Problem 1: Endowment losses. An American university endowmenthas experienced severe losses over the past year. The value of theuniversity'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 endowmentat t=1 if it would like the amount spent to grow by g=4% per yearfrom then on and has no other resources than the endowment? (b) Theplanned spending is, however, much larger. Back when things lookedbetter, the university set up plans to spend $40M at t=1, withfuture spending growing by 4% per year. What is the PV of theplanned spending? How large is the shortfall between the PV of theplanned spending and the value of the endowment? (c) The universitypresident approaches the university's business school forinnovative ideas for how to cover the shortfall to avoid having tocut spending. The business school 1 suggests that the universitysets up a campus in Abu Dhabi and negotiates the following deal:Abu Dhabi will pay the university $200M today (t=0) for the rightto 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 theuniversity. The new campus would be ready to open two years fromnow (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 wouldalso cover the cost of hiring extra faculty and travel cost for USfaculty to go teach on the new campus, so the $24M is theuniversity's per year profit). The deal would end at t=12. What isthe PV of the deal with Abu Dhabi? Is it sufficient to cover theshortfall? (d) The university president is impressed with the PVcalculations but would also like to know exactly how the endowmentwill develop over the years, assuming the deal with Abu Dhabi isaccepted. At t=0 after the initial payment from Abu Dhabi, thevalue of the endowment is $1.2B. What is the value of the endowmentat t=1 (after interest is received and after paying for theuniversity's t=1 spending)? What is the value of the endowment att=12 (after interest is received, after the last payment from AbuDhabi and after paying for the university's t=12 spending)? At whattime will the endowment equal zero if the deal with Abu Dhabi isnot accepted (please report the time at which the endowment restgoes negative)? Hint: Do not bother with Excel functions here, justcalculate the value of the endowment in a spreadsheet year by yearfor the different cases.