The City of Chicago is considering building a park. The initial cost of the park
ID: 2626409 • Letter: T
Question
The City of Chicago is considering building a park. The initial cost of the park is $125,000 and the estimated annual operating cost is $8,000. Every ten years it is anticipated that major maintenance will be required at a cost of $25,000. The city is seeking a donor who would provide an initial amount that would fund the park forever (infinite service life). The city anticipates that it can earn 5% on the investment and would name the park for the donor. How much would the donor have to provide?
Explanation / Answer
Equivalent annual rate = 5%
Equivalent 10 yearly rate = (1+0.05)^10 - 1 = 62.8895%
Donor would have to Provide = Initial Cost + present value of annual operating cost + present Value of Every ten years major maintenance cost
Initial Cost = $ 125000
Present value of annual operating cost = 8000/0.05 = $ 160000
Present Value of Every ten years major maintenance cost = 25000/62.8895% = $ 39752
Donor would have to Provide = 125000+160000 + 39752
Donor would have to Provide = $ 324752
Answer:
Donor would have to Provide = $ 324,752