Question

In: Accounting

Your child is about to enter college a year from now. A local foundation provides scholarships...

  1. Your child is about to enter college a year from now. A local foundation provides scholarships (essentially interest-free loans) each year perpetually for students. Your child has won the scholarship just now. When your child joins college, he/she would receive a scholarship of $ 10,000 per year annually for 4 years. Your child is expected to repay the scholarship amount of $ 40,000 in 15 equal yearly installments, interest-free beginning a year after the expiration of his/her scholarship. The foundation seems to be giving an interest free loan. The market interest rate is 8% and would not change in the future.
    1. What is the PV of the scholarship?
    2. If the foundation invests a lump sum today to fund all future scholarships. What must be that investment today?
  2. solve by formula method and not by excel method

Solutions

Expert Solution

Answer:
a) PV of Scholarship
Repayment of Scolarship of $40000 in 15 equal yearly instalments
So amount of yearly instalment is $40000/15 = $2666.67
PV = CF/(1+r)^n
PV = Present value of all cash flows
CF = Future cash flow in each period
r = rate of interest
n = no. of years
Let us name the denominator in the avove formula i.e (1+r)^n as PV factor
Year FV PV factor PV
1 -10000 1 -10000
2 -10000 1.08 -10800 Here, the annual scholarship of $10000 starts immediately on
3 -10000 1.17 -11664 joining i.e at the beginning of year 1 and so on for Year 2, 3
4 -10000 1.26 -12597 and 4. Repayment starts a year after the expiriration of
5 2666.67 1.47 3918 scholarship i.e at the end of Year 5. Hence the for calculation
6 2666.67 1.59 4232 of PV factor, n for Year 1, 2, 3 & 4 are taken as 0,1,2 and 3. For
7 2666.67 1.71 4570 repayment from the end of Year 5, n in the PV factorare taken
8 2666.67 1.85 4936 as 5, 6 and so on.
9 2666.67 2.00 5331
10 2666.67 2.16 5757 So the PV of the scholarship is $61327
11 2666.67 2.33 6218
12 2666.67 2.52 6715
13 2666.67 2.72 7252
14 2666.67 2.94 7833
15 2666.67 3.17 8459
16 2666.67 3.43 9136
17 2666.67 3.70 9867
18 2666.67 4.00 10656
19 2666.67 4.32 11509
Total 0.00 61327
b) For the foundation to invests a lump sum today to fund all future scholarships, we need to
calculate what sum today if invested will generate a Future Value (FV) of $61327 in 19 years.
Formula of Future Value is given hereunder:
FV = Co x (1+r)^n
FV = Future value of Cash Flow at the beginning
Co = Cash flow at the beginning
r = rate of interest
n = no. of years
Let us name the multiplier in the above formula i.e (1+r)^n as FV factor
Year FV factor
1 1.08 Here the FV factor for n = 19 is computed as 4.32
2 1.17
3 1.26 So, $61327          = Co x 4.32
4 1.36
5 1.47 So, the Cash flow required at the beginning is          $ 14210
6 1.59
7 1.71
8 1.85
9 2.00
10 2.16
ekkarill92 answered 1 year ago
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