Let's consider the following example of an interest rate swap involving two firms, Firm A and Firm B. Firm A prefers a variable interest rate loan, while Firm B prefers a fixed interest rate loan. The banks offer the following lending rates:

Firm A can obtain either a fixed rate loan at 7% or a variable rate loan tied to LIBOR.

Firm B can obtain either a fixed rate loan at 10% or a variable rate loan tied to LIBOR + 1%.

In this scenario, a swap bank has engaged in negotiations with Firm A and Firm B for separate transactions:

Firm A enters into an agreement with the swap bank, whereby Firm A pays the swap bank the variable interest rate LIBOR on the loan, and the swap bank pays Firm A a fixed interest rate of 8% on the loan.

Similarly, the swap bank negotiates an agreement with Firm B, where Firm B pays the swap bank a fixed interest rate of 8.5% on the loan, and the swap bank pays Firm B the variable interest rate LIBOR on the loan.

4.1. Calculate the quality spread differential of this swap.

4.2. Assuming the principal value of this loan is 5 million USD. How much profit the swap bank could earn? How much interest cost saving from firm A and firm B respectively?

4.3. Using one sentence or one calculation result to summarize the connection between your answers in 4.2 and 4.1.