Bond Price Calculator

Introduction

The bond price calculator calculates the price of bonds by inputting the settlement date, maturity date, coupon rate, bond yield, redemption value per $100 face value, frequency of payments, and day count basis convention.

In this article, you will also learn about bonds, the key features of bonds and how to price bonds and the factors affecting bond prices. You will also learn about the day count convention, how it differs across countries, and how it affects bond prices. You can see the difference by changing our bond price calculator’s day count basis dropdown.

A bond is a fixed-income financial instrument representing a loan from an investor to a borrower. For instance, The borrower will issue bonds when they need funds and raise money from investors looking for a return on their capital. The borrower typically will be a corporate or government entity.

The bond buyer lends money to the issuer and expects the issuer to repay the borrowed amount with interest, and most bonds pay regular interest until they mature.

The interest paid is the compensation the borrower provides to the lender for lending them the money.

The price of the bonds will be equal to the present value of future cash flows, such as the interest payments and the principal repayment at maturity.

In summary, the price of a bond is the present value of the future cash flow of a bond.

How to use the Bond Price Calculator?

Using the bond price calculator, you can calculate the bond prices by inputting the settlement date, maturity date, coupon rate, bond yield, redemption value per $100 face value, frequency of payments, and day count basis convention.

Face or Par Value The face or par value

Settlement Date The date when the seller trades the bond security to the buyer. Therefore, it should be after the issue date.

Maturity Date The date on which the debt matures and the bond will expire.

Rate The bond’s annual coupon rate

Yield The bond’s annual yield.

Redemption The security’s redemption value per $100 face value

Frequency The number of coupon payments per year.

Day Count Basis The day count basis used for the calculation

Bond Price The price of the bond

What are Bonds?

A bond is a debt instrument; the bond buyer lends money to the issuer and expects the borrowed amount to be repaid with interest, and most bonds pay regular interest until they mature.

The interest paid is the compensation the borrower provides to the lender for lending them the money. Since the interest the bonds pay the lender is fixed, it’s a fixed-income security.

Governments, corporations, or agencies issue bonds, which can be publicly placed (anyone can buy them) or privately placed (sold only to a few select investors). Bonds can also be secured using collateral or maybe unsecured.

Key Features of Bonds

Maturity

Generally, It is the date on which the borrower will repay the principal, and the bond will cease. The bondholder can expect to receive coupon interest in the period in between. The bond buyer can sell the bond to another buyer before maturity, but the price may vary.

The yield of a bond depends heavily on the bond’s maturity.

The price of the bond will vary depending upon maturity. For example, if the interest rates changes, the effect of the change will be more drastic on the price of a bond with a shorter maturity than that of a bond with a long maturity.

Face Value

The face value also called the par value of a bond, is the amount to be repaid to the investor at maturity.

Coupon Rate

The interest rate the borrower must pay the bondholders during the bond term is called the coupon rate.

We get the coupon paid to the bondholders by multiplying the coupon rate and the par or face value.

Frequency

The coupon payments must be made periodically, whether monthly, quarterly, semiannually, or annually. These terms will be specified during the issue of the bond. Typically, In the United States, the coupon payment is made semiannually. In European bond markets, coupon payment is usually made annually.

Yield

The bond yield is the annualized return of a bond, expressed as the percentage of invested capital.

A bond’s yield depends upon its price, coupon rate, and amount paid at maturity.

You could also use our bond yield calculator to calculate bond yield.

Nominal Yield

the nominal yield is also known as the coupon rate of the bond. The stated interest rate is calculated as a percentage of the par value.

A bond with a $1000 par value that pays 5% interest semiannually will pay out $25 payments every six months totalling $50 at the end of the year, so the nominal yield will be $50 / $1000 = 5%.

\text{Nominal Yield}= \normalsize \dfrac{\text{Annual Interest Payment}}{\text{Par Value}}

The price of the bond and the interest rates are inversely related if interest rates rise, the bond prices will decline, and if the interest rates fall, the bond prices will increase.

So, when the price of a bond changes, the bond’s yield or return will also change.

Current Yield

The buyer can approximate the bond’s yield by calculating the current yield of the bond by dividing the annual coupon payment by the bond price.

\text{Current Yield} = \normalsize \dfrac{\text{Annual Coupon Payment}}{\text{Current Market Price of Bond}}

True Yield or Yield-to-Maturity (YTM)

Yield-to-Maturity (YTM) is the return on the bond if it is held till maturity.

Mathematically, it is the discount rate at which the sum of the present value of all future cash flows from coupon payments and the principal repayment equals the bond’s price.

When the bond is bought at a discount, the YTM will exceed the current yield, and if the bond is purchased at a premium, the YTM will be less than the current yield.

\text{Price} = \sum_{t-1}^T \normalsize \dfrac{\text{Cash Flows}}{(1 + YTM)^t}

Where YTM = Yield-to-Maturity

How are Bonds Priced?

Generally, the price of a financial instrument will be equal to the present value of the expected future cash flows.

The same logic applies to bonds as well. The price of the bonds will be equal to the present value of future cash flows, such as the interest payments and the principal repayment at maturity.

\text{Bond\;Price} = PV(\text{Coupon}_1) + PV(\text{Coupon}_2)+...+PV(\text{Coupon}_n)+PV(\text{Principal})

The bond price above is the clean price. The following factors determine the bond prices.

