Question

Q2 (13) a) (3+3) Feridun announces that it will be offering one UW scholarship every year for an indefinite number of years. The first scholarship is to be offered exactly one year from now. When the scholarship is offered, the student will receive $10,000 annually for a period of four years, beginning from the date the scholarship is offered. This student is then expected to repay the principal amount received ($40,000) in 10 equal annual installments, interest-free, starting one year after the expiration of her scholarship. This implies that Feridun is really giving an interest-free loan under the guise of a scholarship. The current interest is 6% for all maturities and is expected to remain unchanged. (i) What is the PV of the first scholarship? (ii) Feridun invests a lump sum to fund all future scholarships. Determine the size of the investment today.

Answer 1

(I) present value of first scholarship = ($10,000*present value annuity factor*(6%, 4 years))/1.06

= ($10,000*3.465)/1.06

Present value of first scholarship = $32,688.68

(ii) scholarship is to be repaid in 10 equal annual installments after expiry of scholarship I,e repaid after 5 years from now.

Size of investment = present value of future repayments

= ($4000*present value annuity factor*(6%,10years))/(1.06)^5

= ($4000*7.36)/0.747

= $39410.98

Hence investment to be made today = $39,410.98

Thanks,

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