Question

Suppose a seven-year, $1,000 bond with a 7.5% coupon rate and semi-annual coupons is trading with a yield to maturity of 6.72%.

a. Is this bond currently trading at a discount, at par, or at a premlum? Explain.
b. If the yield to maturity of the bond rises to 7.47% (APR with semi-annual compounding), what price will the bond trade for?

Answer 1

The bond is trading at a premium and its price will be $984.59 if the yield to maturity rises to 7.47%.

Step-by-step explanation:

a. To determine whether the bond is trading at a discount, at par, or at a premium, we need to compare the coupon rate with the yield to maturity. In this case, the coupon rate of 7.5% is higher than the yield to maturity of 6.72%. This means that the bond is trading at a premium.

b. If the yield to maturity rises to 7.47%, we can use the present value formula to calculate the new bond price. The bond has semi-annual coupons, so the total number of periods is 14 (7 years multiplied by 2). With the new yield to maturity and the coupon rate, we can calculate the new bond price to be $984.59.