General Information:
a) You must have the correct answer and a correct explanation plus working to gain the marks allocated to each part. Include cash flow maps or tables wherever possible. Avoid rounding error. Providing a formula and the answer is not enough. Some questions have more than one part, where this is the case you must get all parts correct to gain your one mark.
b) Format: Calculation and brief working or short answer with explanation as well as the calculation solved in an Excel spread sheet. For each calculation you must provide a manual solution and a solution using excel. If you have two files you should embed your excel file into your word document and submit only one file. Typing straight into excel without doing the calculations in excel does not qualify as using excel.
c) Word Limit: 300 words as a very rough guide; mostly calculations.
d) It must be done in excel. You can type your explanations in Word if you wish but with an embedded excel file or done all in excel.
e) Make sure to highlight or underline your final answer.
f) Try to be as accurate as possible. Cross-check your answers using excel. Unless otherwise told you should use the following approach:
a. PV and FV accurate to the nearest dollar
b. Prices accurate to two decimal places
c. Rates accurate to one basis point
Outline
You should solve the following ten questions showing your full workings and explanations in brief form. Each question is worth one mark. You must have the correct answer and show your working and correct explanation to get one mark (very brief or one to two line of answers are not acceptable). As well as solving the problems manually using the appropriate formulas you must also solve the problems using Excel functions/calculations. An incorrect answer or an answer without the working will be given zero. Normally no part marks are awarded. For questions where two or more answers are requested you must get all parts correct to guarantee 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 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.
Question 2:
Today is Peter'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?
Question 3:
Peter 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). Peter 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 Peter).
How much is the annual cash flow associated with the annuity?
Question 4:
In exchange for a lump sum payment now, DABsuper 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?
Question 5:
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)