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

## Question:

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

 Alpha Beta Moody's Credit Rating Aa Baa Fixed-rate borrowing cost 10.0% 12.5% Floating-rate borrowing cost LIBOR LIBOR + 1%

a. Calculate the quality spread differential (QSD).

b. Develop an interest rate swap in which a swap bank, Alpha and Beta share the savings equally if any. Assume Alpha desires floating-rate debt and Beta desires fixed-rate debt.

## Fixed interest rate

The fixed interest rate is the fixed rate of percentage charged by the lender on the principal amount for the entire period of the loan. It is reported in the profit and loss account. It is preferred by the borrower because it is not fluctuate due to market rate

a. Calculating the quality spread differential (QSD)

{eq}\begin{align*} \rm\text{Quality spread differential} &= \rm\text{ Differential on fixed rate debt} - \rm\text{ Differential floating rate debt }\\ &= \left( 12.5\% - 10\% \right) - \left( \rm\text{LIBOR } + 1\% \right) - \rm\text{LIBOR}\\ &= 2.5\% - 1 \% \\ &= 1.5\% \end{align*} {/eq}

A positive quality spread differential indicates that SWAP is favor of both parties.

Alpha issues fixed rate of debt at 10%

In the given situation, Alpha desires floating rate debt , Alpha will LIBOR to Beta and receives y% form beta so that quality spread differentials shared equally among both the parties.

Calculating the interest rate for swap effectively:

{eq}\begin{align*} \rm\text{Net payment for Alpha }&= \rm\text{ Floating rate cost} - \dfrac{\rm\text{Quality spread differential saving}}{2}\\ 10\% + \rm\text{LIBOR} - \rm\text{y% } &= \rm\text{LIBOR } - \dfrac{{1.5\% }}{2}\\ \rm\text{y } &= 10.75\% \end{align*} {/eq}

Beta issues floating rate of debt at LIBOR+1%

In the given situation, Beta desires fixed rate debt , Beta will LIBOR+1% and y% to Alpha and receives y% form Alpha so that quality spread differentials shared equally among both the parties.

Calculating the interest rate for swap effectively:

{eq}\begin{align*} \rm\text{Net payment for Alpha } &= \rm\text{ Fixed rate cost } - \dfrac{\rm\text{Quality spread differential saving}}{{2}}\\ \rm\text{LIBOR} + 1\% + \rm\text{y% } &= 12.5\% - \dfrac{{1.5\% }}{{2}}\\ \rm\text{y} &= 10.75\% \end{align*} {/eq}