10.07.2022 - 03:33

# The City of Brandon is installing a new swimming pool in the municipal recreation center. Two designs are under consideration, both of which are to be permanent. The first design is for a reinforced c

Question:

The City of Brandon is installing a new swimming pool in the municipal recreation center. Two designs are under consideration, both of which are to be permanent. The first design is for a reinforced concrete pool that has a first cost of $1,500,000. Every 10 years, the inner surface of the pool would have to be refinished and painted at a cost of$200,000. The second design consists of a metal frame and a plastic liner, which would have an initial cost of $500,000. For this alternative, the plastic liner must be replaced every 5 years for a cost of$100,000, and every 15 years the metal frame would need to be replaced at a cost of $150,000. Extra insurance of$5,000 per year is required for the plastic liner to cover repair costs in case it leaks. The city’s cost of long-term funds is 5%. Determine which swimming pool design has the lower present cost.

The reinforced concrete pool has the lower present cost. To determine the present cost, we need to calculate the present value of all costs associated with each design. For the reinforced concrete pool: - First cost = $1,500,000 - Refinishing and painting cost every 10 years =$200,000, which we'll assume occurs at the end of each 10-year period. Using the present value formula, we can calculate the present value of these costs: $1,500,000 + ($200,000/(1.05)^10) + ($200,000/(1.05)^20) + ($200,000/(1.05)^30) = $2,486,572.81 For the metal frame and plastic liner pool: - First cost =$500,000 - Replacement of plastic liner every 5 years = $100,000 - Replacement of metal frame every 15 years =$150,000 - Additional insurance cost = $5,000 per year Using the present value formula, we can calculate the present value of these costs:$500,000 + ($100,000/(1.05)^5) + ($100,000/(1.05)^10) + ($100,000/(1.05)^15) + ($150,000/(1.05)^15) + (($5,000*15)/1.05) =$2,525,916.17 Therefore, the reinforced concrete pool has the lower present cost of $2,486,572.81 compared to$2,525,916.17 for the metal frame and plastic liner pool.