Your firm is contemplating the purchase of a new $536,500 computer-based order e
ID: 2818030 • Letter: Y
Question
Your firm is contemplating the purchase of a new $536,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $52,200 at the end of that time. You will be able to reduce working capital by $72,500 (this is a one-time reduction). The tax rate is 31 percent and your required return on the project is 23 percent. If your pretax cost savings are $247,950 per year, the NPV for the project is $____ and you will(accept/reject) the project. If your pretax cost savings are $178,500 per year, the NPV for the project is $ and you will(accept/reject) the project. You would be indifferent between accepting the project and rejecting it if your pretax cost savings were $_____ . (Do not include the dollar signs ($). Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
Total investment on the 0th year = $536,500
Salvage value of the investment = $52,200
Total depreciation = $484,300, to be depreciated straight-line to zero over 5 year duration
Annual depreciation = $484,300/5 = $96,860
Present Value of the Cash inflow for the nth year is given by
(Cash Inflow for the nth year)/(1+hurdle rate)n
Net present value = sum of present values of the cash inflows over the 5 years
Here is the calculation table for the first scenario, when pretax cost savings are $247,950 per year:
Annual Depreciation - Straight line to zero method
96860.00
Hurdle Rate
23%
Year
0
1
2
3
4
5
Investment
-536500.00
0.00
0.00
0.00
0.00
0.00
Depreciation
-96860.00
-96860.00
-96860.00
-96860.00
-96860.00
Working Capital
0.00
72500.00
0.00
0.00
0.00
0.00
Pretax Cost savings
0.00
247950.00
247950.00
247950.00
247950.00
247950.00
Total taxable amount(A)
-536500.00
223590.00
151090.00
151090.00
151090.00
151090.00
Tax @ 31%(B)
0.00
69312.90
46837.90
46837.90
46837.90
46837.90
Add Depreciation (C)
0.00
96860.00
96860.00
96860.00
96860.00
96860.00
Net Cash Inflow (A-B+C)
-536500.00
251137.10
201112.10
201112.10
201112.10
201112.10
Present Value
-536500.00
204176.50
132931.52
108074.41
87865.37
71435.26
Net Present Value
67983.07
Hence answer to the first set of questions are:
Calculations when pre-tax savings are $178,500 per year:
Annual Depreciation - Straight line to zero method
96860.00
Hurdle Rate
23%
Year
0
1
2
3
4
5
Investment
-536500.00
0.00
0.00
0.00
0.00
0.00
Depreciation
-96860.00
-96860.00
-96860.00
-96860.00
-96860.00
Working Capital
0.00
72500.00
0.00
0.00
0.00
0.00
Pretax Cost savings
0.00
178500.00
178500.00
178500.00
178500.00
178500.00
Total taxable amount(A)
-536500.00
154140.00
81640.00
81640.00
81640.00
81640.00
Tax @ 31%(B)
0.00
47783.40
25308.40
25308.40
25308.40
25308.40
Add Depreciation (C)
0.00
96860.00
96860.00
96860.00
96860.00
96860.00
Net Cash Inflow (A-B+C)
-536500.00
203216.60
153191.60
153191.60
153191.60
153191.60
Present Value
-536500.00
165216.75
101256.92
82322.70
66929.03
54413.84
Net Present Value
-66360.76
Hence answer to the second set of questions are:
We will be indifferent to the project if NPV is 0
For this, we apply scenario analysis in excel and the table comes out to be:
Annual Depreciation - Straight line to zero method
96860.00
Hurdle Rate
23%
Year
0
1
2
3
4
5
Investment
-536500.00
0.00
0.00
0.00
0.00
0.00
Depreciation
-96860.00
-96860.00
-96860.00
-96860.00
-96860.00
Working Capital
0.00
72500.00
0.00
0.00
0.00
0.00
Pretax Cost savings
0.00
212805.67
212805.67
212805.67
212805.67
212805.67
Total taxable amount(A)
-536500.00
188445.67
115945.67
115945.67
115945.67
115945.67
Tax @ 31%(B)
0.00
58418.16
35943.16
35943.16
35943.16
35943.16
Add Depreciation (C)
0.00
96860.00
96860.00
96860.00
96860.00
96860.00
Net Cash Inflow (A-B+C)
-536500.00
226887.51
176862.51
176862.51
176862.51
176862.51
Present Value
-536500.00
184461.39
116902.98
95043.07
77270.79
62821.78
Net Present Value
0.01
Hence answer to the third set of question is:
Annual Depreciation - Straight line to zero method
96860.00
Hurdle Rate
23%
Year
0
1
2
3
4
5
Investment
-536500.00
0.00
0.00
0.00
0.00
0.00
Depreciation
-96860.00
-96860.00
-96860.00
-96860.00
-96860.00
Working Capital
0.00
72500.00
0.00
0.00
0.00
0.00
Pretax Cost savings
0.00
247950.00
247950.00
247950.00
247950.00
247950.00
Total taxable amount(A)
-536500.00
223590.00
151090.00
151090.00
151090.00
151090.00
Tax @ 31%(B)
0.00
69312.90
46837.90
46837.90
46837.90
46837.90
Add Depreciation (C)
0.00
96860.00
96860.00
96860.00
96860.00
96860.00
Net Cash Inflow (A-B+C)
-536500.00
251137.10
201112.10
201112.10
201112.10
201112.10
Present Value
-536500.00
204176.50
132931.52
108074.41
87865.37
71435.26
Net Present Value
67983.07
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