You are given that the one year spot interest rate is 9%, while the two year spot interest rate is 10.05%. A two-year bond with a fixed coupon is selling at par. Companies A and B are both interested in borrowing money for two years, each in the amount of K, and company A would like to borrow at a variable interest rate, and company B would like to borrow at a fixed rate. A bank is offering loans to companies A and B at the following terms:
Company A Company B
Fixed interest rate 11.5% 13.5%
Variable interest rate LIBOR + 2.25% LIBOR + 3.25%
The firms decided that it would be most beneficial to them to do the following, over the next two years:
• Company A will obtain a fixed interest rate loan.
• Company B will obtain a variable interest rate.
• Companies A and B will enter into a swap with each other, in which Company A will pay Company B at the variable rate LIBOR + c, while company B will pay Company A at the fixed rate of 11%.
Find the value of c, assuming that there is a functioning and efficient market for bonds and loans that both companies can enter, and all transactions, i.e., swaps, bonds, loans, have no additional transaction costs or other costs.