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

The question asks for the percentage price change of bonds with coupon rates of 5% and 11% when interest rates rise by 2%. Bond prices fall when interest rates rise, with bonds having lower coupon rates being more affected. Exact calculations require more information and complex financial formulas.

Step-by-step explanation:

The question asks about the percentage price change of two bonds with different coupon rates when the interest rates rise by 2 percent. Both bonds have the same years to maturity and yield to maturity (YTM), but because Bond J has a lower coupon rate of 5% and Bond K a higher coupon rate of 11%, their sensitivity to interest rate changes will differ.

When interest rates increase, the price of existing bonds typically falls. This is because new bonds are issued at the new higher rates, making the existing bonds with lower rates less attractive. Since Bond J has a lower coupon rate, it is more sensitive to interest rate changes, and its price will decrease more significantly than Bond K's, which has a higher coupon rate.

To determine the exact percentage price change, you would need to perform a bond price calculation using the new yield to maturity, which would be the original YTM plus the 2% increase. However, this requires additional information and more complex financial formulas which go beyond the scope of this explanation.

Answer 2

Bond J -16.33%

Bond K -14.04%

Step-by-step 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%