SME
Engineering Economics · Problem type
After-tax cash flow
Use this for “A machine brings in $30,000 a year before tax and is depreciated $12,000 this year. At a 21% tax rate, what is the after-tax cash flow?”
Chart
ATCF = BTCF − T
30,000 − 3,780 = 26,220
The flows in add and the flows out take away: ATCF = 26,220.
This is an example. Type your own values to start a new problem.
$
TI
=
$
BTCF
−
$
D
$
T
=
t
%
×
$
TI
$
ATCF
=
$
BTCF
−
$
T
Formulas
TI
=
BTCF
−
D
18,000 = 30,000 − 12,000
T
=
t
100
×
TI
3,780
=
21
100
×
18,000
ATCF
=
BTCF
−
T
26,220 = 30,000 − 3,780
Assumptions
•
BTCF is the year’s revenue less its operating expenses.
•
Depreciation is not cash: it only lowers the taxable income, and so the tax.
•
One effective tax rate t; a loss (TI below 0) counts as a credit against other income.
Step-by-step
WE KNOW
BTCF = $30,000, D = $12,000, t = 21%
FIND
taxable income (TI), income tax (T), after-tax cash flow (ATCF)
Step 1 · Find taxable income (TI)
Use TI = BTCF − D
Depreciation is an expense for tax, so it comes off the cash before tax is figured.
TI = 30,000 − 12,000
TI = $18,000
Step 2 · Find income tax (T)
Use T = t ÷ 100 × TI
The tax is the rate times the taxable income; below 0 it is a credit.
T
=
21
100
×
18,000
T
=
0.21
×
18,000
T
=
$3,780
Step 3 · Find after-tax cash flow (ATCF)
Use ATCF = BTCF − T
Only the tax leaves as cash; the depreciation never did.
ATCF = 30,000 − 3,780
ATCF = $26,220
Check
Put the numbers back in. Both sides should match.
18,000 = 30,000 − 12,000 ✓
3,780
=
21
100
×
18,000
✓
26,220 = 30,000 − 3,780 ✓
Topic check
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