Chapter 6, Problem 6.1C

Section 6.1    What is the coupon rate on a bond that has a par value of $1,000, a market value of $1,100, and a coupon interest rate of $100 per year?

Summary Introduction

To determine: The bond’s coupon rate.

Introduction:

A bond refers to the debt securities issued by the governments or corporations for raising capital. The borrower does not return the face value until maturity. However, the investor receives the coupons every year until the date of maturity.

A coupon refers to the interest payment that the issuer guarantees to pay on the bond. The coupon payment per year divided by the face value is the coupon rate of the bond.

Answer to Problem 6.1C

The coupon rate of the bond is 10%.

Explanation of Solution

Given information:

The par value of a bond is $1,000 and its market value is $1,100. The bond pays a coupon interest rate of $100 per year.

The formula to calculate coupon rate:

$\text{Coupon rate}=\frac{\text{Annual coupon payment}}{\text{Face value of the bond}}\times 100$

Compute the coupon rate as follows:

The annual coupon payment of the bond is $100. The face value of the bond is $1,000.

$\begin{array}{c}\text{Coupon rate}=\frac{\text{Annual coupon payment}}{\text{Face value of the bond}}\times 100\\ =\frac{\$100}{\$1,000}\times 100\\ =10\%\end{array}$

Hence, the annual coupon rate is 10%.