Pension fund pay lifetime annuities. If a firm expects to remain in business ind

Question

Pension fund pay lifetime annuities. If a firm expects to remain in business indefinitely, then its pension obligation will resemble a perpetuity Suppose, therefore, that you are managing a person fund with obligation to make perpetual payments of $2million per year to beneficiaries. They yield to maturity on all bonds is 16%, If the duration of 5 years maturity bond with coupon rates of 12% (paid annually)is 4 years and the duration of 20-year maturity with compose 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?

Explanation / Answer

PV of the firm’s “perpetual” obligation = ($2 million/0.16) = $12.5 million. · Based on the duration of a perpetuity, the duration of this obligation = (1.16/0.16) = 7.25 years. Denote by w the weight on the 5-year maturity bond, which has duration of 4 years. Then, w x 4 + (1 – w) x 11 = 7.25, which implies that w = 0.5357. Therefore, 0.5357 x $12.5 = $6.7 million in the 5-year bond and 0.4643 x $12.5 = $5.8 million in the 20-year bond. The total invested amounts to $(6.7+5.8) million = $12.5 million, fully matching the funding needs.

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