Problem 1: Consider a bond paying a coupon rate of 10% per year semiannually when the market interest rate is only 4% per half year. The bond has three year until maturity.
(a) Find the bond's price today and six months from now after the next coupon is paid.
(b) What is the total (six month) rate of return on the bond?
Problem 2: Assume you have one-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1000 at maturity. The second has an 8% coupon rate and pays the $80 coupon once per year. The third has a 10% coupon rate and pays the $100 coupon once per year.
(a) If all three bonds are now priced to yield 8% to maturity. What are their prices?
(b) If you expect their yield to maturity to be 8% at the beginning of next year, what will their prices be then? What is your before-tax holding period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your after-tax rate of return be on each?
(c) Recalculate your answer to (b) under the assumption that you expect the yields to maturity on each bond to be 7% at the beginning of next year.