Financial Management and Business Data Analytics · Dividend Decisions and Dividend Theories

Gordon's Model of Dividend Theory Explained

Updated 10 October 2026 · Fact-checked

Gordon's model says a share's value depends on its dividends. It is a bird-in-the-hand theory: P0 = E1 × (1 − b) ÷ (ke − br), where b is the retention ratio, r the return on investment and br the growth rate. Find E1, b, r and ke, check ke > br, then substitute.

Understand Gordon's Model

Gordon's model is a dividend relevance theory. It says the dividend policy of a firm changes the market price of its shares. So the dividend decision matters to shareholders.

The core idea is the bird-in-the-hand argument. Investors prefer a sure dividend today over an uncertain capital gain later. They see future gains as riskier, so they discount them at a higher rate. A firm that retains more earnings therefore makes its shares riskier in the eyes of investors, and the required return (ke) rises.

The model rests on the dividend growth idea. If a firm retains a fraction b of earnings and earns return r on retained funds, earnings and dividends grow at g = b × r. Share price is the present value of all future dividends, which for a constant growth rate gives P0 = D1 ÷ (ke − g). Here D1 = E1 × (1 − b).

The usual assumptions are: the firm is all-equity financed, there is no external financing, r and ke are constant, the firm has perpetual life, taxes are ignored, the retention ratio is constant so growth is constant, and ke > g (that is, ke > br).

The effect of retention depends on r versus ke. If r > ke, a higher retention raises price, because the firm reinvests at a better rate than investors can. If r < ke, a higher payout raises price. If r = ke, price does not change with payout. Note that Gordon's own view says ke itself rises with retention, so in his argument payout is generally favoured. In exam numericals, ke is usually given as fixed.

Compared with Walter's model: both are relevance theories and both use r, ke and retention. Walter's model, P = [D + (r ÷ ke)(E − D)] ÷ ke, values a share as the dividend plus the capitalised value of retained earnings. It assumes r and ke are constant and has no growth term. Gordon uses a constant growth rate g = br and the dividend growth formula, and he argues that ke rises as retention rises.

Key rules to remember

Share price (Gordon): P0 = E1 × (1 − b) ÷ (ke − br); E1 is next year's EPS, b the retention ratio, r the return on investment, ke the cost of equity. Valid only when ke > br.
Dividend per share: D1 = E1 × (1 − b); Payout ratio = 1 − b. If D1 is given directly, use P0 = D1 ÷ (ke − g).
Growth rate: g = b × r; b is a fraction, r a decimal. For example, b = 0.4 and r = 0.15 give g = 0.06.
Retention ratio: b = 1 − (D ÷ E); Retention is the part of earnings not paid as dividends.
Effect of payout: r > ke: retain more raises P0. r < ke: pay more raises P0. r = ke: P0 is unchanged; This is the decision rule when ke is held constant.

How to solve Gordon's Model questions

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

1Write down the given data: E (or E0), D, b or payout ratio, r, ke. Note whether the earnings given are current (E0) or next year's (E1).
2If E0 is given, find E1 only if the question says earnings grow. Otherwise follow the question's wording and state your assumption.
3Compute the retention ratio b and the payout ratio (1 − b).
4Compute the growth rate g = b × r, in decimals.
5Check that ke > g. If not, the formula does not work, so say so.
6Compute D1 = E1 × (1 − b).
7Compute P0 = D1 ÷ (ke − g).
8For policy questions, repeat for each payout ratio, compare prices, and conclude with the r versus ke rule.

Quickest way: One-line substitution

When to use it: For MCQs and short numericals where E1, b, r and ke are all given.

Convert all percentages to decimals first.
Find g = b × r in one line.
Find the denominator ke − g.
Find the numerator E1 × (1 − b).
Divide. Check that the answer is sensible: a higher payout with r < ke should give a higher price.

