Coupon Rate

Study guide: Exam FM-2

The coupon rate $r$ is the rate applied to the face value $F$ of a bond to determine each periodic interest payment.

$r = \frac{\text{Coupon}}{F}$

For a bond paying semi-annually with a $6\%$ annual coupon rate, the per-period coupon rate is $r = 3\%$ .
The coupon rate is fixed at issuance and does not change over the life of the bond.
It is distinct from the Yield Rate $j$ , which reflects the bond's actual return given its market price.
When the coupon rate equals the yield rate ( $r = j$ for $F = C$ ), the bond prices at par.
The coupon rate determines the size of the coupon cash flows; the yield rate determines how those cash flows are discounted.

Identifying the Coupon Rate A bond with face value $ $1{,}000$ pays annual coupons of $ $45$ . What is the annual coupon rate, and is the bond trading at a premium or discount if the yield rate is $5\%$ ?

Answer $r = \frac{45}{1000} = 4.5\%$ Since the coupon rate ( $4.5\%$ ) is less than the yield rate ( $5\%$ ), we have $Fr < Cj$ , so the bond sells at a discount (price below face value).