Problem $16-13($Algo$)$

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\mathrm{.}3$ million per year to beneficiaries. The yield to maturity on all bonds is $14\mathrm{.}2\%.$

Required:

a$.$ If the duration of $5-$year$-$maturity bonds with coupon rates of $11\mathrm{.}5\%($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?

Note: Do not round intermediate calculations. Enter your answers in millions rounded to $2$ decimal places.

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

Note: Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places.

$\backslash$table$[[$a$.5$ year bond,,million$],[$a$.20$ year bond,,million$],[$b$.$ Par value,,million$]]$