Question

A foundation announces that it will be offering one CUHK (SZ) 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 ￥100,000 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 (￥400,000) in 10 equal annual installments, interest-free, starting two years after the last payment of the scholarship. This implies that the foundation is really giving an interest-free loan under the guise of a scholarship. The current interest is 6% and is expected to remain unchanged. (1) What is the PV of the first scholarship? (2) The foundation invests a lump sum to fund all future scholarships. Determine the size of the investment today

Answer 1

1) PV of first scholarship is:

N = 4

I/y = 6

PV = ?

PMT = -100,000

FV = 0

CMP PV = 346,511

Note - they have not used net Present value... So we will find what they have asked

2) NPV of future scholarshipis calculated as below, use financial calculator:

Cf0 = 0

Cf1 = (100,000)

F1 = 4

Cf2 = 0

F2 = 1

Cf3 = 40,000

F3 = 10

I = 6

CPT NPV = -126,515

Note.. first frequency takes us 4 yrs ahead

Second frequency is put as 1 so it will take you agar by 2 yrs. Ie you will be at -100,000 at yr 4 and then yr5 will be 0 and again yr 6 will be 40,000. So don't make mistake of frequency at 2. It should be 1 only.