Accretion and dilution: what a deal does to earnings per share
The first question asked of any public acquisition is whether it raises or lowers the buyer's earnings per share. The arithmetic is simple, the shortcut is worth knowing, and the answer says less than it seems to.
01the test
- Pro forma EPS
EPSpf = (NIacq + NItgt + (synergies − new interest − lost interest on cash − extra D&A)·(1 − t)) / (sharesacq + new shares)t is the tax rate; every adjustment is taken after tax.- New shares issued
new shares = price paid in stock / acquirer share price- Accretion or dilution
accretion = EPSpf / EPSacq − 1- The yield shortcut
accretive if cost of funding < NItgt / purchase priceStock costs 1 / acquirer P/E; debt costs r·(1 − t); cash costs the interest it stops earning, after tax.
Pro forma EPS against standalone EPS1,2
A merger model estimates the combined company's earnings per share after the deal and compares it with the acquirer's own EPS without it. Higher is accretive; lower is dilutive.
The all-stock shortcut1
In an all-stock deal the acquirer issues new shares to buy the target's earnings. If the acquirer trades on a higher P/E than the target, each new share buys more earnings than an existing one carries, and the deal adds to EPS; Wall Street Prep's worked example has a buyer on 10x taking over a target on 8x. The other way round, it dilutes.
Debt and cash are not free1
Paying with borrowed money adds interest expense and amortised financing fees, both of which come off pre-tax earnings before the target's profit is added. A deal financed with debt is accretive only if what it buys earns more than what it costs.
Why the shortcut works (computed)1
The P/E rule is one case of a general one. Each way of paying has a cost per unit of price: issuing stock gives away the acquirer's earnings yield, 1 / its P/E; debt costs its after-tax interest rate; cash costs the after-tax interest it no longer earns. The target brings its own yield, its earnings over the price paid. If what is bought yields more than the funding costs, EPS goes up. A buyer on 10x has a 10% cost of stock, and a target bought at 8x yields 12.5%, which is why Wall Street Prep's example is accretive.
A deal, worked both ways (illustrative)1,2
The acquirer earns 100 on 100 shares at 20: EPS 1.00, a P/E of 20x. It buys a target earning 20 for 300, a P/E of 15x and a yield of 20 / 300 = 6.7%. All stock: it issues 300 / 20 = 15 shares, and EPS becomes (100 + 20) / 115 = 1.043, 4.3% accretive - a 5% cost of stock against a 6.7% yield. All debt at 6% with a 25% tax rate: interest is 18, or 13.5 after tax, and EPS becomes (100 + 20 − 13.5) / 100 = 1.065, 6.5% accretive - debt at 4.5% after tax is cheaper still. The numbers are invented for the arithmetic.
next: what moves the answer →
02what moves the answer
Synergies add to the combined earnings1
Expected cost and revenue synergies are added to the combined company's operating profit, which is why a deal that dilutes on day one is often presented as accretive by year two or three.
The accounting takes some of it back1
The purchase premium is allocated to the target's assets: part writes up property, plant and equipment and intangibles, and the rest is booked as goodwill. The write-ups are depreciated and amortised, and that extra charge reduces pro forma earnings.
03what it cannot tell you
Accretive is not the same as a good deal1
Accretion and dilution measure earnings per share, not whether the acquisition will pay off - Wall Street Prep's guide says in terms that the analysis cannot determine that. In an interview, say what the number shows and then what it does not.