SME
Construction Engineering · Problem type
Owning and operating cost per unit
Use this for “A $420,000 loader sells for $60,000 after 10,000 h; it costs $48/h to run and its operator earns $45/h. At 150 m³/h, what does each cubic meter cost?”
Chart
Depreciation: $36/h
Operating: $48/h
Operator: $45/h
This is an example. Type your own values to start a new problem.
Dₕ ($/h)
=
$
−
$
N (h)
Cₕ ($/h)
=
Dₕ ($/h)
+
Oₕ ($/h)
+
W ($/h)
c ($/m³)
=
Cₕ ($/h)
P (m³/h)
Cₚ is the purchase price, S the salvage value and N the machine’s life in hours.
Formulas
Dₕ
=
Cₚ −
S
N
36
=
420,000 − 60,000
10,000
Cₕ
=
Dₕ
+
Oₕ
+
W
129 = 36 + 48 + 45
c
=
Cₕ
P
0.86
=
129
150
Assumptions
•
Straight-line depreciation: the machine loses the same value in each of its working hours.
•
Interest, insurance and taxes, when given per hour, are added into Oₕ.
•
P is the hourly production the machine really reaches on the job.
Step-by-step
WE KNOW
Cₚ = $420,000, S = $60,000, N = 10,000 h, Oₕ = 48 $/h, W = 45 $/h, P = 150 m³/h
FIND
depreciation per hour (Dₕ), hourly cost (Cₕ), unit cost (c)
Step 1 · Find depreciation per hour (Dₕ)
Use Dₕ = (Cₚ − S) ÷ N
The value the machine loses over its life, shared equally among its working hours.
Dₕ
=
420,000 − 60,000
10,000
Dₕ
=
360,000
10,000
Dₕ = 36 $/h
Step 2 · Find hourly cost (Cₕ)
Use Cₕ = Dₕ + Oₕ + W
Each hour costs the owning share, the running costs and the operator together.
Cₕ = 36 + 48 + 45
Cₕ = 129 $/h
Step 3 · Find unit cost (c)
Use c = Cₕ ÷ P
Each
hour
costs
Cₕ
and
moves
P
cubic
meters,
so
each
cubic
meter
costs
their
quotient.
c
=
129
150
c
=
0.86
$/
m
3
Check
Put the numbers back in. Both sides should match.
36
=
420,000 − 60,000
10,000
✓
129 = 36 + 48 + 45 ✓
0.86
=
129
150
✓
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