The managing partner of your private equity firm is aghast to discover that a cruise ship line you own has bought a ship $$ a long$-$term asset that will generate revenues in U$.$S$.$ dollars $$ and financed it with $90-$day commercial paper at a rate equivalent to $3-$month SOFR $+\mathrm{.}60\%.$ As she rushes off to catch a flight to Asia she tells you: $$Fix this, fast. Get rid of the risk, and see if you can save us some money in the process. Whatever you do$,$ don$$t get any banks involved $$they are vampires.$$ By noon you have identified a counterparty that is that is willing to do a swap. It is a AA$-$rated U$.$S$.$ aircraft manufacturing firm with long$-$term fixed assets that can issue U$.$S$.$ dollar$-$denominated bonds at $8\%$ or borrow dollars short$-$term at $3-$month SOFR $+\mathrm{.}20\%.$ The cruise ship line you own has a B$+$ rating and would have to pay $9\mathrm{.}5\%$ if it were to issue a long$-$term bond in the U$.$S$.$ market.

$($a$)$ What are the risks the cruise line $($and by extension your firm$)$ faces as a result of the ship acquisition?

$($b$)$ Suggest an interest rate swap that would allow these entities to meet their risk management objectives. Show how the swap would be done and what the payments and receipts would be$.$

$($c$)$ What are the potential gains to the parties to the swaps, and how are they divided up in the swap you suggest?