CFA Level II · CFA Level II Exam

Analysis of Dividends and Share Repurchases: formula sheet

Full chapter guide

Key formulas

Post-split share count: New shares = old shares × split ratio (e.g. 3-for-2 → × 1.5); A 2-for-1 split doubles shares. A reverse split of 1-for-4 multiplies shares by 0.25.
Post-split price: New price = old price ÷ split ratio; Assumes no change in total market value. Market cap stays the same.
Stock dividend price: New price = old price ÷ (1 + stock dividend rate); A 10% stock dividend gives 1.10 shares for each old share, so price is divided by 1.10.
Ex-dividend price (simple): Ex-date price ≈ cum-dividend price − dividend per share; Ignores taxes. With taxes, the drop can be less than the full dividend.
Cash dividend effect on equity: Equity falls by total dividend = DPS × shares outstanding; Cash and equity both fall; no effect for stock dividends or splits on total equity.
Dividend date order: Declaration → Ex-dividend → Record → Payment; Under T+2 the ex-date is one business day before the record date. Under T+1 it is the same day as the record date. Date of payment is last.
Ex-dividend price adjustment (MM, no taxes): Ex-dividend price ≈ Cum-dividend price − Dividend per share; Under MM, wealth is unchanged: price falls by the dividend, and the investor holds cash instead.
Homemade dividend: Shares to sell = Desired cash ÷ Ex-dividend share price; Use it to show that an investor can replicate any payout; useful for 'no dividend, but wants cash' cases.
Price drop with tax differential: Price drop ÷ Dividend = (1 − t_d) ÷ (1 − t_cg); Holds for a marginal investor taxed at t_d on dividends and t_cg on gains. If t_d > t_cg, the drop is less than the dividend.
MM irrelevance conditions: No taxes, no transaction or flotation costs, symmetric information, fixed investment policy; If a question changes one of these, MM no longer holds as stated.
After-tax dividend: After-tax dividend = Dividend × (1 − t_d); Use it when comparing dividends with capital gains.
Double taxation: effective tax on distributed profit: 1 − (1 − corporate rate) × (1 − dividend tax rate); Use for profit paid out as dividends. Example: 30% corporate, 20% dividend gives 1 − 0.70 × 0.80 = 44%.
After-tax dividend to shareholder (double taxation): Pre-tax earnings × (1 − t_corp) × (1 − t_div); Multiply the two retention factors. Do not add the tax rates.
Tax imputation system: Shareholder credit = tax already paid by the company on the dividend; With a full credit, the income is effectively taxed once, at the shareholder's marginal rate. The corporate tax is credited against the shareholder's tax.
Split-rate system: Corporate rate on distributed profit < corporate rate on retained profit; Gives the firm an incentive to pay out.
Relative tax preference for dividends: Compare (1 − t_div) with (1 − t_capital gains); If dividend tax is higher, investors favor retention or repurchases. Deferral of gains tax adds to the preference.
Flotation cost effect: Net proceeds = Gross issue × (1 − flotation cost %); Paying dividends then raising equity loses this fraction of every rupee raised.
Shares repurchased: Shares bought = Cash spent ÷ Repurchase price; Use the buyback price, not the pre-announcement price, if they differ.
EPS after buyback: New EPS = (Net income − after-tax cost of funds) ÷ (Old shares − Shares bought); If funded from cash, the cost is the after-tax interest forgone. If borrowed, the after-tax interest expense. If the question ignores funding cost, use old net income.
Earnings yield test: EPS rises if after-tax cost of funds < E/P = 1 ÷ (P/E); Compare the yield on shares bought with the after-tax cost of funds.
BVPS after buyback: New BVPS = (Old equity − Cash spent) ÷ (Old shares − Shares bought); BVPS falls if the buyback price > old BVPS, and rises if the price < old BVPS.
Old BVPS: BVPS = Shareholders' equity ÷ Shares outstanding; Use the share count before the buyback.
Share price after buyback (fair-value case): Post-buyback price = (Pre-buyback market cap − Cash spent) ÷ Remaining shares; If bought at the market price, the price is unchanged, so the wealth effect is neutral.
Dividend payout ratio: Payout ratio = Dividends ÷ Net income to common = DPS ÷ EPS; Retention ratio = 1 − payout ratio. Use earnings after preferred dividends.
Dividend cover: Dividend cover = Net income ÷ Dividends = EPS ÷ DPS = 1 ÷ payout ratio; Higher means a safer dividend. A value below 1 means dividends exceed earnings.
Total payout ratio: Total payout = (Dividends + Share repurchases) ÷ Net income; Use when the firm returns cash through buybacks as well as dividends.
FCFE coverage ratio: FCFE coverage = FCFE ÷ (Dividends + Share repurchases); A value above 1 means payouts are covered by cash flow available to equity.
Constant payout policy: Dividend = Target payout ratio × Current earnings; Dividends move one-for-one in proportion with earnings, so they are volatile.
Residual dividend: Dividend = Net income − (Capital budget × Equity share of financing); If the equity needed exceeds net income, the residual is zero (or the firm issues equity).
Target payout adjustment: Expected dividend = Previous dividend + (Expected increase in earnings × Target payout ratio × Adjustment factor); Adjustment factor = 1 ÷ number of years to reach the target. Works on per-share or total figures.
Dividend payout ratio: Payout ratio = Dividends ÷ Net income; Use common dividends and net income available to common. Retention ratio = 1 − payout ratio.
Dividend coverage ratio: Dividend coverage = Net income ÷ Dividends = 1 ÷ Payout ratio; Higher means safer on an earnings basis.
FCFE coverage ratio: FCFE coverage = FCFE ÷ (Dividends + Share repurchases); Below 1.0 means the payout exceeds FCFE and must be funded from cash on hand, new debt or new equity. Use dividends only if the question says so.
FCFE from net income: FCFE = NI + NCC − FCInv − WCInv + Net borrowing; NCC is non-cash charges, FCInv is fixed capital investment, WCInv is working capital investment.
Sustainable growth rate: g = b × ROE, where b = retention ratio; A higher payout lowers the growth the firm can fund internally.
Dividend irrelevance (MM): Value is unchanged by dividend policy given fixed investment policy; Holds with no taxes, no transaction costs and symmetric information.

