Bank A needs to borrow $10 million to finance a floating rate Eurodollar loan to

Question

Bank A needs to borrow $10 million to finance a floating rate Eurodollar loan to its client. To avoid the interest rate risk, floating rate note (FRN) is preferable. Company B needs to borrow $10 million to finance an investment project. To avoid the interest rate risk, a fixed rate loan is preferable. Bank A can borrow at a fixed rate of 10.0% and a floating rate of LIBOR flat. Company B can borrow at a fixed rate of 12.5% and a floating rate of LIBOR + 1.0%. A swap bank is used as an intermediary for the deal. The swap bank and the two counterparties of the deal agree that they are going to equally split the total gains from the swap deal.

a. Compute the quality spread differential (QSD).

b. If Bank A agrees to pay LIBOR flat to the swap bank, what interest rate should Bank A

receive from the swap bank?

c. If Company B agrees to pay 10.50% fixed rate to the swap bank, what interest rate should

Company B receive from the swap bank?

Explanation / Answer

Fixed Rate (%)

Floating Rate (%)

Bank A

10%

LIBOR

Company B

12.5%

LIBOR+1%

Bank A has an absolute advantage in both Fixed Rate and Floating Rate. But Company B has a relative advantage while borrowing in Floating Rate than in Fixed Rate.

So if Bank A borrows at fixed rate than Company B then it savings is (12.5%-10%) = 2.5%

Again if Company B borrows at floating rate then loss is (LIBOR-LIBOR-1%) = -1%

So, net savings is 1.5% = (2.5%-1%)

So Quality Spread Differential is 1.5%

Since it is distributed evenly then net savings is 0.75% (since no charges are there for the intermediary)

Now it will mean that Company B will borrow at 12.5% which would mean a loss in cost by 2.5% (10-12.5) %

While a gain in floating rate would be seen by 1%, since it will borrow at a lower rate than Company B (LIBOR% + 1 –LIBOR) = 1%

However a net loss in savings will be seen by => -2.5% + 1% = -1.5%

So net loss in distribution would be -0.75% (since distributed equally)

So it should receive from the bank at 10% but its effective rate of interest would be (10+0.75 = 10.75%)

C. If Company B agrees to pay at 10.5% to the swap bank then Bank A will receive Floating rate.

Now it will mean that Company B will borrow at 10.5% which would mean a loss in cost by 0.5% (10-10.5) %

While a gain in floating rate would be seen by 1%, since it will borrow at a lower rate than Company B (LIBOR% + 1 –LIBOR) = 1%

However a net gain in savings will be seen by => -0.5% + 1% = 0.5%

So net gain in distribution would be 0.25% (since distributed equally)

So it should receive from the bank at (LIBOR+1) but its effective rate of interest would be (LIBOR+1-0.25= LIBOR+0.75) (LIBOR + 0.75%)

Fixed Rate (%)

Floating Rate (%)

Bank A

10%

LIBOR

Company B

12.5%

LIBOR+1%

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