Walk me through how each of the three financing sources (cash on hand, new debt, and new stock) affects pro forma EPS, and where each one shows up in the accretion/dilution build.

Cash and debt hit the numerator by reducing pro forma net income after tax; stock hits the denominator by increasing diluted shares. Here is the walkthrough.

1. Cash on hand. I use existing cash, so I issue no new shares. But that cash had been earning interest, and now that income disappears. In the build, I subtract foregone interest income multiplied by one minus the tax rate from pro forma net income. The impact is a smaller numerator.
2. New debt. Again, no new shares. I borrow and incur interest expense, which is tax-deductible. In the build, I subtract the after-tax interest expense, new debt times the borrowing rate times one minus the tax rate, from net income. The numerator shrinks by that after-tax cost.
3. New stock. Here the income statement is untouched. Instead, I issue new acquirer shares equal to the stock consideration divided by my share price. Those shares are added directly to the diluted share count in the denominator, and that dilution is the entire EPS effect. The cost is measured by my earnings yield. So cash and debt flow through the numerator as after-tax costs; stock flows through the denominator as new shares. Every adjustment must be after-tax to get the true EPS change.

What interviewers are really testing

Accretion/dilution is the single most common merger-math question at every level, and the financing-mix variant is how interviewers separate memorizers from candidates who understand the machine.

First, mechanical fluency. You should be able to take acquirer net income, target net income, a purchase price, and a financing mix, and produce pro forma EPS in under a minute, tax-affecting every adjustment without being prompted. Hesitating on whether interest is pre- or post-tax is an instant tell.

Second, the cost-of-financing intuition. Strong candidates don't just compute; they frame: 'the deal is accretive if the target's earnings yield at the offer price beats the weighted after-tax cost of the funding.' Saying this before doing any arithmetic signals you know why the answer will come out the way it does, and lets you sanity-check your own math.

Third, the limits of the P/E rule. Interviewers love to bait candidates into applying 'higher P/E buys lower P/E = accretive' to a cash deal. Knowing the shortcut only holds for all-stock consideration, and being able to explain what replaces it (after-tax cost of debt vs target earnings yield), is a strong differentiator.

Fourth, judgment. The best candidates volunteer that accretion is cosmetic: a 100% debt-financed deal at a low rate is almost always accretive, yet can still destroy value if the premium exceeds the PV of synergies. At elite boutiques (Evercore, PJT, Lazard), where advisory work is about advising boards on value, this point lands especially well.

Signal mastery by narrating structure before numbers: 'Three things change: the numerator picks up target earnings and synergies and loses financing costs, the denominator picks up new shares if stock is used. Let me size each.' That framing, delivered calmly, is what a superday is listening for.

Common traps

Trap 1: Forgetting to tax-affect the financing cost. Candidates subtract the full interest expense on new debt (or the full foregone interest on cash) from pro forma net income. Interest is a pre-tax expense: the earnings hit is only (1 - t) of it.

Say it out loud: "New debt of $500 at 6% is $30 of interest, but after tax at 25% the net income hit is only $22.5: interest is deductible, so I multiply by one minus the tax rate."

Trap 2: Computing new shares (or the target's earnings yield) off the unaffected price instead of the offer price. The acquirer must fund the full equity purchase price including the premium, and the earnings yield you're buying is target net income over the price you actually pay.

Say it out loud: "The target trades at $40 but we're offering a 25% premium, so I size the consideration, and the P/E paid, off $50 per share, not $40."

Trap 3: Dividing new shares by the wrong price. New shares issued = stock consideration divided by the acquirer's share price (it's the acquirer's paper being printed), not the target's price.

Say it out loud: "We're issuing $2 billion of stock and our shares trade at $100, so that's 20 million new acquirer shares: the target's price only matters for sizing the consideration."

Trap 4: Applying the P/E shortcut to a cash or debt deal. "Acquirer P/E above target P/E means accretive" only compares earnings currencies in an all-stock deal. In a cash/debt deal the comparison is the target's earnings yield versus the after-tax cost of funds.

Say it out loud: "The P/E rule only works for all-stock deals. For a cash deal I compare the target's earnings yield at the offer price against the after-tax cost of debt: if we're paying 20x, that's a 5% yield versus roughly 4.5% after-tax debt cost, so it's modestly accretive."

Trap 5: Ignoring foregone interest on balance-sheet cash. Cash isn't free: using it forfeits interest income, which was in the acquirer's standalone net income.

Say it out loud: "Using $1 billion of cash earning 4% costs us $40 million of pre-tax interest income, or $30 million after tax: cash is cheap financing, but not free."

Trap 6: Mixing pre-tax and after-tax quantities in the accretion rule. Earnings yields are after-tax by construction (net income over price); comparing them against a pre-tax coupon overstates the cost of debt and can flip your answer.

Say it out loud: "I'm comparing after-tax to after-tax: the target's earnings yield is already an after-tax number, so the debt hurdle is the coupon times one minus the tax rate."