Firm A can borrow at $4\%$ fixed or in the floating$-$rate market at Libor flat. Firm B can borrow at $7\%$ fixed or at Libor plus $100$ bps$.$ A wants to borrow floating and B fixed.

Suppose that to reduce financing costs, A borrows fixed, B borrows floating, and they enter into an interest$-$rate swap. Which of the following statements is valid?

A$.$

No improvement in combined financing costs is possible$$what one party gains in financing costs, the other party loses.

B$.$

The combined improvement in cost of financing to A and B with the swap depends on the negotiated fixed rate on the swap between the two counterparties.

C$.$

The combined improvement in cost of financing to A and B with the swap is always equal to the difference between the fixed rate differential $($between A and B$)$ and the floating rate differential which in this case is $200$ basis points.

D$.$

The combined improvement in cost of financing to A and B with the swap is always equal to the floating rate differential, which in this case is $100$ basis points.