uestion 1 (show all workings20 marks)

This question relates to material covered in the Topics 1 to 3. This question addresses the 5th and 6th subject learning outcomes. A thorough understanding of financial mathematics forms the basis of all learning in this subject.

For the following numerical problems, detailed worked answersmustbe shown. This involves providing a brief description of the problem, formulae used, progressive and final answers. For assignments you are expected to show your workings using the appropriate formula entered using the MS Word formula function.

(a)Your daughter has expressed a wish to attend university when she finishes school in five (5) years.You anticipate the cost will be $60,000 at the time she commences university.If your financial institution is offering you 4% pa (compounded monthly), how much do you need to deposit in your account each month in order to save the required amount before your daughter commences university?(5 marks)

(b)You have been offered the opportunity to purchase a start up company building electric cars for the Australian market called Green Motors P/L.Your initial investment is $22,000,000. The term of the project is 5 years. The project has an expected rate of return of 10% pa.All expected cash flows for the project are below and you have an expected rate of return of 10% pa.

End of year

Cash flow ($mil)

1

1.82

3.03

6.54

8.45

12.3

(i)Based on your required rate of return would you purchase this investment? Present all calculations to support your answer.(2.5 marks)

(ii)Would you change your opinion from (i) if the expected rate of return rose to 15%?Present all calculations to support your answer.(2.5 marks)

(c)You have commenced work as a certified Financial Planner. Your supervisor has provided the following financial data for a new client Brant Jerome. The client turned 34 years old today and plans to retire when she turns 67. The client owns a diversified share portfolio which is valued today at $47,000. It is expected that this portfolio will earn (on average) 7% per annum indefinitely. Brant also has a superannuation account with a balance of $78,000 to which he currently contributes $1,000 per month. The superannuation account is expected to continue to earn 8% per annum. At his retirement your client plans to consolidate his financial holdings and purchase a monthly annuity as a pension to fund his planned lifestyle. Brant believes he will need to self-fund his retirement until he reaches the age of 85 at which time he would like to have $120,000 remaining to fund any costs not covered by the age pension. During the pension phase of his retirement Brant will adopt a Balanced investment strategy which will return 5% pa (compounded monthly) on his annuity investment.

(i)What will be the value of Brant's financial assets when he retires at age 67? Present all calculations to support your answer.(5 marks)

(ii)What will be the monthly pension amount that Brant will receive on his retirement?Present all calculations to support your answer.(5 marks)