Acme borrows $4 million at 3% interest on a declining balance to purchase an MRI
ID: 2785721 • Letter: A
Question
Acme borrows $4 million at 3% interest on a declining balance to purchase an MRI. Depreciation is straight-line over five years. The MRI has a trade-in value of $100,000 at the end of the useful life. Maintenance expense is 15,000 per year. Should you buy the equipment or lease it at $75,000 per month for 60 months with maintenance included? What is the net present value of each alternative? Acme borrows $4 million at 3% interest on a declining balance to purchase an MRI. Depreciation is straight-line over five years. The MRI has a trade-in value of $100,000 at the end of the useful life. Maintenance expense is 15,000 per year. Should you buy the equipment or lease it at $75,000 per month for 60 months with maintenance included? What is the net present value of each alternative?Explanation / Answer
Calculation of NPV of the Projects
Period
O/S principal
EMI
Int
Prin
1
$ 40,00,000
$ 71,875
$ 10,000
$ 61,875
2
$ 39,38,125
$ 71,875
$ 9,845
$ 62,029
3
$ 38,76,096
$ 71,875
$ 9,690
$ 62,185
4
$ 38,13,911
$ 71,875
$ 9,535
$ 62,340
5
$ 37,51,571
$ 71,875
$ 9,379
$ 62,496
6
$ 36,89,075
$ 71,875
$ 9,223
$ 62,652
7
$ 36,26,423
$ 71,875
$ 9,066
$ 62,809
8
$ 35,63,615
$ 71,875
$ 8,909
$ 62,966
9
$ 35,00,649
$ 71,875
$ 8,752
$ 63,123
10
$ 34,37,526
$ 71,875
$ 8,594
$ 63,281
11
$ 33,74,245
$ 71,875
$ 8,436
$ 63,439
12
$ 33,10,806
$ 71,875
$ 8,277
$ 63,598
13
$ 32,47,208
$ 71,875
$ 8,118
$ 63,757
14
$ 31,83,451
$ 71,875
$ 7,959
$ 63,916
15
$ 31,19,535
$ 71,875
$ 7,799
$ 64,076
16
$ 30,55,459
$ 71,875
$ 7,639
$ 64,236
17
$ 29,91,223
$ 71,875
$ 7,478
$ 64,397
18
$ 29,26,826
$ 71,875
$ 7,317
$ 64,558
19
$ 28,62,269
$ 71,875
$ 7,156
$ 64,719
20
$ 27,97,550
$ 71,875
$ 6,994
$ 64,881
21
$ 27,32,669
$ 71,875
$ 6,832
$ 65,043
22
$ 26,67,626
$ 71,875
$ 6,669
$ 65,206
23
$ 26,02,420
$ 71,875
$ 6,506
$ 65,369
24
$ 25,37,051
$ 71,875
$ 6,343
$ 65,532
25
$ 24,71,519
$ 71,875
$ 6,179
$ 65,696
26
$ 24,05,823
$ 71,875
$ 6,015
$ 65,860
27
$ 23,39,963
$ 71,875
$ 5,850
$ 66,025
28
$ 22,73,938
$ 71,875
$ 5,685
$ 66,190
29
$ 22,07,748
$ 71,875
$ 5,519
$ 66,355
30
$ 21,41,393
$ 71,875
$ 5,353
$ 66,521
31
$ 20,74,871
$ 71,875
$ 5,187
$ 66,688
32
$ 20,08,184
$ 71,875
$ 5,020
$ 66,854
33
$ 19,41,330
$ 71,875
$ 4,853
$ 67,021
34
$ 18,74,308
$ 71,875
$ 4,686
$ 67,189
35
$ 18,07,119
$ 71,875
$ 4,518
$ 67,357
36
$ 17,39,762
$ 71,875
$ 4,349
$ 67,525
37
$ 16,72,237
$ 71,875
$ 4,181
$ 67,694
38
$ 16,04,543
$ 71,875
$ 4,011
$ 67,863
39
$ 15,36,679
$ 71,875
$ 3,842
$ 68,033
40
$ 14,68,646
$ 71,875
$ 3,672
$ 68,203
41
$ 14,00,443
$ 71,875
$ 3,501
$ 68,374
42
$ 13,32,069
$ 71,875
$ 3,330
$ 68,545
43
$ 12,63,525
$ 71,875
$ 3,159
