Question

# Company A, a lower-rated firm, desires a fixed-rate loan. Company A presently has access to floating...

Company A, a lower-rated firm, desires a fixed-rate loan. Company A presently has access to floating interest rate funds at a margin of 1.7% over LIBOR. In contrast, company B, a higher-rated firm, prefers a floating-rate loan. Company B has access to fixed-rate funds at 11% and floating-rate funds at LIBOR+0.7%. Both companies enter into an interest rate swap with Bank C. Based on the swap, Bank C would gain 0.4% and each of the two companies would gain 0.6%. What is the current fixed rate available for Company A?

Please provide detailed explanation

Since company B prefers a floating rate loan, they would take it from company A and similarly company A, since they want a fixed-rate loan, will take it from company B. Now, the total benefit, in this case, will be the benefit obtained by each firm plus the benefit obtained by the bank. Hence, total benefit = 0.6 + 0.6 + 0.4 = 1.6%. Now, since company A is using its floating rate = Libor + 1.7% and company B is using its fixed-rate = 11%, the total cost will be = Libor + 12.7%. The cost of the reverse option where A takes a fixed-rate loan (let it be at A%) and B takes a floating rate = Libor + 0.7%, the total cost will be = Libor + 0.7 + A. This cost should be more than the current cost by 1.6%. Hence, we have:

Libor + 0.7 + A = Libor + 12.7 + 1.6

Hence, A = 13.6%.

Hence, 13.6% will be the fixed rate available for company A.

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