a) This question relates to the time value of money and deferred perpetuates.
Colin Greenway attended Bunyip High School in the 1970s. After leaving school, Colin became a successful entrepreneur and is now very wealthy. He wishes to establish a perpetual scholarship fund which will provide $10,000 a year, payable to five high performing students at Bunyip High School each year in Year 12, that is, $50,000 a year, starting in early 2020. It is now early 2017. The High School Principal believes that the required funds can be invested at 5 per cent a year in perpetuity.
i) What is the present value in early 2017 of the whole income stream, and thus the amount which Colin must contribute to establish the fund?
ii) The High School Principal, while most appreciative of Colin’s great generosity, mentions that fees at Bunyip High are rising on average by 3 per cent every year because of inflation, and that in several years, $10,000 will not be enough to keep a student in year 12 for a whole year. Colin decides that he will increase the amount to establish the fund so as to provide for increases in the scholarship amount by 3 per cent a year in perpetuity, the first increase occurring in early 2021. How much extra (above the amount calculated in i) above, will Colin need to contribute in early 2017 so as to provide for these inflation increases forever?
[HINT: Consider a formula similar to the dividend growth model.]
QUESTION 2 continued.
b) This question relates to loan repayments and loan terms.
Ron and Robin Reid wish to borrow $540,000 to buy a home. The loan from Biggles Bank requires equal monthly repayments over 20 years, and carries.an interest rate of 7.8% per annum, compounded monthly. The first repayment is due at the end of the first month.
You are required to calculate:
i) the effective annual interest rate on the above loan.
ii) the amount of the monthly repayment (consisting of interest and principal repayment components) if the same amount is to be repaid every month over the 20 year period of the loan.
iii) the amount of $X, if – instead of the above – Biggles Bank agrees that Ron and Robin will repay the loan by paying the bank $3,300 per month for the first 12 months, then $3,750 a month for the next 12 months, and after that $X per month for the balance of the 20 year term.
QUESTION 2 b) continued.
iv) how long (in years and months) it would take to repay the loan if, alternatively, Ron and Robin decide to repay $2,500 per month, with the first repayment again being at the end of the first month after taking the loan, and continuing until the loan was repaid.
v) under option iv) above, the amount of the final repayment. [NOTE: Towards the end of the loan repayment period, after the final full monthly instalment of $2,500 is paid, a lesser amount is likely to be outstanding. That amount, plus interest to the end of the following month, is the final loan repayment amount.]
