A company is considering the purchase of new equipment for $57,000. The projected annual net cash flows are $23,400. The machine has a useful life of 3 years and no salvage value. Management of the company requires a 8% return on investment. The present value of an annuity of 1 for various periods follows: Periods Present value of an annuity of 1 at 12%
1 0.8929
2 1.6901
3 2.4018
What is the net present value of this machine assuming all cash flows occur at year-end?
a. $30,000
b. $4,500
c. $(4,736)
d. $34,500
e. $82,862

Net Present Value = $3,304.069

Explanation:

To determine whether or not the investment was right, we will need to determine the net present value of the investment (NPV).

The NPV is the difference between the present value PV of cash inflows and the PV of cash outflows. A positive NPV implies a good investment decision and a negative figure implies the opposite.

NPV of an investment(NPV)

NPV = PV of Cash inflows - PV of cash outflow

The cash inflow is an annuity.

PV of annuity= A× 1 -(1+r)^(-n)/r

A- Annual cash flow ,- 23,400 r - discount rate - 8%, number of years- 3

Present Value of cash inflow =23,400 × (1- (1.08)^(-3)/0.08 = 60,304.06

Initial cost = 57,000

Net Present Value = 60,304.06 - 57,000 = 3,304.069

Net Present Value = $3,304.069

Kindly note that a discount rate of 8% was used as it is the opportunity cost of capital for the investment.

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