Can soeone help me with part b? Do I have to assume my life expectancy for this
ID: 2811571 • Letter: C
Question
Can soeone help me with part b? Do I have to assume my life expectancy for this qustion?
I would appreciate if you solve it using formulas, not excel...
As a future graduate of the University of Minnesota's prestigious Carlson School of Management, someday you would like to endow a scholarship (meaning give the university money in your name) to pay for tuition expenses for future CSOM students. Assume you just graduated (congratulations!). You plan to work for fifteen years after graduation before endowing this scholarship (at the end of the fifteenth year AFTER graduation). Annual tuition at UMN is $10,000 today, and is expected to grow at the long term average rate of inflation of 3% per year forever. savings is expected to earn a return of 7% per year forever. 3. If the first tuition payment is due one year after the scholarship is endowed, and you would like the scholarship to pay all tuition for one student per year for the twenty years following the creation of the endowment, how much money do you need to endow the scholarship? a.Explanation / Answer
For Part b, you need to take the perpetuity into consideration. Look at Part a, it is for 20 years, so it is like an annuity. Similarly, part b is forever, so it needs to be considered as a perpetuity.
So, soln for part b will be as below,
The tuition today is %10,000 and it is expected to grow at the rate of 3% per year forever.
Given the first tuition payment is done one year after you endowed the scholarship. You endowed the scholarship at the end of year 15. This means. the tuition payments are going to start from Year 16 and they are going to be paid forever as scholarships.
So, you need to endow an amount at the end of year 15 which is equal to the sum of all the tuition payments discounted to year 15 that are done from year 16 to forever (perpetuity)
Tuition fee at year 16 = Tuition fee today * (1+3%)16 = 10,000* (1.0316) = $16,047.06
The perpetuity starts with year 16 i.e $16,047.06 increasing at a rate of 3%
-> Amount to be endowed = Present value of the perpetuity discounted @7% with the perpetuity growing @3%
PV of perpetuity with cash flow of 'C' growing at a rate of 'g' with a return 'r' = C / (r-g)
Therefore, amount to be endowed = 16,047.06 / (7% - 3%)
-> Amount to be endowed at the end of year 15 = $401,176.61