Pension funds pay lifetime annuities to recipients. If a firm remains 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 $16\%.$

$($C$)$ LCO$11-4$

a$.$ If the duration of $5-$year$-$maturity bonds with coupon rates of $12\%($paid annually$)$ is four years and the duration of $20-$year$-$maturity bonds with coupon rates of $6\%($paid annually$)$ is eight 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?

b$.$ What will be the par value of your holdings in the $20-$year coupon bond?