Problem 1: Endowment Losses. An American university endowment has experienced severe losses over the past year. The value of the university's endowment is S1B as of today (t-0). The interest rate (i.e. the expected annual investment return on the endowment) is (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 C-$40M at t=1, with future spending growing by g-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 suggests that the university sets up a campus in Abu Dhabi and negotiates the following deal: Abu Dhabi will pay the university S200M 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 S24M