Question

do not round

Suppose a seven-year, $1,000 bond with an 8.2% coupon rate and semiannual coupons is trading with a yield to maturity of 6.42%. 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 7.28% (APR with semiannual compounding), what price will the bond trade for?

Answer 1

a)

Bond is trading at PREMIUM

When coupon rate is more than yield to maturity, bonds will always sell at premium. This is because the issuer the providing a coupon rate more than what the market is offering. Therefore, the issuer will charge a premium for its bonds.

b)

Coupon = (0.082 * 1000) / 2 = 41

Number of periods = 7 * 2 = 14

Rate = 7.28% / 2 = 3.64%

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

Price = 41 * [1 - 1 / (1 + 0.0364)¹⁴] / 0.0364 + 1000 / (1 + 0.0364)¹⁴

Price = 41 * [1 - 0.606201] / 0.0364 + 606.200569

Price = 41 * 10.818654 + 606.200569

Price = $1,049.77