Problem 4 (20 points, 4 points each) You are the finance manager of a pension plan which pays out $10 million a year forever. The first payment is exactly one year from now. The term structure is currently flat at 5% (i.e. spot rates 0.05 for all years t). (a) Compute the present value of your pension liabilities. (b) Suppose that interest rates decreased by 0.1%. What would be the new value of the liabilites? (c) Compute the modified duration of the pension liabilities. (a) Suppose the pension plan is fully funded (.e. the present value of the assets equals the present value of pension liabilities). As the pension manager you want to invest all the assets in bonds (i.e. you wish to onstruct a bond portfolio) to avoid any interest rate risk. What should be the duration of the bond portfolio? (e) Suppose the portfolio is to be a single 0-coupon bond. What should the maturity and face value be