$ 68,716
44
$ 11,94,809
$ 71,875
$ 2,987
$ 68,888
45
$ 11,25,921
$ 71,875
$ 2,815
$ 69,060
46
$ 10,56,861
$ 71,875
$ 2,642
$ 69,233
47
$ 9,87,628
$ 71,875
$ 2,469
$ 69,406
48
$ 9,18,223
$ 71,875
$ 2,296
$ 69,579
49
$ 8,48,644
$ 71,875
$ 2,122
$ 69,753
50
$ 7,78,890
$ 71,875
$ 1,947
$ 69,928
51
$ 7,08,963
$ 71,875
$ 1,772
$ 70,102
52
$ 6,38,861
$ 71,875
$ 1,597
$ 70,278
53
$ 5,68,583
$ 71,875
$ 1,421
$ 70,453
54
$ 4,98,130
$ 71,875
$ 1,245
$ 70,629
55
$ 4,27,500
$ 71,875
$ 1,069
$ 70,806
56
$ 3,56,694
$ 71,875
$ 892
$ 70,983
57
$ 2,85,711
$ 71,875
$ 714
$ 71,160
58
$ 2,14,551
$ 71,875
$ 536
$ 71,338
59
$ 1,43,212
$ 71,875
$ 358
$ 71,517
60
$ 71,696
$ 71,875
$ 179
$ 71,696
Total
$ 43,12,486
$ 3,12,486
4000000
If the Monthly installemnts amounts were discounted at the 3% rate , the amount we will arrive is 4000000, since the cost of debt and discounting rate effect will set off and the interest amount will get nullified
Since there is no Tax rate was mentioned , the benefit of considering depreciation will not be reflected, Hence ignored for calculating it.
It is assumed that the 3% rate of interest for the loan is Per annum
Also assumed that the 3% will be considered as discounting rate
Year
Cashflow
Presnet calue factor @3%
Amount
1
$ 40,00,000.00
$ 1.00
$ 40,00,000.00
Outflow( refer above EMI table)
1 to 5
$ 15,000.00
$ 4.58
$ 68,700.00
Outflow
5
$ -1,00,000.00
$ 0.86
$ -86,260.88
Inflow
NPV
$ 39,82,439.12
If Leasing option has choosen
Years
Cash outflow p.a
Present value annuity Factor @ 3%
Amount
1 to 5
75000*12 = 900000
$ 4.58
$ -41,21,736.47
Outflow
NPV
$ -41,21,736.47
NPV = Present value of Cash inflows - Present value of cash outflows
By comparing the NPV of the Above two Options it is better to choose the option which is having the NPV low i.e., Borrwing the loan and purchase of Machine
Period
O/S principal
EMI
Int
Prin
1
$ 40,00,000
$ 71,875
$ 10,000
$ 61,875
2
$ 39,38,125
$ 71,875
$ 9,845
$ 62,029
3
$ 38,76,096
$ 71,875
$ 9,690
$ 62,185
4
$ 38,13,911
$ 71,875
$ 9,535
$ 62,340
5
$ 37,51,571
$ 71,875
$ 9,379
$ 62,496
6
$ 36,89,075
$ 71,875
$ 9,223
$ 62,652
7
$ 36,26,423
$ 71,875
$ 9,066
$ 62,809
8
$ 35,63,615
$ 71,875
$ 8,909
$ 62,966
9
$ 35,00,649
$ 71,875
$ 8,752
$ 63,123
10
$ 34,37,526
$ 71,875
$ 8,594
$ 63,281
11
$ 33,74,245
$ 71,875
$ 8,436
$ 63,439
12
$ 33,10,806
$ 71,875
$ 8,277
$ 63,598
13
$ 32,47,208
$ 71,875
$ 8,118
$ 63,757
14
$ 31,83,451
$ 71,875
$ 7,959
$ 63,916
15
$ 31,19,535
$ 71,875
$ 7,799
$ 64,076
16
$ 30,55,459
$ 71,875
$ 7,639
$ 64,236
17
$ 29,91,223
$ 71,875
$ 7,478
$ 64,397
18
$ 29,26,826
$ 71,875
$ 7,317
$ 64,558
19
$ 28,62,269
$ 71,875
$ 7,156
$ 64,719
20
$ 27,97,550
$ 71,875
$ 6,994
$ 64,881
21
$ 27,32,669
$ 71,875
$ 6,832
$ 65,043
22
$ 26,67,626
$ 71,875
$ 6,669
