Question

A $1,000 par value bond with eight years left to maturity pays an interest rate payment semiannually with a 7.75 percent coupon rate and is priced to have a 4.25 percent yield to maturity. If interest rates increase by 1 percent, by how much would the bond's price change

Answer 1

$ 73.66

Step-by-step explanation:

The initial price is derived using the pv formula in excel as below:

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

rate is the yield to maturity of 4.25% divided by 2 i.e =2.125%

nper is the number of coupons the bond would pay which 8 years multiplied by 2 i.e 16

pmt is the semiannual coupon=$1000*7.75%*6/12=$38.75

fv is the face value of $1000

=-pv(2.125%,16,38.75,1000)=$ 1,235.27

1% increase in yield to maturity:

=-pv(5.25%/2,16,38.75,1000)=$ 1,161.61

The price would fall to $ 1,161.61 if interest rate rises by 1%

Change in bond's price=$ 1,235.27-$ 1,161.61 =$ 73.66