The City of Melon is considering a treatment plant with an i

The City of Melon is considering a treatment plant with an initial investment of $35 million and a life of 30 years. The city uses a rate of 4% per year compounded yearly. If the plant would be needed indefinitely, what is the total investment that the city should budget for the project?

$17.35M

$23.27M

$50.6M

$61.03M

Solution

If 30 years project

Initial Investment,PV = 35 Million
Life, n = 30 Years
Interest Rate, i = 4%
Annual Return, PMT = ?

For Finite Period,
PV = PMT * [1 - (1+i)^-n] / i
35 = PMT * [1 - (1+0.04)^-30] / 0.04
35 = PMT * [1 - 0.3083] / 0.04
35 = PMT * 0.6917 / 0.04
35 = PMT * 17.2920
PMT = 35 / 17.2920
PMT = 2.024 Million

If Infinite Project
Initial Investment = Present Value = PMT / i
Initial Investment = 2.024 / 0.04
Initial Investment = $ 50.60 Million

$ 50.6M