Quick revision

Dividend dates run in order: declaration, ex-dividend, holder-of-record, payment. The ex-dividend date is the first day a buyer does not receive the dividend: one business day before the record date under T+2, and the same day as the record date under T+1. Read the vignette for the actual dates.
Stock dividends and splits increase share count but do not change total equity value; a reverse split reduces share count.
Miller and Modigliani: in perfect markets with no taxes or costs, dividend policy does not change firm value.
Tax-disadvantaged dividends favour buybacks and lower payout; low dividend tax favours higher payout.
Flotation costs and investment needs push firms to retain earnings.
Legal and debt covenant limits can cap the dividend a firm may pay.
Buyback shares repurchased = cash used ÷ repurchase price.
If the earnings yield is above the after-tax cost of funds, a buyback raises EPS.
A buyback financed with debt can raise EPS but also raises financial risk.
Payout ratio = dividends ÷ net income; retention rate = 1 − payout ratio.
Dividend cover is the inverse of the payout ratio; compare dividends with FCFE for safety.
A residual policy pays out only what is left after funding positive-NPV projects, so dividends vary.

Common mistakes

Saying a stock dividend or split creates value for shareholders. Fix: Each share is worth proportionally less. Total value and your ownership percentage are unchanged.
Treating a stock dividend and a split as identical in accounting. Fix: A stock dividend transfers an amount from retained earnings to paid-in capital. A split leaves balances unchanged and changes par value per share.
Saying MM implies firms should never pay dividends. Fix: MM says payout does not change value in perfect markets. It makes no claim that zero payout is better.
Applying MM when the vignette mentions taxes or flotation costs. Fix: List the perfect-market conditions first. Any violation means MM is no longer the right answer.
Adding corporate and dividend tax rates under double taxation Fix: Dividends are taxed after corporate tax. Use 1 − (1 − t_corp)(1 − t_div).
Confusing clientele effect with signaling Fix: Clientele is about investors sorting by tax or income needs. Signaling is about managers conveying private information.
Leaving net income unchanged when the question gives a funding cost. Fix: Subtract the after-tax interest forgone or paid from net income before dividing.
Forgetting to apply the tax rate to the interest cost. Fix: Multiply interest by (1 − tax rate) before adjusting net income.
Using total capex instead of the equity portion in the residual model Fix: Multiply the capital budget by the equity percentage first, then subtract from net income.
Leaving out the adjustment factor in the target payout formula Fix: Multiply by 1 ÷ N, where N is the number of years of adjustment, and add to the prior dividend.

Exam tips

Vignettes often give the settlement cycle. Use it to place the ex-date relative to the record date rather than guessing.
Expect a table of before and after shares, price and equity. Check which items change: cash dividends change equity, splits do not.
Watch the wording: 'cum-dividend' means with the dividend, 'ex-dividend' means without it.
Questions on taxes may state that the price drop is less than the dividend. Do not apply the simple rule when told otherwise.
With no penalty for wrong answers, always pick an option. Eliminate any that say a split or stock dividend changes total firm value.
Always check the vignette for taxes, costs or information gaps before choosing MM.
Memorise one-line summaries: MM says no effect, bird-in-the-hand says higher payout is better, tax preference says lower payout is better.
Expect questions that ask which assumption a statement violates; name the assumption, not just the theory.