Consider two firms A and B, which can borrow on the market at the following conditions

Firm A : 8:5% fixed rate or Euribor +3%, for borrowing $10 million for 8 years.

Firm B : 4:5% fixed rate or Euribor +1%, for borrowing $10 million for 8 years.

They both decide to go to the same bank, which will be in charge to design a swap contract between them (and which thus will take a fee).

(a) Depending on the preferences of the firms (fixed rate for A and floating for B, or fixed rate for B and floating for A), find, if they exist, all the swap contracts (including the fees for the bank) which can improve the borrowing conditions of both firms.

(b) What is the maximal fee that the bank can get?