$($Immunization of FI$)$ Consider a financial institution whose asset and liability

both consist of coupon bonds only. The asset is a $10-$year bond with face value

$$100$ million, coupon rate $9\%$ and yield $8\mathrm{.}1\%,$ while the liability is a $15-$year

bond with face value $$100$ million, coupon rate $8\mathrm{.}8\%$ and yield $8\mathrm{.}1\%.$ Both

bonds pay coupon semiannually. Assume parallel yield shift.

Required precision: $4$ digits after decimal point for duration calculation; $2$ digits

after decimal point for dollar amount in million, e$.$g$.$ $$12\mathrm{.}34$ million; $4$ digits

after decimal point for percentage $($coupon$)$ rates, e$.$g$.1\mathrm{.}2345\%.$

$($a$)$ What are the market values of asset, liability and equity of this FI$?$ What

is its leverage$-$adjusted modified duration gap?

$($b$)$ According to the duration model, what would the market value of equity

be for a $10$ basis points decrease in the yield?

$($c$)$ To immunize itself from interest rate risk, the FI plans to restructure its

asset bond by adjusting its face value and coupon rate, while keeping the

bond's value $($and hence the market value of asset$),$ maturity and yield

unchanged. What should be the new face value and coupon rate? $($Hint:

Write out and solve two equations, one for matching the market value of

assets before and after the restructuring, and the other for eliminating the

leverage$-$adjusted modified duration gap after the restructuring.$)$

$($d$)$ Assume the immunization in $($c$)$ is successfully implemented. Immediately

after the implementation, the yields of both bonds decrease from $8\mathrm{.}1\%$ to

$8\%.$ What are the market values of asset, liability and equity now?