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Work out a share's intrinsic value with the dividend discount model

CFA® Level I · Equity Investments · Discounted Cash Flow (DCF) and Growth Models · EQ.1.a

The idea

The dividend discount model values a share as the present value of the dividends it will pay. With dividends growing at a constant rate g forever and a required return r, the Gordon growth form gives V0 = D1 / (r - g), where D1 is next year's dividend. The model only holds when g is below r, and it is highly sensitive to both inputs: small changes in the spread between them swing the valuation sharply. It suits stable, dividend-paying firms and fits poorly where dividends are absent or erratic.

Formulas

One-period dividend discount model

V₀ = (D₁ + P₁) ÷ (1 + r)

D₁
the dividend expected at the end of the year
P₁
the price expected at the end of the year
r
the required return on the equity

A holding of one period, where the value is the dividend plus what the share can then be sold for. Every longer model is this one applied again to P₁.

A practice question

From the question bank, with the reason each wrong option is wrong.

The Gordon growth model expresses intrinsic value as:

  1. D₁ / (r − g) — correct
  2. D₁ / (r + g)Why not: Adding growth shrinks the value, when growth is the thing that makes a dividend stream worth more. The denominator is the *spread* between the required return and growth.
  3. D₀ × (r − g)Why not: Multiplying by the spread rather than dividing, and using the dividend just paid. Both operations are inverted.

Next year's dividend divided by the spread between the required return and the constant growth rate.

A harder one

A share's next dividend is $2.00, its required return 10%, and dividends grow at a constant 4%. Intrinsic value is closest to:

  1. $20.00Why not: 2.00 ÷ 0.10 — growth ignored entirely, which values the dividend as a flat perpetuity.
  2. $33.33 — correct
  3. $50.00Why not: 2.00 ÷ 0.04 — the growth rate used as the denominator instead of the spread.

2.00 / (0.10 − 0.04) = $33.33. Note how much the answer depends on that six-point spread.

The hardest tier

A share has D₁ of $2.00 and a required return of 10%. If the growth estimate is revised from 4% to 5%, intrinsic value rises from $33.33 to approximately:

  1. $35.00Why not: A 5% rise in value, which would follow if the model responded proportionally to the change in g. It responds through the spread, which narrowed from 0.06 to 0.05 — a fifth.
  2. $33.33Why not: The original value, unchanged. The whole point of the question is that a one-point revision to g moves it substantially.
  3. $40.00 — correct

2.00 / 0.05 = $40.00. A one-point change in g moved value by 20%, which is why the model is described as highly sensitive to its inputs.

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