Question

Bond value and changing required returns  Bond X pays an 8% annual coupon and Bond Y pays a 4% annual coupon. Both bonds have 10 years to maturity. The yield to maturity for both bonds is now 8%.

a. If the interest rate suddenly rises by 2%, by what percentage will the price of the two bonds change?

b. If the interest rate suddenly drops by 2%, by what percentage will the price of the two bonds change?

c. Which bond has more interest rate risk? Why?

Answer 1

a ) Initial Price Of Bond

Calculations :

Coupons = Coupon Rate * Face Value(Assumed to be 100 in both cases)

Present Value (PV) = Future Value(FV)/(1+YTM)^(no.of years)

Price of Bond = PV of Coupons + PV of Principal

	BOND X	BOND Y
Coupon	8%	4%
Years to Maturity	10	10
YTM	8%	8%
Bond X		Bond Y
Years	Coupons	PV of Coupon	Principal	PV of Pincipal		Coupons	PV of Coupon	Principal	PV of Pincipal
1	8	7.407407407	0	0		4	3.703704	0	0
2	8	6.858710562	0	0		4	3.429355	0	0
3	8	6.350657928	0	0		4	3.175329	0	0
4	8	5.880238822	0	0		4	2.940119	0	0
5	8	5.444665576	0	0		4	2.722333	0	0
6	8	5.041357015	0	0		4	2.520679	0	0
7	8	4.667923162	0	0		4	2.333962	0	0
8	8	4.322151076	0	0		4	2.161076	0	0
9	8	4.001991737	0	0		4	2.000996	0	0
10	8	3.705547905	100	46.31934881		4	1.852774	100	46.31934881
Sum		53.68065119		46.31934881			26.84033		46.31934881
Price Of Bond		100					73.15967

a) If the interest rate suddenly rises by 2%

Bond X		Bond Y
Years	Coupons	PV of Coupon	Principal	PV of Pincipal		Coupons	PV of Coupon	Principal	PV of Pincipal
1	8	7.272727273	0	0		4	3.636364	0	0
2	8	6.611570248	0	0		4	3.305785	0	0
3	8	6.010518407	0	0		4	3.005259	0	0
4	8	5.464107643	0	0		4	2.732054	0	0
5	8	4.967370584	0	0		4	2.483685	0	0
6	8	4.51579144	0	0		4	2.257896	0	0
7	8	4.105264946	0	0		4	2.052632	0	0
8	8	3.732059042	0	0		4	1.86603	0	0
9	8	3.392780947	0	0		4	1.69639	0	0
10	8	3.084346315	100	38.55432894		4	1.542173	100	38.55432894
Sum		49.15653685		38.55432894			24.57827		38.55432894
Price Of Bond		87.71086579					63.1326
		87.71086579					63.1326

	Old Price	New Price	% Change
Bond X	100	87.71086579	-12.289%
Bond Y	73.15967	63.13259737	-13.706%

b)

	BOND X	BOND Y
Coupon	8%	4%
Years to Maturity	10	10
YTM	6%	6%
Bond X		Bond Y
Years	Coupons	PV of Coupon	Principal	PV of Pincipal		Coupons	PV of Coupon	Principal	PV of Pincipal
1	8	7.547169811	0	0		4	3.773585	0	0
2	8	7.11997152	0	0		4	3.559986	0	0
3	8	6.716954264	0	0		4	3.358477	0	0
4	8	6.336749306	0	0		4	3.168375	0	0
5	8	5.978065383	0	0		4	2.989033	0	0
6	8	5.639684324	0	0		4	2.819842	0	0
7	8	5.320456909	0	0		4	2.660228	0	0
8	8	5.019298971	0	0		4	2.509649	0	0
9	8	4.735187708	0	0		4	2.367594	0	0
10	8	4.467158215	100	55.83947769		4	2.233579	100	55.83947769
Sum		58.88069641		55.83947769			29.44035		55.83947769
Price Of Bond		114.7201741					85.27983
		114.7201741					85.27983
	Old Price	New Price	% Change
Bond X	100	114.7201741	14.720%
Bond Y	73.15967	85.2798259	16.567%

c)Bond Y has more interest rate risk because compared to BondX the percentage change in price of Bond Y is higher whenever interest rate changes.