Question

Suppose a​ seven-year, $1,000 bond with a 11.94 % coupon rate and semiannual coupons is trading with a yield to maturity of 9.79 %. a. Is this bond currently trading at a​ discount, at​ par, or at a​ premuim? Explain. b. If the yield to maturity of the bond rises to 10.26 % ​(APR with semiannual​ compounding), at what price will the bond​ trade? a. Is this bond currently trading at a​ discount, at​ par, or at a​ premuim? Explain. The bond is currently trading...  ​(Select the best choice​ below.)

A. ... at a discount because the coupon rate is greater than the yield to maturity

B. ... at a premium because the yield to maturity is greater than the coupon rate.

C. ... at par because the coupon rate is equal to the yield to maturity

D. ... at a premium because the coupon rate is greater than the yield to maturity Your answer is correct.

b. If the yield to maturity of the bond rises to 10.26 % ​(APR with semiannual​ compounding), at what price will the bond​ trade? The bond will trade for ​$ nothing. ​(Round to two decimal​ places.)

Answer 1

(a) Par Value = $ 1000, Tenure = 7 years, Coupon Rate (Offered Rate) = 11.94% and Yield (Required Rate) = 9.79 %, Coupon Frequency: Semi-Annual

The bond will trade at a premium as the coupon rate (offered rate of return) is greater than the yield to maturity (required/desired rate of return).

Hence, the correct option is (D)

(b) Applicable Yield = 10.26 %, Tenure = 7 years or (7 x 2) = 14 half-years

Semi-Annual Yield = 10.26 / 2 = 5.13 %

Semi-Annual Coupon = 0.1194 x 1000 x 0.5 = $ 59.7

Therefore, Bond Price = 59.7 x (1/0.0513) x [1-{1/(1.0513)^(14)}] + 1000 / (1.0513)^(14) = $ 1082.4617 ~ $ 1082.46