QUESTION 1 TIME VALUE OF MONEY

Following a weekend drive to Noosa on the Sunshine Coast to test out his new BMW X6 car, Mr Jack Bourne identified his 'dream' retirement home at the end of 2010. The property is currently (end 2010) valued at $850,000 and is likely to appreciate in value over the next 15 years (his anticipated retirement date from now) as follows:

-Years 1 to 5 by 8% p.a., -Years 6 to 10 by 10% p.a., and -Years 11 to 15 by 15% p.a.

Jack is told by his financial advisor that he can earn a net 14% p.a. rate of return on any investment funds he puts aside to pay for his 'dream' retirement home over the 15 year term. Moreover, as a result of an inheritance from his grandfather, Jack also anticipates that he will be able to add a lump sum of $300,000 to these investment funds (used to pay for his retirement home) in 3 years from now.

a)Given the information provided above, approximately what amount must Jack invest on an annual basis in order to be able to buy his dream home at retirement?

1. i)At the end of each of the next 15 years?
2. ii)At the beginning of each of the next 15 years?
3. iii)Utilizing your time value of money skills, briefly explain why the amounts calculated in i) and ii) are the same or different. (maximum 100 words)

b)Assuming that the actual amount paid by Jack at the end of 15 years to acquire his dream retirement home was $1.5m, calculate the annual rate of increase in the value of the property expressed as:

i)a nominal interest rate.

ii)an effective interest rate.

iii)Utilizing your time value of money skills, briefly explain why the amounts calculated in i) and ii) are the same or different. (maximum 100 words)

c)Jack unfortunately died exactly 8 years after moving into his dream retirement home and, in his Will, specified that upon his death the house was to be immediately sold and the net proceeds made available to his second son, James Bourne. Calculate the amount that James will receive from the property sale based on the following information collected in relation to the property over the period of ownership by Jack:

• -Property prices in the area where the property was located increased by a nominal 5% p.a. compounded quarterly for the first 3 years after purchase by Jack.
• -Property prices in the area where the property was located increased by a nominal 8% p.a. compounded half-yearly for years 4 to 7 after purchase by Jack.
• -Property prices in the area where the property was located increased by a nominal 18% p.a. compounded monthly in the final year prior to Jack's death.
• -Agent fees on the sale of the property amounted to 1.2% of the gross sales price.
• -Assume that the retirement home was purchased at the price of $1.5m as in Part (b).

d)Assume that James was a graduate from UQ Business School and he learnt that hedge fund managers always outperform the market. Therefore, he decides to use the amount of the net sale proceeds following his father's death to purchase an annuity from the Queensland Investment Fund after paying the fund a fee of $10,000 for their professional services. Calculate the amount that James will receive from the annuity given that the annuity from the Queensland Investment Fund had the following features:

1. - Monthly payments at the end of each month.
2. - Total term of 8 years
3. - Residual value of annuity (at end of the total term) equal to 50% of the purchase price - Nominal rate of return provided by annuity of 8% p.a. compounded monthly.

e)As a business school graduate, James also understands that the net present value is the most important measure for investment appraisal. Using all the information provided above, if James wanted to know what the amount of the residual value of the annuity would have been worth as a present value at the end of 2010 assuming a nominal discount rate of 8% p.a., what would this amount have been?