$3.$ The following table shows the borrowing opportunities for two firms.

Fixed rate Floating rate

Firm A $11\mathrm{.}25\%$ LIBOR $+0\mathrm{.}50\%$

Firm B $9\mathrm{.}25\%$ LIBOR $-0\mathrm{.}50\%$

Firm A can borrow at a floating rate at LIBOR$+0\mathrm{.}50\%.$ However, Firm A would prefer to raise the money by issuing $5-$year fixed$-$rate notes at $11\mathrm{.}25\%.$ On the other hand, Firm B considers issuing $5-$year fixed rate Eurodollar bonds at $9\mathrm{.}25\%,$ while it would make more sense for Firm B to borrow at a floating rate at LIBOR$-0\mathrm{.}50\%.$ Finally, the swap bank makes the following offers to both firms.

a$)$ What is the total gain for this swap? In other words, figure out QSD $($quality spread differential$).(25$points$)$

b$)$ Figure out the gain for Swap bank. $(25$points$)$

c$)$ Figure out the gains for Firm A and Firm B$,$ respectively. $(40$points$)$