Dividend Decisions: formula sheet

Key formulas

Retained earnings

Retained earnings = Profit after tax − Dividends paid

Use this whenever a question gives profit and dividend and asks what is ploughed back.

Dividend payout ratio (D/P ratio)

Payout ratio = Total dividend ÷ Profit after tax × 100 = DPS ÷ EPS × 100

DPS is dividend per share; EPS is earnings per share.

Retention ratio

Retention ratio = 1 − Payout ratio = Retained earnings ÷ Profit after tax

Payout ratio plus retention ratio always equals 100%.

Dividend per share

DPS = Total dividend ÷ Number of equity shares

If dividend is stated as a percentage, apply it to the paid-up face value of the share, not the market price.

Total cash dividend

Total dividend = Dividend per share × Number of shares

If dividend is stated as a percentage, apply it on paid-up (face) value, not on market price.

Dividend per share from rate

DPS = Dividend rate % × Paid-up value per share

A 20% dividend on a ₹10 paid-up share is ₹2.

Bonus shares issued

New shares = Existing shares × Bonus ratio

For 1:2 bonus, ratio is ½. Capitalise: New shares × Face value.

Ex-bonus price (theoretical)

Ex-bonus price = (Old shares × Cum-bonus price) ÷ (Old shares + Bonus shares)

Assumes total market value stays unchanged. It is a theoretical estimate only.

Stock split effect

New shares = Old shares × Split factor; New face value = Old face value ÷ Split factor

Share capital and reserves stay the same.

Ex-dividend price (approx.)

Ex-dividend price ≈ Cum-dividend price − Dividend per share

A simplification that ignores taxes and market effects.

Buyback amount

Buyback outlay = Shares bought back × Buyback price per share

Shares outstanding fall by the number bought back.

Dividend payout ratio

Payout ratio = Dividend ÷ Net profit (or DPS ÷ EPS) × 100

Under constant payout policy, this ratio stays fixed.

Constant payout dividend

Dividend = Fixed payout % × Profit after tax

Dividend moves up and down with profit.

Retention ratio

Retention ratio = 1 − Payout ratio

Retained earnings ÷ Net profit.

Residual dividend

Dividend = Net profit − (Equity share of capital budget)

Equity share = Capital budget × equity % in target capital structure. If the result is negative, dividend is nil.

Walter's share price

P = [D + (r ÷ k) × (E − D)] ÷ k

P = market price per share, D = dividend per share, E = earnings per share, r = return on investment, k = cost of capital (as decimals).

Equivalent form using payout

P = [D + (r ÷ k) × (E − D)] ÷ k, where D = E × payout ratio

Use when the payout ratio is given instead of D.

Retention

Retained earnings per share = E − D

This is the amount that is reinvested at rate r.

Optimal payout rule

r > k: payout 0% | r < k: payout 100% | r = k: any payout

Growth firm, declining firm and normal firm respectively.

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.

MM valuation equation (price)

P0 = (D1 + P1) ÷ (1 + Ke)

P0 = current market price per share, D1 = dividend per share at end of year 1, P1 = market price at end of year 1, Ke = cost of equity (capitalisation rate).

Price at end of year (rearranged)

P1 = P0 × (1 + Ke) − D1

Use this first in most numericals to find the ex-dividend price.

New shares to be issued

ΔN = (I − (E − nD1)) ÷ P1

I = investment required, E = earnings of the period, n = shares at start, D1 = dividend per share, nD1 = total dividend. Use I − E + nD1 in the numerator; it is the same thing.

Value of the firm

nP0 = ((n + ΔN) × P1 − (I − E)) ÷ (1 + Ke)

n = existing shares, ΔN = new shares. The result is the same whatever D1 is.

Quick revision

• Dividend decision means choosing between paying out profit and retaining it for reinvestment.
• Retained earnings are an internal source of finance, so dividend and financing decisions are linked.
• Common forms include cash dividend, bonus shares and other non-cash payouts; know each definition.
• Main policies include stable, constant payout, residual and no-dividend approaches.
• Walter's and Gordon's models treat dividend policy as relevant to share value.
• Walter's model compares the return on investment with the cost of capital to judge the best payout.
• Gordon's model values the share on the dividend, the required return and the growth rate.
• Always list the model's assumptions when asked; they carry marks.
• The Modigliani-Miller hypothesis says dividend policy does not affect firm value under its assumptions, such as perfect markets.
• Write the formula first in every numerical answer, then substitute and conclude.
• Check legal conditions for declaring and paying dividend under the Companies Act, 2013.

Common mistakes

• Treating the dividend decision as only 'how much dividend to declare', ignoring retention. Fix: Always state that the decision splits profit between dividend and retained earnings, and mention the retention ratio.
• Saying higher dividends always maximise shareholder wealth. Fix: Say wealth depends on share value. If retained funds earn more than shareholders' expected return, retention can raise value.
• Saying bonus shares reduce the shareholder's wealth or that a stock dividend is income in cash. Fix: Remember that bonus shares only split the same value across more shares. No cash comes in, and the price per share falls.
• Treating a stock split and bonus issue as the same. Fix: Split changes face value and leaves reserves untouched. Bonus keeps face value and moves reserves into share capital.
• Confusing stable dividend with constant payout ratio. Fix: Stable means a steady amount per share. Constant payout means a steady percentage of profit, so the amount changes.
• In residual policy, subtracting the whole capital budget from profit. Fix: Multiply the budget by the equity share of the target capital structure, then subtract that from profit.
• Using r and k as whole numbers such as 15 and 10 in the formula. Fix: Convert to decimals (0.15, 0.10) before dividing by k. Otherwise the final price is wrong by a factor of 100.
• Using E instead of (E − D) for the retained part. Fix: Always write E − D on its own line first, then multiply by r ÷ k.
• Using ke − b instead of ke − br Fix: Always compute g = b × r first on a separate line, then use ke − g.
• Using E1 as the dividend Fix: Dividend is E1 × (1 − b). Check the payout before using the formula.

Exam tips

• Open every theory answer with a definition and the retention link. It shows you understand the decision, not just a list.
• Group factors as internal and external and add one line of effect for each. Examiners look for structure and reasoning.
• In numericals, show total dividend, DPS, EPS and payout ratio separately so you earn step marks even if one figure slips.
• Keep the legal aspects brief here. Detailed provisions belong to the topic on legal and regulatory aspects of dividend.
• Finish with a conclusion that no single policy fits all companies. It completes the provision-analysis-conclusion pattern.
• Write a short comparison in points for difference questions: source, cash effect, face value, reserves, shareholder wealth.
• For numbers, always show shares, amount capitalised and the before and after balance sheet items.
• Check that reserves are enough before computing any bonus issue.