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You are required to answer the following questions:

**Question 1: **Answer the following questions as directed: [Total 7.5 marks; 2.5 marks for each part]

(a) Sam is planning to retire in 10 years, and buy a house in Byron Bay, Queensland. The house he is currently looking at is priced one million and is expected to grow in value each year at a 5% rate. Assuming that Sam can earn 10% annually on his investments, how much must he invest at the end of each of the next 10 years to be able to buy his dream home when he retires.

(b) ‘The financial director of the ABC company is emphasing the need to create and maximise wealth for the shareholders, while the financial director of the XYZ company believes that maximising profit of the company should be the priority’. Which company do you think adopts the correct strategy? Make a critical evaluation with examples.

(c) You have just borrowed $10,000. You are required to repay equal amounts at the end of each of 7 years, with the first payment starting in four years’ time. Your interest rate is 8% per annum. How much will be the amount of each payment?

**Question 2: **Answer the following questions as directed: [Total 7.5 marks; 2.5 marks for each part]

(a) Rowan has invented a new household device that would earn him $12,000 per annum for the next 10 years. Given an interest rate of 10% compounded annually, would Rowan be willing to sell his invention today for $100,000?

(b) Kate won a lottery that will make a payment $100,000 every year, starting today, for the next 10 years. If she invests the payments at a rate of 4.00% per year, what is the present value of the cash flows over the 10 year period? Interest for the 10 equal payments will be compounded at the end of each year.

(c) Property Trust Bank pays its clients 8% interest per annum,
compounded on a semi-annual basis. To remain competitive, the bank’s
major competitor, Mortgage Trust Bank is willing to match the interest
rate offered by Property Trust Bank, but interest will be compounded on a
quarterly basis. What nominal rate of interest must Mortgage Trust Bank
offer to its clients?

**Question 3: **[Total 7.5 marks; 2.5 marks for each part]

You have had your offer of $1.2 million on a house accepted and have arranged with the bank for a 30 year mortgage equal to 90% of the sale price. The agreement calls for monthly repayments and the bank will charge a nominal annual interest rate of 6%.

(a) If the first payment is due one month after the loan is received, calculate the amount for the regular instalments.

(b) After the 60th payment the interest rate decreases to 5% p.a. Assume you have decided to maintain the monthly repayment. If you choose to pay out the mortgage after the 60th payment, what is the payout figure?

(c) If you choose not to pay out the mortgage after the 60th payment, how much longer will it take you to pay out the loan?

**Question 4: ** [Total 7.5 marks; 2.5 marks for each part]

The following table provides the share return forecasts and associated probabilities for **ABC** Limited and **XYZ**
Limited. Answer parts ‘a’ to ‘c’ using the information provided.
Detailed worked solutions must be presented in your answers, including
formulae used, progressive and final answers to the questions.

**ABC Limited**

**XYZ Limited**

Return (%)

Probability (%)

Return (%)

Probability (%)

16.0

50

18.0

30

12.0

30

10.0

20

10.0

20

8.0

50

(a) Calculate the expected return on each share.

(b) Calculate the variance and standard deviation for each share.

(c) Suppose a portfolio comprised of 60% investment in ABC Limited and 40% investment in XYZ Limited can be constructed. An analyst has estimated that the correlation coefficient of the two-asset portfolio is -0.30, calculate the return and standard deviation of this portfolio. Compare your answer with those reported in parts a. and b. and draw your conclusion.