Dividend Decision: formula sheet

Key formulas

Dividend per share (DPS)

DPS = Total equity dividend ÷ Number of equity shares

Use the number of shares outstanding at the time the dividend is declared.

Earnings per share (EPS)

EPS = (Net profit after tax − Preference dividend) ÷ Number of equity shares

Deduct preference dividend before finding EPS.

Dividend payout ratio

Payout ratio = DPS ÷ EPS × 100 = Total equity dividend ÷ Earnings available to equity × 100

Shows the share of earnings paid out.

Retention ratio

Retention ratio (%) = 100% − Payout ratio (%)

Retained earnings ÷ Earnings available to equity × 100. If you take the payout ratio as a fraction, use 1 − payout ratio instead.

Bonus shares issued

Bonus shares = Existing shares × Bonus ratio

For a 1:4 bonus, holders get 1 new share for every 4 held, so multiply by 1/4.

Theoretical ex-bonus price

Ex-bonus price = Cum-bonus market value of holding ÷ Total shares after bonus

Value of the holding stays the same under the usual assumption of no change in total market value.

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.

Dividend payout ratio

Dividend payout ratio = Dividend per share (DPS) ÷ Earnings per share (EPS)

Shows the share of earnings paid out. Retention ratio = 1 − payout ratio.

Retention ratio

Retention ratio = Retained earnings ÷ Net profit after tax = 1 − payout ratio

A higher retention ratio means more internal funds for growth and a lower dividend.

Direction rule

Higher cash need, higher growth, tighter covenants → lower payout; stable earnings, strong liquidity, shareholder income need → higher payout

A memory aid, not a formula. Apply it using the facts given in the question.

Dividend per share

DPS = Total equity dividend ÷ Number of equity shares

Use this to check whether DPS is stable across years.

Dividend payout ratio

Payout ratio = DPS ÷ EPS = Total dividend ÷ Net profit available to equity

Constant payout policy keeps this ratio fixed.

Constant payout dividend

Dividend = Fixed payout % × Profit after tax (available to equity)

Dividend is nil when profit is nil or a loss.

Residual dividend

Dividend = Profit available − Retained earnings needed for investment (equity portion)

Equity needed = Investment × equity share of target capital structure. If this exceeds profit, dividend is nil and new equity may be raised.

Stock split effect

New number of shares = Old shares × split ratio; new face value = Old face value ÷ split ratio

Total share capital and reserves do not change. Market price per share falls roughly in proportion, all else equal.

Quick revision

• Dividend decision: how much profit to pay out and how much to retain for reinvestment.
• Payout ratio = Dividend ÷ Earnings; retention ratio b = 1 − payout ratio.
• Walter model: P = [D + (r ÷ Ke) × (E − D)] ÷ Ke.
• Walter: if r > Ke, optimal payout is zero; if r < Ke, it is 100%; if r = Ke, dividend is irrelevant.
• Walter assumes only internal financing, constant r and Ke, constant EPS and DPS, and an infinite life.
• Gordon model: P0 = E1 × (1 − b) ÷ (Ke − br), where growth g = br.
• Gordon needs Ke > g, and treats dividends as lowering uncertainty (the bird-in-hand view).
• MM: P0 = (D1 + P1) ÷ (1 + Ke); under its assumptions, dividend policy does not change firm value.
• MM assumptions: perfect capital markets, no taxes, fixed investment policy, no uncertainty.
• MM new shares needed: Δn = [I − (E − n × D1)] ÷ P1.
• Bonus shares move money from reserves to share capital and do not change cash.
• Stability practices: constant DPS, constant payout ratio, stable DPS with extra dividend in good years.

Common mistakes

• Treating a bonus issue as a payment of cash or as income to shareholders. Fix: Remember that a bonus issue only converts reserves into share capital. No cash moves and total shareholder wealth is unchanged.
• Forgetting to deduct preference dividend before calculating EPS and payout. Fix: Always compute earnings available to equity first.
• Using E instead of E − D in Walter's retained-earnings term. 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. Fix: Convert every rate to decimals before substituting. Check that the price is reasonable.
• Listing factors without stating their effect on the dividend. Fix: Add a short phrase to every factor saying whether it increases or decreases the payout and why.
• Treating profit as the only test for paying dividends. Fix: Always check liquidity. A profitable company with little cash cannot comfortably pay a large cash dividend.
• Treating constant payout ratio as a constant dividend amount. Fix: Remember that the ratio is constant, not the rupee dividend. Dividend changes with profit.
• In residual policy, subtracting the whole investment from profit. Fix: Multiply the investment by the equity share of the target capital structure, then subtract that from profit.

Exam tips

• Short notes on types of dividend are common. Cover cash, stock or bonus, and scrip, with the effect of each on cash and reserves.
• In numerical questions, show EPS, DPS and payout as separate lines. Each line can earn a step mark.
• Use the words capitalisation of reserves when you explain bonus shares.
• Learn the dividend dates in order: declaration, then ex-date and record date (the same day under T+1), then payment. A one-line sequence is enough to answer a 2-mark MCQ.
• Always end with a one-line comment on the effect on cash, retention and shareholder wealth.
• 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.