Merger Model Interview Questions: Accretion Retested

The two companies and the offer on the table

Arden Holdings earns $400 million of net income on 200 million shares, so earnings per share are $2.00. It trades at 18.0 times, which puts the share price at $36.00.

Bellweather earns $90 million on 50 million shares, so earnings per share are $1.80. Its unaffected share price is $21.00. Arden offers $27.00 a share, which is a premium of 28.6 percent and values Bellweather's equity at $1,350 million.

At the offer, Bellweather is priced at 27.00 over 1.80, which is 15.00 times earnings. Hold on to that number. Almost every question about this deal resolves by comparing 15.00 times to something else.

Acquisition debt costs 6.50 percent. The five year Treasury constant maturity stood at 5.06 percent and the ten year at 5.26 percent on 29 September 2026, checked 1 October 2026 at federalreserve.gov, so 6.50 percent is the five year point plus 144 basis points. The base is published and the spread is ours.

Tax is 21 percent. The IRS states that corporations "figure their tax by multiplying taxable income by 21% (0.21)", checked 1 October 2026 at irs.gov. Every conversion below runs on that rate.

All cash, and the threshold that governs it

Take the whole $1,350 million from new debt. Interest is 6.50 percent of $1,350 million, which is $87.75 million. After tax that is 87.75 times 0.79, which is $69.32 million.

Pro forma net income is 400 plus 90 less 69.32, which is $420.68 million. The share count does not move, because no shares were issued. Earnings per share are 420.68 over 200, which is $2.1034. Against $2.00 that is 5.17 percent of accretion.

Now the threshold. The after tax cost of debt is 6.50 times 0.79, which is 5.135 percent. Its inverse is 1 divided by 0.05135, which is 19.47 times. A cash deal is accretive when the multiple paid for the target's earnings sits below that.

We paid 15.00 times against a threshold of 19.47 times, so the deal is accretive, and the arithmetic above confirms it. The rule of thumb and the model agree because they are the same statement.

Two things the threshold hides. It ignores forgone interest on cash spent from the balance sheet, which would raise the effective cost. And it ignores every accounting consequence of the purchase, which is the subject of the next two sections.

All stock, and the offer that breaks even

Now pay entirely in Arden shares. At $36.00 a share, $1,350 million of consideration requires 1,350 over 36.00, which is 37.50 million new shares. That is an exchange ratio of 0.75 Arden shares for each Bellweather share.

Pro forma net income is simply 400 plus 90, which is $490 million, because no interest was incurred. The share count becomes 200 plus 37.50, which is 237.50 million. Earnings per share are 490 over 237.50, which is $2.0632. Against $2.00 that is 3.16 percent of accretion.

The stock threshold is cleaner than the cash one. A stock deal is earnings neutral when the multiple paid equals the acquirer's own multiple. Arden trades at 18.0 times, so the neutral offer is 18.0 times Bellweather's $1.80, which is $32.40 a share. That is a premium of 54.3 percent on the unaffected $21.00.

Read the ordering. Cash beats stock here because debt at 5.135 percent after tax is cheaper than equity at an implied 5.56 percent, which is the inverse of 18.0 times. That comparison is the whole answer to "which should they use", and it is two divisions long.

The convention that turns a merger model from accretive to dilutive

Everything above ignored the purchase accounting. Put it back.

Arden pays $1,350 million for a business whose book equity is $420 million. The excess is $930 million. A valuation after closing allocates part of that excess to identifiable intangible assets. Say $300 million, amortized on a straight line over ten years.

Amortization is $30 million a year pre tax, which is $23.70 million after tax. Subtract it. GAAP pro forma net income becomes 420.68 less 23.70, which is $396.98 million. GAAP earnings per share are 396.98 over 200, which is $1.9849.

Against $2.00 standalone, that is dilution of 0.76 percent.

