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

CFA® Level I · Equities · 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.

The Gordon growth model values a share that pays a dividend (a cash payment to shareholders) that grows at a steady rate for ever. The formula is: Value = D1 / (r - g). D1 is next year's dividend, r is the return investors demand (the required return) and g is the dividend growth rate. Example: D1 = 3.00, r = 9%, g = 4% gives 3.00 / (0.09 - 0.04) = 3.00 / 0.05 = $60.00. The other options flip the signs or the operation, which breaks the logic: you divide by the gap between r and g.

A harder one

The Gordon growth model requires that:

  1. the growth rate is below the required return - correct
  2. the growth rate exceeds the required returnWhy not: That makes the denominator negative, producing a negative value for a positive dividend stream.
  3. dividends are paid quarterlyWhy not: Payment frequency affects the arithmetic slightly but is not a condition of the model. Annual dividends are the usual convention.

The formula is Value = D1 / (r - g). For it to make sense, g must be smaller than r. If g equals r, you divide by zero and the value is infinite. If g is bigger than r, the bottom is negative and you get a negative value for a share that pays positive dividends. It also makes no real-world sense for a company to grow faster than investors' required return for ever. Paying dividends quarterly is not a condition of the model.

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: This is only a 5% rise. The value responds through the denominator, which falls from 0.06 to 0.05, so the value rises by a fifth, not by one-twentieth.
  2. $33.33Why not: This is the original value. A one-point rise in g narrows the spread from 0.06 to 0.05, so the value must change.
  3. $40.00 - correct

Use Value = D1 / (r - g) again with the new growth rate. New value = 2.00 / (0.10 - 0.05) = 2.00 / 0.05 = $40.00. The old value was 2.00 / 0.06 = $33.33. A rise of just one percentage point in g shrinks the bottom of the fraction from 0.06 to 0.05, which lifts the value by 20%. This shows why the model is very sensitive to its inputs. The $35.00 answer wrongly assumes the value rises by only 5%.

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