Company AAA, a low$-$rated firm, desires a fixed$-$rate, long$-$term loan. AAA presently has access to floating interest rate funds at a margin of $3\%$ over SOFR. Its direct borrowing cost is $10\%$ in the fixed$-$rate bond market. In contrast, company BBB$,$ which prefers a floating$-$rate loan, has access to fixed$-$rate funds in the Eurodollar bond market at $7\%$ and floating$-$rate funds at SOFR $+1\%.$ A financial institution has brought these two firms together and facilitated the swap by taking the counterparty risk and requires a net total compensation package of $0\mathrm{.}2\%($this does not mean $0\mathrm{.}2\%$ from each, it means $0\mathrm{.}2\%$ total$).$

$($a$)$ What is the size of the mispricing $($if any$)?$

$($b$)$ In terms of financing, describe the relative positions of the two companies using the concepts of absolute and comparative advantages.

$($c$)$ Design a swap acceptable to both companies and the financial institution. Split the benefits evenly between the two companies. Diagram the cash flows of the two

companies and the financial institution. On your diagram clearly indicate the swap rates that the two companies and the institution are using.

$($d$)$ What are the final borrowing rates for each company?

Please answer all questions and show full workings.