The ratio, the shares issued and the ownership split, then what a fixed ratio, a fixed value and a collar do when the acquirer's stock falls before closing.
The exchange ratio is the offer price per target share divided by the acquirer's share price: the number of acquirer shares each target share receives. With the target at 25.00, a 30 per cent premium and the acquirer at 40.00, the offer is 32.50 a share and the exchange ratio is 0.8125. That issues 48,750,000 new shares and gives the target's holders 28.89 per cent of the combined company, against the 23.81 per cent their market value alone would earn.
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 ratio is simple to compute. What needs care is what it fixes: a fixed ratio fixes the ownership split and lets the value move with the acquirer's share price; a fixed value does the opposite. Between signing and closing, that choice decides who bears a fall in the acquirer's stock.
| Input | Acquirer | Target |
|---|---|---|
| Share price | 40.00 | 25.00 |
| Diluted shares outstanding | 120,000,000 | 60,000,000 |
| Equity market value | 4,800,000,000 | 1,500,000,000 |
| Premium offered | 30% |
Step 1: the offer price per target share. Apply the premium to the unaffected target price: 25.00 times 1.30 is 32.50, an offer equity value of 1,950,000,000 and a premium of 450,000,000.
Step 2: the exchange ratio.
Exchange ratio = offer price per target share / acquirer share price = 32.50 / 40.00 = 0.8125
Excel: =TargetPrice*(1+Premium)/AcquirerPrice. A quoted ratio can be read backwards: =Ratio*AcquirerPrice/TargetPrice-1 returns the implied premium, here 30.0 per cent.
Step 3: shares issued and ownership. Every one of the 60,000,000 target shares becomes 0.8125 of an acquirer share.
New shares = 60,000,000 × 0.8125 = 48,750,000
Target ownership = 48,750,000 / (120,000,000 + 48,750,000) = 48,750,000 / 168,750,000 = 28.89%
| Holder | Shares | Ownership |
|---|---|---|
| Acquirer's existing shareholders | 120,000,000 | 71.11% |
| Target's shareholders | 48,750,000 | 28.89% |
| Combined company | 168,750,000 | 100% |
Without a premium the ratio would be 0.6250 (25.00 over 40.00), 37,500,000 shares and 23.81 per cent, exactly the target's share of the two market values. The premium is paid in ownership: 5.08 points of the combined company move from the acquirer's holders to the target's. Whether that is a good trade depends on the synergies, which is the test in how to value synergies net of the cost to achieve them.
Suppose the acquirer's shares fall 10 per cent to 36.00 between signing and closing. Under a fixed ratio the target's holders still receive 0.8125 of a share, now worth 29.25: their premium shrinks to 17.0 per cent, and ownership stays at 28.89 per cent. Under a fixed value the ratio floats to deliver 32.50: 32.50 over 36.00 is 0.9028, the acquirer issues 54,166,667 shares (5,416,667 more) and gives away 31.10 per cent. A collar splits the difference: fixed value while the acquirer trades between 38.00 and 42.00 (5 per cent either side), fixed ratio at 0.8553 or 0.7738 outside it.
| Acquirer price | Fixed ratio: value | Fixed value: ownership | Collar: value | Collar: ownership |
|---|---|---|---|---|
| 32.00 | 26.00 | 33.68% | 27.37 | 29.95% |
| 36.00 | 29.25 | 31.10% | 30.79 | 29.95% |
| 40.00 | 32.50 | 28.89% | 32.50 | 28.89% |
| 44.00 | 35.75 | 26.97% | 34.05 | 27.90% |
| 48.00 | 39.00 | 25.29% | 37.14 | 27.90% |
Read the columns as risk allocation. The fixed ratio leaves the target's holders exposed to the acquirer's stock, which is what they are about to own anyway. The fixed value protects them, and makes the acquirer's holders write the cheque in extra shares if their own stock falls: at 32.00, the target's holders would own a third of the company. The collar holds the target's ownership between 27.90 and 29.95 per cent, whatever the acquirer's stock does.
| Premium | Exchange ratio | New shares | Target ownership |
|---|---|---|---|
| 20% | 0.7500 | 45,000,000 | 27.27% |
| 30% | 0.8125 | 48,750,000 | 28.89% |
| 40% | 0.8750 | 52,500,000 | 30.43% |
The ownership split then drives earnings per share: the 48,750,000 new shares are the denominator in how to calculate EPS accretion or dilution, where, in that illustrative case, funding with stock is the most dilutive of the three routes.
Divide the offer price per target share by the acquirer's price: 0.8125 here, 48,750,000 new shares and 28.89 per cent to the target. Then decide what the agreement fixes, the ratio or the value, because a 10 per cent move in the acquirer's stock before closing is worth 2.21 points of ownership between the two. The free workbook for this book runs the funding of one acquisition with cash, debt and stock side by side.
A fixed ratio sets the number of acquirer shares per target share, so ownership is certain and value moves with the acquirer's stock. A floating, or fixed-value, ratio sets the value, so the share count moves. If the acquirer falls from 40.00 to 36.00, a fixed 0.8125 delivers 29.25 a share; a fixed value of 32.50 needs a ratio of 0.9028 and 31.10 per cent ownership instead of 28.89.
Multiply the ratio by the acquirer's share price to get the value per target share, divide by the target's unaffected price and subtract one. A ratio of 0.8125 with the acquirer at 40.00 gives 32.50 per target share; against an unaffected price of 25.00 that is a premium of 30.0 per cent.
A collar fixes the value within a band of acquirer prices and fixes the ratio outside it. With a band of 38.00 to 42.00 around a 32.50 offer, the ratio floats between 0.7738 and 0.8553. If the acquirer falls to 32.00, the target receives 27.37 a share and 29.95 per cent ownership, against 33.68 per cent under a pure fixed value.
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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