Question

CraMerica has 8% coupon bond issue with 8 years to maturity. Each of these bonds make semi-annual interest payments. These bonds have a yield to maturity of 10%. Suddenly, the yield to maturity on these bonds fall to 8%. What is the percentage change in the price of these bonds. Assume a par value of $1,000. Enter your answer to two decimal plances with no percentage sign. That is, like this: 13.61

Answer 1

Price of semi-annual interest bond

= Semi-annual interest * PVIFA _{[Yield to maturity/2, (Period*2)]} + Maturity value * PVIF _{[Yield to maturity/2, (Period*2)]}

Price of the bond when  yield to maturity is 10%

= $40 * PVIFA _{[5 %, 16]} + $1000 * PVIF _{[5 %, 16]}

=($40 *10.8378) + ($1000 *  0.4581)

= $892

Price of the bond when  yield to maturity is 8%

Note : When coupon rate of the bond =  yield to maturity of the bond, then price of the bond = face value of the bond

= $1000

Percentage change in the price of these bonds

= (Price of the bond when  yield to maturity is 10% - Price of the bond when  yield to maturity is 8%) / Price of the bond when  yield to maturity is 10%

= ($892 - $1000 ) / $892 = 12.11