Question

​(Related to Checkpoint​ 9.3)  ​(Bond valuation) Doisneau 15​-year bonds have an annual coupon interest of 11 ​percent, make interest payments on a semiannual​ basis, and have a ​$1 comma 000 par value. If the bonds are trading with a​ market's required yield to maturity of 15 ​percent, are these premium or discount​ bonds? Explain your answer. What is the price of the​ bonds? a. If the bonds are trading with a yield to maturity of 15​%, then ​ (Select the best choice​ below.) A. the bonds should be selling at a discount because the​ bond's coupon rate is less than the yield to maturity of similar bonds. B. there is not enough information to judge the value of the bonds. C. the bonds should be selling at a premium because the​ bond's coupon rate is greater than the yield to maturity of similar bonds. D. the bonds should be selling at par because the​ bond's coupon rate is equal to the yield to maturity of similar bonds. b.  The price of the bonds is ​$ nothing. ​ (Round to the nearest​ cent)

Answer 1

a. Since the bonds are trading at a yield higher than the coupon rate, the bonds will be trading at a discount. This is because the rate of discount which is higher than the coupon rate will be in the denominator and hence will be reducing the value of the bond more than the coupons can increase it (from a mathematical perspective). Option A.

b. We find the value of the bonds by using the formula for discounting:

Value of bond = 55/1.075^1 + 55/1.075^2 + ...... +55/1.075^29 + 1055/1.075^30

= $763.79