Question

Bond J is a 3 percent coupon bond. Bond K is a 12 percent coupon bond. Both bonds have 9 years to maturity, make semiannual payments, and have a YTM of 8 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead?

Answer 1

Bong J:

Semi Annual Coupon = 1000*3%/2 = $15

		8%		10%		6%
Period	Cash Flow	Discounting Factor [1/(1.04^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.05^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.03^year)]	PV of Cash Flows (cash flows*discounting factor)
1	15	0.961538462	14.42307692	0.952380952	14.28571429	0.970873786	14.5631068
2	15	0.924556213	13.8683432	0.907029478	13.60544218	0.942595909	14.13893864
3	15	0.888996359	13.33494538	0.863837599	12.95756398	0.915141659	13.72712489
4	15	0.854804191	12.82206287	0.822702475	12.34053712	0.888487048	13.32730572
5	15	0.821927107	12.3289066	0.783526166	11.7528925	0.862608784	12.93913177
6	15	0.790314526	11.85471789	0.746215397	11.19323095	0.837484257	12.56226385
7	15	0.759917813	11.3987672	0.71068133	10.66021995	0.813091511	12.19637267
8	15	0.730690205	10.96035308	0.676839362	10.15259043	0.789409234	11.84113851
9	15	0.702586736	10.53880103	0.644608916	9.669133743	0.766416732	11.49625099
10	15	0.675564169	10.13346253	0.613913254	9.208698803	0.744093915	11.16140872
11	15	0.649580932	9.743713973	0.584679289	8.770189336	0.722421277	10.83631915
12	15	0.62459705	9.368955744	0.556837418	8.352561273	0.70137988	10.5206982
13	15	0.600574086	9.008611292	0.530321351	7.95482026	0.68095134	10.2142701
14	15	0.577475083	8.662126242	0.505067953	7.576019295	0.661117806	9.916767087
15	15	0.555264503	8.328967541	0.481017098	7.215256471	0.641861947	9.627929211
16	15	0.533908176	8.008622635	0.458111522	6.87167283	0.623166939	9.347504088
17	15	0.513373246	7.700598688	0.436296688	6.544450314	0.605016446	9.075246688
18	15	0.493628121	7.404421815	0.415520655	6.232809823	0.587394608	8.810919114
18	1000	0.493628121	493.628121	0.415520655	415.5206549	0.587394608	587.3946076
		Price of the Bond = Sum of PVs	683.5175756	Price of the Bond = Sum of PVs	590.8644584	Price of the Bond = Sum of PVs	793.6973038
				% Change = [(590.86-683.52)/683.52]	-0.135553379 = -13.5553%	% Change = [(793.697-683.52)/683.52]	0.161195165 = 16.1195%

Bond K:

Semi Anual Coupon = 1000*12%/2 = $60

		8%		10%		6%
Period	Cash Flow	Discounting Factor [1/(1.04^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.05^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.03^year)]	PV of Cash Flows (cash flows*discounting factor)
1	60	0.961538462	57.69230769	0.952380952	57.14285714	0.970873786	58.25242718
2	60	0.924556213	55.47337278	0.907029478	54.42176871	0.942595909	56.55575455
3	60	0.888996359	53.33978152	0.863837599	51.83025591	0.915141659	54.90849956
4	60	0.854804191	51.28825146	0.822702475	49.36214849	0.888487048	53.30922287
5	60	0.821927107	49.31562641	0.783526166	47.01156999	0.862608784	51.75652706
6	60	0.790314526	47.41887154	0.746215397	44.7729238	0.837484257	50.2490554
7	60	0.759917813	45.59506879	0.71068133	42.64087981	0.813091511	48.78549068
8	60	0.730690205	43.8414123	0.676839362	40.61036172	0.789409234	47.36455406
9	60	0.702586736	42.15520413	0.644608916	38.67653497	0.766416732	45.98500394
10	60	0.675564169	40.53385013	0.613913254	36.83479521	0.744093915	44.64563489
11	60	0.649580932	38.97485589	0.584679289	35.08075735	0.722421277	43.3452766
12	60	0.62459705	37.47582297	0.556837418	33.41024509	0.70137988	42.08279281
13	60	0.600574086	36.03444517	0.530321351	31.81928104	0.68095134	40.8570804
14	60	0.577475083	34.64850497	0.505067953	30.30407718	0.661117806	39.66706835
15	60	0.555264503	33.31587016	0.481017098	28.86102589	0.641861947	38.51171684
16	60	0.533908176	32.03449054	0.458111522	27.48669132	0.623166939	37.39001635
17	60	0.513373246	30.80239475	0.436296688	26.17780126	0.605016446	36.30098675
18	60	0.493628121	29.61768726	0.415520655	24.93123929	0.587394608	35.24367646
18	1000	0.493628121	493.628121	0.415520655	415.5206549	0.587394608	587.3946076
		Price of the Bond = Sum of PVs	1253.185939	Price of the Bond = Sum of PVs	1116.895869	Price of the Bond = Sum of PVs	1412.605392
				% Change = [(1116.896-1253.186)/1253.186]	-0.108754867 = -10.8755%	% Change = [(1412.605-1253.186)/1253.186]	0.127211332 = 12.7211%