Full Accretion/Dilution Analysis

Step 1: Offer Price and Equity Purchase Price

Offer Price per Share = $20.00 × (1 + 1.50) = $50.00

Equity Purchase Price = $50.00 × 50.0m shares = $2,500.0m

Note that at a 150% premium, the acquirer is effectively paying 25.0x the target's net income ($2,500.0m / $100.0m) — well above the acquirer's own 20.0x multiple ($50.00 / $2.50 EPS). Paying a higher multiple for the target than the market pays for the acquirer is usually the first sign a deal could be dilutive.

Step 2: Acquirer Standalone EPS

EPS = $500.0m / 200.0m shares = $2.50

This is the benchmark every pro forma scenario below gets compared against — "accretive" means pro forma EPS ends up above $2.50, "dilutive" means it ends up below.

Step 3: Pro Forma Net Income and EPS — All-Cash Structure

Where: the $2,500.0m purchase price is financed entirely with new debt.

Using the new debt amount ($2,500.0m), the interest rate (6.0%), and the tax rate (25.0%):

After-Tax Interest Expense = $2,500.0m × 6.0% × (1 - 0.25) = $112.5m

Pro Forma Net Income = $500.0m + $100.0m - $112.5m = $487.5m

Pro Forma EPS = $487.5m / 200.0m shares = $2.44 (-2.5% vs. the $2.50 standalone EPS)

The all-cash structure is dilutive here because the after-tax cost of the new debt (6.0% × 0.75 = 4.5%) is higher than the target's earnings yield ($100.0m / $2,500.0m = 4.0%). Whenever the cost of financing a deal exceeds the yield the target's earnings generate on the price paid, cash-funded EPS accretion turns negative — this is one of the fastest sanity checks bankers run before modeling anything else.

Step 4: Pro Forma Net Income and EPS — All-Stock Structure

Using the equity purchase price ($2,500.0m) and the acquirer's share price ($50.00):

New Shares Issued = $2,500.0m / $50.00 = 50.0m shares

Pro Forma Shares Outstanding = 200.0m + 50.0m = 250.0m shares

Pro Forma Net Income = $500.0m + $100.0m = $600.0m (no interest expense enters an all-stock deal)

Pro Forma EPS = $600.0m / 250.0m shares = $2.40 (-4.0% vs. the $2.50 standalone EPS)

The stock structure is also dilutive, and by a wider margin than cash, because the acquirer is issuing shares at its own 20.0x P/E to buy earnings priced at 25.0x — the classic "buying expensive earnings with cheap currency" problem that shows up whenever the transaction multiple exceeds the acquirer's own trading multiple.

Step 5: Synergy Break-Even for Each Structure

Where: Required Net Income is the pro forma net income level that would produce exactly the $2.50 standalone EPS on each structure's own share count.

All-Cash: Required Net Income = $2.50 × 200.0m = $500.0m

Pre-Tax Synergies Needed = ($500.0m - $487.5m) / (1 - 0.25) = $16.7m

All-Stock: Required Net Income = $2.50 × 250.0m = $625.0m

Pre-Tax Synergies Needed = ($625.0m - $600.0m) / (1 - 0.25) = $33.3m

These synergy targets are what a deal team would present to the board as the minimum cost or revenue synergies the combined entity must realize — on a run-rate, pre-tax basis — before the deal can be called EPS-neutral. In practice, boards and analysts also want to see how quickly those synergies are realistic to achieve (year one vs. year three), since a deal that is only breakeven once synergies fully phase in three years out carries very different risk than one that is breakeven from day one.

Final Results

• All-Cash Pro Forma EPS: $2.44 (-2.5%, dilutive)
• All-Stock Pro Forma EPS: $2.40 (-4.0%, dilutive)
• Pre-Tax Synergies Needed to Break Even (Cash): $16.7m
• Pre-Tax Synergies Needed to Break Even (Stock): $33.3m

These four numbers are exactly what feeds into a full merger consequences model — the pro forma EPS, balance sheet, and credit metrics a deal team builds out once a structure is chosen.

Would you like to explore how a blended 50% cash / 50% stock structure changes these results, or how a target's NOL carryforward would affect the after-tax numbers?