$ 65,206
23
$ 26,02,420
$ 71,875
$ 6,506
$ 65,369
24
$ 25,37,051
$ 71,875
$ 6,343
$ 65,532
25
$ 24,71,519
$ 71,875
$ 6,179
$ 65,696
26
$ 24,05,823
$ 71,875
$ 6,015
$ 65,860
27
$ 23,39,963
$ 71,875
$ 5,850
$ 66,025
28
$ 22,73,938
$ 71,875
$ 5,685
$ 66,190
29
$ 22,07,748
$ 71,875
$ 5,519
$ 66,355
30
$ 21,41,393
$ 71,875
$ 5,353
$ 66,521
31
$ 20,74,871
$ 71,875
$ 5,187
$ 66,688
32
$ 20,08,184
$ 71,875
$ 5,020
$ 66,854
33
$ 19,41,330
$ 71,875
$ 4,853
$ 67,021
34
$ 18,74,308
$ 71,875
$ 4,686
$ 67,189
35
$ 18,07,119
$ 71,875
$ 4,518
$ 67,357
36
$ 17,39,762
$ 71,875
$ 4,349
$ 67,525
37
$ 16,72,237
$ 71,875
$ 4,181
$ 67,694
38
$ 16,04,543
$ 71,875
$ 4,011
$ 67,863
39
$ 15,36,679
$ 71,875
$ 3,842
$ 68,033
40
$ 14,68,646
$ 71,875
$ 3,672
$ 68,203
41
$ 14,00,443
$ 71,875
$ 3,501
$ 68,374
42
$ 13,32,069
$ 71,875
$ 3,330
$ 68,545
43
$ 12,63,525
$ 71,875
$ 3,159
$ 68,716
44
$ 11,94,809
$ 71,875
$ 2,987
$ 68,888
45
$ 11,25,921
$ 71,875
$ 2,815
$ 69,060
46
$ 10,56,861
$ 71,875
$ 2,642
$ 69,233
47
$ 9,87,628
$ 71,875
$ 2,469
$ 69,406
48
$ 9,18,223
$ 71,875
$ 2,296
$ 69,579
49
$ 8,48,644
$ 71,875
$ 2,122
$ 69,753
50
$ 7,78,890
$ 71,875
$ 1,947
$ 69,928
51
$ 7,08,963
$ 71,875
$ 1,772
$ 70,102
52
$ 6,38,861
$ 71,875
$ 1,597
$ 70,278
53
$ 5,68,583
$ 71,875
$ 1,421
$ 70,453
54
$ 4,98,130
$ 71,875
$ 1,245
$ 70,629
55
$ 4,27,500
$ 71,875
$ 1,069
$ 70,806
56
$ 3,56,694
$ 71,875
$ 892
$ 70,983
57
$ 2,85,711
$ 71,875
$ 714
$ 71,160
58
$ 2,14,551
$ 71,875
$ 536
$ 71,338
59
$ 1,43,212
$ 71,875
$ 358
$ 71,517
60
$ 71,696
$ 71,875
$ 179
$ 71,696
Total
$ 43,12,486
$ 3,12,486
4000000
If the Monthly installemnts amounts were discounted at the 3% rate , the amount we will arrive is 4000000, since the cost of debt and discounting rate effect will set off and the interest amount will get nullified
Since there is no Tax rate was mentioned , the benefit of considering depreciation will not be reflected, Hence ignored for calculating it.
It is assumed that the 3% rate of interest for the loan is Per annum
Also assumed that the 3% will be considered as discounting rate
Year
Cashflow
Presnet calue factor @3%
Amount
1
$ 40,00,000.00
$ 1.00
$ 40,00,000.00
Outflow( refer above EMI table)
1 to 5
$ 15,000.00
$ 4.58
$ 68,700.00
Outflow
5
$ -1,00,000.00
$ 0.86
$ -86,260.88
Inflow
NPV
$ 39,82,439.12
If Leasing option has choosen
Years
Cash outflow p.a
Present value annuity Factor @ 3%
Amount
1 to 5
75000*12 = 900000
$ 4.58
$ -41,21,736.47
Outflow
NPV
$ -41,21,736.47
NPV = Present value of Cash inflows - Present value of cash outflows
By comparing the NPV of the Above two Options it is better to choose the option which is having the NPV low i.e., Borrwing the loan and purchase of Machine
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