Question

Assuming in twenty years after graduating from ERAU you become extremely wealthy. You want to give back to your school and establish a scholarship endowment that will pay $200,000 per year in perpetuity to support ERAU students in need. Assume a conservative rate of return of 5% per year.

1. If the first payment will be made in one year after establishing the endowment, how much should you invest in it?

2. How much do you need to invest in the endowment if you want the first payment to be made in 6 years from establishing it?

3. In how many years your endowment will be depleted?

4. If you plan to save for this endowment (first payment in one year) over 15 year period and your expected personal rate of return is 12%, how much should you invest every year? Assume equal annual payments.

Answer 1

(1) Target Annual Payout Amount = Annual Endowment = $ 200000 and Rate of Return = 5 %, First Endowment happens at the end of year 1 assuming current time is beginning of year 1,

Therefore, Current Investment = 200000 / 0.05 = $ 4000000

(2) Target Annual Payout Amount = Annual Endowment = $ 200000 and Rate of Return = 5 %, First Endowment happens at the end of year 6 assuming current time is beginning of year 1.

Therefore, Current Investment = [200000/0.05] x [1/(1.05)^(6)] = $ 2984861.59

(3) As the rate of return of 5% matches the rate of depletion of the fund by means of the annual endowment payouts, the current investment will never be depleted in nominal terms.

(4) Savings Tenure = 15 years, Personal Return = 12% and Number of Savings = 15, The last savings is assumed to happen at the end of year 15, with current time being end of year 0 and first endowment payout worth $ 200000 happening at the end of year 16. Let the annul savings be $ M

Therefore, sum of the future values of the annual savings deposits compounded at 12 % at the end of year 15 = Sum of the present values of the annual endowment payouts discounted at 5% at the end of year 15

M x (1.12)^(14) + M x (1.12)^(13) + ..........+ M x (1.12) + M = 200000 / 0.05 = $ 4000000

M x [{(1.12)^(15) - 1} / {1.12-1}] = 4000000

M x 37.2797 = 4000000

M = 4000000 / 37.2797 = $ 107296.9586 ~ $ 107296.96