Problem $4(10$ points$)$

Companies $x$ and $Y$ have been offered the following rates per annum on a $$5$ million $10-$year investment:

$\backslash$table$[[,$Fixed Rate,Floating Rate$],[$Company $x,8\mathrm{.}0\%,$LIBOR$],[$Company $Y,8\mathrm{.}8\%,$LIBOR$]]$

Company $x$ requires a fixed$-$rate investment; company $Y$ requires a floating$-$rate investment.

A$.$ Assuming $x$ and $Y$ split the gains from the swap in such a way that $x$ gets $60\%$ of the gains and $Y$ gets $40\%$ of the gains, what are the net investment rates that $x$ and $Y$ can get?

B$.$ If a Financial Intermediary $($FI$)$ charges $0\mathrm{.}2\%$ a year $($split equally between $x$ and $Y),$ how would this affect the final rates that the two parties are receiving?

C$.$ Illustrate the swap between $x$ and $Y$ in the presence of a financial intermediary with the help of a diagram. Please make sure that all rates are properly labeled.