Your firm is contemplating the purchase of a new $575,000 computer-based order e
ID: 2777691 • Letter: Y
Question
Your firm is contemplating the purchase of a new $575,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $59,000 at the end of that time. You will be able to reduce working capital by $74,000 (this is a one-time reduction). The tax rate is 34 percent and the required return on the project is 14 percent.
If the pretax cost savings are $211,000 per year, what is the NPV of this project?
If the pretax cost savings are $161,000 per year, what is the NPV of this project?
At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?
Explanation / Answer
Calculation of NPV of this project if the pretax cost savings are $211,000 per year:
Cash Flows (CF)
Year
PVF (14%)
PV = CF *PVF
Initial Cost of Purchase
$ (575,000)
0
1.00000
$ (575,000.00)
Reduction of working capital
$ 74,000
0
1.00000
$ 74,000.00
Tax saving on depreciation = (575000/5)*34%
$ 39,100
1 to 5
3.43308
$ 134,233.47
After tax value of Asset = 59000* (1-34%)
$ 38,940
5
0.51937
$ 20,224.22
Post tax cost savings = 211000*(1-34%)
$ 139,260
1 to 5
3.43308
$ 478,090.86
Net Present value (NPV)
$ 131,548.54
Calculation of NPV of this project if the pretax cost savings are $161,000 per year:
Cash Flows (CF)
Year
PVF (14%)
PV = CF *PVF
Initial Cost of Purchase
$ (575,000)
0
1.00000
$ (575,000.00)
Reduction of working capital
$ 74,000
0
1.00000
$ 74,000.00
Tax saving on depreciation = (575000/5)*34%
$ 39,100
1 to 5
3.43308
$ 134,233.47
After tax value of Asset = 59000* (1-34%)
$ 38,940
5
0.51937
$ 20,224.22
Post tax cost savings = 161000*(1-34%)
$ 106,260
1 to 5
3.43308
$ 364,799.18
Net Present value (NPV)
$ 18,256.87
Calculation of Indiffrent level of pretax cost savings:
Cash Flows (CF)
Year
PVF (14%)
PV = CF *PVF
Initial Cost of Purchase
$ (575,000)
0
1.00000
$ (575,000.00)
Reduction of working capital
$ 74,000
0
1.00000
$ 74,000.00
Tax saving on depreciation = (575000/5)*34%
$ 39,100
1 to 5
3.43308
$ 134,233.47
After tax value of Asset = 59000* (1-34%)
$ 38,940
5
0.51937
$ 20,224.22
$ (346,542.32)
Post tax cost savings = X*(1-34%)
0.66 * X
1 to 5
3.43308
2.2658 * X
Net Present value (NPV)
$ -
At Indiffrence level the NPV shall be 0
It means,
2.2658* X - 346542.32 = 0
Hence X = 346542.32 / 2.2658
$ 152,944.80
Indiffrent level of pretax cost savings = $152944.80
Calculation of NPV of this project if the pretax cost savings are $211,000 per year:
Cash Flows (CF)
Year
PVF (14%)
PV = CF *PVF
Initial Cost of Purchase
$ (575,000)
0
1.00000
$ (575,000.00)
Reduction of working capital
$ 74,000
0
1.00000
$ 74,000.00
Tax saving on depreciation = (575000/5)*34%
$ 39,100
1 to 5
3.43308
$ 134,233.47
After tax value of Asset = 59000* (1-34%)
$ 38,940
5
0.51937
$ 20,224.22
Post tax cost savings = 211000*(1-34%)
$ 139,260
1 to 5
3.43308
$ 478,090.86
Net Present value (NPV)
$ 131,548.54
Calculation of NPV of this project if the pretax cost savings are $161,000 per year:
Cash Flows (CF)
Year
PVF (14%)
PV = CF *PVF
Initial Cost of Purchase
$ (575,000)
0
1.00000
$ (575,000.00)
Reduction of working capital
$ 74,000
0
1.00000
$ 74,000.00
Tax saving on depreciation = (575000/5)*34%
$ 39,100
1 to 5
3.43308
$ 134,233.47
After tax value of Asset = 59000* (1-34%)
$ 38,940
5
0.51937
$ 20,224.22
Post tax cost savings = 161000*(1-34%)
$ 106,260
1 to 5
3.43308
$ 364,799.18
Net Present value (NPV)
$ 18,256.87
Calculation of Indiffrent level of pretax cost savings:
Cash Flows (CF)
Year
PVF (14%)
PV = CF *PVF
Initial Cost of Purchase
$ (575,000)
0
1.00000
$ (575,000.00)
Reduction of working capital
$ 74,000
0
1.00000
$ 74,000.00
Tax saving on depreciation = (575000/5)*34%
$ 39,100
1 to 5
3.43308
$ 134,233.47
After tax value of Asset = 59000* (1-34%)
$ 38,940
5
0.51937
$ 20,224.22
$ (346,542.32)
Post tax cost savings = X*(1-34%)
0.66 * X
1 to 5
3.43308
2.2658 * X
Net Present value (NPV)
$ -
At Indiffrence level the NPV shall be 0
It means,
2.2658* X - 346542.32 = 0
Hence X = 346542.32 / 2.2658
$ 152,944.80
Indiffrent level of pretax cost savings = $152944.80
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