Question

1. 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.Confirm 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.

2. 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 payments to mortgage brokers. Returning to the details of question 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 commission 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 payments are only of an amount calculated by you in parts b and d of question 1 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?

Answer 1

sloution for c :

On 19 March 2049, 29 installments of $ 32,622.80 will be paid, the principle will be 31519.56 and interest will be 1103.18.

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