(a) (b) Prove that for an annual coupon bond that if the coupon rate equals the yield to maturity then the bond trades at par. [6 marks] A bond's duration can be used to infer how the bond's price will react to a change in yield to maturity. Give a brief overview of how the duration measure is derived and thus why it is informative about the relationship between prices and yields. What are its shortcomings as a measure of the sensitivity of prices to yields? [8 marks] (d) You are going to enter into a contract to receive cash flows of 10 every year forever with the first cash flow starting at t=2. What is the present value of these cash flows now i.e. t=0 if the relevant semi annual APR is 12%? [6 marks] Company A currently plows back 30% of its earnings and eams a return of 25% on this investment. The forward looking dividend yield on the stock is 5%. Company A continues to plow back 30% of earnings and earns a return of 25% on the investment, at what rate will earnings and dividends grow and what is the expected return on Company A's stock? (5 marks] Suppose that management suddenly announces that there are no future investment opportunities. Company A now intends to pay out all its earings. Calculate the percentage change in the stock price. [8 marks]