6.2 Share Repurchases: Methods, EPS and Book Value Effects & Payout Sustainability

6.2 Share Repurchases: Methods, EPS and Book Value Effects & Payout Sustainability

How this fits: section 6.1 covered dividends. This section covers the repurchase learning outcomes of the same module, and the two coverage ratios that answer the "can this payout be sustained" question for both forms together.

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1. The Four Repurchase Methods

The Dutch auction is the one most often examined, because candidates forget that every accepted shareholder receives the same clearing price, not the price they individually bid.

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2. Effect of a Repurchase on Earnings Per Share

The decision rule is a comparison between the cost of the funds used and the earnings yield of the stock, $E/P$.

Financed with surplus cash

Repurchasing with cash forgoes the after-tax interest that cash was earning:

$\text{New } EPS = \frac{\text{Net income} - (\text{Funds used} \times \text{after-tax return forgone})}{\text{Shares outstanding} - \text{Shares repurchased}}$

• If the after-tax return forgone < earnings yield ($E/P$), EPS rises.
• If the after-tax return forgone > earnings yield, EPS falls.

Worked example. A company has net income of 60m, 20m shares (EPS 3.00), a share price of 25.00, and 50m of surplus cash earning 4.0% pre-tax with a 25% tax rate.

• After-tax return forgone: $4.0% \times (1 - 0.25) = 3.0%$
• Earnings yield: $3.00 / 25.00 = 12.0%$
• Shares repurchased: $50\text{m} / 25.00 = 2.0\text{m}$; remaining shares $= 18.0\text{m}$
• Forgone after-tax income: $50\text{m} \times 3.0% = 1.5\text{m}$; new net income $= 58.5\text{m}$
• New EPS $= 58.5 / 18.0 = 3.25$, up from 3.00

The 3.0% after-tax return forgone is far below the 12.0% earnings yield, so EPS rises — which the rule predicted before any arithmetic.

Financed with debt

$\text{New } EPS = \frac{\text{Net income} - (\text{Debt raised} \times \text{after-tax cost of debt})}{\text{Shares outstanding} - \text{Shares repurchased}}$

• If the after-tax cost of debt < earnings yield, EPS rises; otherwise it falls.

Same company, funding the 50m buyback with debt at 7.0% pre-tax:

• After-tax cost: $7.0% \times 0.75 = 5.25%$; interest after tax $= 50\text{m} \times 5.25% = 2.625\text{m}$
• New net income: $60 - 2.625 = 57.375\text{m}$; shares 18.0m
• New EPS $= 57.375 / 18.0 = 3.19$, still above 3.00 because 5.25% < 12.0%

The critical caution the exam wants stated: a rise in EPS from a debt-financed repurchase is not evidence of value creation. Leverage has increased, so equity risk and the required return have increased, and the higher EPS is discounted at a higher rate. EPS accretion is an accounting outcome, not a valuation conclusion.

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3. Effect of a Repurchase on Book Value Per Share

$\text{New } BVPS = \frac{\text{Book value of equity} - \text{Cash spent on repurchase}}{\text{Shares outstanding} - \text{Shares repurchased}}$

The rule is simple and symmetric:

• Repurchasing above the existing BVPS reduces BVPS;
• Repurchasing below the existing BVPS increases BVPS.

Example. Equity book value 400m, 20m shares, so BVPS = 20.00. The company repurchases 2m shares at 25.00 (above BVPS), spending 50m.

• New book value: $400 - 50 = 350\text{m}$; new shares 18.0m
• New BVPS $= 350 / 18.0 = 19.44$, down from 20.00

Had the share price been 15.00, spending 30m for 2m shares would leave $370/18.0 = 20.56$, an increase. This is why repurchase announcements by companies trading below book — banks in particular — are treated differently from those by companies trading at a large premium to book.

4. Dividends versus Repurchases: Equivalence and Difference

Under a strict set of assumptions — the repurchase is executed at market price, taxes on dividends and capital gains are identical, and information is symmetric — a repurchase and a cash dividend of equal total value leave shareholders equally well off. The shareholder who wants cash sells shares; the shareholder who does not, holds and ends up with a larger proportional stake.

Demonstration. A company with 10m shares at 20.00 (market capitalisation 200m) has 20m to distribute.

• Cash dividend of 2.00 per share: shareholder with 100 shares receives 200 cash and holds 100 shares now worth 18.00 each, total 2,000.
• Repurchase of 1m shares at 20.00: 9m shares remain and equity value is 180m, so the price stays at 20.00. The shareholder who sells 10 shares receives 200 and holds 90 shares worth 20.00, total 2,000.

Identical. Now the real-world differences:

A caution the curriculum stresses: a repurchase used purely to offset dilution from share-based compensation is not a distribution to shareholders at all — it is a cash cost of compensation. Analysts should measure net repurchases, after issuance, when assessing the true payout.

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5. Payout Sustainability: The Two Coverage Ratios

Dividend coverage based on net income

$\text{Dividend coverage} = \frac{\text{Net income}}{\text{Dividends}}$

This is the reciprocal of the payout ratio. It is a weak measure because net income includes non-cash items and ignores the reinvestment the business requires.

Coverage based on free cash flow to equity

$\text{FCFE coverage} = \frac{FCFE}{\text{Dividends} + \text{Share repurchases}}$

This is the ratio that answers the question. It compares the cash actually available to equity holders after working capital, capital expenditure, and net debt movements with the total cash returned, dividends and repurchases together.

• A ratio above 1.0 means the payout is funded from operations.
• A ratio near or below 1.0, sustained across several years, means the payout is being funded by borrowing or asset sales.

Worked example. A company reports net income of 500, FCFE of 380, dividends of 260, and repurchases of 190.

• Dividend coverage on net income: $500/260 = \textbf{1.92}$ — comfortable-looking
• FCFE coverage of total payout: $380/(260+190) = 380/450 = \textbf{0.84}$

The first ratio suggests a safe dividend; the second shows the company is distributing about 18% more cash than the business generates for equity holders. Repeated over several years this must be funded with debt, and the payout is not sustainable at that level. This contrast is the standard Level II item-set construction — the exhibit gives you both numbers and the question asks which conclusion is supported.

Building the screen

A company at risk of cutting its payout typically shows several of the following together:

1. FCFE coverage below 1.0 for three or more consecutive years;
2. rising net debt with a flat or rising dividend;
3. a payout ratio computed off peak-cycle earnings;
4. covenant headroom shrinking in the debt footnote;
5. repurchases funded by debt while the share price is above book value, so BVPS is falling as well;
6. capital expenditure being cut below depreciation to protect the payout — the clearest sign that the distribution has become the priority over the business.

Level II traps in the repurchase module

1. Comparing the pre-tax cost of debt with the earnings yield. Use the after-tax cost.
2. Concluding that EPS accretion proves value creation in a debt-financed buyback.
3. Assuming a repurchase always raises BVPS; it falls whenever shares are bought above book value.
4. In a Dutch auction, assuming each shareholder receives their own bid price rather than the single clearing price.
5. Using dividend coverage on net income as the sustainability test when repurchases are large; the FCFE-based ratio including repurchases is the correct measure.