The break-even is the same either way: synergies equal to the premium. What the method of payment changes is who wins above it and who loses below it.
Pay cash when you are confident the synergies will arrive, and stock when you are not, or when you think your own shares are expensive. In cash the acquirer's shareholders keep all the synergy gain and bear all the risk; in stock they share both with the target's holders. On an illustrative 1,300 million offer at a 300 million premium, the acquirer's shareholder value at risk is 7.50 per cent in cash and 5.66 per cent in stock, and if the 400 million synergy plan is met, cash leaves them 100 million better off against 75.5 million in stock.
Worked in full in Mergers and Acquisitions by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The choice is usually argued on accretion, balance sheet capacity or tax. Those matter, but the first-order question is simpler: who carries the premium if the synergies do not come? Rappaport and Sirower's measure, shareholder value at risk, answers it in one line: the premium as a share of the acquirer's market value, multiplied by the share of the combined company the acquirer's holders will own.
| Input | Acquirer | Target |
|---|---|---|
| Share price before the deal | 40.00 | 20.00 |
| Shares in issue | 100.0 | 50.0 |
| Market value | 4,000 | 1,000 |
| Premium offered | 30.0% | |
| Present value of the synergy plan, net of cost to achieve | 400 |
Both prices are assumed to be fair before the deal, and the cash is assumed to be raised at a fair cost, so the only thing that moves value is the synergies against the premium.
1. Price and premium. Offer 20.00 × 1.30 = 26.00 a share, 1,300 in all; the premium is 300.
2. The stock alternative. At 40.00, paying 1,300 in shares means issuing 32.5 million shares, an exchange ratio of 0.6500. The acquirer's holders keep 100 ÷ 132.5 = 75.47 per cent of the combined company; the target's holders get 24.53 per cent.
3. Shareholder value at risk.
SVAR, cash = premium ÷ acquirer market value = 300 ÷ 4,000 = 7.50%
SVAR, stock = 7.50% × 75.47% = 5.66%
Value to acquirer holders, cash = 4,000 + 1,000 + synergies − 1,300
Value to acquirer holders, stock = 75.47% × (4,000 + 1,000 + synergies)
Excel: =Premium/AcqMV*AcqShares/(AcqShares+Price/AcqPx)
SVAR is the percentage the acquirer's holders lose if the synergies are zero. In stock, the target's holders take 24.53 per cent of that loss, because they own a quarter of the company that overpaid.
| Synergies achieved | Cash: value | Per share | Change | Stock: value | Per share | Change |
|---|---|---|---|---|---|---|
| 0 | 3,700 | 37.00 | −7.50% | 3,773.6 | 37.74 | −5.66% |
| 150 | 3,850 | 38.50 | −3.75% | 3,886.8 | 38.87 | −2.83% |
| 300 (equal to the premium) | 4,000 | 40.00 | 0.00% | 4,000.0 | 40.00 | 0.00% |
| 400 (the plan) | 4,100 | 41.00 | +2.50% | 4,075.5 | 40.75 | +1.89% |
| 600 | 4,300 | 43.00 | +7.50% | 4,226.4 | 42.26 | +5.66% |
The break-even is the same in both columns: synergies equal to the premium. What differs is the slope. In cash, every unit of synergy above or below 300 goes to the acquirer's holders; in stock, 75.47 per cent of it does. If the whole 400 plan fails, the acquirer's holders lose 400 in cash but 301.9 in stock; the target's holders absorb the other 98.1, receiving shares worth 1,226.4 instead of 1,324.5 if the plan had been met, and 73.6 less than the 1,300 they were offered.
So the method of payment is a signal. An acquirer that offers cash is telling the market it believes the synergies; one that insists on stock is asking the seller to underwrite part of them. Sellers know this, which is why stock offers often need a higher headline premium or a collar.
The second reason to pay in stock is that the acquirer's own shares are overvalued. If management believes the shares are worth 36.00, not 40.00, the 32.5 million new shares, valued at 36.00, cost the existing holders 1,170 of true value, not 1,300: a real premium of 170, or 17.0 per cent, instead of 300. That is a saving of 130 against cash. The market knows this too, and an all-stock announcement from an acquirer trading at a high multiple is often read as a statement that its board thinks the shares are rich.
Choosing on accretion alone. Whether cash or stock is more accretive in year one depends only on whether the acquirer's earnings yield is above or below the after-tax cost of debt; it says nothing about who carries the synergy risk. Compute SVAR alongside earnings per share. The second mistake is treating the exchange ratio as the price: once the deal is in stock, the price floats with the acquirer's shares until closing, as shown in how to value a cash-and-stock offer per target share, and the ownership split it creates is worked in how to calculate the exchange ratio in a stock merger.
The book's own deal, priced seven ways with its funding and dilution live, is in the free workbooks for this case.
It is the share of the acquirer's market value lost if no synergies are achieved: the premium divided by the acquirer's market value, times the ownership its holders keep. On the illustrative deal, a 300 premium against a 4,000 acquirer is 7.50 per cent in cash, and 5.66 per cent in stock, where the acquirer's holders keep 75.47 per cent.
Because in stock they keep part of the risk that the buyer overpaid. If the illustrative 400 synergy plan fails entirely, target holders paid in stock receive shares worth 1,226.4: 73.6 less than the 1,300 offered and 98.1 less than if the plan had been met, a quarter of the loss. In cash they keep the full 1,300 whatever happens.
Yes, for the acquirer's existing holders. If shares trading at 40.00 are really worth 36.00, the 32.5 million new shares cost 1,170 of true value rather than 1,300, cutting the real premium from 300 to 170. The market knows this, so an all-stock offer is often read as a sign the board thinks its shares are rich.
This article is one calculation from Mergers and Acquisitions. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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