Calculate the NPV of an investment with the following conditions and conclude wh
ID: 2743685 • Letter: C
Question
Calculate the NPV of an investment with the following conditions and conclude which is better.
Purchase the asset: purchasing the asset requires capital cost of 400,000 dollars (At time zero) that can be depreciated based on MACRS 7 year life depreciation with the half year convention over eight years ( from year 0 to 7). And the salvage value will be 100,000 dollars at the end of year 7.
Lease (operating lease): The asset can be leased for 7 years at annual operating lease payments (LP) of 70,000 dollars( from year 1 to year 7)
The asset would yield the annual revenue of $150,000 and operating cost of $40,000 for seven years (year 1 to 7).
Considering income tax of 40% and minimum ROR of 8%. Calculate ATCF and nPV for both options and conclude which is better.
Explanation / Answer
Calculation of ATCF and NPV :
Purchase Option:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Annual Revenue
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
Less: Annual Operating Costs
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
Less: Depreciation (MACRS)
$ (21,435.00)
$ (36,735.00)
$ (26,235.00)
$ (18,735.00)
$ (13,395.00)
$ (13,380.00)
$ (13,395.00)
(150000*14.29%)
(150000*24.49%)
(150000*17.49%)
(150000*12.49%)
(150000*8.93%)
(150000*8.92%)
(150000*8.93%)
Profit before tax
$ 88,565.00
$ 73,265.00
$ 83,765.00
$ 91,265.00
$ 96,605.00
$ 96,620.00
$ 96,605.00
Less: Tax (40%)
$ (35,426.00)
$ (29,306.00)
$ (33,506.00)
$ (36,506.00)
$ (38,642.00)
$ (38,648.00)
$ (38,642.00)
Profit after tax
$ 53,139.00
$ 43,959.00
$ 50,259.00
$ 54,759.00
$ 57,963.00
$ 57,972.00
$ 57,963.00
Add: Depreciation
$ 21,435.00
$ 36,735.00
$ 26,235.00
$ 18,735.00
$ 13,395.00
$ 13,380.00
$ 13,395.00
After Tax Cash Flows (ATCF)
$ 74,574.00
$ 80,694.00
$ 76,494.00
$ 73,494.00
$ 71,358.00
$ 71,352.00
$ 71,358.00
Cost of Asset
$ (150,000.00)
Add: Salvage value
$ 100,000.00
Less: Tax on Gain on sale
Gain = Sales value - Book value
= 100000 - (150000 * 4.46%) = 93310
Tax on Gain = 93310 * 40% =
$ (37,324.00)
Net Cash Flows
$ (150,000.00)
$ 74,574.00
$ 80,694.00
$ 76,494.00
$ 73,494.00
$ 71,358.00
$ 71,352.00
$ 134,034.00
Present value of $1 (8%)
1.00000
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
Prersent value = Net Cash Flow * PV of $1 =
$ (150,000.00)
$ 69,050.00
$ 69,182.10
$ 60,723.40
$ 54,020.28
$ 48,565.06
$ 44,963.86
$ 78,207.55
Net Present value (Sum )
$ 274,712.26
Operating Lease Option:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Annual Revenue
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
Less: Annual Operating Costs
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
Less: Annual Lease rental
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
Profit before tax
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
Less: Tax (40%)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
After Tax Cash Flows (ATCF)
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
Cost of Asset
$ (150,000.00)
Add: Salvage value
$ 100,000.00
Less: Tax on Gain on sale
Gain = Sales value - Book value
= 100000 - (150000 * 4.46%) = 93310
Tax on Gain = 93310 * 40% =
$ (37,324.00)
Net Cash Flows
$ (150,000.00)
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 86,676.00
Present value of $1 (8%)
1.00000
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
Prersent value = Net Cash Flow * PV of $1 =
$ (150,000.00)
$ 22,222.22
$ 20,576.13
$ 19,051.97
$ 17,640.72
$ 16,334.00
$ 15,124.07
$ 50,574.61
Net Present value (Sum )
$ 11,523.73
Conclusion:
On the basis of above NPV analysis we can see that NPV of Purchase option is more, hence purchase option is better.
Calculation of ATCF and NPV :
Purchase Option:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Annual Revenue
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
Less: Annual Operating Costs
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
Less: Depreciation (MACRS)
$ (21,435.00)
$ (36,735.00)
$ (26,235.00)
$ (18,735.00)
$ (13,395.00)
$ (13,380.00)
$ (13,395.00)
(150000*14.29%)
(150000*24.49%)
(150000*17.49%)
(150000*12.49%)
(150000*8.93%)
(150000*8.92%)
(150000*8.93%)
Profit before tax
$ 88,565.00
$ 73,265.00
$ 83,765.00
$ 91,265.00
$ 96,605.00
$ 96,620.00
$ 96,605.00
Less: Tax (40%)
$ (35,426.00)
$ (29,306.00)
$ (33,506.00)
$ (36,506.00)
$ (38,642.00)
$ (38,648.00)
$ (38,642.00)
Profit after tax
$ 53,139.00
$ 43,959.00
$ 50,259.00
$ 54,759.00
$ 57,963.00
$ 57,972.00
$ 57,963.00
Add: Depreciation
$ 21,435.00
$ 36,735.00
$ 26,235.00
$ 18,735.00
$ 13,395.00
$ 13,380.00
$ 13,395.00
After Tax Cash Flows (ATCF)
$ 74,574.00
$ 80,694.00
$ 76,494.00
$ 73,494.00
$ 71,358.00
$ 71,352.00
$ 71,358.00
Cost of Asset
$ (150,000.00)
Add: Salvage value
$ 100,000.00
Less: Tax on Gain on sale
Gain = Sales value - Book value
= 100000 - (150000 * 4.46%) = 93310
Tax on Gain = 93310 * 40% =
$ (37,324.00)
Net Cash Flows
$ (150,000.00)
$ 74,574.00
$ 80,694.00
$ 76,494.00
$ 73,494.00
$ 71,358.00
$ 71,352.00
$ 134,034.00
Present value of $1 (8%)
1.00000
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
Prersent value = Net Cash Flow * PV of $1 =
$ (150,000.00)
$ 69,050.00
$ 69,182.10
$ 60,723.40
$ 54,020.28
$ 48,565.06
$ 44,963.86
$ 78,207.55
Net Present value (Sum )
$ 274,712.26
Operating Lease Option:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Annual Revenue
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
$ 150,000.00
Less: Annual Operating Costs
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
$ (40,000.00)
Less: Annual Lease rental
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
$ (70,000.00)
Profit before tax
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
$ 40,000.00
Less: Tax (40%)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
$ (16,000.00)
After Tax Cash Flows (ATCF)
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
Cost of Asset
$ (150,000.00)
Add: Salvage value
$ 100,000.00
Less: Tax on Gain on sale
Gain = Sales value - Book value
= 100000 - (150000 * 4.46%) = 93310
Tax on Gain = 93310 * 40% =
$ (37,324.00)
Net Cash Flows
$ (150,000.00)
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 24,000.00
$ 86,676.00
Present value of $1 (8%)
1.00000
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
Prersent value = Net Cash Flow * PV of $1 =
$ (150,000.00)
$ 22,222.22
$ 20,576.13
$ 19,051.97
$ 17,640.72
$ 16,334.00
$ 15,124.07
$ 50,574.61
Net Present value (Sum )
$ 11,523.73
Conclusion:
On the basis of above NPV analysis we can see that NPV of Purchase option is more, hence purchase option is better.
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