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Fundamental Analysisintermediate

The Dividend Discount Model

The dividend discount model (DDM) is an absolute valuation method. A share is worth the present value of all the dividends it will ever pay, discounted at the investor’s required return rr. When dividends grow at a constant rate gg forever, the model collapses to the elegant Gordon growth model, P0=D1r−gP_0 = \dfrac{D_1}{r - g}. The value rises with next year’s dividend D1D_1 and the growth rate gg, and falls as the required return rr rises. The model is valid only when r>gr > g, otherwise the value is infinite or negative and the formula breaks down.

Try it yourself

The Gordon growth model

A share is worth the present value of its growing dividends: P₀ = D₁ / (r − g), with D₁ = D₀(1 + g). Value rises with growth g and falls with the required return r. The denominator is the gap r − g, so as g approaches r the price explodes, and for g ≥ r the model breaks down.

Intrinsic value P₀$41.60
$0$46$91$137$182-6%-2%2%6%10%14%Growth rate g (%)Intrinsic value P₀ ($)g = r$41.60P₀ vs g (r fixed)asymptote g = r
Next dividend D₁ = D₀(1 + g) $2.08Denominator r − g +5.0%
Current dividend D₀$2.00
Growth rate g4.0%
Required return r9.0%
The share is worth $41.60: next year's dividend $2.08 divided by the gap 5.0%. As g rises toward r the gap shrinks and the value climbs steeply.
Try this

Push g toward r and watch P₀ run off the chart. A declining firm (g < 0) still has a finite value: the gap r − g simply widens.

Reflect: a one-point change in g or r can swing P₀ by tens of percent when the two are close. Is that sensitivity a flaw in the model, or an honest signal that the value of a perpetual-growth stock genuinely is fragile to its assumptions?

Why it matters

Owning a share is owning a claim on a stream of future dividends. The DDM simply adds up that stream in today’s money. The Gordon version is a shortcut for a company that grows steadily forever. Notice how sensitive it is. The denominator is the gap between the discount rate and the growth rate, so when rr and gg are close, tiny changes in either swing the value wildly. That fragility is the model’s great teaching point.

Formulas

General dividend discount model
P0=∑t=1∞Dt(1+r)tP_0 = \displaystyle\sum_{t=1}^{\infty} \dfrac{D_t}{(1 + r)^t}
The share price is the present value of every future dividend DtD_t, discounted at the required return rr.
Gordon growth model
P0=D1r−gP_0 = \dfrac{D_1}{r - g}
Valid only when r>gr > g. Here D1D_1 is next year’s dividend, rr the required return and gg the constant growth rate. D1=D0(1+g)D_1 = D_0 (1 + g).

Worked examples

Scenario

A firm just paid a dividend of A$2.00. Dividends are expected to grow at 4 percent forever, and investors require a 10 percent return. What is the share worth?

Solution

Next year’s dividend is D1=2.00×1.04=2.08D_1 = 2.00 \times 1.04 = 2.08. Apply Gordon growth. P0=2.080.10−0.04=2.080.06P_0 = \dfrac{2.08}{0.10 - 0.04} = \dfrac{2.08}{0.06}, which is about A$34.67. Notice the sensitivity. If the required return were 9 percent instead of 10, the denominator falls to 0.05 and the value jumps to A$41.60, a large move from a one-point change in rr.

Common mistakes

  • ✗The DDM only works for companies that pay dividends today. Value can rest on dividends expected to begin later. The model handles a future start, though it is awkward for firms with no foreseeable payout.
  • ✗A higher growth rate always raises the value sharply. Growth raises value only while r>gr > g. As gg approaches rr the formula explodes, which is an artefact, not a real valuation.
  • ✗The required return rr is the same as the dividend yield. The required return is the total return investors demand, combining the dividend yield and expected capital growth.
  • ✗Gordon growth applies to any company. It assumes a single constant growth rate forever, which fits stable, mature firms far better than young high-growth ones.

Revision bullets

  • •A share is worth the present value of all future dividends
  • •Gordon growth: price equals next dividend divided by (r minus g)
  • •Value rises with the dividend and growth, falls as required return rises
  • •Valid only when the required return exceeds the growth rate
  • •Highly sensitive when r and g are close together
  • •The required return can be sourced from CAPM

Quick check

A stock pays a dividend next year of A$3, grows at 5 percent forever, and investors require 11 percent. The Gordon growth value is

The Gordon growth model breaks down when

Connected topics

FundamentalMultiplesFCF / DCFReturn & RiskCAPM & SML

Sources

  1. Brailsford, Heaney & Bilson (2015), Ch. 13
    Brailsford, T., Heaney, R., & Bilson, C. Investments: Concepts and Applications. 5th ed. Cengage Learning Australia, 2015.
    Develops the dividend discount model and the constant-growth (Gordon) valuation.
  2. Gordon (1959), REStat
    Gordon, M. J. "Dividends, Earnings, and Stock Prices." The Review of Economics and Statistics, 41(2), 1959, pp. 99-105.
    Original derivation of the constant-growth dividend valuation model.
How to cite this page
Dr. Phil's Quant Lab. (2026). The Dividend Discount Model. Derivatives Atlas. https://phucnguyenvan.com/concept/im-dividend-discount-model
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