1. A manager is considering the following investment:
Initial capital investment $180,000
Estimated useful life 3 years
Estimated disposal value in 3 years 0
Estimated annual savings in cash operating costs $80,000
Minimum desired rate of return 10%
The net present value of the investment is ________.
A) $(123,652)
B) $18,952
C) $60,000
D) $198,952
To calculate the net present value (NPV) of the investment, we need to discount the future cash flows to their present value and then subtract the initial capital investment.
Step 1: Calculate the present value of the annual savings in cash operating costs.
To calculate the present value of an annuity, we use the formula:
PV = P * [1 - (1 + r)^(-n)] / r,
where PV is the present value, P is the future cash flow, r is the discount rate, and n is the number of years.
In this case, the future cash flow is $80,000 per year for 3 years, the discount rate is 10%, and the number of years is 3.
Plugging in the values into the formula:
PV = 80,000 * [1 - (1 + 0.10)^(-3)] / 0.10
PV = 80,000 * (1 - 0.7513) / 0.10
PV = 80,000 * 0.2487 / 0.10
PV = $198,420
Step 2: Subtract the initial capital investment from the present value of the cash flows.
NPV = PV - Initial capital investment
NPV = $198,420 - $180,000
NPV = $18,420
Therefore, the net present value of the investment is $18,420. This matches option B) $18,952.