Financial Management and Strategic Management · Dividend Decision

Dividend Theories: Relevance and Irrelevance for CA Inter

Updated 4 October 2026 · Fact-checked

Dividend theories ask whether the dividend payout changes a firm's value. Walter and Gordon say it does (relevance). Modigliani-Miller says it does not, in perfect markets (irrelevance). To solve a numerical, pick the model, write its formula, substitute D, E, r, Ke, then compare payouts or find the price.

Understand Dividend Theories: Relevance and Irrelevance

A firm earns profit. It can pay it out as dividend or keep it to reinvest. The dividend decision is the choice of how much to pay out. The big question is: does this choice change the value of the firm or the market price of its share?

Relevance theories say yes. Walter and Gordon argue that dividend policy affects share price. Walter links it to the relation between the return on investment (r) and the cost of capital (Ke). Gordon's 'bird in the hand' view holds that investors prefer certain current dividends to uncertain future gains. So Ke rises as retention rises, because future gains are riskier.

Irrelevance theory says no. Modigliani and Miller (MM) argue that value depends only on the earning power and investment decisions of the firm, not on how earnings are split between dividends and retained earnings. This holds under perfect-market assumptions: no taxes, no transaction or flotation costs, rational investors, and a fixed investment policy.

In Walter's model: if r > Ke (a growth firm), lower payout raises price, so the best payout is 0%. If r < Ke (a declining firm), higher payout raises price, so the best payout is 100%. If r = Ke, price does not change with payout, so every payout ratio is equally good and the firm is indifferent. Walter's key assumptions: financing only by retained earnings, constant r and Ke, constant EPS and DPS, and an infinite life.

In Gordon's model, price depends on the next dividend, Ke and the growth rate g = b × r, where b is the retention ratio. The simple formula P0 = E1(1 − b) ÷ (Ke − b × r) is applied with a given, constant Ke. With constant Ke, for r > Ke price rises with retention; for r < Ke, price falls with retention; for r = Ke, it is unchanged. The 'bird in the hand' argument is the reason Gordon says Ke itself may rise with retention, which would work against the price rise. In numericals, use the Ke given in the question.

Key rules to remember

Walter's model: P = [D + (r ÷ Ke) × (E − D)] ÷ Ke; P = market price per share, D = DPS, E = EPS, r = return on investment, Ke = cost of equity. E − D is retained earnings per share.
Gordon's model: P0 = E1 × (1 − b) ÷ (Ke − b × r); E1 = next year's EPS, b = retention ratio, r = return on investment, Ke = cost of equity. Valid only when Ke > b × r. Use the Ke given in the question as a constant; the 'bird in the hand' view says Ke may rise with retention, but the formula is applied with the stated Ke.
Growth rate in Gordon's model: g = b × r; Retention ratio b = 1 − payout ratio. Equivalent form: P0 = D1 ÷ (Ke − g).
MM hypothesis (price): P0 = (D1 + P1) ÷ (1 + Ke); P0 = price now, D1 = dividend at end of year 1, P1 = price at end of year 1. Under perfect markets, P0 does not change with D1.
MM: new shares needed: ΔN = [I − (E − n × D1)] ÷ P1; I = investment, E = earnings, n = existing shares, ΔN = new shares issued, D1 = DPS. Used to show total value is unchanged.
MM: value of firm: nP0 = [(n + ΔN) × P1 − (I − E)] ÷ (1 + Ke); Dividend D1 does not appear. This is the proof of irrelevance.
Walter's optimal payout rule: r > Ke: payout 0%; r < Ke: payout 100%; r = Ke: every payout is equally good; Gives the best policy to maximise share price. When r = Ke the price is the same at every payout, so the firm is indifferent.

How to solve Dividend Theories: Relevance and Irrelevance questions

Use this method for any dividend theory question, numerical or theory.

1Identify the model asked: Walter, Gordon or MM. If the question says 'dividend relevance' with r and Ke, it is Walter or Gordon.
2List the data: EPS (E), DPS (D) or payout ratio, r, Ke, and retention ratio b = 1 − payout.
3Convert payout percentages into rupees per share: D = payout × E.
4Write the formula before substituting. Examiners give marks for it.
5Substitute carefully. For Walter, compute (E − D) first. For Gordon, compute g = b × r first and check Ke > g.
6If asked for the optimum payout, compare r and Ke, then compute price at the options asked and state the best.
7For MM, compute P1 from the given Ke and P0, find new shares ΔN, then show that value is unchanged.
8Write a one-line conclusion: what the result means for dividend policy.

Quickest way: Fast route for MCQs and written answers

When to use it: Use under time pressure, especially for MCQs on dividend theories and for 5 to 8 mark numericals.

MCQ shortcut: compare r with Ke first. r > Ke means retain (payout 0%). r < Ke means distribute (100%). r = Ke means indifferent. This answers many conceptual MCQs without calculation.
For Walter, split the price into two parts: D ÷ Ke and (r ÷ Ke) × (E − D) ÷ Ke. Calculate each separately to avoid slips.
For Gordon, compute the denominator Ke − b × r first. If it is zero or negative, the model fails.
In MCQs, eliminate options that mix models, such as 'MM says higher dividends raise price'.
Written format: Model name, formula, substitution, answer in rupees, one-line interpretation. This earns step marks even if arithmetic slips.

