A used car can be kept for two more years and then sold for an estimated $3000,
ID: 2613720 • Letter: A
Question
A used car can be kept for two more years and then sold for an estimated $3000, or it could be sold now for $9500. The average annual maintenance cost over the past 7 years has been $500 per year. However, if the car is kept for two more years this cost is expected to be $1800 the first year and $2000 the second year. As an alternative a new car can be purchased for $22,000 and be used for 4 years, after which it can be sold for $8000. The new car will be under warranty for the first 4 years, and not extra maintenance cost will be incurred during those years. If the MARR is 15% per year what is the better option and why?
Explanation / Answer
We need to compute Equivalent annual cost to compare these cars.
Used car
We first need to compute NPV .
Year
Cash flow
PV factor 15%
PV
0
-9500
1.000
-9500
1
-1800
0.870
-1565.22
2
-2000
0.756
-1512.29
2
3000
0.756
2268.431
NPV
-10309.1
Now we need to divide this NPV by the 2 year PVIFA factor to get Annual equivalent cost.
PVIFA factor = 0.870 +0.756 =1.626
Annual equivalent cost = 10,390.10/1.626
=6389.98
New car
Year
Cash flow
PV factor 15%
PV
0
-22000
1.000
-22000
1
0
0.870
0
2
0
0.756
0
3
0
0.658
0
4
8000
0.572
4574.02596
NPV
-17425.97
PVIFA factor for four years = 0.870 +0.756 +0.658+0.572 = 2.856
Annual equivalent cost = 17,425.97/2.856
=6101.53
We can see annual equivalent cost of new car is lower. Therefore new car is a better option.
Year
Cash flow
PV factor 15%
PV
0
-9500
1.000
-9500
1
-1800
0.870
-1565.22
2
-2000
0.756
-1512.29
2
3000
0.756
2268.431
NPV
-10309.1
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