Outline
You should have the correct answer and show your working or correct explanation to get one mark (very brief or one line answers are not acceptable). An incorrect answer or an answer without the working will be given zero. No part marks. For questions where two or more answers are requested you must get all parts correct to get the one mark. Include cash flow maps or tables wherever possible. Avoid rounding error.
Read the questions carefully
Question 1
Now that they have accumulated a deposit of 85,000 Jack and Jill take out a housing loan to purchase a home. The house costs $655,000. It is to be repaid in equal monthly instalments over a term of 20 years. The interest rate quoted by the bank is an effective annual rate of 7.5%pa. Jack has misplaced the paperwork showing the annual nominal rate (j12) with monthly compounding.
i. How much is the monthly repayment?
ii. How much do Jack and Jill owe the bank immediately before making the 120th repayment?
iii. After making the 160th repayment Jack and Jill receive an amount of $50,000, which they use to reduce their loan. They wish to keep the same term of the loan and reduce their repayments. How much is the new repayment, if the interest rate remains the same?
(Answers to must be accurate to the nearest dollar)
Question 2
Today is Stanley's 55th birthday. He plans to retire on his 65th birthday. He wants to put aside the same sum of money every birthday (starting next birthday) up to and including his 65th. He then wants to be able to withdraw $8000 every birthday (starting with his 65th) up to and including his 85th birthday. He believes that an interest rate of 7% pa is a reasonable estimate of the opportunity cost of funds. How much does he need to put away each birthday?
(Your answers should be accurate to the nearest dollar)
Question 3
A perpetuity with the first annual cash flow paid at the beginning of year 5 is equivalent to receiving $109,000 in 18 years' time. Assume that the perpetuity and the lump sum are of equivalent risk and that j12 = 14.32% pa is the appropriate interest rate.
How much is the annual cash flow associated with the perpetuity?
(Accurate to the nearest dollar)
Question 4
In exchange for a lump sum payment now, Polysuper offers an annual pension over thirty years beginning with a payment of $30,000 at the end of the first year. There are thirty payments in total and the payments will increase at an annual rate of 3%pa. The appropriate opportunity cost of funds is j2 = 8%pa what is the amount of lump sum needed to purchase the pension?
(Accurate to the nearest dollar)
Question 5
a) A ninety day bank bill with 90 days to maturity has a price of $99227.95. What is the effective annual yield implied by this price and maturity? Be careful I am not asking for the annual nominal yield, which by convention is normally quoted in financial markets. Face value is $100,000.
b) What would be the price of this bank bill if you decide to sell it with 80 days left to maturity and the appropriate interest rate was 4.21%pa effective?
c) Calculate the geometric average rate of return over three years given the following annual rates, year 1 = 5.55%, year 2 = 6.75%, year 3 = 8.37%. (geometric nor arithmetic)
(Rates as a percentage accurate to one basis point and prices accurate to two decimal places)
Question 6
Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $1,500,000. The bonds were issued seven years and three months ago and still have two years and nine months to maturity. They pay a coupon rate of interest of 6.5% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.02% pa. The convention in Zanadu financial markets is that the market yield and coupon rate are quoted as annual nominal rates. What is the current market value of the bonds?
(In dollars accurate to three decimal places)
Question 7
Polycorp has a dividend of $5.00 due in a year's time and is expected to pay a dividend $5.50 at the end of the second year. Its dividend is expected to grow at 8% pa for the following year. Dividends are then expected to grow at 4% pa for another two years, after which they are expected to grow at 3.5%pa forever. Shareholders required return on equity is 10.85% pa. What is the current price (cum-dividend) of Polycorp shares? Polycorp has just paid a dividend of $4.75.
(Accurate to the nearest cent)
Question 8
Gamma Ltd is not expecting to pay dividends for three years, at the end of year four, a dividend of $2.65 is planned and dividends are expected to be constant forever after that. The required rate of return for Gamma Ltd equity is j4 = 12.5% pa. What is the expected price (cum-dividend) of Gamma Ltd's shares at the beginning of year nine? Explain your logic.
(Accurate to the nearest cent)
Question 9
Mooncorp Insurance has quoted you an annual premium to insure your car of $3100. You are offered a 15% discount if you pay the lump sum immediately. They also offer an alternative payment method. You can pay the account in full by making 11 equal end-of-the month payments of $280, rather than the lump sum. The first payment is at the end of the second month. What is the effective annual opportunity cost of paying monthly?
You must provide one complete manual calculation of the IRR to demonstrate that you understand the process. Failure to follow this instruction will attract a mark of zero.
(Accurate to one basis point)
Question 10
Calculate the return for each of these investments (capital gain/loss plus dividend).
a) My portfolio ends the year with a value of $12.72 million after paying dividends at the end of the year to the value of $255,000. The value of the fund at the beginning of the year was $12.13 million.
b) At the same time the All Ordinaries Index ended the year at 5695 after starting at 5226.
c) A share in BHP was selling for $23.45 at the beginning of the year and selling for $27.42 at the end of the year after paying a dividend of $1.13.
(Your answers should be as a percentage accurate to one basis point)