Question

I need help understanding how to answer this and the proper way to answer this - I attempted it twice the way I thought and came up with the wrong answers.

If you solve this in excel, if you can show the formulas used as well as the values it generates, it would be greatly appreciated.

Maintenance money for an athletic complex has been sought. Mr. Kendall, Athletic Director, would like to solicit a donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to be $1.1 million each year for the first five years, $1.4 million each year for years 6 through 10, and $1.7 million each year after that. (The building has an indefinite service life.) If the money is placed in an account that will pay 6% interest compounded annually, how large should the gift be? Click the icon to view the interest factors for discrete compounding when i-6% per year. The gift should be $mn. (Round to two decimal places.)

Answer 1

Answer:

Maintenance Cost Cash flow

Years	Cash flow (CF)
1-5 years	$1.1 millions
6-10 years	$1.4 millions
11 years onwards	$1.7 Millions

Interest Rate r=6%

So Gift Size= PV of cash flow from 1-5 years+PV of cash flow from 6-10 years+PV of cash flow from 11 years onwards

PV of cash flow from 1-5 years=CF*(1-(1+r)^-5)/r=1.1 *(1-(1+6%)^-5)/6%=$4.63 millions

PV of cash flow from 6-10 years=CF*(1-(1+r)^-5)/(r*(1+r)^5)=1.4 *(1-(1+6%)^-5)/(6%*(1+6%)^5)=$4.41 millions

PV of cash flow from 11 years onwards=CF/(r*(1+r)^10)=1.7 /(6%*(1+6%)^10)=$15.82 millions

Gift Size =4.63+4.41+15.82=$24.86 millions