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

a$.$ Calculate the quality spread differential $($QSD$).$

b$.$ Develop 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. No swap bank is involved in this transaction. What rate should Alpha pay to

Beta? What rate will Beta pay to Alpha? Calculate the all$-$in$-$cost of borrowing for Alpha and Beta, respectively.

Do problem $1$ over again, this time assuming more realistically that a swap bank is involved as an intermediary. Assume the swap bank is

quoting five$-$year dollar interest rate swaps at $10\mathrm{.}7-10\mathrm{.}8$ percent against SOFR $+.72$ percent. Compute the rates Alpha and Beta should

pay to the swap bank in this swap, and calculate the all$-$in$-$cost of borrowing for Alpha and Beta and the earnings for the swap bank.