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Chapter 1 of 6 · 10 min

Depreciation through the three statements

The walk-through almost every interview starts with, and why an expense can raise cash.

By the end of this chapter you can
  • Walk a change in depreciation through all three statements, in order
  • Explain why cash rises by depreciation × tax rate
  • Show that the balance sheet still balances
  • Work back from the change in cash to the depreciation that caused it
1

The intuition

You buy a delivery van for $50,000 cash. The day you buy it, the cash is gone. Over the next five years the van wears out, so your accountant charges $10,000 of depreciation each year, spreading its cost across the years you use it.

That $10,000 is an expense, but no cash leaves in those years: you paid for the van on day one. What does change is your tax bill. Depreciation is tax-deductible, so you pay less tax. The expense is on paper; the tax saving is real cash.

The key idea

Extra depreciation lowers net income by D × (1 − t) but raises cash by D × t. Profit goes down and cash goes up.

2

Why it works

Interviewers love depreciation because it touches every statement and every link between them. Walk it in the same order every time:

  • Income statement. Depreciation is an expense, so pre-tax income falls by D. Tax expense falls by D × t, so net income falls by only D × (1 − t).
  • Cash flow statement. It starts from net income, which is down D × (1 − t). Depreciation used no cash, so it is added back in full. Cash from operations ends up D × t higher: exactly the tax saved.
  • Balance sheet. Cash is up D × t and PP&E (the van) is down D, so total assets fall by D × (1 − t). On the other side, retained earnings fall by the drop in net income, D × (1 − t). Both sides move by the same amount, so it balances.
$10 more depreciation at a 25% tax rate
Income statement: pre-tax income−10.0
Tax expense−2.5
= Net income−7.5
Cash flow statement: net income−7.5
+ Add back depreciation+10.0
= Change in cash+2.5
Balance sheet: cash +2.5, PP&E −10.0assets −7.5
= Retained earnings−7.5, balances
3

The formulas

Δ Net income = −D × (1 − t)

The expense, after the tax it saves.

Δ Cash from operations = −D × (1 − t) + D = D × t

Add the non-cash expense back and only the tax saving is left.

Δ PP&E = −D

The asset's book value falls by the full depreciation.

Δ Total assets = D × t − D = −D × (1 − t)

More cash, less PP&E.

Δ Equity = −D × (1 − t)

Retained earnings fall with net income, so both sides match.

4

Worked example

The classic three-statement walk-through, with fresh numbers. Say each line out loud before you reveal it.

Drawing the numbers…
5

See it move

Same company. Move the depreciation and the tax rate and watch all three statements change together.

Drawing the numbers…
Try this
  • Set the tax rate to zero. Net income falls by the full depreciation, and cash does not move at all.
  • Double the depreciation. Every figure doubles, because every effect is proportional to D.
  • Move the tax rate. The fall in net income plus the rise in cash always adds up to exactly the depreciation.
  • Whatever you change, the balance check stays green: assets and liabilities plus equity move together.
6

Run it backwards

Same company, reversed: you only see cash moving. How much depreciation caused it?

Drawing the numbers…

Cash only moved because of tax, so the change in cash is D × t. Divide by the tax rate to get D.

This is the question that separates students who memorized "cash goes up by the tax shield" from students who understand why. With a zero tax rate it could not be answered at all: nothing would have moved.

7

Traps

Saying cash falls because depreciation is an expense.
Depreciation uses no cash. The only cash effect is the lower tax bill, so cash rises by D × t.
Saying cash is unchanged because depreciation is non-cash.
The expense is non-cash, but it lowers taxes, and taxes are paid in cash.
Adding back only the after-tax depreciation on the cash flow statement.
Add back the full D. The tax effect is already inside net income.
Forgetting PP&E on the balance sheet.
The asset falls by the full D. Without it, assets rise while equity falls, and nothing balances.
Saying EBITDA falls.
Depreciation sits below EBITDA, so EBITDA does not change. EBIT falls by D.
8

Say it in the interview

The interviewer asks

“Depreciation goes up by $10 at a 25% tax rate. Walk me through the three statements.”

Say yours out loud first, then compare.
9

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
  • Net income: −D × (1 − t).
  • Cash: +D × t, the tax shield.
  • PP&E −D; retained earnings −D × (1 − t): it balances.
  • EBITDA does not move; EBIT falls by D.