Question

4 a. Suppose you are the fixed rate payer in a $10million interest rate swap where the floating rate is the 3-month LIBOR rate and the fixed rate is 3%. The tenor is one year and the rate is reset quarterly. Calculate what you will pay or receive on June 1, Sept 1, Dec 1, and March 1 next year if LIBOR rates turn out to be: June 1: 2%; Sept 1: 2.5%; Dec 1: 3%, and March 1 (next year): 4%.

b. Suppose you have a loan agreement for a $10m 1-year loan at LIBOR plus 150 basis points starting June 1, 2011 with the rate reset quarterly. Combined with the swap in question a, what are your hedged payments in June, Sept, Dec and next March?

Answer 1

4a. In the first case where I am the fixed ratepayer of a $10 million interest rate swap, I will pay according to the fixed rate of 3% on each of the 4 dates -

June 1- (10 million *3%*3/12) = 0.075 million

Sept 1- (10 million *3%*3/12) = 0.075 million

Dec 1- (10 million *3%*3/12) = 0.075 million

March 1 (next year)- (10 million *3%*3/12) = 0.075 million

According to the floating rate which is 3 month LIBOR rate, I will receive the following-

June 1- (10 million*2%*3/12)=0.05 million

Sept 1- (10 million*2.5%*3/12)=0.0625 million

Dec 1- (10 million*3%*3/12)=0.075 million

March 1 (next year)- (10 million*4%*3/12)=0.1 million

So according to the above calculations, we get the following cash flows-

DATE	3 MONTH LIBOR RATE	FLOATING CASH FLOW RECEIVED (MILLION)	FIXED CASH FLOW PAID (MILLION)	NET CASH FLOW(MILLION)
JUNE 1	2%	+0.05	-0.075	-0.025
SEP 1	2.5%	+0.0625	-0.075	-0.0125
DEC 1	3%	+0.075	-0.075	0
MAR 1	4%	+0.1	-0.075	0.025

4b. For the calculation of the hedged loan payments using the rate as LIBOR plus 150 basis points, we do the following-

DATE	LIBOR PLUS 150 BASIS POINTS	LOAN INSTALMENT TO BE PAID(MILLION)	HEDGED AMOUNT(MILLION)
JUNE 1	3.5%	(10 MILLION*3.5%*3/12)=-0.0875	-0.0875-0.025=-0.1125
SEP 1	4%	-0.1	-0.1-0.0125=-0.1125
DEC 1	4.5%	-0.1125	-0.1125+0=-0.1125
MAR 1	5.5%	-0.1375	-0.1375+0.025=-0.1125

So from the above table it is clear that we have to pay 0.1125 million every quarter.