Problem 1: Consider a bond paying a coupon rate of 6% per year semiannually (i.e. it pays $30 every six months) when the market interest rate at all maturities is only 2.5% per half year. The bond has three years until maturity.
a. What is the bond’s price today?
b. What will the bond’s price be in six months after the next coupon is paid?
c. What is the total (six month) return on this bond?
Problem 2: The yield to maturity on one-year zero-coupon bonds is currently 4%. The YTM on two-year zeros is 5%. The Treasury plans to issue a two-year maturity coupon bond, paying coupons once per year with a coupon rate of 5.5%. The face value of the bond is $1000.
a. At what price will the bond sell?
b. What will the yield to maturity on the bond be?
c. If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year?
Problem 3: What is the duration of an eight year bond which pays a single annual coupon of $60 if interest rates are 6%. What is the value of this bond? What will its value be if interest rates suddenly (and immediately) jump to 8%? Compare the percentage change in this bond’s value to the percentage change in the value of a eight-year zero-coupon bond.