The P/E Arbitrage Rule, Explained
The question
State the intuitive P/E-arbitrage rule for when an all-stock deal is accretive versus dilutive to the acquirer's EPS, with no synergies assumed.
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The answer
A stock deal is accretive when the acquirer's own P/E is higher than the P/E it is effectively paying for the target's earnings, and dilutive when the acquirer's P/E is lower. The intuition is simple: the acquirer trades its own shares, which are priced at its own multiple, for the target's earnings stream.
If the acquirer's shares are more expensive per dollar of earnings than what it is paying for the target's earnings, it hands over relatively few shares to pick up that earnings stream. So combined EPS rises. But I would immediately add that accretion is just a mechanical outcome of relative P/E and financing choice. It does not tell me whether the deal creates value.
To assess that I would want to check whether the expected return on the target exceeds our cost of capital. Accretion is a useful quick sanity check for market perception, not a substitute for a rigorous return analysis.
Accretion / dilution
| Acquirer standalone net income | 300 |
| + Target net income | 80 |
| + After-tax synergies | 15 |
| − After-tax incremental interest | (10) |
| Pro forma combined net income | 385 |
| Acquirer standalone EPS | $3.00 |
| Pro forma share count | 125 |
| Pro forma EPS | $3.08 |
| Accretion | 2.7% |
Also asked as
- Acquirer trades at 24x earnings; target trades at 15x earnings with $100M of net income. Acquirer offers a 20% premium in an all-stock deal. Is the deal accretive or dilutive on a no-synergy basis? Show the deal-implied P/E paid.
- List every term that belongs in the pro forma EPS numerator and denominator for a mixed cash/stock/debt deal, and state which terms are after-tax.
- Derive the formula for breakeven premium in an all-stock, no-synergy deal, and explain in words what it represents.
- Explain why debt-funded acquisitions are accretive far more easily than stock-funded acquisitions, and why this makes a bare 'is it accretive' question a weak test of deal quality for debt deals specifically.
- A stock deal is dilutive by $25M of after-tax net income at the proposed price. Tax rate 21%. Compute the pre-tax run-rate synergies required to reach exact EPS breakeven, and explain why you gross up by (1 - tax rate) rather than crediting the synergy figure as stated.
- Acquirer trades at 19x earnings, EPS of $6.00, 200M shares. Target has net income of $180M and currently trades at 13x earnings. Acquirer proposes an all-stock deal at a 35% premium. Compute the deal-implied P/E paid, determine accretion/dilution, and then compute the exact breakeven premium (holding synergies at zero) at which the deal-implied P/E would equal the acquirer's own P/E.
- An acquirer funds a $4,000M acquisition with 50% new debt at 5.5% pre-tax and 50% cash on hand earning 2.5% pre-tax, tax rate 25%. The target contributes $260M of net income. Purchase accounting adds $50M of annual pre-tax incremental D&A. Compute pro forma net income and determine whether the deal is accretive given the acquirer's standalone net income of $1,500M and 120M shares outstanding (no new shares issued, since it's debt/cash funded).
- A board is being pressured to raise its all-stock offer from a 25% premium (which is EPS breakeven with zero synergies) to a 40% premium to beat a rival bidder. Management says $85M of pre-tax synergies 'easily' covers the gap. Walk through how you would test whether that synergy claim is credible, including how the cost-vs-revenue synergy mix and execution risk should change your confidence, and explain what analysis you'd run in parallel to accretion/dilution before advising the board on the higher premium.
- Compare the GAAP accretion/dilution outcome to the 'cash EPS' (excluding deal amortization) outcome for a stock deal where after-tax incremental D&A from write-ups is $45M and the deal is GAAP-dilutive by 2% but cash-accretive by 1.5%. Explain why management might emphasize the cash EPS figure publicly, and what a skeptical analyst should ask in response.
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The rest of this topic
Accretion and dilution