Bond Pricing Formula

What is Bond Pricing Formula?

The formula for bond pricing is basically the calculation of the present value of the probable future cash flows which comprises of the coupon payments and the par value which is the redemption amount on maturity. The rate of interest which is used to discount the future cash flows is known as the yield to maturity (YTM.)

The bond pricing formula for coupon paying bonds is mathematically represented as,

or

where C = Periodic coupon payment,

• F = Face / Par value of bond,
• r = Yield to maturity (YTM) and
• n = No. of periods till maturity

On the other, the bond valuation formula for deep discount bonds or zero coupon bonds can be computed simply by discounting the par value to present value which is mathematically represented as,

Zero Coupon Bond Price =  (as the name suggests, there are no coupon payments)

Explanation of the Bond Pricing Formula

The formula for Bond Pricing calculation by using the following steps:

Step 1: Firstly, the face value or par value of the bond issuance is determined as per the funding requirement of the company. The par value is denoted by F.

Step 2: Now, the coupon rate, which is analogous to interest rate, of the bond and the frequency of the coupon payment is determined. The coupon payment during a period is calculated by multiplying coupon rate and the par value and then dividing the result by the frequency of the coupon payments in a year. The coupon payment is denoted by C.

C = Coupon rate * F / No. of coupon payments in a year

Step 3: Now, the total number of periods till maturity is computed by multiplying the number of years till maturity and the frequency of the coupon payments in a year. The number of periods till maturity is denoted by n.

n = No. of years till maturity * No. of coupon payments in a year

Step 4: Now, the yield to maturity (YTM) is the discounting factor and it is determined based on the current market return from an investment with similar risk profile. The YTM is denoted by r.

Step 5: Now, the present value of the first, second, third coupon payment and so on so forth along with the present value of the par value to be redeemed after n periods is derived as,

Step 6: Finally, adding together the present value of all the coupon payments and the par value gives the bond price as below,

Examples of Bond Pricing Formula (with Excel Template)

Below are some of the Examples of Bond Pricing Formula.

Example #1

Let us take an example of a bond with annual coupon payments. Let us assume a company XYZ Ltd has issued a bond having a face value of $100,000 carrying an annual coupon rate of 7% and maturing in 15 years. The prevailing market rate of interest is 9%.

• Given, F = $100,000
• C = 7% * $100,000 = $7,000
• n = 15
• r = 9%

The price of the bond calculation using the above formula as,

• Bond price Equation = $83,878.62

Since the coupon rate is lower than the YTM, the bond price is less than the face value and as such the bond is said to be traded at discount.

Example #2

Let us take an example of a bond with semi-annual coupon payments. Let us assume a company ABC Ltd has issued a bond having the face value of $100,000 carrying a coupon rate of 8% to be paid semi-annually and maturing in 5 years. The prevailing market rate of interest is 7%.

Hence, the price of the bond calculation using the above formula as,

• Bond price Equation = $104,158.30

Since the coupon rate is higher than the YTM, the bond price is higher than the face value and as such, the bond is said to be traded at a premium.

Example #3

Let us take the example of a zero coupon bond. Let us assume a company PQR Ltd has issued zero coupon bond having face value of $100,000 and maturing in 4 years. The prevailing market rate of interest is 10%.

Hence, the price of the bond calculation using the above formula as,

• Bond price Equation= $68,301.35 ~ $68,301

Relevance and Uses of Bond Pricing Formula

The concept of bond pricing is very important because bonds form an indispensable part of the capital markets, and as such investors and analysts are required to understand how the different factors of a bond behave in order to determine its intrinsic value. Similar to stock valuation, the pricing of a bond is helpful in understanding whether it is a suitable investment for a portfolio and consequently forms an integral part of bond investing.

Recommended Articles

This has been a guide to Bond Pricing Formula. Here we discuss how to perform bond pricing calculations along with practical examples and downloadable excel templates. You may learn more about Fixed Income from the following articles –

• Absolute Valuation Formula
• Terms Related to Coupon Bond
• Sinking Fund Formula | Examples
• Explanation of Coupon Rate Formula
• Intrinsic Value Formula
• Calculate Convexity of a Bond
• Bonds Payable Balance Sheet
• What is Bond Sinking Fund?
• Compare Bonds and Debentures