Problem:
Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2.6 million per year to beneficiaries. The yield to maturity on all bonds is 20%.
Required:
Question 1: If the duration of 5-year maturity bonds with coupon rates of 16% (paid annually) is 4 years and the duration of 25-year maturity bonds with coupon rates of 9% (paid annually) is 16 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?
Question 2: What will be the par value of your holdings in the 25-year coupon bond?
Note: Provide thorough explanation of the given question.