Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 18 years to maturity.

   

	If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam?
	-5.16% -5.44% -5.14% 5.22%

    

	If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Dave?
	19.07% -17.67% -17.65% -21.46%

    

	If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then?
	-5.11% 5.22% 5.49% 5.51%

    

	If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Dave be then?
	23.56% 23.54% 19.07% -17.62%

Answer 1

As Both Bonds are Price at Par Value, Current Interest Rate is Equal to Coupon Rate i.e. 7%

Therefore, Semi Annual Rate = 7%/2 = 3.5%

Coupons = Par Value*Semi Annual Coupon Rate = 1000*3.5% = $35

Semi Annual Interest Rate on 2% Rise = (7+2)/2 = 4.5%

Semi Annual Interest Rate on 2% Fall = (7-2)/2 = 2.5%

Bond Sam:

Period Remaining to maturity = 3 years*2 = 6

		7%		9%		5%
Period	Cash Flow	Discounting Factor [1/(1.035^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.045^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.025^year)]	PV of Cash Flows (cash flows*discounting factor)
1	35	0.966183575	33.81642512	0.956937799	33.49282297	0.975609756	34.14634146
2	35	0.9335107	32.67287451	0.915729951	32.05054829	0.951814396	33.31350387
3	35	0.901942706	31.5679947	0.876296604	30.67038114	0.928599411	32.50097938
4	35	0.871442228	30.50047797	0.838561344	29.34964703	0.905950645	31.70827257
5	35	0.841973167	29.46906084	0.802451047	28.08578663	0.883854288	30.93490007
6	35	0.813500644	28.47252255	0.767895738	26.87635084	0.862296866	30.18039031
6	1000	0.813500644	813.5006443	0.767895738	767.8957383	0.862296866	862.296866
		Price of the Bond = Sum of PVs	1000	Price of the Bond = Sum of PVs	948.4212752	Price of the Bond = Sum of PVs	1055.081254
				% Change = [(948.42-1000)/1000]	-0.051578725	% Change = [(1055.08-1000)/1000]	0.055081254

Bond Dave:

Period Remaining to Maturity = 18 years*2 = 36

		7%		9%		5%
Period	Cash Flow	Discounting Factor [1/(1.035^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.045^year)]	PV of Cash Flows (cash flows*discounting factor)	Discounting Factor [1/(1.025^year)]	PV of Cash Flows (cash flows*discounting factor)
1	35	0.966183575	33.81642512	0.956937799	33.49282297	0.975609756	34.14634146
2	35	0.9335107	32.67287451	0.915729951	32.05054829	0.951814396	33.31350387
3	35	0.901942706	31.5679947	0.876296604	30.67038114	0.928599411	32.50097938
4	35	0.871442228	30.50047797	0.838561344	29.34964703	0.905950645	31.70827257
5	35	0.841973167	29.46906084	0.802451047	28.08578663	0.883854288	30.93490007
6	35	0.813500644	28.47252255	0.767895738	26.87635084	0.862296866	30.18039031
7	35	0.785990961	27.50968362	0.734828458	25.71899602	0.841265235	29.44428323
8	35	0.759411556	26.57940447	0.703185127	24.61147944	0.820746571	28.72612998
9	35	0.733730972	25.68058403	0.672904428	23.55165497	0.800728362	28.02549266
10	35	0.708918814	24.81215848	0.643927682	22.53746887	0.781198402	27.34194406
11	35	0.684945714	23.97309998	0.616198739	21.56695586	0.762144782	26.67506738
12	35	0.661783298	23.16241544	0.589663865	20.63823527	0.743555885	26.02445598
13	35	0.639404153	22.37914535	0.564271641	19.74950744	0.725420376	25.38971315
14	35	0.61778179	21.62236266	0.539972862	18.89905018	0.707727196	24.77045185
15	35	0.596890619	20.89117165	0.516720442	18.08521548	0.690465557	24.16629449
16	35	0.576705912	20.18470691	0.494469323	17.3064263	0.673624934	23.57687267
17	35	0.557203779	19.50213228	0.473176385	16.56117349	0.657195057	23.001827
18	35	0.53836114	18.84263988	0.452800369	15.84801291	0.641165909	22.44080683
19	35	0.52015569	18.20544916	0.433301788	15.16556259	0.625527716	21.89347008
20	35	0.502565884	17.58980596	0.41464286	14.51250009	0.610270943	21.359483
21	35	0.485570903	16.9949816	0.396787426	13.88755989	0.595386286	20.83852
22	35	0.469150631	16.42027208	0.379700886	13.289531	0.580864669	20.33026341
23	35	0.453285634	15.86499718	0.36335013	12.71725454	0.566697238	19.83440333
24	35	0.437957134	15.32849969	0.347703474	12.16962157	0.552875354	19.3506374
25	35	0.423146989	14.81014462	0.332730597	11.64557088	0.539390589	18.87867063
26	35	0.408837671	14.30931848	0.318402485	11.14408697	0.526234721	18.41821525
27	35	0.395012242	13.82542848	0.304691373	10.66419806	0.513399728	17.96899049
28	35	0.38165434	13.35790191	0.291570692	10.20497422	0.500877784	17.53072243
29	35	0.368748155	12.90618542	0.279015016	9.765525567	0.488661252	17.10314383
30	35	0.356278411	12.46974437	0.267000016	9.345000543	0.476742685	16.68599398
31	35	0.344230348	12.04806219	0.255502407	8.942584251	0.465114815	16.27901852
32	35	0.332589709	11.6406398	0.244499911	8.557496891	0.453770551	15.88196929
33	35	0.321342714	11.24699498	0.233971207	8.18899224	0.442702977	15.49460418
34	35	0.310476052	10.86666181	0.223895892	7.836356211	0.431905343	15.11668701
35	35	0.299976862	10.49919016	0.214254442	7.498905465	0.421371066	14.74798732
36	35	0.289832717	10.14414508	0.205028174	7.175986091	0.411093723	14.38828032
36	1000	0.289832717	289.8327166	0.205028174	205.028174	0.411093723	411.0937233
		Price of the Bond = Sum of PVs	1000	Price of the Bond = Sum of PVs	823.3395942	Price of the Bond = Sum of PVs	1235.562511
				% Change = [(823.34-1000)/1000]	-0.176660406	% Change = [(1235.56-1000)/1000]	0.235562511

i) Rises....Sam...... -5.16%

ii) Rises....Dave..... -17.67%

iii) Falls....Sam..... 5.51%

iv) Falls....Dave.... 23.56%