Question

9) The Elysian Trust has set up a program that provides free school education for an Trust will provide, as underprivileged children in India and Nepal. The Elysian Trust will provide, as endowment, S1 million each year-end in perpetuity. The interest rate is 8% per year What is the value of this gift today? Suppose, instead, Elysian provides an endowment that pays $2 million every two years in perpetuity, what is the value of this gift today? Suppose, instead, Elysian provides an endowment that pays $500,000 every six months in perpetuity, what is the value of this gift today? a) b) c)

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Answer 1

(9) (a) Annual Perpetual Payouts = $ 1million and Interest Rate = 8 %

Value of the Gift = Present Value of the Perpetuity = 1000000 / 0.08 = $ 12500000 or $ 12.5 million

(b)  Payouts are $ 2 million every 2 years. The present value experession of this payout stream will be as shown below:

PV = 2 / (1.08) + 2 / (1.08)^(2) + 2 / (1.08)^(3) + 2 / (1.08)^(4) + 2 / (1.08)^(5) + ............tp infinity

Substitute (1+K) for (1.08)^(2). The above expression changes to

PV = 2 / (1+K) + 2 / (1+K)^(2) + ........... to infinity

PV = 2 x (1/K) x [1-{1/(1+K)^($\infty$)}] = 2 / K

Now, (1+K) = (1.08)^(2)

K = 1.1664 - 1 = 0.1664

Therefore, PV = 2 / 0.1664 = $ 12.019 million

Value of Gift = PV = $ 12.019 million

(c) Periodic perpetual payouts = $ 500000 and Period = 6 months

PV = 500000 / (1.08)^(0.5) + 500000 / (1.08)^(1) + ..... to infinity

Substitute (1+R)^ for (1.08)^(0.5) to yield the following expression:

PV = 500000 / (1+R) + 500000 / (1+R)^(2) + ............... to infinity

PV = 500000 x (1/R) x [1-{1/(1+R)^($\infty$)}] = 500000 / R

Now, (1+R) = (1.08)^(0.5)

R = 1.03923 - 1 = 0.03923

Therefore, Value of Gift = PV = 500000 / 0.03923 = $ 12745190.52 ~ $ 12.7452 million