Price of bonds excel

Bond Pricing Formula

Formula to Calculate Bond Price

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

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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

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

Table of contents

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 company’s funding requirement. The par value is denoted by F.

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

The total number of periods till maturity is computed by multiplying the 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

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

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,

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

Practical Examples (with Excel Template)

Example #1

Let us take an example of a bond Example Of A Bond Bonds refer to the debt instruments issued by governments or corporations to acquire investors’ funds for a certain period. 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 = $83,878.62

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

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

$68,301

Use and Relevance

The concept of bond pricing is very important because bonds form an indispensable part of the capital markets. As such, investors and analysts must understand how a bond’s different factors behave to calculate its intrinsic value. Similar to stock valuation, the pricing of a bond helps understand 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, practical examples, and downloadable excel templates. You may learn more about Fixed Income from the following articles –

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How to Calculate PV of a Different Bond Type With Excel

Pete Rathburn is a copy editor and fact-checker with expertise in economics and personal finance and over twenty years of experience in the classroom.

A bond is a type of loan contract between an issuer (the seller of the bond) and a holder (the purchaser of a bond). The issuer is essentially borrowing or incurring a debt that is to be repaid at «par value» entirely at maturity (i.e., when the contract ends). In the meantime, the holder of this debt receives interest payments (coupons) based on cash flow determined by an annuity formula. From the issuer’s point of view, these cash payments are part of the cost of borrowing, while from the holder’s point of view, it’s a benefit that comes with purchasing a bond.

The present value (PV) of a bond represents the sum of all the future cash flow from that contract until it matures with full repayment of the par value. To determine this—in other words, the value of a bond today—for a fixed principal (par value) to be repaid in the future at any predetermined time—we can use a Microsoft Excel spreadsheet.

Specific Calculations

We will discuss the calculation of the present value of a bond for the following:

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Excel PRICE Function

PRICE is an Excel function that calculates the price of a bond. A bond’s price is determined by discounting the bond’s future cash flows, which comprise of periodic coupon payments and/or redemption value, using the bond’s yield (termed as YLD) over the remaining term of the bond.

The periodic coupon payments are based on the coupon RATE, the annual percentage rate at which the bond pays periodic interest payments and payment FREQUENCY, the number of coupon payments per year.

Price of a bond is expressed by the following algebraic function:

Syntax

PRICE function syntax is:

PRICE(settlement, maturity, rate, redemption, frequency, [basis])

Excel PRICE function works out a bond’s price per $100 face value of a bond given the bond’s

SETTLEMENT is the date on which we intend to work out the price (i.e. the purchase/pricing date), MATURITY (date) is the date on which the bond expires and the principal amount is paid back by the issuer to the bond-holder, (coupon) RATE is the annual interest rate at which coupon payments are made , yield referred to as YLD is the annual market interest rate representative of the risk of the bond, REDEMPTION (value) is the value per $100 of the principal amount that is paid back at the redemption date, FREQUENCY is the number of coupon payments per year and (day-counting) [BASIS].

Example

The following screenshot illustrates how PRICE function can be used to price a bond:

Since the PRICE function works out the price per $100 par value of a bond, we have manually worked out the price per $1,000 of par value by dividing the result of the PRICE function by the $100 par value and multiplying it with the actual par value of $1,000.

by Obaidullah Jan, ACA, CFA and last modified on Jan 27, 2018

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Bond price formula – Excelchat

Bonds essentially refer to a contract between an investor and a borrower. It is a type of loan to be repaid at the end of the maturity period. Some bonds have annual or semi-annual coupons which are basically predetermined interest payments. These coupons are incurred as additional cost of borrowing, and are paid to investors on a regular basis until the bond’s maturity.

This article will show us how to calculate the bond value or bond price for a zero coupon bond, an annual coupon bond and a semi-annual coupon bond.

Figure 1. Final result: Bond price formula

Calculate bond price

Bond price is the current discounted value of a future cash flow. In simple terms, a bond price is the sum of the present value of the principal payment and the interest payments. In order to calculate the bond price , we can use the PV function.

Syntax of PV function

=PV(rate, nper, pmt, [fv], [type])

• Rate is the interest rate per period
• Nper is the total number of payment periods
• Pmt is the payment made each period and is fixed until bond maturity
• Fv is the future value at bond maturity
• Type is either 0 ((if payment is at the end of the period) or 1 (payment at the beginning of the period)

Figure 2. Sample data to calculate bond price

Price of zero coupon bond

Our example is a ten-year bond with a face value of 10,000 and an interest rate of 5%. In order to calculate the bond price with no coupons, we enter this formula in C8:

=PV(C6,C5,0,C3)

• Interest rate = 5%
• Number of periods = 10
• Payment made each period = 0 (zero coupons)
• Face value = 10,000

Figure 3. Bond price formula for zero coupons

The resulting bond price is -6,139.13. In accounting, the negative sign means it is an outgoing cash flow.

Price of annual coupon bond

There are bonds wherein the investors get a coupon each year. In order to calculate the price of an annual coupon bond, we enter this formula in D8:

=PV(D6,D5,D3*D7,D3)

• Discount rate = 4%
• Number of periods = 10
• Payment made each period = 10,000 x 2.5%
• Face value = 10,000

Figure 4. Bond price formula for annual coupon bond

As a result, the bond price is 8783.37.

Price of semi-annual coupon bond

There are also bonds that give out coupons twice in a year. The formula for bond price is:

=PV(E6/2,E5,E3*E7/2,E3)

• Discount rate = 4%/2 = 2%
• Number of periods = 10×2 = 20
• Payment made each period = 10,000 x 2.5%/2
• Face value = 10,000

Figure 5. Bond price formula for semi-annual coupon bond

Note that for semi-annual coupons, we divide the discount rate and coupon rate by 2, and the number of periods is twice the number of years. The resulting bond price is 8773.64.

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