Maintenance money for a new building at a college is being solicited from potent

Question

Maintenance money for a new building at a college is being solicited from potential alumni donors. You would like to make a donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to be $40,000 each year for the first five years, $50,000 for each of years six through 10, and $60,000 each year after that (The building has an infinite service life)

a) If the money is placed in an account that will pay 13% interest compounded annually, how large should the gift be?

b) What is the equivalent annual maintenance cost over the infinite service life?

Explanation / Answer

a) Calculating the future value of the amount at 13% interest rate: The future value of annuity is calculated using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "FV" function as we are finding the future value of annuity in this case. Step3: Enter the values as Rate = 13%; Nper = 5; PMT = 40000; PV = 0 Step4: Click "OK" to get the desired value. The value comes to $259,210 This future value of annuity becomes present value for the 6th year: Calculating the future value of cash flows from year 6 to year 10: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "FV" function as we are finding the future value of annuity in this case. Step3: Enter the values as Rate = 13%; Nper = 5; PMT = 50000; PV = 259210 Step4: Click "OK" to get the desired value. The value comes to "$801,591" Therefore, the future value of the deposit after 10years would be $801,591 Since we cannot the future value of perpetuity, we calculated the future value for 10years. b) Equivalent annual cost is calculated as EAC = (Asset price x Discount rate)/ (1 + Discount rate)^-nuber of periods But here the number of periods is infinity. The discount rate is 13% We know that anything power infinity is equal to "1" If we substitute the values in the above formula, we get the denominator equal to "1"

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