BOND

9. 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 percent.

a. If the duration of 5-year-maturity bonds with coupon rates of 12 percent (paid annually) is

4 years and the duration of 20-year-maturity bonds with coupon rates of 6 percent (paid

annually) is 11 years, how much of each of these coupon bonds (in market value) will you

want to hold to both fully fund and immunize your obligation?

b. What will be the par value of your holdings in the 20-year coupon bond?