Question

Suppose a​ seven-year, $1,000 bond with a 8.58% coupon rate and semiannual coupons is trading with a yield to maturity of 7.09%.

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 7.40% ​(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 a premium because the coupon rate is greater than the yield to maturity

D.

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

Answer 1

Bond whose coupon rate is equal to the YTM, trades at par value.

Bond whose coupon rate is greater than YTM, trades at premium.

Bond whose coupon rate is lower than YTM, trades at discount.

In the present case, coupon rate is greater than YTM and hence the bond must be trading at a premium.

So, the correct answer is option C.

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 8.58% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 42.9

The YTM will be as follows:

= 7.40% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.7% or 0.037

N will be as follows:

= 7 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 14

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 42.9 x [ [ (1 - 1 / (1 + 0.037)¹⁴ ] / 0.037 ] + $ 1,000 / 1.037¹⁴

= $ 42.9 x 10.77544342 + $ 601.3085935

= $ 1,063.58

Feel free to ask in case of any query relating to this question