Question

Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 8 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds?

Answer 1

Answer:

Bond J -16.33%

Bond K -14.04%

Explanation:

In order to determine the percentage price change it is incumbent to establish the bonds' prices with YTM of 8% as well as when interest rises by 2% so as to calculate the price change percentage.

The pv formula can be used to establish the prices as follows:

=-pv(rate,nper,pmt,fv)

rate is semiannual yield to maturity of both bonds which 8%/2=4%

nper is the number of coupon interest payable by the bonds which 14 years multiplied by 2 i.e 28

pmt is the semiannual coupon payment by the bonds:

Bond J=$1000*5%/2=$25

Bond K=$1000*11%/2=$55

fv is the face of the bonds which is $1000 in  both cases

Price of bond J;

=-pv(4%,28,25,1000)=$ 750.05  

Price of Bond K:

=-pv(4%,28,55,1000)=$1,249.95  

New price with 2% increase in interest

Yield previously 8%

plus increase      2%'

total                     10%

divided by 2=10%/2=5%

Price of bond J;

=-pv(5%,28,25,1000)=$627.55  

Price of Bond K:

=-pv(5%,28,55,1000)=$ 1,074.49  

Change in price=new price-old price/old price

Bond J=($627.55-$ 750.05)/$ 750.05=-16.33%

Bonk K=($1,074.49-$1,249.95)/$1,249.95  =-14.04%