A repurchase changes arithmetic before it creates value

Learning goals

• Calculate EPS after the cash repurchase.
• Explain why a smaller share denominator under the assumptions applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 80 minutes, excluding further revision.

Shared case and decision context

A company has earnings 100, 50 shares and surplus cash 200 earning nothing. It buys 10 shares at 20 using cash. Assume no taxes, transaction costs or operating effects. Management says the EPS increase proves value creation.

Economic or professional mechanism

Dividends distribute cash across eligible shares; a repurchase pays selling shareholders and reduces shares outstanding. Under frictionless fairly priced assumptions the distribution changes the division of value rather than creating operating value. Taxes, information, agency costs, constraints and the price paid can matter in practice.

Apply, challenge and communicate

EPS increases from 2 to 2.5 because shares fall to 40 while earnings stay 100. A debt-funded repurchase additionally changes interest expense and leverage. Evaluate distribution sustainability using recurring cash after investment, and distinguish a stable dividend policy from a promise that payments can never fall.

Distinguish distributions and share-count changes

A cash dividend transfers cash from issuer to shareholders; all else equal ex-dividend value falls by the cash distribution before tax and market effects. Stock dividends and splits change share count and per-share figures without by themselves creating enterprise value. A two-for-one split doubles shares and approximately halves price under the simple unchanged-value assumption. Liquidating dividends return capital and must be distinguished from distributions of recurring earnings.

Compare dividend-policy explanations

Dividend irrelevance under restrictive frictionless assumptions contrasts with tax preferences, signaling and agency explanations. Investors can differ in tax status and cash needs, creating clientele effects. A dividend increase can signal confidence but can also constrain investment; context determines interpretation. The irrelevance proposition is a benchmark for isolating frictions, not a claim that payout policy never matters in real markets.

Read payout signals with financing evidence

An unexpected dividend increase may convey management confidence in sustainable cash flow, while a cut can reflect stress or a deliberate funding shift toward valuable investment. Borrowing to preserve a dividend can make the signal less persuasive if operating cash generation is weak. Compare the action with prior guidance, investment opportunities and coverage. A price reaction alone does not reveal the manager’s true private information.

Connect payout with agency costs

Distributing surplus cash can limit managerial spending on negative-NPV projects, but excessive payout can force costly external financing or underinvestment. Creditors can prefer restrictions protecting their claims; shareholders may prefer distributions before risk increases. Evaluate governance, investment opportunities, covenants and liquidity jointly. No single payout ratio minimizes agency costs for every issuer.

Calculate combined corporate and investor taxes

Under a simple classical double-tax system a unit of pretax profit first pays corporate tax Tc and the distributed remainder pays investor dividend tax Td. Combined effective rate is1−(1−Tc)(1−Td), not Tc+Td. For25% corporate and20% investor tax it is40%. Imputation systems credit specified corporate tax to eligible investors, while split-rate systems can apply different corporate rates to distributed and retained income. Actual credits and eligibility require jurisdiction-specific rules.

Compare stable dividends and fixed payout ratios

A constant payout ratio multiplies current earnings by a target percentage, so dividends move with earnings. A stable-dividend policy smooths changes and can partially adjust toward a target. If prior dividend.5, target dividend1.2 and adjustment fraction.25, the next dividend is.675 under that stated rule. Smoothing does not guarantee an uncuttable dividend; cash constraints and investment requirements still bind.

Evaluate payout evidence by market and period

The mix of dividends and repurchases differs across markets, legal regimes, tax systems, issuer maturity and periods. Mature cash-generating firms may distribute more; growing firms may retain cash, but exceptions are common. Any statement of a broad empirical trend requires a dated dataset and definitions distinguishing announced from completed repurchases. A generic classroom example cannot establish today’s global payout trend.

Compare buyback mechanisms and prices

Open-market repurchases buy over time at market prices, while tender offers specify terms for holders to sell and negotiated repurchases target particular holders. Execution certainty, price premium, disclosure, fairness and control effects differ. An authorization is not the same as shares actually repurchased. In evaluating the main case, verify quantity, average price and funding from completed transactions rather than assuming the announced maximum was fully executed.

Recalculate book value after repurchase

Repurchase reduces book equity by cash paid and reduces shares by the quantity acquired, absent other effects. With book equity100,10 shares and2 shares bought at15, equity becomes70 and shares8, so book value per share falls from10 to8.75. Buying above book value lowers book value per share under this simple setup; buying below raises it. This arithmetic does not by itself determine economic value creation.

Compare earnings and cash dividend coverage

Net-income dividend coverage is earnings divided by common cash dividends under the specified definition. Cash coverage can use cash available after necessary investment. If earnings100, cash after reinvestment60 and dividends80, earnings coverage1.25 contrasts with cash coverage.75. Persistent reliance on borrowing to fund the gap is a sustainability concern. Be explicit whether preferred dividends, capital spending or debt payments are included in the selected denominator or cash numerator.

Formula and assumptions

EPS after cash repurchase=unchanged earnings/(initial shares−repurchased shares)

Case analysis with explicit assumptions

1. A company has earnings 100, 50 shares and surplus cash 200 earning nothing. It buys 10 shares at 20 using cash. Assume no taxes, transaction costs or operating effects. Management says the EPS increase proves value creation.
2. Method: EPS after cash repurchase=unchanged earnings/(initial shares−repurchased shares)
3. Case result: 2.50. EPS increases from 2 to 2.5 because shares fall to 40 while earnings stay 100. A debt-funded repurchase additionally changes interest expense and leverage. Evaluate distribution sustainability using recurring cash after investment, and distinguish a stable dividend policy from a promise that payments can never fall.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• EPS growth alone is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov