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Stock Market & Efficiencyintermediate

Valuing a Stock: Dividends and Gordon Growth

A share is worth the present value of the dividends it will pay. The one-period and generalized dividend models say this directly, and the Gordon growth model gives a clean closed form when dividends grow at a constant rate below the required return.

Try it yourself

Gordon growth model

A share is the present value of its future dividends. With constant growth P₀ = D₁ / (kₑ − g). Watch the price blow up as growth g climbs toward the required return kₑ: the denominator shrinks to zero, so value gets extremely sensitive to the growth assumption.

Stock value P₀$40.00= $2.00 ÷ (8.0% − 3.0%)
$0$38$75$113$1500%2%4%6%8%Dividend growth g (%)Stock price P₀ ($)g = kₑ$40.00
Capped at 7.9% so growth stays below kₑ.
Try this
Bumping g from 3% to 4% lifts P₀ from $40 to $50, a 25% jump from a one-point change. Why does a tiny growth revision move value so much, and what does that say about trusting a single point estimate of g?

Why it matters

Owning a share is owning a claim on a future cash stream, so the same discounting that prices a bond prices a stock. When dividends grow steadily, the whole infinite stream collapses into one simple expression.

Formulas

One-period valuation
P0=D1+P11+keP_0 = \frac{D_1 + P_1}{1 + k_e}
D1D_1 is next year’s dividend, P1P_1 the expected price then, and kek_e the required return on equity.
Gordon growth model
P0=D1ke−gP_0 = \frac{D_1}{k_e - g}
Valid only when the required return kek_e exceeds the constant dividend growth rate gg.

Worked examples

Scenario

A stock will pay a $2 dividend next year, the required return is 8%, and dividends grow at 3%. Value it, then raise growth to 4%.

Solution

Gordon gives P = 2 / (0.08 - 0.03) = $40. Raising growth to 4% gives P = 2 / (0.08 - 0.04) = $50, which shows how sensitive value is to the growth assumption.

Common mistakes

  • ✗A stock is worth its current dividend or earnings. It is worth the present value of all future dividends, not a single year’s payout.
  • ✗The Gordon model works for any growth rate. It needs the required return to exceed growth. If growth meets or beats the required return, the formula breaks down.

Revision bullets

  • •A share equals the present value of future dividends
  • •Gordon growth model: P0=D1/(ke−g)P_0 = D_1/(k_e - g)
  • •Requires the required return above the growth rate
  • •Value is very sensitive to the growth assumption

Quick check

In the Gordon growth model, raising the assumed dividend growth rate (still below the required return)

Connected topics

Present ValueEfficient MarketsRational Expectations

Sources

  1. Mishkin (2018), Ch. 7
    Mishkin, F. S. The Economics of Money, Banking, and Financial Markets. 12th ed. Pearson, 2018. ISBN 978-1-292-26885-9.
    The one-period, generalized-dividend, and Gordon growth models of stock valuation.
How to cite this page
Dr. Phil's Quant Lab. (2026). Valuing a Stock: Dividends and Gordon Growth. Derivatives Atlas. https://phucnguyenvan.com/concept/mb-stock-valuation
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