Management is considering purchasing a machine for $780,000 that would have a us

ID: 2450801 • Letter: M

Question

Management is considering purchasing a machine for $780,000 that would have a useful life of 8 years and $52,000 salvage value. The asset would generate annual net cash inflows of $121,500 throughout its useful life. The project would require additional working capital of $95,000. The company’s discount rate is 5%. In year 6 the machine will require $28,000 overhaul.

What is the net present value of the machine salvage value in year 8?

What is the PV factor used to calculate the NPV of the Annual net cash flows?

What is the net present value of the annual net cash flows?

Should we accept or reject the purchase of the new machine?

Explanation / Answer

Calculation of net present value of the machine salvage value in year 8:

Salvage value at the end of year 8

$ 52,000.00

PVF (5%, 8 years )

0.67684

Net present value of the machine salvage value in year 8 = 52000 * 0.67684

$ 35,195.65

PV factor used to calculate the NPV of the Annual net cash flows shall be annuity factor taken at 5% discount rate and for 8 years period =

PVAF (5%, 8 years ) =

6.46321

Calculation of net present value of the annual net cash flows:

Annual net cash flows

$ 121,500.00

PVAF (5%, 8 years ) =

6.46321

Net present value of the annual net cash flows = 121500*6.46321

$ 785,280.35

Calculation of Net present value for machine :

Initial cost of purchasing

$ (780,000.00)

Additional working capital

$ (95,000.00)

Present value of overhaul in year 6 = 28000* PVF (5%, 6 years ) = 28000*0.74622

$ (20,894.16)

Net present value of the annual net cash flows

$ 785,280.35

Net present value of the machine salvage value in year 8

$ 35,195.65

Net present value for machine

$ (75,418.16)

The net present value of the machine is negative , hence we should reject the purchase of the new machine