Now that they have accumulated a deposit of 65,000 Jack and his partner Jill wish to take out a housing loan to purchase a home. The house costs $555,000. The loan is to be repaid in equal monthly instalments over a term of 25 years. The interest rate quoted by the bank is an effective annual rate of 6.42%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 interest will be paid in the second year?
iii. How much do Jack and Jill owe the bank immediately before making the 180th repayment?
iv. Produce a repayment schedule in Excel for the loan. Use it to confirm the answers in parts i to iii.
(Answers should be accurate to the nearest dollar)
Today is Stanley’s 54th 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 $29000 every birthday (starting with his 65th) up to and including his 85th birthday. He believes that an interest rate of 6.5% 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)
Stanley has received a bequest of a lump sum of 110,000 from his Aunt’s will, but it is not due to be available for him for seventeen years (t = 17). Stanley wants to receive the cash earlier than this. He is investigating a deferred annuity with the first annual cash flow of the annuity is to be paid at the beginning of year 3 (fifteen cash flows). Assume that the annuity and the lump sum are of equivalent risk and that j12 = 7.20% pa is the appropriate interest rate (opportunity cost of funds for Stanley).
How much is the annual cash flow associated with the annuity?
(Accurate to the nearest dollar)
In exchange for a lump sum payment now, Polysuper offers an annual pension over twenty five years beginning with a payment of $55,000 at the end of the first year. There are twenty five 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 the lump sum needed today to purchase the pension?
(Accurate to the nearest dollar)
a) A ninety day bank bill with 90 days to maturity has a price of $98078. 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 70 days left to maturity and the appropriate interest rate is 7.22%pa effective?
c) Calculate the geometric average rate of return over four years given the following annual rates, year 1 = 5.24%, year 2 = 6.79%, year 3 = 8.57%, year 4 = 9.23%. (geometric nor arithmetic)
(Rates as a percentage accurate to one basis point and prices accurate to two decimal places)
Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $3,000,000. The bonds were issued six years and nine months ago and still have three years and three 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 5.52% 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)
Polycorp has a dividend of $5.00 due in a year’s time and is expected to pay a dividend $5.60 at the end of the second year. Its dividend is expected to grow at 7% pa for the following year. Dividends are then expected to grow at 3% pa for another three years, after which they are expected to grow at 2%pa forever. Shareholders required return on equity is 10.15% pa. What is the current price (cum-dividend) of Polycorp shares? D0 is $4.55.
The required rate of return on the shares in the companies identified below is 16% pa. Calculate the current share price in each case.
(a) The current earnings per share of Alpha Ltd are $2.60. The company does not reinvest any of its earnings. Earnings are expected to remain constant.
(b) Beta Ltd’s current dividend is $1.75 and dividends are expected to grow at 4% pa indefinitely.
(c) Gamma Ltd is not expecting to pay dividends for three years, at the end of year four a dividend or $2.30 is planned and dividends are expected to grow at 4% pa forever after that.
(d) Delta limited plans to pay dividends of 1.50, 2.00, and 3.00 at the end of years 4, 5, 6 respectively followed by a dividend of 4.00 in perpetuity after that
Mooncorp Insurance has quoted you an annual premium to insure your car of $2640. You are offered a 20% 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 $240, rather than the lump sum, with no payment in the first month (ie the first payment is at the end of the second month). What is the effective annual opportunity cost of paying monthly?