Formula to Calculate Coupon Rate
Coupon Rate Formula is used for the purpose of calculating the coupon rate of the bond and according to the formula coupon rate of the bond will be calculated by dividing the total amount of annual coupon payments with the par value of the bonds and multiplying the resultant with the 100.
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.
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.
Coupon Rate Calculation (Step by Step)
The coupon rate can be calculated by using the following steps:
- Step 1: Firstly, figure out the face value or par value of the issued bonds. 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 the 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 coupon rate is calculated by dividing the total annual coupon payment by the par value of the bond and multiplied by 100%, as shown above.
Examples
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.
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 –
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Coupon Rate of the Bond will be –
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.
Therefore, the calculation of the coupon rate of the bond is as follows,
Coupon Rate of the Bond will be –
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%
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 of the Bond will be –
Therefore, Dave is correct. [Harry has mistakenly used the 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
It is important to understand the concept of coupon rate 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 the market value of the bond.
Based on the 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.
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