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Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely,...

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Finance

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 million per year to beneficiaries. The yield to maturity on all bonds is 16%. Note: duration of perpetuity is (1+i)/i.

a What is the present value and duration of the pension obligations?

b To fund the liabilities, you decide to choose two types of bonds to invest: the 5-year maturity bonds with coupon rates of 12% (paid annually) and the 20-year maturity bonds with coupon rates of 6% (paid annually). What is the duration of the 5-year coupon bond and 20-year coupon bond?

c To immunize your obligation, what is the asset weight (w) of the 5-year coupon bond and what is the asset weight of the 20-year coupon bond?

d To fully fund and immunize your obligation, how much of each of these coupon bonds you want to hold?

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