Merger Accretion and Dilution

Merger Accretion and Dilution

Merger Accretion and Dilution: What a Deal Does to Earnings per Share

What it does

When one company buys another, its earnings per share (EPS) change: it gains the target's profit, and it pays for it with new shares, with interest on borrowed cash, or with both. A deal is called accretive when the buyer's EPS after the deal is higher than its EPS without the deal, and dilutive when it is lower. The page works through this arithmetic in the order it is done by hand and reports the change in money per share and in percent. The words describe the arithmetic only; they are not a verdict on the deal.

The method

Subscript B is the buyer, T the target. NI is net income (profit after tax), Sh the shares outstanding, P the share price, t the tax rate.

Each company alone. EPS = NI/Sh. The price-to-earnings ratio is P/E = P/EPS: what the market pays for one unit of yearly earnings.

The price paid. With an offer premium p over the target's share price:

P_off = P_T(1 + p)
equity purchase price Eq = P_off Sh_T
P/E paid = P_off/EPS_T

Paying for it. A fraction s of the price is paid in new buyer shares, valued at the buyer's share price; the rest is cash, borrowed at the interest rate i:

new shares = s Eq/P_B = s × ER × Sh_T, with the exchange ratio ER = P_off/P_B (buyer shares per target share)
new debt = (1 − s) Eq
interest after tax = debt × i × (1 − t)

Interest is deducted before tax, so it lowers net income by only (1 − t) of its amount.

The combined company (pro forma). Synergies, Syn, are the yearly savings or extra profit from combining the two, before tax:

NI_PF = NI_B + NI_T + Syn(1 − t) − interest after tax
Sh_PF = Sh_B + new shares
EPS_PF = NI_PF/Sh_PF

Accretion or dilution. EPS_PF − EPS_B in money per share, and (EPS_PF − EPS_B)/EPS_B in percent.

Break-even synergies. Setting EPS_PF = EPS_B and solving for the synergies gives the pre-tax amount at which the deal leaves EPS unchanged:

Syn_BE = [EPS_B Sh_PF − (NI_PF without synergies)]/(1 − t)

A negative value means the deal is accretive with no synergies at all.

The P/E rule. For a deal paid wholly in stock, with no synergies, EPS_PF = (NI_B + NI_T)/(Sh_B + Eq/P_B). This is above EPS_B exactly when NI_T/Eq is above EPS_B/P_B, that is, when the buyer's P/E is above the P/E paid. The page computes the all-stock EPS and prints the two P/Es so the rule can be seen as a consequence of the arithmetic.

Ownership. The buyer's shareholders hold Sh_B/Sh_PF of the combined company and the target's former shareholders hold the new shares, new shares/Sh_PF.

Advanced. The buyer's own cash C is used before debt is raised; it stops earning interest at the rate i_c, a cost of C i_c(1 − t) a year. Transaction fees F are paid in cash at closing, so the cash needed is (1 − s) Eq + F and the debt is that less C; their one-time expense is left out of EPS. Purchase-price allocation: the buyer records the target's assets at fair value; a write-up W is charged against earnings over N years, costing (W/N)(1 − t) a year. All three are subtracted in NI_PF. Second year: each net income grows at its entered rate, the synergies counted are the entered share of the full amount in each year, and the debt and the shares are unchanged. Contribution analysis: each company's share of the combined net income and market value beside its shareholders' share of ownership.

What it assumes

The net incomes entered are those expected for the first year after the deal, each company alone. New shares are issued at the buyer's current share price, which does not move on the announcement. All of the cash part not covered by the buyer's own cash is borrowed at one interest rate and is not repaid in the two years shown. One tax rate applies to interest, synergies and amortisation. The target has no debt that must be refinanced and no options or convertible securities that add shares. Synergies cost nothing to achieve. The write-up is the only accounting adjustment: goodwill is not amortised, and deferred taxes are not shown separately.

When it misleads

EPS accretion is not value creation. EPS rises whenever the earnings bought cost less, per unit, than the financing used: a buyer with a high P/E makes almost any all-stock purchase accretive, and cheap debt makes almost any cash purchase accretive. Neither says the price is right. Value depends on whether the target, with its synergies, is worth more than the price paid, which a discounted cash flow addresses and this arithmetic does not.

Debt raises EPS and risk together. Paying in cash adds interest but no shares, so it often shows more accretion than stock. The combined company also carries more debt, and its earnings become more variable; the market may value each unit of those earnings lower.

One year is a snapshot. Synergies arrive late and cost money to achieve, and a fast-growing target dilutes at first and adds later. The second-year section shows the direction, not the whole path.

The buyer's P/E need not survive the deal. The P/E rule compares today's multiples. If the market applies a lower multiple to the combined earnings, a deal that is accretive to EPS can still lower the share price.

The inputs are estimates. Forecast earnings, synergies and the premium needed to win the target are all uncertain; the table of accretion against premium and stock percentage shows how far the answer moves.

Worked example

The default case is two illustrative companies, not real ones; money and shares are in millions. Buyer: net income 500, 200 shares, price 40. Target: net income 100, 50 shares, price 30. Premium 30 percent, half paid in stock, debt at 6 percent, tax 25 percent, synergies 40.

EPS_B = 500/200 = 2.50 and P/E = 40/2.50 = 16.0. EPS_T = 100/50 = 2.00 and P/E = 30/2.00 = 15.0.

Offer price = 30 × 1.30 = 39.00; purchase price = 39 × 50 = 1,950; P/E paid = 39/2.00 = 19.5.

Stock part 975: new shares = 975/40 = 24.375 (exchange ratio 39/40 = 0.975). Cash part 975, borrowed: interest after tax = 975 × 0.06 × 0.75 = 43.875.

NI_PF = 500 + 100 + 40 × 0.75 − 43.875 = 586.125. Sh_PF = 224.375. EPS_PF = 586.125/224.375 = 2.6123.

Accretion = 2.6123 − 2.5000 = 0.1123 a share, or 4.49 percent.

Break-even synergies = (2.50 × 224.375 − 556.125)/0.75 = 6.42: without synergies the deal would be dilutive, and 6.42 a year before tax brings EPS back to 2.50.

All stock, no synergies: shares = 200 + 1,950/40 = 248.75, EPS = 600/248.75 = 2.4121, a change of −3.52 percent. The buyer's P/E of 16.0 is below the 19.5 paid, as the rule says.

Ownership: the buyer's shareholders hold 200/224.375 = 89.1 percent and the target's 10.9 percent.

Advanced, with 200 of the buyer's own cash earning 3 percent, fees of 20, a write-up of 300 over 10 years and half of the synergies in the first year: debt = 975 + 20 − 200 = 795, interest after tax 35.775, lost interest 4.50, amortisation 22.50, NI_PF = 600 + 15 − 62.775 = 552.225, EPS_PF = 2.4612, a dilution of 1.55 percent. In the second year, with growth of 5 and 8 percent and the full synergies, NI_PF = 525 + 108 + 30 − 62.775 = 600.225 and EPS_PF = 2.6751 against 2.6250 alone, an accretion of 1.91 percent.

A calculator for education and analysis, not investment advice.