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A company is considering the purchase of new equipment for $45,000. The projected annual net cash flows are $19,000. The machine has a useful life of 3 years and no salvage value. Management of the company requires a 12% return on investment. The present value of an annuity of $1 for various periods follows: Period Present value of an annuity of $1 at 12%1 0.89292 1.69013 2.4018 What is the net present value of this machine (rounded to the nearest whole dollar) assuming all cash flows occur at year-end?

Question

A company is considering the purchase of new equipment for 45,000.Theprojectedannualnetcashflowsare45,000. The projected annual net cash flows are 19,000. The machine has a useful life of 3 years and no salvage value. Management of the company requires a 12% return on investment. The present value of an annuity of 1forvariousperiodsfollows: PeriodPresentvalueofanannuityof1 for various periods follows: Period Present value of an annuity of 1 at 12%1 0.89292 1.69013 2.4018 What is the net present value of this machine (rounded to the nearest whole dollar) assuming all cash flows occur at year-end?

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Solution

To calculate the net present value (NPV) of the machine, we need to discount the projected annual net cash flows to their present value and then subtract the initial cost of the machine.

Step 1: Calculate the present value of the cash flows.

The present value of an annuity formula is:

PV = Cash flow * Present value of an annuity factor

In this case, the cash flow is $19,000 per year and the present value of an annuity factor for 3 years at 12% is 2.4018 (given in the question).

So,

PV = 19,0002.4018=19,000 * 2.4018 = 45,634.2

Step 2: Calculate the NPV.

The NPV formula is:

NPV = PV - Initial cost

In this case, the initial cost is $45,000.

So,

NPV = 45,634.245,634.2 - 45,000 = $634.2

Therefore, the net present value of the machine, rounded to the nearest whole dollar, is $634.

This problem has been solved

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