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 $$4\mathrm{.}2$ million per year to beneficiaries. The yield to

maturity on all bonds is $20\%.$

Required:

a$.$ If the duration of $5-$year maturity bonds with coupon rates of $16\%($paid

annually$)$ is $3\mathrm{.}7$ years and the duration of $20-$year maturity bonds with coupon

rates of $10\%($paid annually$)$ is $6\mathrm{.}2$ 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? $($Do not round intermediate calculations. Enter your answers

in millions rounded to $5$ decimal places.$)$

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

$($Enter your answer in dollars not in millions. Do not round intermediate

calculations. Round your answer to the nearest dollar amount.$)$