Question

Problem 10-18 Interest Rate RIS (LUS, CP44) 10 points Bond J has a coupon of 74 percent. Bond K has a coupon of 11.4 percent. Both bonds have 12 years to maturity and have a YTM of 78 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (A negative value should be Indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) eBook % A in Price References Bond J Bond K b. If interest rates suddenly falby 2 percent, what is the percentage price change of these bonds? (Do not round Intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) SA In Price Bond Bond K

Answer 1

Based on information given Duration is calculated as below

Bond J						Bond K
Bond Price	$100					Bond Price	$100
Coupon rate	7.40%					Coupon rate	11.40%
Years for Maturity	12					Years for Maturity	12
YTM	7.80%					YTM	7.80%

Year (1)	Yearly Cashflow (2)	PV factor @ 7.8% (3)	PV of Cashflow 4 = (3x2)	PV x Yearly Weights 5 = (4 x 1)		Year (1)	Yearly Cashflow (2)	PV factor @ 7.8% (3)	PV of Cashflow 4 = (3x2)	PV x Yearly Weights 5 = (4 x 1)
1	7.4	0.93	6.86	6.86		1	11.40	0.93	10.58	10.58
2	7.4	0.86	6.37	12.74		2	11.40	0.86	9.81	19.62
3	7.4	0.80	5.91	17.72		3	11.40	0.80	9.10	27.30
4	7.4	0.74	5.48	21.92		4	11.40	0.74	8.44	33.77
5	7.4	0.69	5.08	25.42		5	11.40	0.69	7.83	39.15
6	7.4	0.64	4.72	28.29		6	11.40	0.64	7.26	43.59
7	7.4	0.59	4.37	30.62		7	11.40	0.59	6.74	47.17
8	7.4	0.55	4.06	32.46		8	11.40	0.55	6.25	50.01
9	7.4	0.51	3.76	33.88		9	11.40	0.51	5.80	52.19
10	7.4	0.47	3.49	34.92		10	11.40	0.47	5.38	53.79
11	7.4	0.44	3.24	35.63		11	11.40	0.44	4.99	54.89
12	107.4	0.41	43.61	523.31		12	111.40	0.41	45.23	542.80
Total			96.95	803.77		Total			127.41	974.85
Duration of Bond J = Weighted PV of Cashflow/PV of Cashflows				8.2902		Duration of Bond K = Weighted PV of Cashflow/PV of Cashflows				7.6511

a) If interest rates increase by 2%, the prices of bonds will decrease as below

Change in Price of Bond J = (- Duration of Bond J) x Interest rate increase

= -8.2902 x 2% = - 16.58% i.e price will decrease by 16.58%

Change in Price of Bond K = (- Duration of Bond K) x Interest rate increase

= -7.6511 x 2% = - 15.30% i.e price will decrease by 15.30%

b) If interest rates decrease by 2%, the prices of bonds will decrease as below

Change in Price of Bond J = (- Duration of Bond J) x( -Interest rate decrease)

= -8.2902 x -2% = 16.58% i.e price will increase by 16.58%

Change in Price of Bond K = (- Duration of Bond K) x (-Interest rate decrease)

= -7.6511 x -2% = 15.30% i.e price will increase by 15.30%