$2.$ Decision on Long$-$Term Physical Capital

Case of Nonannuity: Computing Present Value of Investment

Suppose you are the Chief Financial Officer $($CFO$)$ of the YMCA South Bend. The YMCA is planning to build a new swimming pool this year. The YMCA Board of Trustees $($BOT$)$ asked you to evaluate the present value of this project. The construction of the swimming pool will cost $$110$ in $2024($current year$).$ And the new swimming pool will generate revenues in the following five years: $2025$: $$40/2026$: $$32/2027$: $$24/2028$:$$15/2029$: $$8.$ Finally, the average annual interest rate for the next five years would be $4$ percent.

$(1)$ Show your computing process $($Show your completed Excel template$).$

$(2)$ Will you recommend BOT to construct the new swimming pool? Why or why not?