25 Pts.) 4. A small paint company owns an air compressor that should possibly be
ID: 2648412 • Letter: 2
Question
25 Pts.) 4. A small paint company owns an air compressor that should possibly be replaced. A new model which sells for $1500 will last 7 years with annual costs estimated to be $100 the first year and increasing $50 each year thereafter, and a zero salvage value. The old compressor can be sold at the following prices: $400 now, $300 next year, or $50 the last year. The company will keep the compressor for a maximum of two more years since the operating expenses are expected to increase to $175 next year and $350 the following yea r. When should the company buy the new compressor, assuming all cost projections remain as estimated now. The investment rate is 12% per year.Explanation / Answer
Case-1: If replaced Now
Year
0
1
2
3
4
5
6
7
Initial cost
1500
Proceed from sale
-400
Annual cost
100
150
200
250
300
350
400
Net Cost
1100
100
150
200
250
300
350
400
P.V@12%
1100.00
89.29
119.58
142.36
158.88
170.23
177.32
180.94
NPV
2138.59
Equivalent annual cost=NPV/Annuity Factor(7years,12%) =NPV/4.56
282.882143
Equivalent annual cost (282)>operating expense (175).
Thus using the older machine will have lower operating expense
Cae-2:If replaced by next year
Year
0
1
2
3
4
5
6
7
Initial cost
1500
Proceed from sale
-300
Annual cost
100
150
200
250
300
350
400
Net Cost
1200
100
150
200
250
300
350
400
P.V@12%
1200.00
89.29
119.58
142.36
158.88
170.23
177.32
180.94
NPV
2238.59
Equivalent annual cost=NPV/Annuity Factor(7years,12%) =NPV/4.56
296.109656
Equivalent annual cost (296)>operating expense (350).
Thus using the older machine will have higher operating expense now.
Case-3: If replaced last year
Year
0
1
2
3
4
5
6
7
Initial cost
1500
Proceed from sale
-50
Annual cost
100
150
200
250
300
350
400
Net Cost
1450
100
150
200
250
300
350
400
P.V@12%
1450.00
89.29
119.58
142.36
158.88
170.23
177.32
180.94
NPV
2488.59
Equivalent annual cost=NPV/Annuity Factor(7years,12%) =NPV/4.56
329.178439
Thus machine should be replace after 1 year, when the operating cost of using old machine is much higher than equivalent annual cost of new machine
Year
0
1
2
3
4
5
6
7
Initial cost
1500
Proceed from sale
-400
Annual cost
100
150
200
250
300
350
400
Net Cost
1100
100
150
200
250
300
350
400
P.V@12%
1100.00
89.29
119.58
142.36
158.88
170.23
177.32
180.94
NPV
2138.59
Equivalent annual cost=NPV/Annuity Factor(7years,12%) =NPV/4.56
282.882143
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