Explain the relationship between the yield to maturity of a par bond and its coupon rate. (1 mark)

Duncan recently completed ACST1001 and is hoping to apply what he has learned to start investing.

Duncan is interested in a $1,000 18-year bond paying half-yearly coupons with a coupon rate of 7.5%. The yield to maturity for such bonds is 8% p.a. compounding half-yearly.

b) Calculate the fair price Duncan should pay for one such bond, given the market conditions described above. (2 marks)

c) Suppose that 6 months after he initially purchases this bond, immediately after receiving the coupon on that date, Duncan decides to sell his bond to his friend Ian. Ian pays a price that yields 7% p.a. effective. Calculate the price Ian paid, ignoring any other costs (such as brokerage). (2 marks)

d) Calculate the return on Duncan's 6 month investment, expressed as a percentage. (1 mark)

Duncan is also considering investing in shares in a new company, Greene Daeye Ltd.

e) Duncan has predicted that the first dividend will be paid will be exactly two years from today, and amount to $4.5. From there, Duncan believes the dividend will grow at 25% p.a. for 4 years. After that, the dividend will grow at 3% p.a. indefinitely.

Based on the riskiness of this share, Duncan requires a return of 12% on his investment. Calculate the maximum price he is willing to pay for this share. (3 marks)

f) State, and then explain the key difference between bonds and shares.