Chattanooga and the State of Tennessee Development Board wants to build an incub

Question

Chattanooga and the State of Tennessee Development Board wants to build an incubator on the east side. The initial investment will be $325,000 and the endowment principal will earn 9% per year.The operating and maintenance cost for the incubator is eastimated to be $53,000 each year, and $42,000 to upgrade the equipment at the end of every tenth year. What is the amount of the endowment required to establish the center and supply the funds to maintain this center forever? (ANS. $XXX,XXX) (show your work)

Explanation / Answer

To maintain the center forever PV of all future cash should equal to $325,000

rate = 9%

since it is a perpetuity

PV of cost for incubator = -53000/.09 = -$588888.8888

Let annual endwmwnt = $X

PV of all the future endowment = X/.09

since it is need to upgrade every fifth year and it is perpetuity

we need to calculate effective rate for 5 years

effective rate for 5 year = 1.09^5-1 = 0.538623 = 53.8623%

PV of upgrade cost = -42000/.538623 = -$77976.61815

NOW, to continue endowmwnt for perpetuity

325,000 = (X/.09)-77976.61815-588888.8888

X = 325000+77976.61815+588888.8888)*.09 = $89267.8956 = 089,268

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