The Face value or Par value.
The coupon rate.
Accrued interest.
Prevailing interest rates in the market.
Credit rating of the issuer.

During the bond issue, it is generally sold at par, which is the amount that will be repaid at maturity. Due to interest rate fluctuations and supply and demand changes, the bond’s price may vary during the bond’s life. It can sell higher or lower than par.

When the interest rate rises, the bond prices decline, and when the interest rate falls, the bond prices rise.

The bond price will also include the accrued interest earned between the coupon payment dates. The interest earned but not paid.

Clean bond prices are bond prices without the accrued interest, and dirty prices will include the accrued interest.

\text{Clean\;Bond\;Price} = \normalsize \dfrac{C_1}{(1+\dfrac{r}{k})^1} + \dfrac{C_2}{(1+\dfrac{r}{k})^2} + ... + \dfrac{C_n}{(1+\dfrac{r}{k})^{kn}} + \dfrac{P}{(1+\dfrac{r}{k})^{kn}}

Where

C = Coupon Payment

k = Frequency of Coupon Payments in a Year

n = Number of Years until maturity

r = Annualised Interest Rate

P = Par/Face Value of Bond

Bond’s Dirty Price

The bond’s dirty price equals the clean price plus the accrued interest.

\text{Dirty Price = Clean Price + Accrued Interest}

Where Accrued interest is

\text{Accrued Interest} = \text{Interest Payment} *( \normalsize \dfrac{\text{Days since last payment}}{\text{Days between Payments}})

This bond price calculator calculates the clean price of the bond.

You can also calculate only the accrued interest using our accrued interest calculator.

Bond Day-Count Conventions

The Day count conventions are standardized practices for calculating the number of days between two dates.

The Day count convention is one of the factors affecting bond price calculation in the bond price calculator. Day Count conventions are used for calculating the Accrued Interest, where we need to find the days between the previous coupon date and the value date.

The following are the day count conventions used to calculate the number of days between two dates.

Actual / Actual

Most bonds, like treasury coupon securities, use the Actual / Actual day count convention in a month’s actual number of days. The actual number of days in the coupon period is used for the calculations.

But there are different day count conventions where the accrued interest might vary.

Actual / 360

Actual / 360 is a Day Count Convention where the accrued interest is given by multiplying the coupon rate with the actual number of days and dividing by 360.

\text{Accrued \;Interest = Coupon\; Rate}\times \normalsize \dfrac{\text{Days}}{360}

Actual / 365

Actual / 365 is a Day Count Convention where the accrued interest is given by multiplying the coupon rate with the actual number of days and dividing by 365.

\text{Accrued \;Interest = Coupon\; Rate}\times \normalsize \dfrac{\text{Days}}{365}

The accrued interest calculated with the Actual / 360 day count convention will be slightly more than that calculated by the Actual / Actual or the Actual / 365 method.

US (NASD) 30/360

In the US (NASD) 30/360 day count convention, regardless of the number of days in a month, we consider that there are 30 days, and irrespective of the number of days in a year, we consider that there are 360 days in a year.

To Calculate the Day Count:

Start Date: M1/D1/Y1

End Date: M2/D2/Y2

If $D_1 = 31$ , we set $D_1 = 30$

If $(D_2 = 31)$ and $(D_1 = 30\; \text{or}\; 31)$ , then we set $D_2 = 30$

\text{Day Count} = (Y_2 - Y_1)\times360 + (M_2 - M_1)\times30+(D_2-D_1)

\text{Day Count Fraction} = \normalsize \dfrac{\text{Day Count}}{360}

European 30/360

In the European 30/360 Day count convention, regardless of the number of days in a month, we consider that there are 30 days, and irrespective of the number of days in a year, we consider that there are 360 days.

To Calculate the Day Count:

Start Date: M1/D1/Y1

End Date: M2/D2/Y2

If $(D_2 = 31)$ , then we set $D_2 = 30$

\text{Day Count} = (Y_2 - Y_1)\times360 + (M_2 - M_1)\times30+(D_2-D_1)

\text{Day Count Fraction} = \normalsize \dfrac{\text{Day Count}}{360}

The 30 / 360 Day Count conventions are the easiest ones to use. They were primarily used before the advent of calculators or computers to easily calculate the days between the coupon date and the value date.

Day Count Conventions Used in US Bond Markets

Bond Market	Day Count Basis
US Treasury Notes	Actual / Actual
Money Market Instruments	Actual / 360
Corporate, Agency, and Municipal Bonds	30 / 360

Day Count Conventions in US Bond Markets

Bond Markets outside of the US use the Actual/Actual convention except the following

Bond Market	Day Count Basis
Eurobonds	30 / 360
Denmark, Sweden, Switzerland	30E / 360
Norway	Actual / 365

Day Count Conventions in other markets

Example

The face value of the bond is $1000, it has a 6.40% annual coupon rate and a yield-to-maturity of 7.2%, the coupons are paid semiannually, and the bond term is 8 years. What is the price of the bond today?

Settlement – 1/1/2020

Maturity – 1/1/2028

Rate – 6.4%

Yield – 7.2%

Redemption – 100

Frequency – 2

The price of the bond after inputting the values in the calculator, we get the answer as $951.9848