Question

INTEREST RATE SENSITIVITY

An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 10% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell, and each then had a new YTM of 6%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places. Enter all amounts as positive numbers.

Price @ 10% Price @ 6% Percentage Change

10-year, 10% annual coupon: $ ________   $ ________ _________ %
10-year zero:    ________ ________    ________
5-year zero: ________ ________ ________
30-year zero:     _______ ________    ________
$100 perpetuity: _______ ________    ________

Answer 1

We use pv formaule in excel to find the price of bond in each case
=pv(rate,nper,pmt,fv,type)
1)at 10%
=pv(10%,10,(1000*10%),1000,0)=1000
at 6%
=pv(6%,10,(1000*10%),1000,0)=1294.40
% changee=(new/old)-1
=(1294.40/1000)-1=29.44%
2)10 year zero coupon
=pv(10%,10,(1000*0%),1000,0)=385.54
at 6%
=pv(6%,10,(1000*0%),1000,0)=558.39
% changee=(new/old)-1
=(558.39/385.54)-1=44.83%
3)5 year zero
=pv(10%,5,(1000*0%),1000,0)=620.92
at 6%
=pv(6%,5,(1000*0%),1000,0)=747.26
% changee=(new/old)-1
=(747.26/620.92)-1=20.35%
4)30 year zer0
=pv(10%,30,(1000*0%),1000,0)=57.31
at 6%
=pv(6%,30,(1000*0%),1000,0)=174.11
% changee=(new/old)-1
=(174.11/57.31)-1=203.81%
5)$100 perpituy
old price=100/10%=1000
new price=100/6%=1666.67
% changee=(new/old)-1
=(1666.67/1000)-1=66.67%