From the offer price to the enterprise value paid, through diluted shares at the offer and every claim the buyer takes on, then the five multiples one deal can report.
The EV/EBITDA multiple paid is the offer's equity value on fully diluted shares, plus net debt and the other claims the buyer takes on, divided by the target's EBITDA. An illustrative offer of 32.00 a share on 52,000,000 diluted shares is 1,664,000,000 of equity and 1,954,000,000 of enterprise value, 9.77 times LTM EBITDA. Basic shares alone would report 9.45 times, and the 0.32 of a turn is where most reported deal multiples go wrong.
Worked in full in Mergers and Acquisitions by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Every deal has several multiples, all arithmetically correct: on basic or diluted shares, on net debt or on all debt-like items, on trailing, forward or synergised EBITDA. The one to quote is the one whose numerator and denominator describe the same business on the same date, and the one to compare against is a comparable deal computed the same way.
| Input | Value |
|---|---|
| Offer price per share (unaffected 25.00, a 28.0% premium) | 32.00 |
| Basic shares outstanding | 50,000,000 |
| Options, all vesting on change of control, strike 20.00 | 4,000,000 |
| Restricted stock units, vesting on change of control | 500,000 |
| Gross debt | 400,000,000 |
| Cash | 150,000,000 |
| Pension deficit | 30,000,000 |
| Non-controlling interests | 20,000,000 |
| Investments in associates | 10,000,000 |
| EBITDA: last twelve months; next twelve months | 200,000,000; 215,000,000 |
| Run-rate synergies expected by the buyer | 30,000,000 |
Step 1: diluted shares at the offer price. In a takeover the options vest and are cashed out or exercised, so the treasury stock method is run at the offer price, not at the market price before the bid.
Option proceeds = 4,000,000 × 20.00 = 80,000,000
Shares repurchased = 80,000,000 ÷ 32.00 = 2,500,000; net new shares = 1,500,000
Diluted shares = 50,000,000 + 1,500,000 + 500,000 = 52,000,000
Equity purchase price = 52,000,000 × 32.00 = 1,664,000,000
Step 2: the bridge to enterprise value.
EV = 1,664,000,000 + 400,000,000 − 150,000,000 + 30,000,000 + 20,000,000 − 10,000,000 = 1,954,000,000
Excel: =Offer*(Basic+MAX(0,Opt-Opt*Strike/Offer)+RSU)+Debt-Cash+Pension+NCI-Assoc
The non-controlling interests are added because consolidated EBITDA includes 100 per cent of the subsidiaries; the associates are deducted because their profit is not in EBITDA at all. The pension deficit is a debt the buyer assumes; tax-effect it where the contributions will be deductible. The full list of what belongs in this bridge is in the enterprise value to equity value bridge.
Step 3: divide by EBITDA. 1,954,000,000 over 200,000,000 is 9.77 times LTM; over the forward 215,000,000 it is 9.09 times; over LTM plus the 30,000,000 of synergies, 230,000,000, it is 8.50 times.
| Measure | EV | Multiple |
|---|---|---|
| Basic shares, all claims, LTM | 1,890,000,000 | 9.45x |
| Diluted shares, net debt only, LTM | 1,914,000,000 | 9.57x |
| Diluted, all claims, LTM | 1,954,000,000 | 9.77x |
| Diluted, all claims, NTM | 1,954,000,000 | 9.09x |
| Diluted, all claims, LTM plus synergies | 1,954,000,000 | 8.50x |
The buyer's board paper will tend to quote the bottom row and the target's the top one. Only the third row is the price of the business as it stands. The synergised multiple is the buyer's own view of what it will be worth in its hands, which is useful for its decision but not comparable with another deal, and the synergies have a cost to achieve that the multiple ignores. Before the bid, the same company traded at 1,572,500,000 of enterprise value, 7.86 times LTM, so the 28.0 per cent premium on the shares is 24.3 per cent on enterprise value: debt dilutes the premium, which is why a premium on the equity always looks larger than the same premium on the business.
| Offer | Diluted shares | Equity value | EV | LTM | NTM |
|---|---|---|---|---|---|
| 30.00 | 51,833,333 | 1,555,000,000 | 1,845,000,000 | 9.22x | 8.58x |
| 32.00 | 52,000,000 | 1,664,000,000 | 1,954,000,000 | 9.77x | 9.09x |
| 34.00 | 52,147,059 | 1,773,000,000 | 2,063,000,000 | 10.31x | 9.60x |
| 36.00 | 52,277,778 | 1,882,000,000 | 2,172,000,000 | 10.86x | 10.10x |
Each extra 1.00 a share adds about 54,500,000 of enterprise value, a little more than the 52,000,000 diluted shares alone suggest, because the share count itself rises with the price: at a higher offer the option proceeds buy back fewer shares.
Seven ways of quoting the same acquisition, and why three of them are one number, are rebuilt in the free workbook for this case.
Quote both and label them; comparable deal databases mostly report LTM. On an illustrative 1,954,000,000 enterprise value, 200,000,000 of LTM EBITDA gives 9.77 times and 215,000,000 of forward EBITDA gives 9.09 times. A forward multiple on one deal against an LTM multiple on another flatters the forward one.
Yes. Options vest and are settled at the offer, so the repurchase is computed at that price. With 4,000,000 options at a 20.00 strike, the offer of 32.00 gives 1,500,000 net new shares; at the 25.00 pre-bid price it would give 800,000, understating the equity price.
Because the debt is paid at face value whatever the premium, so the same extra money is spread over a larger base. A 28.0 per cent premium on the shares, from 25.00 to 32.00, raises enterprise value from 1,572,500,000 to 1,954,000,000, a premium of 24.3 per cent.
The same acquisition quoted seven ways is worked in chapters 1 to 4 of 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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