A mixed offer is a fixed amount of cash plus a floating amount of stock. The value per share, the premium, the dilution, and what proration does to holders who elect cash.
A cash-and-stock offer is worth the cash per share plus the exchange ratio times the acquirer's share price. An offer of 18.00 in cash plus 0.40 acquirer shares, with the acquirer at 45.00, is worth 36.00 a share, a 28.6 per cent premium to a 28.00 unaffected price. Half of it floats: if the acquirer falls to 40.00 before closing, the offer is worth 34.00 and the premium 21.4 per cent.
Worked in full in Mergers and Acquisitions by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An acquirer pays partly in cash and partly in shares to balance three constraints: how much debt it can raise, how much dilution its own shareholders will accept, and how much of the deal's risk it wants the target's shareholders to keep. For the target's board the question is simpler and harder: what is the offer worth today, and how much of that is guaranteed. The arithmetic below answers both, and then follows what happens when shareholders may choose their mix.
| Item | Value |
|---|---|
| Cash per target share | 18.00 |
| Acquirer shares per target share | 0.40 |
| Acquirer share price at announcement | 45.00 |
| Target unaffected share price | 28.00 |
| Target shares outstanding | 60,000,000 |
| Acquirer shares outstanding | 200,000,000 |
Offer value = 18.00 + 0.40 × 45.00 = 18.00 + 18.00 = 36.00
Premium = 36.00 / 28.00 − 1 = 28.6%
Cash share of the consideration = 18.00 / 36.00 = 50.0%
Excel: =Cash+Ratio*AcqPrice and =(Cash+Ratio*AcqPrice)/Unaffected-1
The premium should be measured against an unaffected price, before any leak or rumour, exactly as for a cash offer; see how to calculate a control premium.
Cash = 18.00 × 60,000,000 = 1,080,000,000
New shares = 0.40 × 60,000,000 = 24,000,000
Target holders' share of the combined company = 24,000,000 / (200,000,000 + 24,000,000) = 10.71%
Equity value of the offer at 45.00 = 2,160,000,000
The cash is fixed. The share count is fixed. Only the value of the share component moves, and with it the headline price and the premium.
| Acquirer price | Mixed offer | Premium | Cash elector, prorated | Stock elector |
|---|---|---|---|---|
| 35.00 | 32.00 | 14.3% | 33.00 | 28.00 |
| 40.00 | 34.00 | 21.4% | 34.50 | 32.00 |
| 45.00 | 36.00 | 28.6% | 36.00 | 36.00 |
| 50.00 | 38.00 | 35.7% | 37.50 | 40.00 |
| 55.00 | 40.00 | 42.9% | 39.00 | 44.00 |
The mixed offer moves 0.40 for each 1.00 on the acquirer's price. The cash cushions it: the acquirer would have to fall to 25.00, 44.4 per cent below 45.00, before the offer was worth no more than the unaffected price. In an all-stock deal of the same value, 0.80 shares, it would only take a fall to 35.00.
Many mixed deals let each holder elect all cash or all stock, subject to a fixed total. Suppose the agreement offers 36.00 in cash or 0.8000 shares per target share, with the cash pool capped at the 1,080,000,000 of the standard mix. That pool pays 36.00 on 30,000,000 shares, 50.0 per cent of the total.
If 80% of holders elect cash: proration factor = 50.0% / 80% = 62.5%
Each cash elector receives cash on 62.5% of their shares and stock on 37.5%
Per share: 0.625 × 36.00 = 22.50 in cash + 0.375 × 0.8000 = 0.3000 shares
Stock electors receive 0.8000 shares, undiluted by the proration
At 45.00 everyone receives 36.00. Away from it they do not: the cash elector holds 0.3000 shares, the stock elector 0.8000, so at 40.00 they receive 34.50 and 32.00. Whether a holder should elect cash therefore depends on where the acquirer's price is expected to be at closing, and on tax, since cash is usually taxable at once and stock may roll over.
Many agreements equalise the elections instead, setting the cash and stock alternatives by reference to the acquirer's average price over a window before closing. Then every holder receives the same value whatever they elect, and proration changes only the mix of cash and shares, which still matters for tax and for how much of the acquirer each holder ends up owning.
Treating the announced 36.00 as a fixed price. It is 36.00 on the day of announcement only. A fairness analysis, a merger arbitrage spread or a board's comparison with a competing all-cash bid must value the stock component at the acquirer's price at the time, and recognise that the 18.00 of stock is a claim on a combined company whose own value depends on the synergies and the financing. The exchange ratio side of that calculation is worked in how to calculate the exchange ratio in a stock merger.
The book sets out the seven prices one deal can be quoted at and which of them is true; the free workbooks for the case carry the funding, the dilution and the accretion conventions side by side.
Value the offer at the acquirer's current price, then divide by the target's unaffected price and subtract one. 18.00 of cash plus 0.40 shares at 45.00 is 36.00, a 28.6 per cent premium to 28.00. The premium is not fixed: at an acquirer price of 40.00 the offer is 34.00 and the premium 21.4 per cent.
When holders can choose cash or stock but the total cash is capped, oversubscribed elections are scaled back. In the worked case the cash pool covers 50.0 per cent of the shares; if 80 per cent elect cash, each cash elector receives cash on 62.5 per cent of their shares and stock on the other 37.5 per cent.
Only the stock part moves. With 0.40 shares per target share, each 1.00 change in the acquirer's price moves the offer by 0.40. A holder who elected all stock at 0.80 shares moves twice as much, and the offer only falls back to the 28.00 unaffected price if the acquirer drops to 25.00, a 44.4 per cent fall.
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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