Bond Pricing Formula

Formula to Calculate Bond Price

The formula for bond pricingBond PricingThe bond pricing formula calculates the present value of the probable future cash flows, which include coupon payments and the par value, which is the redemption amount at maturity. The yield to maturity (YTM) refers to the rate of interest used to discount future cash flows.read more 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.)

Bond Price = ∑i=1n C/(1+r)n + F/(1+r)n

or

Bond Price = C*  (1-(1+r)-n/r ) + F/(1+r)n

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For eg:
Source: Bond Pricing Formula (wallstreetmojo.com)

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 bondsZero-coupon BondsIn contrast to a typical coupon-bearing bond, a zero-coupon bond (also known as a Pure Discount Bond or Accrual Bond) is a bond that is issued at a discount to its par value and does not pay periodic interest. In other words, the annual implied interest payment is included into the face value of the bond, which is paid at maturity. As a result, this bond has only one return: the payment of the nominal value at maturity.read more can be computed simply by discounting the par value to the present value, which is mathematically represented as,

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

Bond Pricing Calculation (Step by Step)

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

  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.

  2. Now, the coupon rate, which is analogous to the interest rate of the bond and the frequency of the coupon payment, is determined. The coupon payment during a period is calculated by multiplying the 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

  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

  4. Now, the YTM is the discounting factor, and it is determined based on the current market return from an investment with a similar risk profile. The YTM is denoted by r.

  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,


    PV of 1st coupon payment

    PV of 2nd coupon payment

    PV of 3rd coupon payment

    PV of nth coupon payment

    PV of Par Value

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


    bond price

Practical Examples (with Excel Template)

You can download this Bond Pricing Formula Excel Template here – Bond Pricing Formula Excel Template

Example #1

Let us take an example of a bondExample Of A BondA bond is financial instrument that denotes the debt owed by the issuer to the bondholder. Issuer is liable to pay the coupon (an interest) on the same. These are also negotiable and the interest can be paid monthly, quarterly, half-yearly or even annually whichever is agreed mutually.read more 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 formula example1
Bond price Example 1
  • Bond price = $83,878.62
Bond price Example 1-1

Since the coupon rateCoupon RateThe coupon rate is the ROI (rate of interest) paid on the bond's face value by the bond's issuers. It determines the repayment amount made by GIS (guaranteed income security). Coupon Rate = Annualized Interest Payment / Par Value of Bond * 100%read more 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 a 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%.

Bond price Example 2-2

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

Bond price formula example1
Example 2-3
  • Bond price = $104,158.30
Example 2-4

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 QPR Ltd has issued a zero-coupon bond with having a face value of $100,000 and maturing in 4 years. The prevailing market rate of interest is 10%.

Example 3
Zero Coupon Bond Price formula

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

Example 4
  • Bond price = $68,301.35 ~ $68,301
Example 3-1

Use and Relevance

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 calculate 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.

Bond Pricing Formula Video

 

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 –

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