What is Coupon Bond Formula?
The term “coupon bond” refers to bonds that pay coupons which is a nominal percentage of the par value or principal amount of the bond. The formula for calculation of the price of this bond basically uses the present value of the probable future cash flows in the form of coupon payments and the principal amount which is the amount received at maturity. The present value is computed by discounting the cash flow using yield to maturity.
Mathematically, it the price of a coupon bond is represented as follows,
where
- C = Periodic coupon payment,
- P = Par value of bond,
- YTM = Yield to maturity
- n = No. of periods till maturity
Calculation of the Coupon Bond (Step by Step)
The formula for coupon bond calculation can be done by using the following steps:
- Step 1: Firstly, determine the par value of the bond issuance and it is denoted by P.
- Step 2: Next, determine the periodic coupon payment based on the coupon rate of the bond based, the frequency of the coupon payment and the par value of the bond. The coupon payment is denoted by C and it is calculated as, C = Coupon rate * P / Frequency of coupon payment
- Step 3: Next, determine the total number of periods till maturity by multiplying the frequency of the coupon payments during a year and the number of years till maturity. The number of periods till maturity is denoted by n and it is calculated as, n = No. of years till maturity * Frequency of coupon payment
- Step 4: Now, determine the yield to maturity on the basis of the current market return from an investment with similar risk profile. The yield to maturity is denoted by YTM.
- Step 5: Next, determine the present value of the first coupon, second coupon and so on. Then, determine the present value of the par value of the bond.
- Step 6: Finally, the formula for determination of the coupon bond calculation is done by adding the present value of all the coupon payments and the par value as shown below.
Examples
Example #1
Let us take an example of bonds issued by company XYZ Ltd that pays coupons annually. The company plans to issue 5,000 such bonds and each bond has a par value of $1,000 with a coupon rate of 7% and it is to mature in 15 years. The effective yield to maturity is 9%. Determine the price of each bond and the money to be raised by XYZ Ltd through this bond issue.
Below is given data for the calculation of the coupon bond of XYZ Ltd.
The price of each bond is calculated using the below formula as,
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Therefore, calculation of the Coupon Bond will be as follows,
So it will be –
= $838.79
Therefore, each bond will be priced at $838.79 and said to be traded at discount (bond price lower than par value) because the coupon rate is lower than the YTM. XYZ Ltd will be able to raise $4,193,950 (= 5,000 * $838.79).
Example #2
Let us take an example of bonds issued by company ABC Ltd that pays semi-annual coupons. Each bond has a par value of $1,000 with a coupon rate of 8% and it is to mature in 5 years. The effective yield to maturity is 7%. Determine the price of each C bond issued by ABC Ltd.
Below is given data for the calculation of the coupon bond of ABC Ltd.
Therefore, the price of each bond can be calculated using the below formula as,
Therefore, calculation of the Coupon Bond will be as follows,
So it will be –
= $1,041.58
Therefore, each bond will be priced at $1,041.58 and said to be traded at a premium (bond price higher than par value) because the coupon rate is higher than the YTM.
Relevance and Uses
The concept of pricing of this kind of bond is very important from the perspective of an investor because bonds are an indispensable part of the capital markets. The purchaser of a bond receives these coupon payments during the period between the issuance of the bond and the maturity of the bond. In the bond market, bonds with higher coupon rates are considered to be more attractive for investors because they offer higher yields.
Further, bonds trading at a value higher than their par value is said to be traded at a premium, while the bonds trading at a value lower than their par value is said to be traded at discount. Nowadays, these bonds are quite uncommon because most recent bonds are not issued in coupon or certificate form, rather the bonds are issued electronically.
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