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- Certificate in Quantitative Finance (CQF) Exam Guide
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**Table of Contents**

## What is Coupon Rate Formula?

The term “coupon rate” refers to the rate of interest paid to the bondholders by the bond issuers. In other words, it is the stated rate of interest paid on fixed income securities, primarily applicable to bonds. The formula for coupon rate is computed by dividing the sum of the coupon payments paid annually by the par value of the bond and then expressed in terms of percentage.

Mathematically, Coupon Rate Formula represented as,

**Coupon Rate Formula= Total Annual Coupon Payment / Par Value of Bond * 100%**

Conversely, the equation of the coupon rate of a bond can be seen as the percentage of the face value or par value of the bond paid every year.

### Explanation of the Coupon Rate Formula

The formula for coupon rate can be computed by using the following steps:

**Step 1: **Firstly, figure out the face value or par value of the issued bond. It will be easily available in the funding proposal or the accounts department of the company.

**Step 2:** Next, determine the no. of periodic payments made during the course of a year. Then all the periodic payments are added up to calculate the total coupon payment during the year. In case of equal periodic payments, the total annual coupon payment can be computed by multiplying the periodic payments and the no. of payments made in the year.

**Total annual coupon payment = ****Periodic payment * No. of payments in a year**

**Step 3: **Finally, the equation of the coupon rate of the bond is calculated by dividing the total annual coupon payment by the par value of the bond and multiplied by 100% as shown above.

**Examples of Coupon Rate Formula (with Excel Template)**

Let’s see some simple to advanced examples of the Coupon Rate Formula to understand it better.

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#### Coupon Rate Formula – Example #1

**Let us take an example of bond security with half-yearly coupon payments. Let us assume a company PQR Ltd has issued a bond having the face value of $1,000 and quarterly interest payments of $25. Do the Calculation of the coupon rate of the bond.**

Use the following data for the calculation of Coupon Rate Formula.

**Annual Coupon Payment**

- Annual coupon payment = 2 * Half yearly coupon payment
- = 2 * $25
- = $50

Therefore, the calculation of the coupon rate of the bond is as follows –

- Coupon Rate Formula
**=**$50 / $1,000 * 100%

**Coupon Rate of the Bond will be –**

Therefore, the coupon rate of the bond issued by PQR Ltd is 5%.

#### Coupon Rate Formula – Example #2

**Let us take another example of bond security with unequal periodic coupon payments. Let us assume a company XYZ Ltd has paid periodic payments of $25 at the end of 4 months, $15 at the end of 9 months and another $15 at the end of the year. Do the Calculation of the coupon rate of the bond if the par value is $1,000.**

Use the following data for the calculation of Coupon Rate Formula.

Therefore, the calculation of the coupon rate of the bond is as follows,

- Coupon Rate Formula
**=**$55 / $1,000 * 100%

**Coupon Rate of the Bond will be –**

- Coupon Rate of The Bond = 5.50%

Therefore, the coupon rate of the bond issued by XYZ Ltd is 5.5%.

#### Coupon Rate Formula – Example #3

**Dave and Harry are two bondholders of ABC Ltd. The company has made equal quarterly payments of $25. The par value of the bond is $1,000 and it is trading $950 in the market. Determine which statement is correct:**

**Dave said that the coupon rate is 10.00%****Harry said that the coupon rate is 10.53%**

Use the following data for the calculation of Coupon Rate Formula.

**Annual Coupon Payment**

- Annual coupon payment = 4 * Quarterly coupon payment
- = 4 * $25
- = $100

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

- Coupon Rate Formula
**=**$100 / $1,000 * 100%

**Coupon Rate of the Bond will be –**

- Coupon rate of bond = 10.00%

Therefore, Dave is correct. [Harry has mistakenly used market price of $950 in the place of par value for the calculation of coupon rate i.e. $100 / $950 * 100% = 10.53%]

### Relevance and Uses of Coupon Rate Formula

It is important to understand the concept of coupon rate equation because almost all types of bonds pay annual payment to the bondholder, which is known as coupon payment. 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 market value of the bond.

Based on coupon rate and the prevailing market rate of interest, it can be determined whether a bond will trade at a premium, par or discount.

- A bond trades at a premium when the coupon rate is higher than the market interest rate, which means that the price of the bond will fall because an investor will be reluctant to purchase the bond at that value.
- Again the bond will trade at a discount when the coupon rate is lower than the market interest rate, which means the price of the bond will increase because an investor will be willing to purchase the bond at a higher value.
- A bond trades at par when the coupon rate is equal to the market interest rate.

### Recommended Articles

This has been a guide to what is Coupon Rate Formula. Here we discuss how to calculate the Coupon Rate of the Bond using practical examples and downloadable excel template. You can learn more about Accounting from the following articles –

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