Question

Heather​ O'Reilly, the treasurer of CB​ Solutions, believes interest rates are going to​ rise, so she wants to swap her future floating rate interest payments for fixed rates.​ Presently, she is paying LIBOR plus 2.00​% per annum on $5,200,000 of debt for the next two​ years, with payments due semiannually. LIBOR is currently 3.98​% per annum. Heather has just made an interest payment​ today, so the next payment is due six months from today. Heather finds that she can swap her current floating rate payments for fixed payments of 7.008​% per annum. ​ (CB Solutions' weighted average cost of capital is 12​%, which Heather calculates to be 6​% per​ six-month period, compounded​ semiannually).

a. If LIBOR rises at the rate of 50 basis points per​ six-month period, starting​ tomorrow, how much does Heather save or cost her company by making this​ swap?

b. If LIBOR falls at the rate of 25 basis points per​ six-month period, starting​ tomorrow, how much does Heather save or cost her company by making this​ swap?

Answer 1

	a	LIBOR rises 50 basis point per six month period starting tomorrow
		Libor rate tomorrow=3.98+0.5=			4.48%		4.48
		N	A	B=(A*7.008%)/2	C	D=C+2%	E=(A*D)/2	F=E-B	G=F/(1.06^N)
		Semi annual Period	Amount of Debt	Fixed payment	Libor rate	Interest rate on current loan	Interest payment without swap	Savings/(Cost)	Present Value of Savings/(cost)
		1	$5,200,000	$182,208	4.48%	6.48%	$168,480	-$13,728	-$12,951
		2	$5,200,000	$182,208	4.98%	6.98%	$181,480	-$728	-$648
		3	$5,200,000	$182,208	5.48%	7.48%	$194,480	$12,272	$10,304
		4	$5,200,000	$182,208	5.98%	7.98%	$207,480	$25,272	$20,018
							Total Savings/(Cost)		$16,723
		Savings	$16,723
	b	LIBOR falls 25 basis point per six month period starting tomorrow
		Libor rate tomorrow=3.98-0.25=			3.73%		3.73
		N	A	B=(A*7.008%)/2	C	D=C+2%	E=(A*D)/2	F=E-B	G=F/(1.06^N)
		Semi annual Period	Amount of Debt	Fixed payment	Libor rate	Interest rate on current loan	Interest payment without swap	Savings/(Cost)	Present Value of Savings/(cost)
		1	$5,200,000	$182,208	3.73%	5.73%	$148,980	-$33,228	-$31,347
		2	$5,200,000	$182,208	3.48%	5.48%	$142,480	-$39,728	-$35,358
		3	$5,200,000	$182,208	3.23%	5.23%	$135,980	-$46,228	-$38,814
		4	$5,200,000	$182,208	2.98%	4.98%	$129,480	-$52,728	-$41,766
							Total Savings/(Cost)		-$147,284
		Costs	$147,284