Dividend Decisions and Dividend Theories: formula sheet

Key formulas

Retained earnings for the year

Retained earnings = PAT − Dividends

Use total dividend on equity, after preference dividend if asked for equity retention.

Dividend payout ratio

Payout ratio = Dividend per share ÷ Earnings per share

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

Retention ratio

Retention ratio = Retained earnings ÷ Net profit after tax

A higher ratio suggests growth needs or liquidity constraints.

Classification of factors

Internal: profitability, liquidity, growth, debt repayment, control. External: law, contracts, tax, market conditions, shareholder expectations

Use this as your answer skeleton.

Cash available for dividend

Cash available = Closing cash − minimum cash balance needed − committed outflows

A simple check of capacity to pay, not a formal ICMAI formula.

Dividend per share

DPS = Total dividend ÷ Number of equity shares

Use shares outstanding on which dividend is payable.

Constant payout ratio

Dividend = Payout ratio × Profit after tax (available to equity)

Payout ratio = DPS ÷ EPS. DPS changes whenever EPS changes.

Retention ratio

Retention ratio = 1 − Payout ratio

Equals retained earnings ÷ earnings.

Residual dividend

Dividend = Net income − (Equity share of new investment) = Net income − (Target equity % × Capital budget)

If the result is negative, dividend is nil and extra equity is needed. Assumes the company keeps its target debt-equity mix.

Walter's share price

P = [D + (r ÷ Ke) × (E − D)] ÷ Ke

P = market price per share, D = DPS, E = EPS, r = return on investment, Ke = cost of equity. Use r and Ke as decimals.

Equivalent form with payout

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

Payout ratio = D ÷ E. Retention ratio = 1 − payout ratio. Use this to find D from a given payout ratio.

Decision rule: growth firm

r > Ke ⇒ optimum payout = 0%

Price falls as payout rises. Retain everything.

Decision rule: normal firm

r = Ke ⇒ price unchanged at any payout

Price equals E ÷ Ke. No optimum payout.

Decision rule: declining firm

r < Ke ⇒ optimum payout = 100%

Price rises with payout. Distribute all earnings.

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.

MM share price at start of year

P0 = (D1 + P1) ÷ (1 + ke)

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

Funds to be raised by new issue

ΔnP1 = I − (E − nD1)

I = total investment, E = total net profit of the year, n = existing shares, D1 = dividend per share, Δn = number of new shares. Equivalent form: Δn × P1 = I − E + nD1.

Number of new shares

Δn = [I − (E − nD1)] ÷ P1

Use the P1 found from the first formula, not P0.

Value of the firm

nP0 = [(n + Δn)P1 − I + E] ÷ (1 + ke)

This value is the same for any dividend D1, which proves irrelevance.

Value using existing shares only

nP0 = n(D1 + P1) ÷ (1 + ke) when no new shares are needed (Δn = 0 and funds are enough)

Use only when retained earnings cover the investment fully.

Tax preference condition

Effective tax on dividends > effective tax on capital gains ⇒ investors prefer retention

A conceptual rule, not a formula. Always state it as depending on the prevailing tax rates.

Post-tax dividend received

Post-tax dividend = Dividend × (1 − tax rate)

Use for numerical comparison of dividend income and capital gain after tax.

Post-tax capital gain

Post-tax gain = Gain × (1 − capital gains tax rate)

Compare with post-tax dividend of the same pre-tax amount.

Signalling reading

Dividend increase ⇒ favourable signal; dividend cut ⇒ unfavourable signal

Holds under information asymmetry. The share price reacts to the information content.

Clientele effect reading

Payout policy ⇒ attracts investors whose tax position and income needs match it

Change in policy leads to shifts between investor groups.

Quick revision

• A dividend decision is the split of profit between payout and retention.
• Retained earnings are an internal source of finance, so dividend policy affects financing.
• Common forms: cash dividend, bonus shares, stock split and buy-back each work differently.
• Factors include profitability, liquidity, growth needs, taxes, legal limits, and shareholder expectations.
• Main policy types: stable, constant payout ratio, residual and no dividend.
• Walter: if r > k, a lower payout raises share value; if r < k, a higher payout does; if r = k, payout does not matter.
• Gordon: share value depends on dividend, k and growth g, and retention affects g through g = b × r.
• Walter and Gordon both treat dividend policy as relevant to value.
• MM: in a perfect market, value depends on earning power and investment policy, not on payout.
• MM assumes no taxes, no transaction costs, rational investors and a fixed investment policy.
• Tax preference: if dividends are taxed more heavily than gains, investors may prefer retention.
• Signalling: a dividend change can convey management's view of future earnings.

Common mistakes

• Saying a bonus issue brings cash to shareholders or the company. Fix: Remember bonus shares are free shares issued by capitalising reserves. No cash moves.
• Showing share capital increasing in a stock split. Fix: Multiply: shares × new face value gives the same total. Capital is unchanged.
• Treating profit as the same as cash available for dividend. Fix: State that dividends need cash. A profitable firm with weak liquidity may pay little or issue bonus shares.
• Saying a growing firm should pay high dividends. Fix: Explain that high growth needs usually mean higher retention and lower payout.
• Treating stable and constant payout policies as the same thing. Fix: Stable fixes the amount (DPS). Constant payout fixes the percentage of profit. Only the second makes DPS move with EPS.
• In the residual policy, deducting the whole capital budget from earnings. Fix: Deduct only the equity portion: target equity % × capital budget.
• Using the wrong sign comparison and recommending dividends for a growth firm. Fix: Say it aloud: r > Ke means retain. r < Ke means distribute. r = Ke means indifferent.
• Putting E instead of (E − D) in the retention term. Fix: Only retained earnings are reinvested. Always write E − D as a separate line before substituting.
• Using the retention ratio instead of the payout ratio in the numerator 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 Fix: Compute g = b × r first. The denominator is ke − g, never ke − r.

Exam tips

• In MCQs, first ask whether cash leaves the company. That removes two options quickly.
• For bonus questions, always show the transfer from reserves to share capital in your working.
• Write one line of interpretation, for example no cash outflow and total equity unchanged, to earn the step mark.
• For buyback versus dividend theory questions, compare who receives cash, effect on shares and effect on EPS.
• Always organise the answer as internal and external factors; examiners look for this structure.
• In case questions, link each fact in the case to a named factor and say whether it raises or lowers dividend.
• For MCQs, remember: more growth, less liquidity or tighter covenants mean lower dividend; stable earnings mean higher dividend.
• Do not quote tax rates unless the question gives them; explain the principle only.