One illustrative 180,000,000 acquisition, measured on what the acquirer actually paid rather than on the target's own balance sheet.
The ROIC of an acquisition is the target's NOPAT plus the after-tax synergies, divided by everything the acquirer spent to get them: the purchase price, the transaction fees and the after-tax cost to achieve the synergies. On an illustrative 180,000,000 purchase at 9.0x EBITDA, invested capital is 189,750,000 and ROIC is 7.27 per cent in year 1 and 9.08 per cent in year 3, so the deal clears an 8.5 per cent WACC only once synergies reach run rate.
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 buys a business with 20,000,000 of EBITDA at 9.0 times, an enterprise value of 180,000,000. The target has 4,000,000 of depreciation and amortisation, so EBIT of 16,000,000, growing 3.0 per cent a year. The deal case promises 6,000,000 of pre-tax cost synergies, phased in at 40, 80 and then 100 per cent, and costs 7,000,000 to achieve. Fees are 4,500,000. Tax is 25 per cent and the acquirer's WACC is 8.5 per cent. All figures are illustrative.
| Item | Value |
|---|---|
| Target EBITDA | 20,000,000 |
| Multiple paid | 9.0x |
| Purchase price (enterprise value) | 180,000,000 |
| Target EBIT, year 1 | 16,000,000 |
| Run-rate synergies, pre-tax | 6,000,000 |
| Cost to achieve, pre-tax | 7,000,000 |
| Transaction fees | 4,500,000 |
| Tax rate | 25% |
| WACC | 8.5% |
The denominator is the acquirer's outlay, not the target's balance sheet. That means the enterprise value paid (equity plus the debt assumed or refinanced), the fees, and the cost to achieve the synergies net of the tax relief on it, because that cash buys the synergies in the numerator.
Invested capital = price + fees + cost to achieve × (1 − tax)
= 180,000,000 + 4,500,000 + 7,000,000 × 75% = 180,000,000 + 4,500,000 + 5,250,000 = 189,750,000
Excel: =Price+Fees+CTA*(1-Tax)
NOPAT is the target's EBIT plus the synergies realised that year, taxed as if unlevered. Interest on any acquisition debt stays out: financing is in the WACC, not in the return. Amortisation of acquired intangibles is also usually left out, since it is a non-cash allocation of the same price that already sits in the denominator.
NOPATt = (target EBITt + synergiest) × (1 − tax)
Year 3: (16,974,400 + 6,000,000) × 75% = 17,230,800
ROIC3 = 17,230,800 / 189,750,000 = 9.08%
Excel: =(EBIT+Syn)*(1-Tax)/IC
| Year | Target EBIT | Synergies | NOPAT | ROIC | Economic profit |
|---|---|---|---|---|---|
| 1 | 16,000,000 | 2,400,000 | 13,800,000 | 7.27% | -2,328,750 |
| 2 | 16,480,000 | 4,800,000 | 15,960,000 | 8.41% | -168,750 |
| 3 | 16,974,400 | 6,000,000 | 17,230,800 | 9.08% | 1,102,050 |
| 4 | 17,483,632 | 6,000,000 | 17,612,724 | 9.28% | 1,483,974 |
| 5 | 18,008,141 | 6,000,000 | 18,006,106 | 9.49% | 1,877,356 |
Economic profit is NOPAT less a capital charge of 8.5 per cent of 189,750,000, which is 16,128,750 a year. The deal destroys value in years 1 and 2, crosses in year 3, and then earns a spread of 0.58 points that widens slowly with the target's own growth. That is a thin margin for a deal of this size: it depends entirely on the synergies arriving on schedule.
To earn exactly 8.5 per cent in year 3, NOPAT must be 16,128,750, which needs 21,505,000 of pre-tax profit. The target alone brings 16,974,400, so synergies must reach 4,530,600: 75.5 per cent of the plan. Below that, the deal misses its cost of capital in year 3 and crosses later only if the target's own growth carries it.
The two levers are the multiple paid, which moves the denominator, and how much of the synergy plan is delivered, which moves the numerator. Year-3 ROIC:
| Multiple | Price | Invested capital | No synergies | 50% delivered | 100% delivered |
|---|---|---|---|---|---|
| 8.0x | 160,000,000 | 169,750,000 | 7.50% | 8.83% | 10.15% |
| 9.0x | 180,000,000 | 189,750,000 | 6.71% | 7.90% | 9.08% |
| 10.0x | 200,000,000 | 209,750,000 | 6.07% | 7.14% | 8.21% |
| 11.0x | 220,000,000 | 229,750,000 | 5.54% | 6.52% | 7.50% |
At 10.0x the deal fails to earn its WACC even with every synergy delivered. At 8.0x it clears with half of them. One turn of multiple is worth roughly the whole difference between full and half delivery, which is why the price negotiation matters as much as the integration plan. The arithmetic behind pricing synergies in the first place is in how to value synergies net of the cost to achieve them.
The most frequent error is to quote the target's own ROIC. On its balance sheet the target has 60,000,000 of invested capital and earns 12,000,000 of NOPAT: 20.00 per cent. That is a fact about the business, and it is why the seller could ask 9.0 times EBITDA. It says nothing about the acquirer, who paid 180,000,000 for the same 12,000,000. The premium over book value has moved into goodwill, and goodwill is capital the acquirer has to earn a return on.
The second error is subtler: dividing full run-rate NOPAT by the price alone, which gives 9.17 per cent from year 1. It leaves out the fees and the cost to achieve, which are real cash spent on this deal, and it pulls year-3 synergies into year 1. Both flatter the result, and together they hide the two years in which the deal earns less than it costs.
The free workbook for this case sets the board's value-created figure beside the arithmetic one and reconciles the two line by line, which is the same discipline applied to the whole deal rather than to one ratio.
Yes, when the question is whether the deal earned its cost of capital. Goodwill is part of what the acquirer paid. Excluding it measures the operating business, which is useful for comparing units, but it hides the premium. In this case ROIC including goodwill is 9.08 per cent in year 3; on the target's book capital of 60,000,000 it would look like 20.00 per cent.
There is no rule, but boards often look for the third year, once synergies reach run rate. Here ROIC is 7.27 per cent in year 1 and 8.41 per cent in year 2, below an 8.5 per cent WACC, and clears it in year 3 at 9.08 per cent. A deal that needs more than five years to cross usually rests on growth assumptions rather than synergies.
ROIC on the full invested capital must exceed the WACC used to price the deal, and stay above it. The economic profit is NOPAT less WACC times invested capital: 17,230,800 less 16,128,750, or 1,102,050 in year 3 here. If year-3 synergies fall below 4,530,600, 75.5 per cent of plan, the spread disappears that year.
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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