Based on the following, calculate the costs of buying and of leasing a motor veh
ID: 2649506 • Letter: B
Question
Based on the following, calculate the costs of buying and of leasing a motor vehicle.
Purchase Costs
Leasing Costs
Down payment $1,500
Security deposit $500
Loan payment $450 for 48 months
Lease payment $450 for 36 months
Estimated value at
End of loan $4,000
End of lease charges $600
Opportunity cost interest rate: 4 percent
Purchase Costs
Leasing Costs
Down payment $1,500
Security deposit $500
Loan payment $450 for 48 months
Lease payment $450 for 36 months
Estimated value at
End of loan $4,000
End of lease charges $600
Opportunity cost interest rate: 4 percent
Explanation / Answer
Answer
Opportunity cost interest rate: 4 percent per annum. So monthly interest rate is 0.33 % per month (4%/12).
Option 1 : Leasing Option
Month
Lease rent
End lease charges
Security deposits
Cashflow
Disc Rate
Present value
A
B
C
D
E
D*E
A+B+C
0.33%
0
0
0
-500
-500
1.00
-500
1
-450
0
0
-450
1.00
-448.52
2
-450
0
0
-450
0.99
-447.04
3
-450
0
0
-450
0.99
-445.57
4
-450
0
0
-450
0.99
-444.11
5
-450
0
0
-450
0.98
-442.65
6
-450
0
0
-450
0.98
-441.19
7
-450
0
0
-450
0.98
-439.74
8
-450
0
0
-450
0.97
-438.29
9
-450
0
0
-450
0.97
-436.85
10
-450
0
0
-450
0.97
-435.42
11
-450
0
0
-450
0.96
-433.98
12
-450
0
0
-450
0.96
-432.56
13
-450
0
0
-450
0.96
-431.13
14
-450
0
0
-450
0.95
-429.72
15
-450
0
0
-450
0.95
-428.30
16
-450
0
0
-450
0.95
-426.89
17
-450
0
0
-450
0.95
-425.49
18
-450
0
0
-450
0.94
-424.09
19
-450
0
0
-450
0.94
-422.69
20
-450
0
0
-450
0.94
-421.30
21
-450
0
0
-450
0.93
-419.92
22
-450
0
0
-450
0.93
-418.54
23
-450
0
0
-450
0.93
-417.16
24
-450
0
0
-450
0.92
-415.79
25
-450
0
0
-450
0.92
-414.42
26
-450
0
0
-450
0.92
-413.06
27
-450
0
0
-450
0.91
-411.70
28
-450
0
0
-450
0.91
-410.35
29
-450
0
0
-450
0.91
-409.00
30
-450
0
0
-450
0.91
-407.65
31
-450
0
0
-450
0.90
-406.31
32
-450
0
0
-450
0.90
-404.97
33
-450
0
0
-450
0.90
-403.64
34
-450
0
0
-450
0.89
-402.31
35
-450
0
0
-450
0.89
-400.99
36
-450
-600
500
-550
0.89
-488.49
NPV
-15839.85
So, Cost of leasing is $15839.85
Option 2 : Borrow and buy option
First we have to find Present value of loan Amount
Month
Cash flow
Disc Rate
Present value
0.33%
A
B
A*B
0
-1500
1
-1500.00
1
-450
1.00
-448.52
2
-450
0.99
-447.04
3
-450
0.99
-445.57
4
-450
0.99
-444.11
5
-450
0.98
-442.65
6
-450
0.98
-441.19
7
-450
0.98
-439.74
8
-450
0.97
-438.29
9
-450
0.97
-436.85
10
-450
0.97
-435.42
11
-450
0.96
-433.98
12
-450
0.96
-432.56
13
-450
0.96
-431.13
14
-450
0.95
-429.72
15
-450
0.95
-428.30
16
-450
0.95
-426.89
17
-450
0.95
-425.49
18
-450
0.94
-424.09
19
-450
0.94
-422.69
20
-450
0.94
-421.30
21
-450
0.93
-419.92
22
-450
0.93
-418.54
23
-450
0.93
-417.16
24
-450
0.92
-415.79
25
-450
0.92
-414.42
26
-450
0.92
-413.06
27
-450
0.91
-411.70
28
-450
0.91
-410.35
29
-450
0.91
-409.00
30
-450
0.91
-407.65
31
-450
0.90
-406.31
32
-450
0.90
-404.97
33
-450
0.90
-403.64
34
-450
0.89
-402.31
35
-450
0.89
-400.99
36
-450
0.89
-399.67
37
-450
0.89
-398.36
38
-450
0.88
-397.05
39
-450
0.88
-395.74
40
-450
0.88
-394.44
41
-450
0.87
-393.14
42
-450
0.87
-391.85
43
-450
0.87
-390.56
44
-450
0.87
-389.28
45
-450
0.86
-387.99
46
-450
0.86
-386.72
47
-450
0.86
-385.45
48
-450
0.85
-384.18
Present value of loan amount
-21445.78
So in Year zero , Cost of the fixed asset will be $ 21445.78 & Loan amount taken will be $ 21445.78.
Tax rate is not given so depreciation and interest cost are irrelevant because we are not going get any tax benefit on it.
