, the infinite series collapses to a closed form: value equals next period's expected dividend divided by the required return minus the growth rate. Equivalently, the current dividend multiplied by one plus the growth rate, over the same denominator. The formula holds only when the required return exceeds the growth rate; as growth approaches the discount rate the value explodes, which signals that a perpetual growth assumption above the cost of equity is economically impossible.

Growth is normally estimated as the sustainable growth rate: the retention ratio, meaning one minus the payout ratio, multiplied by return on equity. This links the valuation directly to the firm's reinvestment policy and profitability rather than treating growth as a free parameter. The required return typically comes from CAPM or a build-up approach.

Most firms do not grow at a single constant rate. The two-stage model forecasts dividends explicitly through a high-growth phase, then applies the Gordon formula at the end of that phase to capture the mature period. Care is required with timing: the terminal value computed from the first stable-phase dividend sits at the end of the final explicit forecast year and must be discounted back over that many periods, alongside the individual dividends.

The H-model offers a shortcut when growth declines linearly from an initial high rate to a long-run rate over a specified period. Its value equals the current dividend grown at the long-run rate and capitalised in the usual way, plus an additional term equal to the current dividend times half the transition length times the excess of the initial growth rate over the long-run rate, all divided by the required return less the long-run rate. Three-stage variants add an explicit constant-growth middle phase.

On an exam and in practice, the constant-growth relationship is used as often in reverse as forward. Given a market price and a dividend forecast, solving for the discount rate yields the market-implied required return, which equals the forward dividend yield plus the growth rate. Solving instead for growth yields the growth rate the market is currently pricing in, a common sanity check against sustainable growth estimated from ROE and retention. Dividing both sides by earnings converts the model into a justified price-to-earnings multiple: the payout ratio divided by the required return minus growth, on a leading basis.

Candidates should be able to move fluidly among these forms, build a two-stage valuation with correct discounting, and articulate why the output is highly sensitive to small changes in the spread between the required return and the growth rate.