• You have $5,000 in a term deposit account that provides 2.8% p.a. interest compounded semi-annually. To what amount will your investment grow after 4 years? [2 marks]
• How many years will it take an investment of $10,000 to grow to $30,500 if the investment pays 2.8% p.a. compounded every two months? [2 marks]
• A zero-coupon bond matures in 30 years. The interest is compounded semi-annually and the face value of the bond is $1,000. The market interest rate for similar bonds is 3.99%. What is the value of this bond? How many of these bonds sold will raise $1m?  [2.5 marks]
• For a rapidly growing British company, the growth rate forecast suggests an expected 27% per annum for the next two years and 15% for the subsequent year (i.e. 3 years from now). At the end of 3 years, the growth rate settles to an expected 8% per annum and remain so for the near future. The company expects to pay a dividend of £220 per share next year. Assume that the investors’ required rate of return for the company’s shares is 17%. Determine the value of this company’s share. Is the share a desirable purchase if its market price is £3,500 per share? [£ = Pound Sterling] [3.5 marks]

 

Hints:

All these math problems involve very few steps and can be solved quite quickly.

For (a), please note week 1 resources. Please also note what information (i.e., PV, FV, i, m, & n) are given and which information the question asks to determine. Please then use the relevant formula – a straightforward and quick calculation.

For (b), please note week 2 resources – a straightforward calculation.

For (c), please determine the price of the bond using the formula – this is what is referred to as the value of the bond. Then determine the number of bonds. Please note the week 4 slides.

For (d), please note the concepts introduced in week 5 slides and the relevant section of the book. Notably, although we are using Deutsche mark (DM) as the currency, the approach introduced for similar math in lecture slides and tutorials and entailing Dollar ($) applies here also. The answer should be indicated in the currency the question refers to. By the way, please also note the dividend information to understand whether D₀ is given or D₁ is given. Please also note when the constant growth starts and proceed with the calculation accordingly. Once the value has been determined, compare it with the market price to decide whether it is a desirable purchase.