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Corporate Accounting and Financial Management · Dividend Decisions

Gordon's Model of Dividend Policy: Formula and Numericals

Updated 11 October 2026 · Fact-checked

Gordon's model says dividend policy affects share value. Its rationale is bird-in-the-hand: investors see retained gains as riskier, so ke rises with retention. In numericals ke is held constant: P0 = E1 × (1 − b) ÷ (ke − br), where b is retention and r is return. Compare r with ke for the best payout.

Understand Gordon's Model

Every company must decide how much profit to pay out as dividend and how much to keep. Dividend relevance theories ask whether this choice changes the market price of the share. Gordon's model says it does.

Myron Gordon's argument is the bird-in-the-hand argument. A dividend received today is certain. Capital gain from retained profit comes later and is risky. So investors discount distant gains at a higher rate and prefer dividends. In Gordon's fuller argument, ke is assumed to rise with the retention ratio, so a higher payout is favoured. In the simplified numerical form, ke is held constant, and the r versus ke rule decides the optimal policy.

The model is a growth model. Growth comes only from retained earnings: g = b × r. Here b is the retention ratio and r is the return the firm earns on new investment. The price is the next dividend divided by (ke − g). The dividend is E1 × (1 − b), the payout ratio times earnings.

The model rests on assumptions. The firm is all-equity financed, with no debt. Investment is financed only from retained earnings, with no new external equity. The return r is constant. The firm has an infinite life. Retention ratio b is constant, so growth g = br is constant. Also ke > br, otherwise the price is infinite or meaningless. Corporate taxes are ignored. In Gordon's fuller argument, ke depends on the retention ratio. In the simplified textbook form used in numericals, ke is given as a constant for each calculation, so you can apply the formula directly.

The effect depends on r versus ke. If r > ke, a higher retention raises price. If r < ke, a higher payout raises price. If r = ke, price does not change. In the simplified form with constant r and ke, this conclusion is similar to Walter's model. The valuation formulas differ. Walter values the share as the present value of dividends plus the capitalised value of retained earnings, with no explicit growth rate. Gordon uses a growth perpetuity, P0 = D1 ÷ (ke − br), and explains the investor's preference for dividends through risk.

Key rules to remember

Gordon's share price
P0 = E1 × (1 − b) ÷ (ke − br)
E1 is expected earnings per share next year, b is retention ratio, ke is the cost of equity (as a decimal).
Dividend per share
D1 = E1 × (1 − b)
(1 − b) is the payout ratio. If given D1 directly, use it.
Growth rate
g = b × r
r is the return on retained funds. Retained earnings generate growth.
Equivalent dividend-growth form
P0 = D1 ÷ (ke − g)
Use this when D1 and g are given directly. Valid only if ke > g.
Retention and payout ratio
b = 1 − payout ratio; payout ratio = D ÷ E
Retention plus payout always equals 1 (100%).
Optimal policy rule
r > ke: retain more; r < ke: distribute more; r = ke: indifferent
Same conclusion as Walter's model. State it in conclusions.

How to solve Gordon's Model questions

Use this method for any numerical or theory question on Gordon's model.

  1. 1Write down E1 (or E0 and growth), r, ke and the retention ratio b given in the question. Convert percentages to decimals.
  2. 2Check whether the question gives D1 or the payout ratio. If D1 is not given, compute D1 = E1 × (1 − b).
  3. 3Compute growth g = b × r.
  4. 4Check that ke > g. If not, say the model fails.
  5. 5Apply P0 = D1 ÷ (ke − g) and compute the price per share.
  6. 6If the question has several payout ratios, repeat the steps for each and tabulate the prices.
  7. 7State the conclusion: compare r with ke and say which policy maximises price.
  8. 8If E0 is given instead of E1, first find E1 = E0 × (1 + g) only if the question says earnings grow at g. Otherwise read the question wording.

Quickest way: Table method for multiple payout ratios

When to use it: Use when the question asks for share price at different retention ratios, such as 0%, 25%, 50%.

  1. Draw a small table with columns: b, 1 − b, D1, g = br, ke − g, P0.
  2. Fill E1 and r once; they stay constant in all rows.
  3. Compute each row quickly: D1 = E1 × (1 − b), then P0 = D1 ÷ (ke − g).
  4. Look at the pattern: if r > ke, price rises as b rises; if r < ke, it falls.
  5. Write one line of conclusion using this pattern.

Common mistakes in Gordon's Model

  • Using ke − b instead of ke − br

    Students forget that growth is retention times return.

    Fix: Always compute g = b × r first on a separate line, then use ke − g.

  • Using E1 as the dividend

    The formula has E1 in the numerator, and students skip the (1 − b) factor.

    Fix: Dividend is E1 × (1 − b). Check the payout before using the formula.

  • Using percentages without converting

    Writing 15 instead of 0.15 distorts the answer.

