Question

A town's recreation department is trying to decide how to use a piece of land. One option is to put up basketball courts with an expected life of 8 years. Another is to install a swimming pool with an expected life of 24 years. The basketball court would cost $180,000 to construct and yield net benefits of $40,000 at the end of each year, for 8 years. The swimming pool would cast $2.25 million to construct and yield net benefits of $170,000 at the end of each year, for 24 years. Each project is assumed to have zero salvage value at the end of its life. Using a real discount rate of 5 percent, which project offers larger net benefits? Approach the problem using the Roll-Over and the Equivalent Annual Net Benefit methods.

Answer 1

The basketball court offers larger net benefits compared to the swimming pool based on a real discount rate of 5 percent.

Step-by-step explanation:

To determine which project offers larger net benefits, we can use the Roll-Over and the Equivalent Annual Net Benefit methods.

1. Roll-Over Method: Calculate the net benefits for each project over their respective lifetimes. For the basketball court, the total net benefits would be $40,000 * 8 = $320,000. For the swimming pool, the total net benefits would be $170,000 * 24 = $4,080,000.
2. Equivalent Annual Net Benefit Method: Find the equivalent annual net benefit (EANB) for each project by dividing the total net benefits by the present value interest factor of an annuity (PVIFA) of the project's expected life and discount rate. For the basketball court, EANB = $320,000 / (0.8621) = $371,759. For the swimming pool, EANB = $4,080,000 / (16.6857) = $244,573.

Comparing the EANB values, we can see that the basketball court offers a larger net benefit of $371,759 compared to the swimming pool's net benefit of $244,573. Therefore, the basketball court project offers larger net benefits based on a real discount rate of 5 percent.