The multi-period excess earnings method for a purchase price allocation, with the contributory asset charges and the tax amortisation benefit worked line by line.
Customer relationships acquired in a deal are valued with the multi-period excess earnings method: forecast the after-tax earnings of the customers on the books at closing as they attrite, charge every other asset that helps earn them a fair return, discount what is left, and add the tax amortisation benefit. On an illustrative target with 120.0 million of revenue from existing customers, 15 per cent annual attrition and an 11 per cent discount rate, the excess earnings are worth 60.4 million and the relationships 69.1 million with the amortisation benefit. Leave out the contributory asset charges and the figure rises to 88.4 million, 27.9 per cent too high.
Worked in full in Mergers and Acquisitions by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
In many acquisitions of a business-to-business company the customer relationships are the largest identifiable intangible, and one that auditors review closely. The method is not complicated. Its errors are almost always in what is charged against the earnings, not in the discounting.
| Input | Value |
|---|---|
| Revenue from customers existing at closing, last 12 months | 120.0 |
| Price growth on retained customers | 3.0% |
| Customer attrition a year | 15.0% |
| EBITA margin (after depreciation, before intangible amortisation) | 22.0% |
| Tax rate | 25.0% |
| Discount rate for the relationships (WACC 9.0%) | 11.0% |
| Forecast horizon, mid-year discounting | 20 years |
| Tax amortisation period (US Section 197) | 15 years |
Only existing customers count. Revenue from customers the target will win after closing belongs to goodwill, so the forecast starts from the closing book and only shrinks: 120.0 × 1.03 × 0.85 = 105.1 in year one, a retention factor of 0.8755 a year. The discount rate sits above the 9.0 per cent WACC because these cash flows are riskier than the business as a whole; working capital would sit below it, goodwill above.
The customers do not generate earnings alone. They need working capital, equipment, a brand and trained staff. Each of those assets is charged a fair return, expressed here after tax as a share of revenue.
| Contributory asset | Charge | Year 1 |
|---|---|---|
| Net working capital, return on | 0.5% | 0.53 |
| Fixed assets, return on | 1.0% | 1.05 |
| Trade name, royalty forgone | 1.5% | 1.58 |
| Assembled workforce, return on | 0.6% | 0.63 |
| Total | 3.6% | 3.8 |
The fixed assets are charged a return on only. The return of the capital, depreciation, is already deducted inside the 22.0 per cent EBITA margin, and charging it again is a double count. The workforce is not recognised as an asset under IFRS 3 or US GAAP, but it still contributes, so it is charged here and its value falls into goodwill.
Revenue 105.1 × 22.0% = EBITA 23.1; tax at 25.0% = 5.8; after-tax 17.3
Less contributory charges 105.1 × 3.6% = 3.8
Excess earnings = 13.6; discount factor 1 ÷ 1.110.5 = 0.9492; present value 12.9
Excel, year t in row 2: =Rev0*((1+g)*(1-a))^t*(m*(1-tax)-CAC)/(1+r)^(t-0.5)
| Year | Revenue | EBITA | Tax | Charges | Excess | Factor | PV |
|---|---|---|---|---|---|---|---|
| 1 | 105.1 | 23.1 | 5.8 | 3.8 | 13.6 | 0.9492 | 12.9 |
| 2 | 92.0 | 20.2 | 5.1 | 3.3 | 11.9 | 0.8551 | 10.1 |
| 3 | 80.5 | 17.7 | 4.4 | 2.9 | 10.4 | 0.7704 | 8.0 |
| 4 | 70.5 | 15.5 | 3.9 | 2.5 | 9.1 | 0.6940 | 6.3 |
| 5 | 61.7 | 13.6 | 3.4 | 2.2 | 8.0 | 0.6252 | 5.0 |
| 6 to 20 | 48.4 | 18.1 | |||||
| Total | 60.4 |
The first five years carry 70.1 per cent of the value; everything after year 10 adds 8.5 per cent. That is why the horizon matters much less than the attrition rate.
A market participant buying the relationships on their own would amortise them for tax, and that deduction is part of what the asset is worth. Valuers therefore gross up the present value, whether or not this particular acquirer gets the deduction; that question is handled through deferred tax instead.
TAB factor = n ÷ (n − tax × AF), with AF the present value of 1 a year for n years at the discount rate
AF over 15 years at 11%, mid-year = 7.5761
Factor = 15 ÷ (15 − 0.25 × 7.5761) = 1.1445
Value = 60.4 × 1.1445 = 69.1, of which the benefit is 8.7
The 15 years is the US Section 197 period for acquired intangibles; in other jurisdictions use the tax life that a market participant there would get. The factor is circular by nature, since the deduction depends on the value it helps create, and the closed form solves it in one step.
Take an enterprise value of 600.0 against 150.0 of net tangible assets: 450.0 to allocate. Recognising the relationships at 69.1 takes 11.5 per cent of the price out of goodwill. In a share deal with no tax step-up, a deferred tax liability of 69.1 × 25% = 17.3 goes on the balance sheet beside it, and goodwill falls by only 51.8, to 398.2 before the trade name and any other intangibles are valued. The intangible is then amortised through the income statement, 6.9 a year over an illustrative ten-year useful life, while goodwill is not. The goodwill calculation shows the full allocation.
| Attrition | Implied average life | At 10% | At 11% | At 12% |
|---|---|---|---|---|
| 10% | 10.0 years | 97.1 | 92.0 | 87.4 |
| 15% | 6.7 years | 72.3 | 69.1 | 66.2 |
| 20% | 5.0 years | 55.7 | 53.6 | 51.7 |
| 25% | 4.0 years | 44.1 | 42.7 | 41.4 |
Five points of attrition move the value by a fifth to a third; a point of discount rate moves it by about 3 to 6 per cent. Attrition should come from the target's own customer history, by cohort and by revenue rather than by customer count, because large accounts often stay longer than the small ones.
Value = Σ (after-tax earnings of existing customers − contributory charges) discounted, × the TAB factor. Here: 60.4 × 1.1445 = 69.1 million. Attrition decides most of the answer and the charges decide whether it is defensible. The method is the multi-period version of the logic in the excess earnings method; the price allocation, the deferred tax and the amortisation that follow are in the free workbook for this case.
They are the fair returns charged for the other assets the customers need to generate earnings: working capital, fixed assets, the trade name and the assembled workforce. In the example they total 3.6 per cent of revenue after tax, 3.8 million in year one. Leaving them out credits those assets' earnings to the customers and raises the value from 69.1 to 88.4 million.
Multiply the present value of the excess earnings by n divided by (n minus the tax rate times the annuity factor), where n is the tax amortisation period. Over the 15-year US Section 197 period at 11 per cent with mid-year discounting the annuity factor is 7.5761, so at a 25 per cent tax rate the factor is 1.1445 and 60.4 million becomes 69.1 million.
Because it sets how fast the earnings run off. At 15 per cent a year the relationships are worth 69.1 million at 11 per cent; at 10 per cent attrition they are worth 92.0 million and at 20 per cent 53.6 million. A point of discount rate moves the value by about 3 to 6 per cent, so attrition, measured by revenue cohort, deserves most of the diligence.
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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