Alpha and Beta Companies can borrow for a five-year term at the following rates:

Question

Alpha and Beta Companies can borrow for a five-year term at the following rates:

QUESTIONS: 2 questions

(1) Calculate the quality spread differential (QSD).

(2) Develop an interest rate swap on behalf of the swap bank, in which the swap bank will earn a
profit of 10 basis points. In addition, Alpha and Beta would have equal cost savings by doing the
swap. Assume Alpha desires floating-rate debt and Beta desires fixed-rate debt.

Alpha Beta Moody’s credit rating Aa Baa Fixed-rate borrowing cost 10.5% 12.0% Floating-rate borrowing cost LIBOR LIBOR + 1%

Explanation / Answer

Question 1.

QSD =12.5% - 10.5% - (LIBOR+1% - LIBOR) = 1.5%-1%

Therefore QSD = 0.5%

Question 2.

Alpha will issue at fixed-rate debt at 10.5% and Beta will issue at floating rate-debt at LIBOR + 1%. So, Alpha in such case will pay LIBOR to Beta. Beta will pay 10.75% to Alpha. If this is done, Alpha’s floating-rate costs: 10.5% + LIBOR - 10.75% = LIBOR - 0.25%, and a 0.25% savings over issuing floating-rate. Beta’s fixed-rate costs: LIBOR+ 1% + 10.75% - LIBOR = 11.75%, So, Savings will be 12%-11.75% = 0.25% and a .25% savings over issuing fixed-rate debt.

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