The sign of the answer is decided by one comparison per funding source: the target's earnings yield after amortisation against the cost of the money.
Add the target's net income to the acquirer's, subtract the after-tax cost of the funding and the after-tax amortisation of acquired intangibles, and divide by the share count after any new shares are issued. Compare the result with the acquirer's standalone EPS. In the illustrative case below, buying a target on 18 times earnings is 1.49 per cent dilutive paid in stock, 0.47 per cent dilutive paid in debt and 4.93 per cent accretive paid from cash.
Worked in full in Mergers and Acquisitions by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Accretion and dilution is the first question a board asks about a deal and the first screen in any merger model. The arithmetic is short. What makes it useful is knowing which single comparison decides the sign for each form of funding, because that tells you the price at which the answer flips before the model is built.
| Input | Value |
|---|---|
| Acquirer net income | 150.0 |
| Acquirer shares in issue | 100.0 |
| Acquirer EPS, standalone | 1.50 |
| Acquirer share price (P/E 20.0x) | 30.00 |
| Target net income | 20.0 |
| Equity purchase price (P/E 18.0x) | 360.0 |
| Identified intangibles, amortised over 10 years | 60.0 |
| Pre-tax cost of new debt | 6.0% |
| Pre-tax yield on cash used | 3.0% |
| Tax rate | 25% |
Synergies and transaction fees are left out so that the funding effect is visible on its own. Fees are usually excluded from the accretion test as one-off; synergies are added later as the variable that closes a gap.
Pro forma NI = acquirer NI + target NI − new interest × (1 − t) − lost interest on cash × (1 − t) − new amortisation × (1 − t)
Pro forma shares = acquirer shares + stock consideration ÷ acquirer share price
Accretion = pro forma EPS ÷ standalone EPS − 1
In Excel: =(NI_A+NI_T-Debt*Rd*(1-t)-Cash*Rc*(1-t)-Amort*(1-t))/(Sh_A+Stock/Px_A)/EPS_A-1.
Step 1, amortisation. 60.0 of intangibles over 10 years is 6.0 a year, 4.5 after tax. It applies whatever the funding.
Step 2, all stock. 360.0 ÷ 30.00 = 12.0 new shares. Net income is 150.0 + 20.0 − 4.5 = 165.5 over 112.0 shares: EPS 1.4777, −1.49 per cent.
Step 3, all debt. Interest of 360.0 × 6.0 per cent is 21.6, or 16.2 after tax. Net income is 170.0 − 16.2 − 4.5 = 149.3 over 100.0 shares: EPS 1.4930, −0.47 per cent.
Step 4, cash on hand. The acquirer loses 3.0 per cent on 360.0, 8.1 after tax. Net income is 157.4: EPS 1.5740, +4.93 per cent.
| Funding | Pro forma NI | Shares | EPS | Accretion | Before amortisation |
|---|---|---|---|---|---|
| All stock | 165.5 | 112.0 | 1.4777 | −1.49% | +1.19% |
| All debt | 149.3 | 100.0 | 1.4930 | −0.47% | +2.53% |
| 50% debt, 50% stock | 157.4 | 106.0 | 1.4849 | −1.01% | +1.82% |
| Cash on hand | 157.4 | 100.0 | 1.5740 | +4.93% | +7.93% |
Each form of funding has a one-line test. Compare the target's earnings yield on the price paid, net of the amortisation, with the cost of the money:
The target earns 20.0 ÷ 360.0 = 5.56 per cent on the price, but only 4.31 per cent after the amortisation. That is below 5.00 and 4.50, so stock and debt dilute, and above 2.25, so cash accretes. Before amortisation, 5.56 per cent clears all three, which is why the right-hand column is positive throughout. The usual shorthand, "buying a lower P/E with stock is accretive", holds before purchase accounting; once the amortisation is charged it can fail, as it does here.
| Price | P/E paid | All debt | All stock |
|---|---|---|---|
| 300 | 15.0x | +1.33% | +0.30% |
| 330 | 16.5x | +0.43% | −0.60% |
| 360 | 18.0x | −0.47% | −1.49% |
| 400 | 20.0x | −1.67% | −2.65% |
The break-even prices follow directly from the yield test. Debt-funded, EPS is neutral at 15.5 ÷ 4.50 per cent = 344.4, a P/E of 17.2x. Stock-funded, it is neutral at 15.5 ÷ 5.00 per cent = 310.0, a P/E of 15.5x. At the agreed 360.0 the gap closes with 0.93 of pre-tax synergies on a debt deal, or 3.33 on a stock deal, where net income must reach 168.0 to hold EPS at 1.50 on 112.0 shares.
The convention can be worth more than the deal. The acquisition worked in Mergers and Acquisitions runs from −15.7134 per cent on a statutory basis to +11.2171 per cent on the cash convention, on the same deal and the same accounts. Always state which earnings an accretion figure is on.
The common mistake is to read accretion as value creation. A cash deal is accretive whenever the target's yield beats the interest forgone on deposits, which at 2.25 per cent is almost any price. A debt-funded deal can be accretive at a price that destroys value, because the after-tax cost of debt is far below the cost of capital the business must earn. Accretion tells you what happens to a reported number in year one. Whether the price is covered by the target's cash flows and the synergies is a separate calculation, and the one that matters.
Compute the target's earnings yield on the price after amortisation, and compare it with the acquirer's earnings yield for stock, the after-tax interest rate for debt and the after-tax deposit rate for cash. The sign of the answer is already decided. The full statutory and cash conventions, with the twelve-line bridge from standalone to combined EPS, are in the free workbook for this case, and how to value synergies net of the cost to achieve answers the value question that accretion does not.
Not necessarily once purchase accounting is included. A target on 18x bought by an acquirer on 20x with stock is 1.19 per cent accretive before amortisation of intangibles; once 4.5 of after-tax amortisation is charged, it is 1.49 per cent dilutive, because the target's yield falls from 5.56 to 4.31 per cent, below the acquirer's 5.00.
When the target's earnings yield on the price, after amortisation, exceeds the after-tax interest rate. At 6 per cent pre-tax and 25 per cent tax the hurdle is 4.50 per cent; with 15.5 of post-amortisation earnings the break-even price is 344.4, a P/E of 17.2x.
No. Accretion compares the target's yield with the cost of funding, and after-tax debt or forgone deposit interest is far cheaper than the cost of capital. In the illustrative case a cash purchase at 360.0 is 4.93 per cent accretive simply because cash earned only 2.25 per cent after tax.
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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