Final answer:
The future value of all the costs of owning and operating this machine is $2,840,680.
Step-by-step explanation:
To calculate the future value of all the costs of owning and operating the machine, we first need to calculate the future value of the initial cost, monthly maintenance costs, and the major overhaul cost.
We will use the formula for future value of a series of cash flows.
Calculate the future value of the initial cost of $1.2M at the end of 10 years using the formula:
FV = PV * (1 + r)^n, where FV is the future value, PV is the present value, r is the nominal interest rate, and n is the number of periods.
In this case, FV = $1.2M * (1 + 0.09/12)^(10*12) = $1.2M * 1.791 = $2.1492M.
Calculate the future value of the monthly maintenance costs for the first 7 years using the formula:
FV = PMT * ((1 + r)^n - 1)/r, where PMT is the monthly payment, r is the nominal interest rate, and n is the number of months.
In this case, FV = $2000 * ((1 + 0.09/12)^(7*12) - 1)/(0.09/12) = $2000 * (1.0932 - 1)/0.0075 = $260,800.
Calculate the future value of the monthly maintenance costs for the remaining years using the same formula.
In this case, FV = $2500 * ((1 + 0.09/12)^(3*12) - 1)/(0.09/12) = $2500 * (1.3152 - 1)/0.0075 = $262,680.
Calculate the future value of the major overhaul cost of $100,000 at the end of the fifth year using the formula:
FV = PV * (1 + r)^n.
In this case, FV = $100,000 * (1 + 0.09/12)^(5*12) = $100,000 * 1.680 = $168,000.
Add all the future values together to get the total future value of all the costs:
$2.1492M + $260,800 + $262,680 + $168,000 = $2,840,680.