Question

Problem 6-25 Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%....

 Problem 6-25 Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%. You hold the bond for five years before selling it. Note: assume \$100 face value. a. If the bond’s yield to maturity is 6% when you sell it, what is the annualized rate of return of your investment? b. If the bond’s yield to maturity is 7% when you sell it, what is the annualized rate of return of your investment? c. If the bond’s yield to maturity is 5% when you sell it, what is the annualized rate of return of your investment? d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain. Maturity (years) 30 Face value \$               100 Yield to maturity 6% Holding period (years) 5 a. If the bond’s yield to maturity is 6% when you sell it, what is the annualized rate of return of your investment? Purchase price Maturity when sold (years) Bond price when sold Rate of return b. If the bond’s yield to maturity is 7% when you sell it, what is the annualized rate of return of your investment? Yield to maturity 7% Bond price when sold Rate of return c. If the bond’s yield to maturity is 5% when you sell it, what is the annualized rate of return of your investment? Yield to maturity 5% Bond price when sold Rate of return d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain. If you sell prior to maturity, you are exposed to the risk that the may change.

a) Purchase Price = FV / (1 + r)^n = \$100 / (1 + 6%)^30 = \$17.41

Sell Price = 100 / (1 + 6%)^25 = \$23.30

Rate of return = (23.30 / 17.41)^(1/5) - 1 = 6%

b) Sell Price = 100 / 1.07^25 = \$18.42

Rate of return = (18.42 / 17.41)^(1/5) - 1 = 1.14%

c) Sell Price = 100 / 1.05^25 = \$29.53

Rate of return = (29.53 / 17.41)^(1/5) - 1 = 11.14%

d) No. There are interest rate risk when you invest in bond markets, which will impact returns on bond. Hence, the realized returns would be different than expected if interest rates change over a period of time.