Chapter 4 of 5 · 12 min

Purchase accounting: goodwill and the step-up

Where the purchase price goes on the balance sheet, and the extra amortization it creates.

By the end of this chapter you can

Calculate goodwill with and without an asset write-up
Explain the deferred tax liability a stock deal creates
Work back from reported goodwill to the write-up
Calculate the yearly net income hit from amortizing the step-up

The intuition

You buy a company for $1,000. Its books say its assets, less its debts, are worth $400. But the books are old: its factory and its customer list are really worth $200 more than recorded. So you rewrite them at their true value. That is the step-up, or write-up.

Even after that, you paid more than everything you can put a name to. The rest is goodwill: the price of the brand, the workforce and the synergies you expect. It sits on the balance sheet as an asset.

The key idea

Goodwill = purchase price − fair value of the net assets acquired. In a stock deal the write-up is not tax-deductible, so it creates a deferred tax liability, which lowers net assets and raises goodwill by the same amount.

Why it works

No write-up. Goodwill = purchase price − book equity.
A write-up raises the book value of assets, so less of the price is unexplained: goodwill falls.
The deferred tax liability. When you buy the shares, the tax authority keeps the old tax basis. The higher book value will be depreciated without any tax deduction, so the company will pay more tax than its books suggest. That future tax is recorded now as a liability: write-up × t.
So net assets = book equity + write-up − DTL, and goodwill = price − book equity − write-up × (1 − t).
An asset deal is different: the tax basis steps up too, no DTL is created, and goodwill is lower by exactly the DTL.
The earnings hit. The write-up is amortized over the assets' life. Net income falls by amortization × (1 − t) each year, as the DTL releases. Goodwill is not amortized; it is tested for impairment.

Price $1,000; book equity $400; write-up $200; tax 25%; 10-year life

Goodwill with no write-up: 1,000 − 400	600
Deferred tax liability: 200 × 25%	50
Net assets: 400 + 200 − 50	550
Goodwill, stock deal: 1,000 − 550	450
Goodwill, asset deal: 1,000 − 400 − 200	400
Yearly amortization: 200 ÷ 10	20
Yearly net income hit: 20 × (1 − 25%)	−15

The formulas

Goodwill (no write-up) = purchase price − book equity

The premium over the books.

DTL created = write-up × t (stock deal)

Future tax on depreciation that can never be deducted.

Goodwill = price − (book equity + write-up − DTL) = price − book equity − write-up × (1 − t)

Each dollar of write-up removes only (1 − t) of goodwill.

Yearly amortization = write-up ÷ life; Δ net income = −amortization × (1 − t)

The step-up becomes a yearly charge, softened by the DTL releasing.

Asset deal: no DTL, goodwill = price − book equity − write-up

The tax basis steps up with the books.

Worked example

A stock purchase with a write-up. Create the DTL first, then rebuild net assets, then goodwill.

Drawing the numbers…

See it move

Same deal. Change the write-up, the tax rate and the assets' useful life.

Drawing the numbers…

Try this

Raise the write-up. Goodwill falls, but only by the write-up × (1 − t): the deferred tax liability claws the rest back.
Raise the tax rate. The deferred tax liability grows and stock-deal goodwill rises with it; asset-deal goodwill does not move.
Compare the two goodwill bars: the stock deal's is always higher, by exactly the deferred tax liability.
Lengthen the useful life. The yearly charge shrinks, but over the whole life it still adds up to the write-up.

Run it backwards

Same deal, reversed: you know the price, the book equity and the goodwill reported. How big was the write-up?

Drawing the numbers…

Price less book equity is the premium over book. Whatever part of it is not goodwill was explained by the write-up, net of its deferred tax. So (premium over book − goodwill) = write-up × (1 − t); divide by (1 − t).

The business combinations note in a filing shows this allocation. Running it backwards tells you how much of the price the acquirer could pin to real assets.

Traps

Adding the write-up to goodwill.

A write-up explains part of the price, so it reduces goodwill, by write-up × (1 − t) in a stock deal.

Forgetting the deferred tax liability in a stock deal.

The tax basis does not step up, so the write-up creates a DTL of write-up × t, and goodwill is higher by that amount.

Amortizing goodwill.

Under US GAAP and IFRS goodwill is not amortized; it is tested for impairment. The write-up to PP&E and intangibles is what gets amortized.

Leaving the step-up amortization out of accretion / dilution.

It is a real yearly charge that a simple net income plus net income model misses. Interviewers expect you to name it.

Adding the target's book equity to the acquirer's.

The target's equity is eliminated in consolidation. It is replaced by the price paid, split between net assets and goodwill.

Say it in the interview

The interviewer asks

“How is goodwill calculated, and how does an asset write-up change it?”

Say yours out loud first, then compare.

Check yourself

4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.

Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.

0 of 4

Drawing your questions…

Remember

Goodwill = price − fair value of net assets.
Stock deal: DTL = write-up × t, so goodwill = price − book − write-up × (1 − t).
Asset deal: no DTL, lower goodwill.
The write-up is amortized; goodwill is impairment-tested.