Question

2.7 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 $2.7 million per year to beneficiaries. The yield to maturity on all bonds is 12.5%.

a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4.0 years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 7.9 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?

Answer 1

Answer: indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $1.4 million per year to beneficiaries. The yield to maturity on all bonds is 13.0%. a. If the duration of 5-year maturity bonds with coupon rates of 9.0% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 decimal place. Omit the "$" sign in your response.) b. What will be the par value of your holdings in the 20-year coupon bond? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places. Omit the "$" sign in your response.)

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