Month
Loan payment
fixed assets
Loan taken
Cashflow
Disc rate
Present value
A
B
C
D
E
D*E
A+B+C
0.33%
0
-1500
-21445.78
21445.78
-1500.00
1.00
-1500.00
1
-450
0
0
-450.00
1.00
-448.52
2
-450
0
0
-450.00
0.99
-447.04
3
-450
0
0
-450.00
0.99
-445.57
4
-450
0
0
-450.00
0.99
-444.11
5
-450
0
0
-450.00
0.98
-442.65
6
-450
0
0
-450.00
0.98
-441.19
7
-450
0
0
-450.00
0.98
-439.74
8
-450
0
0
-450.00
0.97
-438.29
9
-450
0
0
-450.00
0.97
-436.85
10
-450
0
0
-450.00
0.97
-435.42
11
-450
0
0
-450.00
0.96
-433.98
12
-450
0
0
-450.00
0.96
-432.56
13
-450
0
0
-450.00
0.96
-431.13
14
-450
0
0
-450.00
0.95
-429.72
15
-450
0
0
-450.00
0.95
-428.30
16
-450
0
0
-450.00
0.95
-426.89
17
-450
0
0
-450.00
0.95
-425.49
18
-450
0
0
-450.00
0.94
-424.09
19
-450
0
0
-450.00
0.94
-422.69
20
-450
0
0
-450.00
0.94
-421.30
21
-450
0
0
-450.00
0.93
-419.92
22
-450
0
0
-450.00
0.93
-418.54
23
-450
0
0
-450.00
0.93
-417.16
24
-450
0
0
-450.00
0.92
-415.79
25
-450
0
0
-450.00
0.92
-414.42
26
-450
0
0
-450.00
0.92
-413.06
27
-450
0
0
-450.00
0.91
-411.70
28
-450
0
0
-450.00
0.91
-410.35
29
-450
0
0
-450.00
0.91
-409.00
30
-450
0
0
-450.00
0.91
-407.65
31
-450
0
0
-450.00
0.90
-406.31
32
-450
0
0
-450.00
0.90
-404.97
33
-450
0
0
-450.00
0.90
-403.64
34
-450
0
0
-450.00
0.89
-402.31
35
-450
0
0
-450.00
0.89
-400.99
36
-450
0
0
-450.00
0.89
-399.67
37
-450
0
0
-450.00
0.89
-398.36
38
-450
0
0
-450.00
0.88
-397.05
39
-450
0
0
-450.00
0.88
-395.74
40
-450
0
0
-450.00
0.88
-394.44
41
-450
0
0
-450.00
0.87
-393.14
42
-450
0
0
-450.00
0.87
-391.85
43
-450
0
0
-450.00
0.87
-390.56
44
-450
0
0
-450.00
0.87
-389.28
45
-450
0
0
-450.00
0.86
-387.99
46
-450
0
0
-450.00
0.86
-386.72
47
-450
0
0
-450.00
0.86
-385.45
48
-450
4000
0
3550.00
0.85
3030.74
Net Present value
-18030.86
So cost of borrowing and buying is $ 18030.86
Month
Lease rent
End lease charges
Security deposits
Cashflow
Disc Rate
Present value
A
B
C
D
E
D*E
A+B+C
0.33%
0
0
0
-500
-500
1.00
-500
1
-450
0
0
-450
1.00
-448.52
2
-450
0
0
-450
0.99
-447.04
3
-450
0
0
-450
0.99
-445.57
4
-450
0
0
-450
0.99
-444.11
5
-450
0
0
-450
0.98
-442.65
6
-450
0
0
-450
0.98
-441.19
7
-450
0
0
-450
0.98
-439.74
8
-450
0
0
-450
0.97
-438.29
9
-450
0
0
-450
0.97
-436.85
10
-450
0
0
-450
0.97
-435.42
11
-450
0
0
-450
0.96
-433.98
12
-450
0
0
-450
0.96
-432.56
13
-450
0
0
-450
0.96
-431.13
14
-450
0
0
-450
0.95
-429.72
15
-450
0
0
-450
0.95
-428.30
16
-450
0
0
-450
0.95
-426.89
17
-450
0
0
-450
0.95
-425.49
18
-450
0
0
-450
0.94
-424.09
19
-450
0
0
-450
0.94
-422.69
20
-450
0
0
-450
0.94
-421.30
21
-450
0
0
-450
0.93
-419.92
22
-450
0
0
-450
0.93
-418.54
23
-450
0
0
-450
0.93
-417.16
24
-450
0
0
-450
0.92
-415.79
25
-450
0
0
-450
0.92
-414.42
26
-450
0
0
-450
0.92
-413.06
27
-450
0
0
-450
0.91
-411.70
28
-450
0
0
-450
0.91
-410.35
29
-450
0
0
-450
0.91
-409.00
30
-450
0
0
-450
0.91
-407.65
31
-450
0
0
-450
0.90
-406.31
32
-450
0
0
-450
0.90
-404.97
33
-450
0
0
-450
0.90
-403.64
34
-450
0
0
-450
0.89
-402.31
35
-450
0
0
-450
0.89
-400.99
36
-450
-600
500
-550
0.89
-488.49
NPV
-15839.85
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