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

Alpha Beta

Moody$$s credit rating Aa Baa

Fixed$-$rate borrowing cost $12\mathrm{.}5\%16\mathrm{.}0\%$

Floating$-$rate borrowing cost SOFR $+0\mathrm{.}72\%$ SOFR $+1\mathrm{.}72\%$

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 $14\mathrm{.}712\mathrm{.}8$ percent against SOFR $+0\mathrm{.}72$ 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.

Required:

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

b$-1.$ 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. Compute the rates Alpha and Beta should pay to the swap bank in this swap.

b$-2.$ Calculate the all$-$in$-$cost of borrowing for Alpha and Beta and the earnings for the swap bank.