Accretion and dilution in a merger, with a worked example

How do you walk through a merger model?

The merger model question and the accretion question are one answer. Give the steps, then explain that accretion is just pro forma EPS compared with the buyer's EPS on its own.

1. Project both companies' income statements on their own.
2. Set the purchase price and premium, and how it is paid: cash on hand, new debt, new stock, or a mix.
3. Calculate the cost of each: interest the cash would have earned, interest on new debt, and the new shares issued at the buyer's share price.
4. Combine net incomes, subtract the after tax financing costs, and add after tax synergies and any new amortization from writing up the target's assets.
5. Divide pro forma net income by the new share count and compare with the buyer's standalone EPS.

What is the earnings yield shortcut?

Every way of paying has a cost you can express as a yield. Compare each with the target's earnings yield, which is the target's net income divided by the price paid, or one over the P/E you are paying. If the target yields more than the funding costs, EPS goes up.

The cost of stock is the buyer's earnings yield, one over its own P/E, because every new share has to share in the earnings. That is why the old rule says a buyer with a higher P/E than the price it pays is accretive in an all stock deal: it is paying with expensive currency.

• Cost of cash: the interest rate the cash was earning, times one minus the tax rate.
• Cost of debt: the interest rate on new debt, times one minus the tax rate.
• Cost of stock: the buyer's net income divided by its market value, or one over its P/E.
• Target earnings yield: target net income divided by the purchase price.

What does a worked example look like?

Assumptions: the buyer has net income of 100 and 50 shares at 40, so EPS is 2.00 and its P/E is 20. The target earns 20 of net income and is bought for 300, a P/E of 15 and an earnings yield of about 6.7 percent. Cash on hand earns 4 percent, new debt costs 6 percent, the tax rate is 25 percent, and there are no synergies, fees, or asset write ups.

All three are accretive because the target's 6.7 percent earnings yield beats the after tax cost of each: 3 percent for cash, 4.5 percent for debt, and 5 percent for stock. The cheapest funding gives the most accretion.

1. All cash: lost interest after tax is 300 times 4 percent times 0.75, which is 9. Pro forma net income is 100 plus 20 minus 9, or 111, over 50 shares: EPS 2.22, about 11 percent accretive.
2. All debt: new interest after tax is 300 times 6 percent times 0.75, which is 13.5. Net income is 106.5 over 50 shares: EPS 2.13, about 6.5 percent accretive.
3. All stock: 300 divided by the 40 share price is 7.5 new shares. Net income is 120 over 57.5 shares: EPS about 2.09, about 4.3 percent accretive.

What does a dilutive deal look like, and how much synergy fixes it?

Change one assumption: the buyer's shares trade at 20, not 40, so its P/E is 10. It buys a target earning 20 for 400, all in stock. It must issue 400 divided by 20, or 20 new shares. Pro forma EPS is 120 over 70 shares, about 1.71, roughly 14 percent dilutive. It paid 20 times earnings with a currency worth 10 times earnings.

To break even, pro forma EPS must be 2.00, so net income must be 2.00 times 70 shares, or 140. That needs 20 of after tax synergies, or about 26.7 before tax at a 25 percent rate. Saying the breakeven synergy number unprompted is how you stand out on this question.

Why is accretion not the same as a good deal?

EPS accretion only says the target's earnings yield beats the cost of funding, which is easy when debt is cheap. It says nothing about whether the return on the price paid beats the buyer's cost of capital, whether the synergies are real, or what the extra leverage does to risk. A deal can be accretive and destroy value, and a dilutive stock deal can still be the right one if the buyer's shares are richly valued or the balance sheet cannot take more debt.

Interviewers love this follow up because it separates people who memorized a rule from people who understand it. Drill the modeling questions below; they include both worked examples from this guide.

Questions students ask

Is an all stock deal accretive if the buyer has a higher P/E?

Yes, ignoring synergies, fees, and new amortization: the buyer issues fewer shares per dollar of target earnings than the target's multiple implies. If the buyer's P/E is lower than the P/E it pays, the deal is dilutive.

Why does the P/E shortcut sometimes give the wrong answer?

It only works for a pure stock deal with nothing else going on. Real deals mix funding, add amortization from asset write ups, refinance target debt, pay fees, and include synergies, each of which changes pro forma net income.

Do synergies count in accretion and dilution?

Yes, after tax. Banks usually show the deal with and without synergies and the synergy needed to break even, since cost synergies are more believable than revenue synergies.

Why would a company do a dilutive deal?

Its stock may be richly valued, the deal may be too large to fund with debt, it may want to protect its credit rating, or the target's growth may make later years accretive. EPS dilution in year one is not the same as destroying value.

Is a debt funded buyback accretive?

When the after tax cost of the debt is below the earnings yield. With net income of 100, 100 shares at 20, and 200 borrowed at 5 percent and a 25 percent tax rate, it buys 10 shares, net income falls to 92.5, and EPS rises from 1.00 to about 1.03.