Answer :
The coupon rate of a corporate bond with a current yield of 6.39 percent and a price quote of 97.8 is calculated by dividing the annual coupon payment by the bond's price to find the payment amount and then dividing that by the face value of the bond. The correct coupon rate is 6.25 percent. Therefore the correct answer is option b.
To determine the coupon rate of a corporate bond with a current yield of 6.39 percent and a price quote of 97.8, we need to understand the relationship between the bond's price, its current yield, and its coupon rate. The current yield is calculated by dividing the annual coupon payment by the bond's price. In this case, let the coupon payment be represented by 'C'.
Current Yield = Annual Coupon Payment / Bond Price
6.39% = C / 97.8
To find the annual coupon payment in dollar terms, we multiply both sides of the equation by the bond price: C = 6.39% \ imes 97.8. Once we have the dollar amount for 'C,' we can find the coupon rate by dividing it by the face value of the bond, typically $1,000 for corporate bonds:
Coupon Rate = (C / $1,000) \ imes 100
Executing the computation, if we assume the face value is $1,000 (as it is standard for most corporate bonds), we find the coupon rate by first calculating C:
C = 0.0639 \ imes 97.8
= $6.25
Then the coupon rate is:
Coupon Rate = ($6.25 / $1,000) \ imes 100
= 6.25%
Therefore, the coupon rate of the bond is 6.25 percent, which corresponds to option b.