Firm A wants to borrow $10 million at a variable interest rate and Firm B wants to borrow $10 million at a fixed rate.

Firm A goes to Citibank and Citibank quotes Firm A a variable interest rate equal to the LIBOR (which at the time Firm A goes to Citibank is equal to 4%). Citibank also informs Firm A that if Firm A wanted to borrow at a fixed rate that it could borrow at a 5% rate.

Firm B goes to Bank of America and Bank of America quotes Firm B a fixed interest rate of 12%. The Bank of America informs Firm B that if it wanted to borrow at a variable rate it could do so at a rate equal to LIBOR + 3%

• Assume that Firm A borrows from Citibank at the variable and Firm B borrows from Bank of America at a fixed rate. What is the total amount of interest paid by both firms? (Express this in dollar terms.)
• Assume now that Firm A borrows from Citibank at the fixed rate and Firm B borrows from the Bank of America at the variable rate. What is the total amount of interest paid by both firms? (Express this in dollar terms.)
• Subtract the value in (b) from the value in (a). This gives the total savings. Explain why it makes sense that the total cost of borrowing is less in part (b) than in part (a).
• While total costs are lower when Firm A borrows at a fixed and Firm B borrows at a variable, Firm A wants to borrow at a variable rate and Firm B wants to borrow at a fixed rate. Therefore, if Firm A borrows at a fixed and Firm B borrows at a variable rate they have to work out a swap so that each firm ends up with the desired loan.

Assume that Firm A agrees to borrow at a fixed and then pay Firm B the LIBOR rate. Firm B agrees to pay Firm A a fixed rate of 7%.

Calculate the total interest Firm A payswhich is equal to the amount Firm A pays Citibank, plus the amount Firm A pays Firm B, minus the amount Firm A receives from Firm B.

Calculate the total interest Firm B payswhich is equal to the amount Firm B pays Bank of American, plus the amount Firm B pays Firm A, minus the amount Firm B receives from Firm B.

Verify that the total amount of interest paid by both firms is equal to the amount you found in part (b).

Assume that a swap bank is involved in the transaction. If anyone pays the swap bank the LIBOR the swap bank will pay that bank firm a fixed rate of 7%. If anyone pays the swap bank a fixed rate of 7.5% the swap bank will pay that bank firm the LIBOR.

• Firm A will show up and agree to pay the swap bank the LIBOR and receive a fixed rate of 7%. Calculate how much firm A pays the swap bank, how much it receives from the swap bank, and how much it pays Citibank. After all of this how much is Firm A paying for the $10 million loan? Show all your work.
• Firm A will show up and agree to pay a fixed of 7.5% in exchange for receiving the LIBOR. Calculate how much firm B pays the swap bank, how much it receives form the swap bank, and how much it pays Bank of America. After all of this how much is Firm B paying of the $10 million loan? Show all your work.
• How much does the swap bank make from this transaction? Express things in dollar terms.
• Verify that the total amount that all three parties gain is equal to the total amount you calculated in part (c).