$2)$ Alpha and Beta Companies can borrow for a five$-$year term at the following rates:

$\backslash$begin$\{$tabular$\}\{$l$|$ll$\}$

& $\backslash$multicolumn$\{1\}\{$c$\}\{$ ALPHA $\}$ & BETA $\backslash \backslash$

$\backslash$hline MOODY'S CREDIT RATING & Aa & Baa $\backslash \backslash$

FIXED$-$RATE BORROWING COST & $\backslash (9\mathrm{.}5\backslash \%\backslash )$ & $\backslash (11\mathrm{.}0\backslash \%\backslash )\backslash \backslash$

$\backslash$begin$\{$tabular$\}\{$l$\}$

FLOATING$-$RATE BORROWING $\backslash \backslash$

COST

$\backslash$end$\{$tabular$\}$ & LIBOR & LIBOR $\backslash (+1\backslash \%\backslash )\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$)$ Calculate the quality spread differential $($QSD$).$ Describe an interest rate swap in which both Alpha and Beta have an equal cost savings in their borrowing costs. Assume Alpha desires floating$-$rate debt and Beta desires fixed$-$rate debt. Assume no swap bank is involved.

b$)$ Repeat the above assuming that a swap bank is involved as an intermediary. Assume the swap bank is quoting five$-$year dollar interest rate swaps at $9\mathrm{.}7-9\mathrm{.}8$ percent against LIBOR flat.$|$