The shortcut capitalises the run rate from day one and charges nothing for getting there. Timed and paid for, the same synergies are worth a fifth less.
Tax the run-rate synergy, discount the ramp years one by one, capitalise the full run rate as a growing perpetuity from the year it is reached, and subtract the after-tax, discounted cost to achieve. On the acquisition of Balmacara in Mergers and Acquisitions, 7,200,000 of run-rate synergies are worth 58,841,565, not the 73,260,000 the shortcut gives, and against a premium, fees and an earn-out totalling 76,372,420 the deal destroys 17,530,855.
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 shortcut is familiar: take the run rate after tax, divide by the cost of capital less growth, and call that the value of the synergies. It assumes the full saving arrives on day one and costs nothing to achieve. Neither is true of any integration, and the gap between the shortcut and the proper figure is often larger than the margin by which a deal clears its hurdle.
| Input | Value |
|---|---|
| Run-rate cost synergies, pre-tax | 7,200,000 |
| Ramp: share of run rate in years 1, 2, 3 | 30% / 70% / 100% |
| Cost to achieve, pre-tax | 9,400,000 |
| Cost spent in years 1, 2, 3 | 55% / 30% / 15% |
| Tax rate | 25% |
| Cost of capital | 9.25% |
| Perpetual growth | 1.75% |
The cost to achieve is 1.3056 times the run rate: redundancy, systems migration and site closures often cost more than one year of the saving they produce.
Value = Σ ramp synergyt × (1 − tax) ÷ (1 + WACC)t + run rate × (1 − tax) × (1 + g) ÷ (WACC − g) ÷ (1 + WACC)3 − Σ costt × (1 − tax) ÷ (1 + WACC)t
In Excel, with after-tax synergies in C5:E5, after-tax costs in C6:E6 and the run rate in B2: =NPV(WACC,C5:E5)+B2*(1-Tax)*(1+g)/(WACC-g)/(1+WACC)^3-NPV(WACC,C6:E6).
| Year | Synergy | After tax | Cost | After tax | Factor | PV synergy | PV cost |
|---|---|---|---|---|---|---|---|
| 1 | 2,160,000 | 1,620,000 | 5,170,000 | 3,877,500 | 0.9153 | 1,482,838 | 3,549,199 |
| 2 | 5,040,000 | 3,780,000 | 2,820,000 | 2,115,000 | 0.8378 | 3,167,006 | 1,772,015 |
| 3 | 7,200,000 | 5,400,000 | 1,410,000 | 1,057,500 | 0.7669 | 4,141,231 | 810,991 |
| Total | 8,791,074 | 6,132,205 |
Step 1, the ramp years. The three years of partial and then full synergy are worth 8,791,074 today.
Step 2, the perpetuity. From year four the after-tax run rate of 5,400,000, growing at 1.75 per cent, is capitalised at 1.0175 ÷ 0.075 = 13.5667 times: 73,260,000 at the end of year three, discounted three years to 56,182,696.
Step 3, the cost. The cost to achieve is deductible, so 9,400,000 becomes 7,050,000 after tax, front-loaded and therefore discounted little: 6,132,205 today.
Step 4. 8,791,074 + 56,182,696 − 6,132,205 = 58,841,565.
| Step | Amount |
|---|---|
| Shortcut: perpetuity from today, no cost | 73,260,000 |
| − Perpetuity starts at year 4, not today | −17,077,304 |
| + Ramp years actually delivered | 8,791,074 |
| − Cost to achieve, after tax, discounted | −6,132,205 |
| Value of the synergies | 58,841,565 |
The proper value is 80.3 per cent of the shortcut. Each unit of run rate is worth 9.0241 before the cost to achieve, against 10.1750 on the shortcut.
The synergies then have to cover what the buyer paid above the target's standalone value: a premium of 59,823,333 over its discounted cash flow value, 6,900,000 of fees and an earn-out with a fair value of 9,649,087, a total of 76,372,420. The synergies fall 17,530,855 short. The run rate needed to break even is 9,142,663, 1.2698 times the figure announced and 4.9688 per cent of the target's revenue.
| Variant | Synergy value | Change | Value created |
|---|---|---|---|
| Base case | 58,841,565 | 0 | −17,530,855 |
| Full run rate from year 1, no cost to achieve | 69,791,013 | +10,949,448 | −6,581,407 |
| Full run rate from year 1, with the cost | 63,658,808 | +4,817,243 | −12,713,612 |
| Slower ramp: 0% / 30% / 70% | 54,306,641 | −4,534,925 | −22,065,779 |
| Cost to achieve 14,100,000 (50% over) | 55,775,462 | −3,066,103 | −20,596,958 |
| Cost of capital 8.75% | 63,738,227 | +4,896,661 | −12,634,193 |
| Cost of capital 9.75% | 54,564,964 | −4,276,601 | −21,807,456 |
| No growth in the synergy | 47,428,930 | −11,412,635 | −28,943,490 |
Even with the full run rate on day one and nothing spent to get it, the deal still destroys 6,581,407: the premium is simply too large for this run rate. The single most powerful assumption is the growth rate on the synergy. Cost savings that grow with inflation for ever are an assumption, not a finding, and setting growth to nil removes 11,412,635.
Revenue synergies need their own treatment. A cost saving falls straight to operating profit and is taxed as above. Revenue synergies are worth only the contribution margin on the extra sales, after the working capital and capex they require, and usually deserve a slower ramp and a probability.
The common mistake is to compare the shortcut value of the synergies, 73,260,000, with the premium alone, 59,823,333, and conclude that the deal creates value with room to spare. Both sides of that comparison are wrong: the synergies are worth less once timed and paid for, and the bill includes fees and the earn-out. Value the synergies on the timeline the integration plan actually commits to, and compare them with everything paid above standalone value.
Synergy value = ramp years + perpetuity from the year the run rate is reached − cost to achieve, all after tax and discounted. Then solve for the break-even run rate and set it beside the one announced. The full Balmacara case, with the earn-out, the standalone value and the cost of capital grid, is in the free workbook for this case; for the items that come out of the price before any of this, see whether uncapitalised leases count as debt.
Yes. Cost savings raise taxable profit, so they are worth the run rate times one minus the tax rate, and the cost to achieve is deductible too. In the Balmacara case 7,200,000 of pre-tax run rate is 5,400,000 after 25 per cent tax, and the 9,400,000 cost to achieve is 7,050,000 after tax.
Usually the cost of capital of the business that will deliver them, with any doubt about delivery handled in the ramp or a probability rather than an arbitrary premium on the rate. At 9.25 per cent the Balmacara synergies are worth 58,841,565; half a point either way moves them by about 4.3 to 4.9 million.
Add up everything paid above standalone value, add the present value of the cost to achieve, and divide by the value of one unit of run rate after ramp and tax. For Balmacara: 76,372,420 plus 6,132,205, divided by 9.0241, gives 9,142,663, which is 1.2698 times the run rate announced.
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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