Consider two firms AAA and BBB. Each firm needs to borrow $1M. AAA wants to borrow at a floating interest rate while BBB

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Consider two firms AAA and BBB. Each firm needs to borrow $1M.
AAA wants to borrow at a floating interest rate while BBB wants to
borrow at a fixed interest rate. AAA can borrow either at 9% or
LIBOR+3% and BBB can borrow either at 8% or at LIBOR +1%. The
companies entered into a swap agreement in which both companies
borrowed $1M from outside lenders. According to the swap agreement,
one of the companies pays the other one annual interest payments
equal to LIBOR rate times $1M in exchange for fixed-rate payments
of x% times $1M. Given that this swap agreement is beneficial for
both firms, find the maximum and minimum possible value for
x.