Common mistakes in Dividend Theories: Relevance and Irrelevance

Using E instead of E − D in Walter's retained-earnings term.
The formula looks like it uses EPS twice, so students plug in E.
Fix: Underline E − D as retained earnings per share. Compute it on its own line before substituting.
Writing Ke as a whole number such as 12 instead of 0.12.
Percentages are copied directly from the question.
Fix: Convert every rate to decimals before substituting. Check that the price is reasonable.
In Gordon's model, using the payout ratio instead of the retention ratio in g = b × r.
Students confuse b with the dividend payout.
Fix: Remember b means 'burn into the business', i.e. retention. b = 1 − payout. The dividend in the numerator is E1 × (1 − b).
Claiming MM says dividends never matter in any situation.
The summary is learned without the assumptions.
Fix: Always add 'in perfect capital markets: no taxes, no transaction costs, rational investors, fixed investment policy'.
Stating Walter's optimum payout as 'high' or 'low' instead of 0% or 100%.
The model's conclusion is remembered loosely.
Fix: Write the exact rule: r > Ke gives 0% payout, r < Ke gives 100% payout, r = Ke means every payout ratio is equally good, so the firm is indifferent.
Treating Walter and Gordon as the same model in a difference question.
Both are relevance theories with r and Ke.
Fix: Distinguish them clearly. Walter takes constant r and Ke and values retained earnings at the return r. Gordon capitalises the expected dividend at (Ke − g), with growth g = b × r.

Worked examples

Example 1

A firm has EPS ₹10, r = 15% and Ke = 10%. Using Walter's model, find the market price per share if the dividend payout is (a) 40% and (b) 100%. State the optimum payout.

Show the solution

Since r (15%) > Ke (10%), this is a growth firm, so a low payout should raise price.
(a) D = 40% × 10 = ₹4. E − D = ₹6.
P = [4 + (0.15 ÷ 0.10) × 6] ÷ 0.10 = [4 + 1.5 × 6] ÷ 0.10 = [4 + 9] ÷ 0.10 = 13 ÷ 0.10 = ₹130.
(b) D = ₹10. E − D = 0.
P = [10 + 0] ÷ 0.10 = ₹100.
Price falls as payout rises, which matches r > Ke.

Answer: Price is ₹130 at 40% payout and ₹100 at 100% payout. The optimum payout is 0%, because r > Ke.

Example 2

A company has EPS of ₹20 expected next year, Ke = 12%, r = 15%. Using Gordon's model, find the price per share if the retention ratio is (a) 40% and (b) 60%.

Show the solution

Use P0 = E1 × (1 − b) ÷ (Ke − b × r).
(a) b = 0.40. Dividend = 20 × 0.60 = ₹12. g = 0.40 × 0.15 = 0.06.
P0 = 12 ÷ (0.12 − 0.06) = 12 ÷ 0.06 = ₹200.
(b) b = 0.60. Dividend = 20 × 0.40 = ₹8. g = 0.60 × 0.15 = 0.09.
P0 = 8 ÷ (0.12 − 0.09) = 8 ÷ 0.03 = ₹266.67 (approx).
Check Ke > g in both cases: 0.12 > 0.06 and 0.12 > 0.09. Valid.
Price rises with retention because r (15%) > Ke (12%), with Ke held constant at 12%.

Answer: Price is ₹200 at 40% retention and about ₹266.67 at 60% retention. With Ke held constant, higher retention increases price since r > Ke.

Exam tips

Know the assumptions of each model. Theory questions often ask for 'assumptions and criticisms of Walter, Gordon or MM' as a short written answer.
Always begin with the r versus Ke comparison. It tells you the direction of your answer and helps you catch calculation errors.
Learn the difference between Walter and Gordon as a short table-style list in words: price basis, treatment of growth, and role of Ke.
For MM numericals, show each step: P1, ΔN, then value. Marks are given for the process.
MCQs have no negative marking, so attempt every one. Use the r versus Ke rule to eliminate wrong options.

Practice questions from Dividend Decision

Dividend Theories: Relevance and Irrelevance in other exams

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

Dividend Theories: Relevance and Irrelevance: frequently asked questions

What is the main difference between Walter's and Gordon's models?

Both say dividend policy affects value. Walter values the share using dividend plus the return earned on retained earnings, discounted at Ke. Gordon values the share as the next dividend capitalised at (Ke − g), where g = b × r.

Why does MM say dividends are irrelevant?

In perfect markets, a firm's value depends on its earning power and investments. If a firm pays more dividend, it raises new shares to fund investment, and the fall in ex-dividend price offsets the dividend. So shareholder wealth is unchanged.

What happens in Walter's model when r equals Ke?

The share price is the same at every payout ratio. Every payout is equally good, so the firm is indifferent between retaining and distributing.

Do I need to remember the criticisms of these models?

Yes, for descriptive questions. Walter is criticised for assuming no external financing and constant r and Ke. MM is criticised for assuming perfect markets, ignoring taxes, flotation costs and investor preference for current income.