Question

Problem 1: Endowment losses. An American university endowment has experienced severe losses over the past year. The value of the university's endowment is $1B as of today (t=0). The interest rate (i.e. the expected annual investment return on the endowment) is r = 7%. (a) What amount can the university spend from the endowment at t=1 if it would like the amount spent to grow by g=4% per year from then on and has no other resources than the endowment? (b) The planned spending is, however, much larger. Back when things looked better, the university set up plans to spend $40M at t=1, with future spending growing by 4% per year. What is the PV of the planned spending? How large is the shortfall between the PV of the planned spending and the value of the endowment? (c) The university president approaches the university's business school for innovative ideas for how to cover the shortfall to avoid having to cut spending. The business school 1 suggests that the university sets up a campus in Abu Dhabi and negotiates the following deal: Abu Dhabi will pay the university $200M today (t=0) for the right to name the campus after the famed university for the next 12 years (i.e. up to t=12) and have classes taught by professors from the university. The new campus would be ready to open two years from now (t=2). At the end of each of the following 10 years (t=3, 4, 5, 6, ...,12) Abu Dhabi would pay the university $24M (Abu Dhabi would also cover the cost of hiring extra faculty and travel cost for US faculty to go teach on the new campus, so the $24M is the university's per year profit). The deal would end at t=12. What is the PV of the deal with Abu Dhabi? Is it sufficient to cover the shortfall? (d) The university president is impressed with the PV calculations but would also like to know exactly how the endowment will develop over the years, assuming the deal with Abu Dhabi is accepted. At t=0 after the initial payment from Abu Dhabi, the value of the endowment is $1.2B. What is the value of the endowment at t=1 (after interest is received and after paying for the university's t=1 spending)? What is the value of the endowment at t=12 (after interest is received, after the last payment from Abu Dhabi and after paying for the university's t=12 spending)? At what time will the endowment equal zero if the deal with Abu Dhabi is not accepted (please report the time at which the endowment rest goes negative)? Hint: Do not bother with Excel functions here, just calculate the value of the endowment in a spreadsheet year by year for the different cases.

Answer 1

a.

Calculation of amount spend by the university from endowment

Formula to calculate payment spend by the university:

Substituting Equation (1) with $1B(Billion) for PV, 7% or 0.07 for r and 4% or 0.04 for g to calculate payment spend by the university.

Hence, the payment spend by the university is $30M (Million).

Where,

PV is present value

r is the interest rate

g is the growth rate

b.

Calculation of Present value of planned spending

Formula to calculate Present value:

Substituting Equation (2) with $40 M for payment, 7% or 0.07 for r and 4% or 0.04 for g to calculate present value.

Hence, the present value is $1,333M.

Calculation of shortfall in between the planned value of PV and the value of endowment:

Hence, the value of shortfall is $333M.

c. Calculation of Present value of the deal of Abu Dhabi:

Substituting Equation (3) with $200 M for payment, 0.07 for r to calculate present value.

Hence, the present value is $347.2M.

As per this deal it is enough to overcome the shortfall because $347.2M is greater than the value of last shortfall that is $333M.

d.

Calculation of endowment at t1 and t12:

Hence, the value of endowment at t1 is $1,244M and t12 is $2,166M