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 $2.3 million per year to beneficiaries. The yield to maturity on all bonds is 14.2%. a. If the duration of 5-year maturity bonds with coupon rates of 11.5% (paid annually) is four 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?

Question

Alissa Grant

Business

16 August, 18:13

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 $2.3 million per year to beneficiaries. The yield to maturity on all bonds is 14.2%. a. If the duration of 5-year maturity bonds with coupon rates of 11.5% (paid annually) is four 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?

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Lizeth Carpenter · Answer 1

Solution:

PV of the firm's "perpetual" obligation = ($2.3 million/0.14) = $16.4 million.

Based on the duration of a perpetuity, the duration of this obligation = (1.14/0.14) = 8.14 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 = 8.14, which implies that w = 0.4085.

w x 4 + (11-11w) = 8.14

- 7W + 11 = 8.14

7W = 2.86

w = 0.4085

Therefore, 0.4085 x $16.4 = $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.