1. You are operating an old machine that is expected to produce a cash inflow of
ID: 2742532 • Letter: 1
Question
1. You are operating an old machine that is expected to produce a cash inflow of $5,000 in each of the next 3 years before it fails. You can replace it now with a new machine that costs $20,000, but is much more efficient and will provide a cash flow of $10,000 a year for 4 years. a) What is the NPV of the purchase of the new machine if you take into account only the incremental cash flows it can generate relative to the old machine? Given your computations, should you replace the old machine now? b) What is the EAA of the new machine if you look only at the cash flows associated to that machine? Does that computation suggest that you should replace your old equipment now? [Hint: the EAA of the old machine can be considered to be just the annual cash inflows it generates]
Please show how to do it in a BA II Plus financial calculator
Explanation / Answer
Solution A
We have
Incremental initial cash flow = -20,000
Incremental cash flow (year 1-3) = 10,000-5000 = 5000
Incremental cash flow year 4 = 10,000-0 = 10,000
NPV is the sum of present values of all cash flows. Present value is calculated by multiplying cash flow with PV factor:
Year
Cash flow
PV factor 8%
PV
0
-20000
1
-20000
1
5000
0.925926
4629.63
2
5000
0.857339
4286.694
3
5000
0.793832
3969.161
4
10000
0.73503
7350.299
235.78
Since NPV is positive, the old machine should be replaced.
Solution A
Taking cash flows of new machine:
Year
Cash flow
PV factor 8%
PV
0
-20000
1
-20000
1
10000
0.925926
9259.259
2
10000
0.857339
8573.388
3
10000
0.793832
7938.322
4
10000
0.73503
7350.299
3.312127
13,121.27
EAA = NPV/ sum of pv factors except year 0
= 13,121.27/ 3.312127
= 3961.58
Since the EAA is lower than current machine, the machine should not be replaced.
Year
Cash flow
PV factor 8%
PV
0
-20000
1
-20000
1
5000
0.925926
4629.63
2
5000
0.857339
4286.694
3
5000
0.793832
3969.161
4
10000
0.73503
7350.299
235.78
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