Question

Suppose a​ seven-year, $1,000 bond with a 7.6% coupon rate and semiannual coupons is trading with a yield to maturity of 6.54%.

a. Is this bond currently trading at a​ discount, at​ par, or at a​ premium? Explain.

b. If the yield to maturity of the bond rises to 7.33% (APR with semiannual​ compounding), what price will the bond trade​ for?

a. Is this bond currently trading at a​ discount, at​ par, or at a​ premium? Explain.  ​(Select the best choice​ below.)

A. Because the yield to maturity is greater than the coupon​ rate, the bond is trading at a premium.

B. Because the yield to maturity is less than the coupon​ rate, the bond is trading at a premium.

C. Because the yield to maturity is less than the coupon​ rate, the bond is trading at a discount.

D. Because the yield to maturity is greater than the coupon​ rate, the bond is trading at par.

b. If the yield to maturity of the bond rises to7.33% ​(APR with semiannual​ compounding), what price will the bond trade​ for?The new price of the bond is

​$______. (Round to the nearest​ cent.)

Answer 1

a)

B. Because the yield to maturity is less than the coupon​ rate, the bond is trading at a premium.

When yield to maturity is less than coupon rate, bond will sell at premium. This is because the bond is offereing a coupon rate more than what is being offered in the market. So the bond is offering 7.6% whereas the market is offering 6.54%. Since bond is offereing a higher coupon rate, company will also demand a premium from the investor.

b)

Semi annual coupon = (7.6% of 1000) / 2 = 38

Number of periods = 7 * 2 = 14

Semi annual rate = 7.33% / 2 = 3.665%

Price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price = 38 * [1 - 1 / (1 + 0.03665)^14] / 0.03665 + 1000 / (1 + 0.03665)^14

Price = 38 * [1 - 0.604157] / 0.03665 + 604.157083

Price = 38 * 10.800629 + 604.157083

Price = $1,014.58