    Fix: Convert everything to decimals before subtracting.

  • Ignoring the condition ke > br

    Students plug numbers in without checking.

    Fix: Compute ke − g first. If it is zero or negative, state that the model gives no meaningful value.

  • Mixing up Walter and Gordon formulas

    Both models use a constant r and ke and reach similar conclusions on r versus ke, so students assume the valuation formulas are the same. They are not.

    Fix: Walter: P = (D + r(E − D) ÷ ke) ÷ ke. Gordon: P = E(1 − b) ÷ (ke − br). The r versus ke conclusion is similar, but the formulas differ. Write the formula before substituting.

  • Stating that Gordon says dividend is irrelevant

    Confusion with Modigliani-Miller.

    Fix: Gordon is a relevance theory. Irrelevance belongs to Modigliani-Miller.

Worked examples

Example 1

A company has expected earnings per share of ₹10, cost of equity 12% and return on investment 15%. Find the market price per share using Gordon's model if the retention ratio is (a) 40% and (b) 60%.

Show the solution
  1. Given: E1 = ₹10, ke = 0.12, r = 0.15.
  2. Case (a): b = 0.40. D1 = 10 × 0.60 = ₹6.
  3. g = 0.40 × 0.15 = 0.06.
  4. ke − g = 0.12 − 0.06 = 0.06.
  5. P0 = 6 ÷ 0.06 = ₹100.
  6. Case (b): b = 0.60. D1 = 10 × 0.40 = ₹4.
  7. g = 0.60 × 0.15 = 0.09.
  8. ke − g = 0.12 − 0.09 = 0.03.
  9. P0 = 4 ÷ 0.03 = ₹133.33 (approx.).
  10. Since r (15%) > ke (12%), a higher retention raises the price.

Answer: (a) ₹100; (b) ₹133.33 approx. Retention of 60% is better because r exceeds ke.

Example 2

A firm has EPS of ₹20 expected next year, ke of 10% and r of 8%. Using Gordon's model, find the price at retention ratios of 25% and 50%. State the optimal policy.

Show the solution
  1. Given: E1 = ₹20, ke = 0.10, r = 0.08.
  2. At b = 0.25: D1 = 20 × 0.75 = ₹15.
  3. g = 0.25 × 0.08 = 0.02.
  4. ke − g = 0.10 − 0.02 = 0.08.
  5. P0 = 15 ÷ 0.08 = ₹187.50.
  6. At b = 0.50: D1 = 20 × 0.50 = ₹10.
  7. g = 0.50 × 0.08 = 0.04.
  8. ke − g = 0.10 − 0.04 = 0.06.
  9. P0 = 10 ÷ 0.06 = ₹166.67 (approx.).
  10. Price falls as retention rises because r (8%) < ke (10%).
  11. So the firm should distribute more; zero retention gives 20 ÷ 0.10 = ₹200, the highest.

Answer: ₹187.50 at 25% retention and ₹166.67 approx. at 50%. As r < ke, the optimal policy is full payout, giving ₹200.

Exam tips

  • Write the formula first, then substitute. Method marks are given even if arithmetic slips.
  • In theory questions, list the assumptions as short numbered points: all-equity, no external financing, constant r and ke, constant retention, perpetual life, ke > g.
  • For a Walter versus Gordon question, make a two-column comparison: both are relevance theories, both assume no external financing, both use constant r and ke, and both give the same r versus ke conclusion. Walter values the share as dividends plus capitalised retained earnings with no explicit growth rate. Gordon uses the growth perpetuity P0 = D1 ÷ (ke − br) and ties dividend preference to risk.
  • Always end a numerical with a conclusion on r versus ke and the optimal payout.

Practice questions from Dividend Decisions

Gordon's Model in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Gordon's Model: frequently asked questions

What is Gordon's model in simple words?

It is a share valuation model that says dividend policy affects share price. The reasoning is that investors prefer certain current dividends to uncertain future capital gains, so in the full argument ke rises with retention. In numericals ke is held constant, and comparing r with ke decides whether more retention or more payout raises the price.

What is the difference between Walter's and Gordon's model?

Both say dividends matter, both assume no external financing, and both use a constant r and ke. Walter values the share as the present value of dividends plus the capitalised value of retained earnings, with no explicit growth rate. Gordon uses a growth perpetuity, P0 = E1(1 − b) ÷ (ke − br), and argues that investors see retained gains as riskier than dividends.

What are the assumptions of Gordon's model?

The firm is all-equity financed and uses only retained earnings for investment. Return r and cost of equity ke are constant, the retention ratio is constant, the firm has an infinite life, ke is greater than br, and taxes are ignored.

What are the main criticisms of Gordon's model?

Its assumptions are unrealistic. Firms use debt and external equity, r and ke change over time, and growth is not constant forever. Modigliani and Miller also argue that dividend policy does not change value when markets are perfect.