2. Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%. Note: duration of perpetuity is (1+i)/i.

a (0.25). What is the present value and duration of the pension obligations?

b (0.25). To fund the liabilities, you decide to choose two types of bonds to invest: the 5-year maturity bonds with coupon rates of 12% (paid annually) and the 20-year maturity bonds with coupon rates of 6% (paid annually). What is the duration of the 5-year coupon bond and 20-year coupon bond?

c (0.25). To immunize your obligation, what is the asset weight (w) of the 5-year coupon bond and what is the asset weight of the 20-year coupon bond?

d (0.25). To fully fund and immunize your obligation, how much of each of these coupon bonds you want to hold?

e (0.25). What will be the par value of your holdings in the 20-year coupon bond? Assume the par value for each bond contract is $1000. Hint: first use financial calculator to calculate the PV of individual 20-year coupon bond. Then calculate # of bond contracts to hold.