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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