- Security A: a risky stock with an expected return of 10%, a payout ratio of 60%, a constant Return on Equity (ROE) of 15%, and an expected dividend one year from now of $1 per share. - Security B: a two-year default-free bond with a face value of $1000, a coupon rate of 4% and a yield to maturity of 4%. - Security C: a risky stock whose current dividend (just paid, so the current price is ex-dividend) is $1 and whose dividend is expected to grow once by 60% this year and then remain constant at that level forever, also with an expected return of 10%. Assume any cash flows are paid annually with the first cash flow due one year from today. (a) Determine the present value and the Modified duration of Security B. [5 marks] (b) Consider the following statement: "The duration approximation will understate the fall in the Security B's price if its yield rises". Explain whether this statement is correct or incorrect. [5 marks] (c) Determine the present value of security A, stating any assumptions you need to make. [4 marks] (d) Would Security A's present value be higher/lower/the same as in part (c) if the company chose to pay out all its earnings as dividends in all years? Explain. [4 marks] (e) What is the present value of security C ? [4 marks] (f) Suppose that after one year the price of security A rises while the price of all default-free bonds is unchanged, and the price of security C rises by twice the rise in A's price. Discuss the different possible reasons why security A's price has risen, assuming that there is only one common risk factor to asset returns and that the three securities' sensitivities to this risk factor do not change. Make sure your reasons account for the observed behaviour of securities B and C. [6 marks] (g) Consider another security, Security D, with an expected return of 15%, which pays $1 in one year, with subsequent annual payments growing by $0.30 per year, forever. Determine the present value of security D. [6 marks]