Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension...

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Pension funds pay lifetime annuities to recipients. If a firmremains in business indefinitely, the pension obligation willresemble a perpetuity. Suppose, therefore, that you are managing apension fund with obligations to make perpetual payments of $2.0million per year to beneficiaries. The yield to maturity on allbonds is 16%.
a. If the duration of 5-year maturity bonds with coupon rates of12% (paid annually) is 4.0 years and the duration of 20-yearmaturity bonds with coupon rates of 4% (paid annually) is 8.6years, how much of each of these coupon bonds (in market value)will you want to hold to both fully fund and immunize yourobligation? (Do not round intermediate calculations. Enter youranswers in millions rounded to 1 decimal place.)
b. What will be the par value of your holdings in the 20-yearcoupon bond? (Enter your answer in dollars not in millions. Do notround intermediate calculations. Round your answer to the nearestdollar amount.)

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4.3 Ratings (884 Votes)

a PV of the firms perpetual obligation 20 million016 125 million Based on the duration of a perpetuity the duration of this obligation 116016 725 years Denote See Answer

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Pension funds pay lifetime annuities to recipients. If a firmremains in business indefinitely, the pension obligation willresemble a perpetuity. Suppose, therefore, that you are managing apension fund with obligations to make perpetual payments of $2.0million per year to beneficiaries. The yield to maturity on allbonds is 16%.a. If the duration of 5-year maturity bonds with coupon rates of12% (paid annually) is 4.0 years and the duration of 20-yearmaturity bonds with coupon rates of 4% (paid annually) is 8.6years, how much of each of these coupon bonds (in market value)will you want to hold to both fully fund and immunize yourobligation? (Do not round intermediate calculations. Enter youranswers in millions rounded to 1 decimal place.)b. What will be the par value of your holdings in the 20-yearcoupon bond? (Enter your answer in dollars not in millions. Do notround intermediate calculations. Round your answer to the nearestdollar amount.)