Common mistakes in Gordon's Model

Using the retention ratio instead of the payout ratio in the numerator
Students see b in the formula and put E1 × b.
Fix: Dividend is the part not retained. Always use E1 × (1 − b).
Forgetting that growth g = b × r, and using r as the growth rate
The terms r and g are confused.
Fix: Compute g = b × r first. The denominator is ke − g, never ke − r.
Not converting percentages to decimals
Working in a hurry with 15% and 0.40 together.
Fix: Write every rate as a decimal before substituting, such as 0.15 and 0.40.
Ignoring the condition ke > br
Students substitute without checking.
Fix: Check the denominator is positive. If ke ≤ br, the model gives no meaningful price.
Mixing up Walter's and Gordon's formulas
Both use r, ke and retention.
Fix: Gordon: P0 = E1(1 − b) ÷ (ke − br). Walter: P = [D + (r ÷ ke)(E − D)] ÷ ke. Gordon has a growth term, Walter does not.
Using E0 as E1 without comment
The question gives current EPS only.
Fix: Follow the question's wording. If E1 is not stated, state your assumption clearly and use the given EPS if no growth is mentioned.

Worked examples

Example 1

A company expects EPS of ₹10 next year. Its retention ratio is 40%, return on investment is 15% and cost of equity is 12%. Find the share price using Gordon's model.

Show the solution

b = 0.40, r = 0.15, ke = 0.12, E1 = ₹10.
g = b × r = 0.40 × 0.15 = 0.06.
Check: ke = 0.12 > g = 0.06, so the model is valid.
D1 = 10 × (1 − 0.40) = ₹6.
P0 = 6 ÷ (0.12 − 0.06) = 6 ÷ 0.06 = ₹100.

Answer: The share price is ₹100.

Example 2

Meera Textiles has expected EPS of ₹20, r = 16% and ke = 12%. Compare the share price at payout ratios of 40% and 80%, and state which policy is better.

Show the solution

Case 1: payout 40%, so b = 0.60. g = 0.60 × 0.16 = 0.096. Check: ke = 0.12 > 0.096, so the model is valid.
D1 = 20 × 0.40 = ₹8. P0 = 8 ÷ (0.12 − 0.096) = 8 ÷ 0.024 = ₹333.33.
Case 2: payout 80%, so b = 0.20. g = 0.20 × 0.16 = 0.032. Check: ke = 0.12 > 0.032, so the model is valid.
D1 = 20 × 0.80 = ₹16. P0 = 16 ÷ (0.12 − 0.032) = 16 ÷ 0.088 = ₹181.82.
Since r (16%) > ke (12%), the price falls as payout rises: ₹333.33 at 40% payout against ₹181.82 at 80%.

Answer: At 40% payout the price is ₹333.33 and at 80% payout it is ₹181.82. Because r > ke, retaining more earnings is better, so the 40% payout policy is preferred.

Exam tips

Always write the formula first and state the assumption ke > br. It earns step marks even if arithmetic slips.
Check whether the question gives E1 or E0. Use what the wording supports and say so.
In theory questions, link the bird-in-the-hand idea to the fact that investors treat retained earnings as riskier.
For comparison questions, use a small table of payout ratio, g, D1 and P0, then conclude with the r versus ke rule.
For difference-between-Walter-and-Gordon questions, give points: growth term, valuation basis and the treatment of ke.

Practice questions from Dividend Decisions and Dividend Theories

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 the bird-in-the-hand theory in Gordon's model?

It says investors prefer a sure dividend now to an uncertain future capital gain. Retained earnings are seen as riskier, so a firm that retains more faces a higher required return. That is why dividends are relevant to share value.

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

Both say dividends affect value. Walter discounts the dividend plus the capitalised value of retained earnings, assuming r and ke are constant, with no growth term. Gordon uses the dividend growth formula P0 = D1 ÷ (ke − g) with g = br, and argues that ke rises as retention rises.

Why must ke be greater than br in Gordon's model?

The denominator is ke − br. If ke equals br, the price is infinite. If ke is less than br, the price is negative. Neither result is meaningful, so the model needs ke > br.

Is Gordon's model the same as the Gordon growth model?

They use the same dividend growth logic, P0 = D1 ÷ (ke − g). In the dividend policy chapter the model is framed with retention, so g = br and D1 = E1(1 − b).