SME
Engineering Economics · Problem type
MACRS depreciation
Use this for “An $84,000 machine is 7-year MACRS property. Its year-3 rate is 17.49%, and 56.27% to date. What are D₃ and BV₃?”
Chart
BVⱼ = C − ΣD
84,000 − 47,270 = 36,730
The flows in add and the flows out take away: BVⱼ = 36,730.
This is an example. Type your own values to start a new problem.
$
Dⱼ
=
rⱼ
%
×
$
C
$
ΣD
=
Σr
%
×
$
C
$
BVⱼ
=
$
C
−
$
ΣD
Formulas
Dⱼ
=
rⱼ
100
×
C
14,691.6
=
17.49
100
×
84,000
ΣD
=
Σr
100
×
C
47,266.8
=
56.27
100
×
84,000
BVⱼ
=
C
−
ΣD
36,733.2 = 84,000 − 47,266.8
Assumptions
•
Type rⱼ and Σr from the IRS MACRS table for the property class (half-year convention).
•
MACRS ignores salvage: the rates add to 100%, so the book value ends at 0.
•
The table has one more row than the class has years: the first and last years are half years.
Step-by-step
WE KNOW
C = $84,000, rⱼ = 17.49%, Σr = 56.27%
FIND
depreciation this year (Dⱼ), depreciation to date (ΣD), book value (BVⱼ)
Step 1 · Find depreciation this year (Dⱼ)
Use Dⱼ = rⱼ ÷ 100 × C
MACRS takes the year’s rate times the whole cost basis, not times the book value.
Dⱼ
=
17.49
100
×
84,000
Dⱼ = 0.1749 × 84,000
Dⱼ = $14,691.60
Step 2 · Find depreciation to date (ΣD)
Use ΣD = Σr ÷ 100 × C
Every year’s depreciation is its rate times the same basis, so the rates to date give the total.
ΣD
=
56.27
100
×
84,000
ΣD = 0.5627 × 84,000
ΣD = $47,266.80
Step 3 · Find book value (BVⱼ)
Use BVⱼ = C − ΣD
The book value is the basis less all the depreciation taken so far.
BVⱼ = 84,000 − 47,266.8
BVⱼ = $36,733.20
Check
Put the numbers back in. Both sides should match.
14,691.6
=
17.49
100
×
84,000
✓
47,266.8
=
56.27
100
×
84,000
✓
36,733.2 = 84,000 − 47,266.8 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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