Coupon Rate of a Bond (Formula, Definition)

What is the Coupon Rate of a Bond?

Coupon Rate is mostly applied to bonds and it is usually the ROI (rate of interest) that is paid on the face value of a bond by the issuers of bond and it is also used to calculate the repayment amount that is made by GIS (guaranteed income security).

Formula

The coupon rate of a bond can be calculated by dividing the sum of the annual coupon payments by the par value of the bond and multiplied by 100%. Therefore, the rate of a bond can also be seen as the amount of interest paid per year as a percentage of the face value or par value of the bond. Mathematically, it is represented as,

Coupon Rate = Annualized Interest Payment / Par Value of Bond * 100%

The bond price varies based on the coupon rate and the prevailing market rate of interest. If the coupon rate is lower than the market interest rate, then the bond is said to be traded at discount, while the bond is said to be traded at a premium if the coupon rate is higher than the market interest rate. Nevertheless, the bond is said to be traded at par if the coupon rate is equal to the market interest rate

Steps to Calculate the Bond’s Coupon Rate

The steps to calculate the coupon rate of a bond are the following:

Step #1: Firstly, the face value or par value of the bond issuance is determined as per the funding requirement of the company.
Step #2: Now, the number of interest paid during the year is determined and then the annualized interest payment is calculated by adding up all the payments during the year.

Annual interest payment = Periodic interest payment * No. of payments in a year

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Step #3: Finally, the formula of the coupon rate of the bond is calculated by dividing the annualized interest payments by the par value of the bond and multiplied by 100% as shown below.

Examples

Let us take the example of a bond with quarterly coupon payments. Let us assume a company XYZ Ltd has issued a bond having a face value of $1,000 and quarterly interest payments of $15.

If the prevailing market rate of interest is 7%, then the bond will be traded at _______
If the prevailing market rate of interest is 6%, then the bond will be traded at _______
If the prevailing market rate of interest is 5%, then the bond will be traded at _______

As per the given question,

Par value of bond = $1,000

Annual interest payment = 4 * Quarterly interest payment

= 4 * $15
= $60

Therefore, the coupon rate of the bond can be calculated using the above formula as,

Since the coupon (6%) is lower than the market interest (7%), the bond will be traded at discount.
Since the coupon (6%) is equal to the market interest (7%), the bond will be traded at par.
Since the coupon (6%) is higher than the market interest (5%), the bond will be traded at a premium.

Drivers of Coupon Rate of a Bond

When a bond is issued in the open market by a company, it arrives at the optimal coupon rate based on the prevailing rate of interest in the market to make it competitive. Also, the issuer’s creditworthiness drives the coupon rate of a bond i.e. a company rated “B” or below by any of the top rating agencies is likely to offer a higher coupon rate than the prevailing market interest rate to counterbalance the additional credit risk taken by the investors. In short, the coupon rate is influenced by the market interest rates and the issuer’s creditworthiness.

Relevance and Uses

Coupon Rate is referred to the stated rate of interest on fixed income securities such as bonds. In other words, it is the rate of interest that the bond issuers pay to the bondholders for their investment. It is the periodic rate of interest paid on the bond’s face value to its purchasers. It is to be noted that the coupon rate is calculated based on the bond’s face value or par value, but not based on the issue price or market value.

It is quintessential to grasp the concept of the rate because almost all types of bonds pay annual interest to the bondholder, which is known as the coupon rate. Unlike other financial metrics, the coupon payment in terms of the dollar is fixed over the life of the bond. For example, if a bond with a face value of $1,000 offers a coupon rate of 5%, then the bond will pay $50 to the bondholder until its maturity. The annual interest payment will continue to remain $50 for the entire life of the bond until its maturity date irrespective of the rise or fall in the market value of the bond.

Another important facet of the rate is that if the prevailing market interest rate is higher than the rate of the bond, then the price of the bond is expected to fall because an investor will be reluctant to purchase the bond at that face value now, as they can get a better rate of return elsewhere. On the other hand, if the prevailing market interest rate is lower than the coupon rate of the bond, then the price of the bond is expected to increase because it will pay a higher return on investment than an investor can make by purchasing a similar bond now, as the coupon rate will be lower resulting in the in an overall decline in interest rates.