A twelve-year corporate bond has a coupon rate of 9%, a face value of $1,000, and a yield to maturity of 11%. Assume annual interest payments.
(i) What is the current price?
(ii) What is the duration (Macaulay’s)?
(iii) Compare this bond to a eight-year zero coupon bond. Which has more interest-rate risk (which bond price changes more given a 1 percentage point change in the interest rate)?
(iv) Using duration, what is the change in price of the bond if there was a parallel shift in interest rates and rates rose 3 percentage points?
(v) What is the true current price if interest rates rose 3 percentage points?
(vi) Why are the answers different?