You are considering an investment in two different bonds. One bond matures in seven years and has a face value of $1,000. The bond pays an annual coupon of 5.25% and has an 8% yield to maturity. The other bond is a 6-year zero coupon bond with a face value of $1,000, and it also has a yield to maturity of 8%.
What is the price of each bond?
What is the duration of each bond? Refer to Web Appendix 7B and the Web App 7B tab in the Chapter 7 spreadsheet model (both are on the e-Learning site).
If the yield to maturity of each bond were to immediately increase to 11%, what would be the percentage change (including the correct sign) in the price of each bond (from the price found in part a)?
If the yield to maturity of each bond were to immediately decrease to 5%, what would be the percentage change (including the correct sign) in the price of each bond (from the price found in part a)?
Assume that you plan on holding the coupon bond for seven years and reinvesting all the coupons when they are received at the going interest rate (which is the yield to maturity). Assume that after the zero matures you invest in a 1-year security that earns the going interest rate.
Set up a table where you show what happens to the value of each investment (zero and coupon bond) over time if the yield to maturity remains at 8%. Specifically, show what the cumulative value of each investment (including the value of the reinvested coupons for the coupon bond) would be at the end of each of the next seven years. For example, at the end of Year 1, you would calculate the value of the coupon bond (with one year less remaining until maturity) and you would receive the interest coupon payment. However, no interest would be earned on that interest coupon payment in Year 1. (However, that coupon payment will remain in your account and earn interest in the years that follow.) The sum of these two amounts would be the cumulative value for the coupon bond at the end of Year 1.
Set up a table where you show what happens to the value of each investment (zero and coupon bond) over time if the yield to maturity immediately and permanently increases to 11%. Specifically, show what the cumulative value of each investment (including the value of the reinvested coupons for the coupon bond) would be at the end of each of the next seven years.
Set up a table where you show what happens to the value of each investment (zero and coupon bond) over time if the yield to maturity immediately and permanently decreases to 5%. Specifically, show what the cumulative value of each investment (including the value of the reinvested coupons for the coupon bond) would be at the end of each of the next seven years.
Plot on two graphs (one for the coupon bond and one for the zero) the cumulative value of the investment over the next seven years under each of the three scenarios outlined above.
Roughly speaking, after how many years would the value of the investment be the same regardless of what happens to interest rates? What can explain this?