Question

Please answer all the questions below.

Questions: (a) How many years will it take an investment of $1,000 to grow to $2,500 if the investment pays 5% p.a. compounded monthly? [2 marks] (b) A zero-coupon bond matures in 10 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 3.25%. What is the value of this bond? [3 marks] II. How many of these bonds need to be sold to raise $1.4m? mark] iii. Does the bond sell at par, premium or discount? Explain. [1 mark] iv. If an investor purchases the bond now for $850 and holds it until maturity, what will be the investor's yield to maturity? [2 marks] V. If an investor purchases the bond now for $850 and then sells the bond after 5 years for $950, what will be the investor's realised yield? [2 marks] (c) For a rapidly growing Japanese company, the growth rate is projected to be 20% for the next two years and 10% for the following year. At the end of 3 years, the growth rate is expected to settle to 5% and remain so for the foreseeable future. The company has recently paid a dividend of X220 per share. Assume that the investors' required rate of return for the company's shares is 17%. i. Determine the value of this company's share. [3 marks] ii. If the market price of the share is 42,500 per share, is the share a desirable purchase? Explain. [1 mark]

Answer 1

Answer a

Future value = Present value * (1+ (rate per period/compounding per year))^ (no. of periods*compounding per year)

2500 = 1000*(1+(.05/12))^12n

1.00416666667^12n = 2500/1000

= 2.5

12n = log 2.5 / log 1.00416666667

= 0.39794000867/0.00180580086

= 220.367603917 months

= 220.367603917/12 years

= 18.36 years

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