QuestionQuestion

Question 1
Gladys buys a 270-day bank bill with a face value of $100 000 at a yield of 6.1% p.a. (simple interest). After 66 days she sells it at a yield of 5.9% p.a. (simple interest)
a. Draw a fully labelled cash flow diagram (from Gladys’ perspective) that describes Gladys’ purchase and sale of the bank bill.
b. What is the value of yield (simple interest) that Gladys earned on this transaction? Support your answer with
• your chosen valuation date and
• your equation of value.
c. Explain what would happen to the value of the yield you calculated above if Gladys was able to sell her bill at a yield of 6.4% p.a. (simple interest) rather than the 5.9% p.a. given above. (Do not do any further calculations, just explain in words.)

Question 2
An 11-year 7% p.a. Treasury bond (coupon payable half-yearly) is available for purchase at a market yield to maturity of j2 = 6% p.a.
a. Find the bond’s price (per $100 face value, rounded to three decimal places) at this yield. Include in your answer
• a fully labelled cash flow diagram (drawn from the perspective of the bond issuer),
• your chosen valuation date and
• an equation of value.
b. Find the bond’s price (to three decimal places) at a nominal annual yield two hundred basis points higher.
c. Using the phrase ‘par bond’ answer the following: how do you know your answers in parts a and b are reasonable?

Question 3
Bill has bought a new home in Canberra. He borrowed $600 000 at a rate of 3.5% p.a., which is to be repaid in annual instalments over a thirty year period. The first instalment is due on 19 March 2020.
a. Choosing a valuation date of 19 March 2019, write down the equation of value that will give Bill’s annual repayments.
Support your answer with a fully labelled cash flow diagram, drawn from Bill’s perspective.
b. What are Bill’s annual repayments?
c. Choosing a valuation date of 19 March 2049, write down the equation of value that will give Bill’s annual repayments. Your equation of value should include the sn function.
d. that solving part c gives the same answer as your response to part b. To earn full marks for this question, you must give all the values of the functions that appear in part c above.

Question 4
Like Bill, in question 3 above, Scott has bought a house in Canberra, bor- rowing the same amount, and on the the same terms. Scott’s bank, however, offers an ‘interest offset’ account facility with the loan. Like Bill, Scott’s first payment is on 19 March 2020. On the day Scott takes the loan of $600 000 out (19 March 2019), Mal- colm gives Scott $100 000. Scott immediately puts the money into his inter- est offset account. This account also earns 3.5% p.a. (compound interest). Over the term of the loan Scott does not put any more money into the in- terest offset account. The interest offset account pays interest annually, and its first payment will be on 19 March 2020.
a. Draw a cash flow diagram, from Scott’s perspective, that describes the actions of his interest offset account. Scott’s interest offset account pays its interest payments to Scott’s loan.
b. What is the amount of Scott’s total loan repayment on 19 March 2020?
c. Show that Scott can make the total repayments calculated in part b for only 25 years, and that in the 26th year Scott will only pay $2 047.95 (plus the interest payment from his interest offset account) to extinguish his loan.

Question 5
The recently released recommendations of the Banking Royal Commission (the Royal Commission into Misconduct in the Banking, Superannuation and Financial Services Industry) include the elimination of commission pay- ments to mortgage brokers.
Returning to the details of question 3 above: Theresa was Bill’s mortgage broker. Bill’s bank will pay her commission amounts of $1 000 annually from 19 March 2020 through to 19 March 2049 (inclusive).
If we view the bank’s mortgage business as making neither a profit nor a loss, then (in the absence of any internal capital transfers) Theresa’s com- mission payments have to effectively come from Bill.
a. As at 19 March 2019, what is the total value of Theresa’s commission (use a valuation interest rate of 3.5% p.a.)?
Your answer needs to be supported by
• a cash flow diagram (from Theresa’s perspective),
• a valuation date and
• an equation of value.
If the value of Theresa’s commission comes from Bill, then the total amount of Bill’s loan is $600 000 plus your answer to part a above. But Bill’s pay- ments are only of an amount calculated by you in parts b and d of question 3 above. This suggests that the effective interest rate the bank requires on its funds is not the 3.5% p.a. that it communicates publicly.
b. Is the effective interest rate that bank requires on its funds higher or lower than the 3.5% p.a. that it communicates publicly? Why? (Answer this last part by reference to an appropriate equation of value and cash flow diagram. No numerical calculations are required.)
c. Calculate the effective interest rate discussed in part b above. Carefully explain how you reached your answer.
d. If Bill had been offered the effective rate discussed in part b above, by how much would his annual payments increase or decrease?

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