Although the Chen Company\'s milling machine is old, it is still in relatively g
ID: 2718876 • Letter: A
Question
Although the Chen Company's milling machine is old, it is still in relatively good working order and would last for another 10 years. It is inefficient compared to modern standards, though, and so the company is considering replacing it. The new milling machine, at a cost of $28,400.00 delivered and installed, would also last for 10 years and would produce after-tax cash flows (labor savings and depreciation tax savings) of $9,500.00 per year. It would have zero salvage value at the end of its life. The firm's WACC is 13.75%, and its marginal tax rate is 35%.
1. What is the NPV?
2. What is the IRR?
3. Should Chen buy the machine ? Based on NPV or IRR rule explain briefly.
SHOW YOUR WORK AND EXPLAIN ANSWERS.
Explanation / Answer
1
Calculation of NPV:
Year
Cash Flows (CF)
PVF (13.75%)
PV = CF *PVF
Initial Cost of the Machine
0
$ (28,400.00)
1.00000
$ (28,400.00)
Annual After-tax cash flows
1 to 10
$ 9,500.00
5.26741
$ 50,040.39
NPV = Sum of PVs
$ 21,640.39
2
Calculation of IRR:
At IRR NPV shall be zero, lets assume IRR be 30%
Calculation of NPV:
Year
Cash Flows (CF)
PVF (30%)
PV = CF *PVF
Initial Cost of the Machine
0
$ (28,400.00)
1.00000
$ (28,400.00)
Annual After-tax cash flows
1 to 10
$ 9,500.00
3.09154
$ 29,369.63
NPV = Sum of PVs
$ 969.63
At 30%, NPV is postive , hence we should take higer rate
Lets Assume IRR be 32%
Calculation of NPV:
Year
Cash Flows (CF)
PVF (32%)
PV = CF *PVF
Initial Cost of the Machine
0
$ (28,400.00)
1.00000
$ (28,400.00)
Annual After-tax cash flows
1 to 10
$ 9,500.00
2.93041
$ 27,838.94
NPV = Sum of PVs
$ (561.06)
Now At 32 %, NPV is Negative
It means IRR is in between 30% to 32%
Now we shall calculate exact IRR as under:
Rate
NPV
30%
$ 969.63
32%
$ (561.06)
Difference
2%
$ 1,530.69
IRR = 30% + 2% * (969.63 / 1530.69) =
31.27%
3
Decision Based on NPV:
NPV is positive $21640.39, hence machine is good to buy
Decision Based on IRR:
IRR 31.27% is more than WACC 13.75%, hence machine is good to buy
1
Calculation of NPV:
Year
Cash Flows (CF)
PVF (13.75%)
PV = CF *PVF
Initial Cost of the Machine
0
$ (28,400.00)
1.00000
$ (28,400.00)
Annual After-tax cash flows
1 to 10
$ 9,500.00
5.26741
$ 50,040.39
NPV = Sum of PVs
$ 21,640.39
2
Calculation of IRR:
At IRR NPV shall be zero, lets assume IRR be 30%
Calculation of NPV:
Year
Cash Flows (CF)
PVF (30%)
PV = CF *PVF
Initial Cost of the Machine
0
$ (28,400.00)
1.00000
$ (28,400.00)
Annual After-tax cash flows
1 to 10
$ 9,500.00
3.09154
$ 29,369.63
NPV = Sum of PVs
$ 969.63
At 30%, NPV is postive , hence we should take higer rate
Lets Assume IRR be 32%
Calculation of NPV:
Year
Cash Flows (CF)
PVF (32%)
PV = CF *PVF
Initial Cost of the Machine
0
$ (28,400.00)
1.00000
$ (28,400.00)
Annual After-tax cash flows
1 to 10
$ 9,500.00
2.93041
$ 27,838.94
NPV = Sum of PVs
$ (561.06)
Now At 32 %, NPV is Negative
It means IRR is in between 30% to 32%
Now we shall calculate exact IRR as under:
Rate
NPV
30%
$ 969.63
32%
$ (561.06)
Difference
2%
$ 1,530.69
IRR = 30% + 2% * (969.63 / 1530.69) =
31.27%
3
Decision Based on NPV:
NPV is positive $21640.39, hence machine is good to buy
Decision Based on IRR:
IRR 31.27% is more than WACC 13.75%, hence machine is good to buy
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