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 $3.6million per year to beneficiaries. The yield to maturity on allbonds is 20%.

a. If the duration of 5-year maturity bonds withcoupon rates of 16% (paid annually) is 3.7 years and the durationof 20-year maturity bonds with coupon rates of 10% (paid annually)is 6.2 years, how much of each of these coupon bonds (in marketvalue) will you want to hold to both fully fund and immunize yourobligation? (Do not round intermediate calculations. Enteryour answers in millions rounded to 1 decimalplace.)

b. What will be the par value of yourholdings in the 20-year coupon bond? (Enter your answer indollars not in millions. Do not round intermediate calculations.Round your answer to the nearest dollar amount.)

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4.0 Ratings (501 Votes)

Duration of the perpetuity 1rr where r YTM on all bonds 12020 6 years a For immunization duration of the liability has to match the sum of the weighted durations of the bonds Let the weight of the 5year 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 $3.6million per year to beneficiaries. The yield to maturity on allbonds is 20%.a. If the duration of 5-year maturity bonds withcoupon rates of 16% (paid annually) is 3.7 years and the durationof 20-year maturity bonds with coupon rates of 10% (paid annually)is 6.2 years, how much of each of these coupon bonds (in marketvalue) will you want to hold to both fully fund and immunize yourobligation? (Do not round intermediate calculations. Enteryour answers in millions rounded to 1 decimalplace.)b. What will be the par value of yourholdings in the 20-year coupon bond? (Enter your answer indollars not in millions. Do not round intermediate calculations.Round your answer to the nearest dollar amount.)