Same deal. Same price. Same interest rate. Same tax rate. Every number above is arithmetically correct, and the deal is accretive on one measure and dilutive on the other. A candidate who says "accretive" without naming the measure has a coin flip's chance of being right.

This is why the convention gets documented rather than assumed. One employer writes in its own risk factors that its advisory role "involves complex analysis and the exercise of professional judgment, including, in particular, in rendering fairness opinions in connection with mergers and other transactions", checked 1 October 2026 at sec.gov. Professional judgment here means writing down which earnings measure you used.

Synergies, and the tax that eats a fifth of them

Suppose Arden identifies $25 million a year of cost synergies. Those are pre tax savings, so they arrive in net income after tax: 25 times 0.79, which is $19.75 million.

Add that to the cash case. Net income becomes 420.68 plus 19.75, which is $440.43 million. Earnings per share are $2.2021, and accretion rises to 10.11 percent.

Count the synergies before tax instead and you would report 445.68 of net income, $2.2284 of earnings per share, and 11.42 percent of accretion. That is 1.3 points of accretion manufactured by skipping a multiplication.

Three follow ups are standard and each has a short answer.

1. How much in savings does the deal need. None. It is accretive at $27.00 on either financing route before any cost savings at all, so the savings are upside rather than justification.
2. What premium do synergies support. The $19.75 million of after tax savings, capitalized at Arden's 18.0 times multiple is $355.5 million of value, which is $7.11 a Bellweather share on 50 million shares.
3. What about costs to achieve. A one time restructuring charge hits the year it is taken and not the run rate. Say which year and keep it out of the recurring earnings per share.

What purchase price allocation creates in a merger model

Work the balance sheet entries, because interviewers ask for goodwill and most answers forget one line.

Purchase equity value is $1,350 million. Target book equity is $420 million. The excess is $930 million. Allocate $300 million to identifiable intangibles.

Here is the line that gets dropped. Writing up an intangible for book purposes without a matching step up in tax basis creates a deferred tax liability. At 21 percent, that is 21 percent of $300 million, which is $63 million.

Goodwill is therefore 1,350 less 420 less 300 plus 63, which is $693 million.

Omit the deferred tax liability and goodwill comes out at $630 million, which is 9 percent light. The error never shows up in the income statement, because the amortization base is unchanged. It shows up only on the balance sheet, which is exactly why it survives so many models.

One more consequence worth a sentence. The deferred tax liability unwinds as the intangible amortizes, so it reduces the tax charge by $6.3 million a year for ten years. That is a book entry with no cash in it.

The consideration mix interview questions, answered

Four more come up, and all four are decided by the same two thresholds.

1. Why would an acquirer use stock when cash is cheaper. Because it thinks its own shares are expensive, or because it wants the target's shareholders exposed to the combination, or because it cannot raise the debt. Earnings per share is one input into that choice.
2. What if the acquirer pays from existing cash rather than new debt. Then the cost is the interest it stops earning. At the three month Treasury bill rate of 4.07 percent on 29 September 2026, forgone interest on $1,350 million is $54.95 million pre tax and $43.41 million after tax, which is cheaper than the 6.50 percent debt and therefore more accretive.
3. What happens to the combined multiple. Arden's 18.0 times buys earnings at 15.00 times, so the combined entity is worth more than the sum of the parts on a multiple basis alone. That gap is the entire mechanism behind multiple arbitrage.
4. Does accretion mean the deal creates value. No. Accretion is an earnings statement about one year. Paying a 28.6 percent premium destroys value if the target is worth less than $27.00, and earnings per share will still rise.

The fourth is the one that separates answers. Earnings accretion and value creation are different tests, and a model that only runs the first has not answered the board's question.

How a merger model answer gets scored

Our math rubric puts four weights on a calculation, and the weights are ours. No bank publishes a marking scheme, and one named employer's 119 open requisitions read on 1 October 2026 at its Workday portal name a merger model exactly once, under the term "merger consequence". The reasoning behind each weight sits on how an answer is assessed.