Break-even synergies for an illustrative 660,000,000 acquisition, under stock, debt and mixed funding.
Break-even synergies are the pre-tax savings that bring pro forma EPS back to the acquirer's standalone EPS: take standalone EPS times pro forma shares, subtract pro forma net income, and gross the gap up for tax. In an illustrative 660,000,000 acquisition at 22.0 times earnings, the deal needs 8,000,000 a year of pre-tax synergies if paid in stock and 3,600,000 if paid with debt. Ignoring tax and the new amortisation would put the stock figure at 3,000,000, less than half the real number.
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 acquirer earns 120,000,000 on 100,000,000 shares, an EPS of 1.20, and trades at 20.0 times, so 24.00 a share. It offers 22.0 times the target's 30,000,000 of net income: 660,000,000 for the equity. The purchase price allocation creates 4,000,000 a year of new intangible amortisation, 3,000,000 after tax at 25 per cent. New debt, if used, costs 6.0 per cent before tax, 4.50 per cent after. All figures are illustrative.
| Item | Value |
|---|---|
| Acquirer net income | 120,000,000 |
| Acquirer shares | 100,000,000 |
| Acquirer EPS / share price | 1.20 / 24.00 |
| Target net income | 30,000,000 |
| Offer P/E / equity price | 22.0x / 660,000,000 |
| New amortisation, pre-tax | 4,000,000 |
| Tax rate | 25% |
| Cost of new debt, pre-tax | 6.0% |
Paid entirely in stock at 24.00, the offer issues 660,000,000 / 24.00 = 27,500,000 new shares. Pro forma net income is the two incomes less the after-tax amortisation: 120,000,000 + 30,000,000 − 3,000,000 = 147,000,000. On 127,500,000 shares that is an EPS of 1.1529, 3.92 per cent below 1.20. The mechanics of this step are set out in full in how to calculate EPS accretion or dilution; here the question is what closes the gap.
To hold EPS at 1.20 on 127,500,000 shares, the combined company must earn 153,000,000. It earns 147,000,000 without synergies, so it needs 6,000,000 more after tax. Synergies are taxed like any other profit, so the pre-tax figure is larger.
Break-even synergies (pre-tax) = (EPSacquirer × pro forma shares − pro forma net income) / (1 − tax)
= (1.20 × 127,500,000 − 147,000,000) / 75% = 6,000,000 / 75% = 8,000,000
Excel: =(EPS_A*(Sh_A+Offer*Stock%/Price_A)-PF_NI)/(1-Tax)
That is 20.0 per cent of the target's 40,000,000 of pre-tax profit, a demanding cost-saving target for a single year.
| Funding | New shares | New debt | Interest after tax | Pro forma EPS | Dilution | Synergies needed |
|---|---|---|---|---|---|---|
| All stock | 27,500,000 | 0 | 0 | 1.1529 | -3.92% | 8,000,000 |
| Half and half | 13,750,000 | 330,000,000 | 14,850,000 | 1.1618 | -3.19% | 5,800,000 |
| All debt | 0 | 660,000,000 | 29,700,000 | 1.1730 | -2.25% | 3,600,000 |
Debt is the cheapest currency for EPS here because its after-tax cost, 4.50 per cent, is below the acquirer's earnings yield of 5.00 per cent (one over a P/E of 20.0). That is the general test: stock is dilutive whenever the offer P/E exceeds the acquirer's, and debt is dilutive whenever the target's earnings yield at the offer, here 4.55 per cent, falls below the after-tax cost of debt. At 22.0 times the target clears the debt test by a hair; the amortisation then tips the result into dilution.
Synergies rarely arrive in full in year 1. If 40 per cent of the run rate is realised in the first year, the all-stock deal needs a run rate of 20,000,000 to avoid year-1 dilution, and the all-debt deal 9,000,000. Ask which year the board is promising break-even in.
| Offer P/E | Equity price | All stock | Half and half | All debt |
|---|---|---|---|---|
| 18.0x | 540,000,000 | 0 | none (1.01% accretive) | none (2.25% accretive) |
| 20.0x | 600,000,000 | 4,000,000 | 2,000,000 | 0 |
| 22.0x | 660,000,000 | 8,000,000 | 5,800,000 | 3,600,000 |
| 24.0x | 720,000,000 | 12,000,000 | 9,600,000 | 7,200,000 |
| 26.0x | 780,000,000 | 16,000,000 | 13,400,000 | 10,800,000 |
In the all-stock column each extra turn of offer P/E costs 2,000,000 of pre-tax synergies a year. At 18.0 times the stock deal would be accretive on earnings alone, and the 3,000,000 of after-tax amortisation brings it exactly back to zero. At 20.0 times the debt deal breaks even before any synergy, because the target's 5.00 per cent earnings yield less the amortisation just covers the 4.50 per cent interest.
The shortcut is to compute the after-tax earnings gap on the raw incomes and call it the synergy target. Without amortisation, the stock deal earns 150,000,000 against 153,000,000 needed, a gap of 3,000,000, and that figure is often presented as the required saving. The real number is 8,000,000: 2.67 times as large, because the amortisation adds 3,000,000 to the after-tax gap and the tax gross-up turns 6,000,000 after tax into 8,000,000 before it. The amortisation is non-cash, but it is in reported EPS, and reported EPS is what break-even is measured on.
The second mistake is to treat break-even EPS as success. Accretion says nothing about the cost of equity: the all-debt deal is the least dilutive and also the one that loads the most risk on to the balance sheet. Whether the price is earned is a separate test, set out in how to calculate the ROIC of an acquisition. The value version of the break-even, the run-rate synergies whose present value covers the premium and the cost to achieve, is a different number; it is worked in how to value synergies net of the cost to achieve them. The free workbook for this case prints the combined income statement under four accretion conventions at once, which is the quickest way to see how much of a headline depends on the convention chosen.
Before synergies and new amortisation, when the offer P/E exceeds the acquirer's own P/E: the acquirer gives up more earnings per new share than it buys. Here an acquirer on 20.0x paying 22.0x dilutes; paying 18.0x would be accretive on the earnings alone, though 4,000,000 of new amortisation brings that case exactly back to zero.
When the target's earnings yield at the offer price exceeds the after-tax cost of debt. At 22.0x the yield is 4.55 per cent, just above a 4.50 per cent after-tax cost of 6.0 per cent debt, so the earnings are marginally accretive; 3,000,000 of after-tax intangible amortisation then turns the deal 2.25 per cent dilutive.
No. EPS ignores the cost of equity, so a debt-funded deal can be accretive and still earn less than its WACC. Break-even synergies tell you what the market will see in the first reported year; whether the deal is worth doing depends on return on invested capital against the cost of capital, which here needs a separate test.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: corporate finance, valuation and markets → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.