Question

Interest Rate Sensitivity A bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediately after she purchased the bonds, interest rates fell to 6%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table. Assume annual coupons and annual compounding. Do not round intermediate calculations. Round the monetary values to the nearest cent and percentage values to two decimal places. Price @ 8% Price @ 6% Percentage Change 10-year, 10% annual coupon 10-year zero 5-year zero 30-year zero Perpetuity, $100 annual coupon

Answer 1

	Price @8%	Price @6%	Percentage Change
10 year ,10% annual coupon	1134.2	1294.4	14.12	%
10 Year zero	463.2	558.4	20.55	%
5 year zero	680.6	747.3	9.80	%
30 year zero	99.4	174.1	75.20	%
Perpetuity, $100 annual coupon	1250.0	1666.7	33.33	%

Workings:

10 year 10% annual coupon:

NPER	10.00
FV	1000
PMT	100.0
Rate	8%
PV	$1,134.20	[-pv(rate,nper,pmt,fv,0)

NPER	10.00
FV	1000
PMT	100.0
Rate	6%
PV	$1,294.40	[-pv(rate,nper,pmt,fv,0)

10 year zero : YTM 8% = 1000/ (1.08)10 = 463.2

YTM 6% = 1000/ (1.06)10 = 558.4

5 year zero:

YTM 8% = 1000/ (1.08)5 = 680.6

YTM 6% = 1000/ (1.06)5 = 747.3

30 year zero:

YTM 8% = 1000/ (1.08)30 = 99.4

YTM 6% = 1000/ (1.06)30 = 174.1

Perpetuity:

YTM 8% = 100/ 0.08 = 1250

YTM 6% = 1000/ 0.08 = 1666.7