Question

You decide you want to gift Stanford with an endowed professorship in three years, when you graduate. The Lipton Endowed Chair in Finance will pay a new Finance professor 125000$ per year, forever (year 4 and forever after), at the end of every year. You can earn a return of 8% on investments, and so can Stanford. How much would you have to invest today to give Stanford the endowment gift in 3 years?

Answer 1

To endow a professorship paying $125,000 per year starting in year four, you need to first calculate the present value of the perpetuity beginning in year four, which is $1,562,500, and then discount that back to today's value, leading to an investment of $1,162,963.92 required now at an 8% interest rate.

Step-by-step explanation:

To calculate how much you would have to invest today to create an endowed professorship that will pay a Finance professor $125,000 per year from the fourth year onwards, you would use the formula for the present value of a perpetuity. The present value of a perpetuity can be found using the formula PV = P / r, where PV is the present value, P is the payment per period, and r is the interest rate per period. However, because you want to make the gift in 3 years, you must discount that amount back to the present value using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate per period, and n is the number of periods until the payment.

The calculation steps are:

1. Calculate the present value of the perpetuity that begins in year 4: PV(endowment) = 125,000 / 0.08 = $1,562,500.
2. Discount that back to the present value at the beginning of year 1: PV(today) = PV(endowment) / (1 + 0.08)^3 = $1,162,963.92.

Therefore, you would have to invest $1,162,963.92 today to give Stanford an endowment that will pay out $125,000 a year starting from the fourth year onwards.