Questions -

Question 1 - Now that they have accumulated a deposit of 55,000 Jack and Jill take out a housing loan to purchase a home. The house costs $755,000. It is to be repaid in equal monthly instalments over a term of 30 years. The interest rate quoted by the bank is an effective annual rate is 7.5%pa. Jack has lost 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 130th repayment?

iii. After making the 150th repayment Jack and Jill receive an amount of $50,000, which they use to reduce their loan. The bank allows them to make the same monthly payment. How much will the term of the loan be reduced by if the interest rate remains the same?

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 today) up to and including his 65th. He then wants to be able to withdraw $9000 every birthday (starting with his 66th) 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?

Question 3 - A perpetuity with the first annual cash flow paid at the beginning of year 4 is equivalent to receiving $103,000 in 15 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?

Question 4 - Many creditors of your firm offer early payment discounts. The accounts payable supervisor does not believe in paying early "as the bank overdraft rate of j12 = 8% pa is more than the average 2% offered for payment within 10 days from date of invoice". The supervisor stretches the accounts to 40 days from the last date of early payment discount. If average creditors terms are 2%, 10: net 30, what is the minimum number of days beyond the net date that accounts must be stretched to make stretching a viable alternative? Use the effective annual rate approach as described on pages 773-774 of your textbook (11th edition).

Question 5 - A ninety day bank bill with 90 days to maturity has a price of $99427.95. 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.

Question 6 - Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $2,000,000. The bonds were issued seven years and nine months ago and still have two years and three months to maturity. They pay a coupon rate of interest of 6.25% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.62% 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?

Question 7 - Polycorp has a current dividend of $5.00 due tomorrow and is expected to pay a dividend $5.50 at the end of the first 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. Then they are expected to grow at 3.5%pa forever after that. Shareholders required return on equity is 11.85% pa. What is the current price (cum-dividend) of Polycorp shares?

Question 8 - Gamma Ltd is not expecting to pay dividends for three years, at the end of year four, a dividend of $2.45 is planned and dividends are expected to be constant forever after that. The required rate of return for Gamma Ltd equity is j4 = 12.25% pa. What is the expected price (cum-dividend) of Gamma Ltd's shares at the beginning of year eight? Explain your logic.

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 12 equal beginning of the month payments of $270, rather than the lump sum. What is the effective annual opportunity cost of paying monthly?

Question 10 - One of your customers is having trouble paying her account. You agree to a repayment schedule of $300 per month. You charge 1% per month interest on late accounts. If the current balance is $2000, how long will it take to pay off the debt?