Two bonds, A and B, are currently trading in the market. Bond A is a 3-year coupon bond with a face value of $100, selling for $113.616; coupons are paid annually. Bond B is a perpetuity with an initial cash flow of $1 in one years time, with cash flows growing thereafter at 1% per year. Determine Bond As coupon rate and the price of Bond B. (6 marks) Calculate Bond As Modified Duration. Without recalculating the bond price, estimate the percentage change in the price of Bond A if the entire term structure were to immediately shift downwards by 100 basis points (1 basis point is one hundredth of 1 percent, i.e. 0.01%) (6 marks) Show that the Modified Duration of a growing perpetuity with initial cash flow C1 (at time 1), cash flow growth rate g, and discount rate r is given by: D_Mod=1/(r-g) Using this expression, calculate the Macaulay Duration of Bond B. (6 marks) To manage its interest rate risk exposure, LNP proposes creating a portfolio of bonds A and B such that the following two conditions are met: The current values of the bond portfolio and the companys liability are the same. The change in the value of the bond portfolio in response to a small, parallel shift in the term structure matches the change in the value of the companys liability. How many units of Bond A and B must the company purchase today? Briefly explain why this strategy is not static, i.e. why the number of units of each bond will need to change over time. (8 marks)