Question

Poe Company is considering the purchase of new equipment costing $86,000. The projected annual cash inflows are $36,200, to be received at the end of each year. The machine has a useful life of 4 years and no salvage value. Poe requires a 10% return on its investments. The present value of an annuity of $1 and present value of an annuity of $1 for different periods are presented below, Compute the net present value of the machine (rounded to the nearest whole dollar).

Answer 1

Step-by-step explanation:

To compute the net present value (NPV) of the machine, we need to calculate the present value of the cash inflows and subtract the initial cost of the equipment.

The formula for calculating the present value of an annuity is:

PV = A x [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

A = Annual cash inflow

r = Discount rate (10% or 0.10)

n = Number of periods (4 years)

Let's calculate the present value of the annual cash inflows:

PV of cash inflows = $36,200 x [(1 - (1 + 0.10)^(-4)) / 0.10]

PV of cash inflows = $36,200 x [(1 - 0.683013455) / 0.10]

PV of cash inflows = $36,200 x (0.316986545 / 0.10)

PV of cash inflows = $36,200 x 3.16986545

PV of cash inflows = $114,744.13 (rounded to two decimal places)

Now, subtract the initial cost of the equipment:

NPV = PV of cash inflows - Initial Cost

NPV = $114,744.13 - $86,000

NPV = $28,744.13

So, the net present value of the machine is approximately $28,744 (rounded to the nearest whole dollar).