Please show all workings including any formula used.

Question 1 - This question relates to material covered in the Topic 3 on Financial Mathematics. This question addresses the 6th subject learning outcome.

a. A couple wants to accumulate $10,000 by making payments of $800 at the end of each half year into a savings account that earns interest of 10% per annum. Find the number of full payments required and the size of the concluding payment.

b. A woman wins $200,000 in a lottery. She takes only $20,000 in cash and invests the balance at a rate of interest of 10% with the understanding that she will receive 180 equal monthly payments, with the first one to be made in 4 years. Find the size of the payments.

c. Dr.Ritz has been depositing $4,000 in her savings account every December since 2007. Her account earns 5% compounded annually. How much will she have in December 2017? (Assume a deposit will be made in the year 2017).

d. Mary Tune will receive $20,000 every year for the next 10 years as a payment for a new song she has written. If a 6.0% rate is applicable, should she be willing to sell out her future rights now for $150,000?

e. Mr. Tomas wants to buy an annuity of $1,000 a year for 10 years that is protected against inflation. The ABC Trust Company offers to sell him an annuity where payments increase each year by exactly 10%. Find the cost of this annuity if the rate of interest is 12% per annum.

Question 2 - This question relates to material covered in the Topic 1. This question addresses the 1st, 2nd and 3rd subject learning outcomes.

Write a short essay of 300 words for each of the following questions. For each question, illustrate your answer with an appropriate example.

a. Describe the 'maximisation of shareholder wealth' concept and contrast it with the notion of 'maximisation of profit'.

b. 'Risk aversion implies that only risk-free investments will be undertaken by corporate managers'. Critically evaluate this statement (indicate whether you agree or disagree in your answer).

Question 3 - This question relates to material covered in the Topics 3-5. This question addresses the 1st, 2nd and 3rd subject learning outcomes.

i. Find the monthly holding period returns for 2016 for Commonwealth Bank (CBA), Rio Tinto (RIO) and the market (MKT) as proxied by the All Ordinaries index. The monthly holding period return is the return you would receive if you bought an asset on the first day of the month (opening price) and sold it on the last day of the month (closing price). Using Excel, graph your % return results on one graph with returns on the y axis and time on the xaxis to enable comparison between options. (Use 'Close' rather than 'Adjusted Close' for the selling price) Note: Monthly opening price MUST equal previous month closing price. When calculating return students should use the previous period closing value as the opening value for their next calculation. It is recommended that students use a line graph within the Excel chart options to allow effective comparison of performance between the different securities.

ii. For each investment, what is the average monthly holding period return?

iii. For each investment, what is the annual holding period return?

iv. Calculate the standard deviation of the monthly rates of return for each share and the market.

v. Using Excel plot your results from (iii) and (iv) above with risk on the x axis and return on the y axis.

v. If the 10 year government bond rate is 3.25% and the long term return on the market is 7%, assuming the beta (β) for CBA is 1.11 and for RIO is 0.95, use the Capital Asset Pricing Model (CAPM) to find the expected returns for CBA and RIO.

vi. Construct the Security Market Line (SML) showing where CBA and RIO lie.

vii. Based on your findings construct a portfolio made up of 60% CBA and 40% RIO. Calculate the estimated return and β for this portfolio.

viii. Based on your understanding of the CAPM and the SML, which of these asset(s) or portfolio(s) would you invest in and which would you not invest in. Explain your choice.