Question

Bond J has a coupon rate of 4 percent. Bond K has a coupon rate of 14 percent. Both bonds have 17 years to maturity, a par value of $1,000, and a YTM of 8 percent, and both make semiannual payments. 

a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) 

b.If interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) 

Answer 1

a.	Bond J	-18.61%
	Bond K	-14.72%
Working:
	# 1	Existing price of Bond J	=	=-pv(rate,nper,pmt,fv)		Where,
			=	$     631.78		rate	=	8%*(6/12)	=	0.04
						nper	=	17*(12/6)	=	34
						pmt	=	1000*4%*(6/12)	=	$       20.00
						fv			=	$ 1,000.00
		Existing price of Bond K	=	=-pv(rate,nper,pmt,fv)		Where,
			=	$ 1,552.34		rate	=	8%*(6/12)	=	0.04
						nper	=	17*(12/6)	=	34
						pmt	=	1000*14%*(6/12)	=	$       70.00
						fv			=	$ 1,000.00
	# 2	Price after rise of interest rate by 2 percent:
		New price of Bond J	=	=-pv(rate,nper,pmt,fv)		Where,
			=	$     514.21		rate	=	10%*(6/12)	=	0.05
						nper	=	17*(12/6)	=	34
						pmt	=	1000*4%*(6/12)	=	$       20.00
						fv			=	$ 1,000.00
		New price of Bond K	=	=-pv(rate,nper,pmt,fv)		Where,
			=	$ 1,323.86		rate	=	10%*(6/12)	=	0.05
						nper	=	17*(12/6)	=	34
						pmt	=	1000*14%*(6/12)	=	$       70.00
						fv			=	$ 1,000.00
	# 3	Percentage change in the price of:
		Bond J	=	(b-a)/a		Where,
			=	-18.61%		a	Existing price	=	$     631.78
						b	New Price	=	$     514.21
		Bond K	=	(b-a)/a		Where,
			=	-14.72%		a	Existing price	=	$ 1,552.34
						b	New Price	=	$ 1,323.86
b.	Bond J	24.84%
	Bond K	18.87%
Working:
	# 1	Price after fall of interest rate by 2 percent:
		New price of Bond J	=	=-pv(rate,nper,pmt,fv)		Where,
			=	$     788.68		rate	=	6%*(6/12)	=	0.03
						nper	=	17*(12/6)	=	34
						pmt	=	1000*4%*(6/12)	=	$       20.00
						fv			=	$ 1,000.00
		New price of Bond K	=	=-pv(rate,nper,pmt,fv)		Where,
			=	$ 1,845.27		rate	=	6%*(6/12)	=	0.03
						nper	=	17*(12/6)	=	34
						pmt	=	1000*14%*(6/12)	=	$       70.00
						fv			=	$ 1,000.00
	# 2	Percentage change in the price of:
		Bond J	=	(b-a)/a		Where,
			=	24.84%		a	Existing price	=	$     631.78
						b	New Price	=	$     788.68
		Bond K	=	(b-a)/a		Where,
			=	18.87%		a	Existing price	=	$ 1,552.34
						b	New Price	=	$ 1,845.27