Bond Price Calculator: Calculate Bond Prices

A Bond Price Calculator can be used to work out the market price of a bond based on its face value, interest rate, current market rate and years until maturity. Bonds are commonly used for income purposes, diversifying and managing a portfolios finances by investors in the United States.

A bond is a type of security used to borrow money that is issued by governments, municipalities and companies. If you purchase a bond you are typically providing an loan for the bond issuer. In return you receive regular interest payments and your principal will be returned at the maturity date.

Common bonds used within the market in the United States include US Treasuries, municipal bonds and bonds from companies. Bond prices can vary depending on the current market interest rates, creditworthiness and investor demand.

If a bond has a 5% interest rate but new bonds in the market have a 6% interest rate, it may not be as attractive. This means that the bonds market price will decrease to below face value.

A Bond Price Calculator can help you work out what the current value of the bond is. It will help you compare bond prices, understand how sensitive it is to interest rates and see if it could be a good investment opportunity.

Using the Bond Price Calculator

To work out how much the bond is worth follow the steps below:

Face Value – Enter how much the bond issuer will return at the maturity date. For example $1,000.

Annual Coupon Rate – Enter the annual interest rate stated on the bond. For example 5%.

Market Interest Rate – Enter the yield/discount rate you would like to use.

Years Until Maturity – Enter how many years until the bond matures.

Coupon Frequency – Enter if the bond pays annually or semi-annually.

Calculate – Click calculate to work out what the bond is worth.

Check what the market price is compared to the face value.

Most bonds in the United States including Treasuries and many corporate bonds, pay interest every six months. Make sure to check the terms of the bond you are looking at.

Bond Price Formula

The bond price can be calculated by finding out what the future coupon payments and principal to be returned are worth today.

Bond Price Formula:

P = C [1 − (1 + r)^-n ] / r + F / (1 + r)^n

Variables:

P = The current theoretical price

C = Coupon payment

r = The market yield for each period. Must be expressed as decimals.

n = Number of coupons left.

F = Face value.

If the bond pays coupons yearly then:

C = F x Coupon Rate.

If paying semi-annually the formula will typically have half the yearly coupon payment, half the yearly nominal yield and double the number of years left.

It is assumed that the coupons are paid on time, the bond is held according to the terms and the market yield is suitable.

Example

Let’s say we want to work out how much a United States corporate bond is worth with the following details:

Face Value = $1,000

Annual Coupon Rate = 5%

Market Yield = 6%

Years Until Maturity = 5 Years

Coupon Frequency = Annually

We first need to work out how much the bond pays in annual coupons:

Coupon Payment = $1,000 x 5%.

Coupon Payment = $50.

We now need to discount the annual coupons over 5 years and the $1,000 principal.

P = $50 × [1 − (1.06)^(-5)] / 0.06 + $1,000 / (1.06)^5.

This will give us a present value of approximately $210.62, while the present value of the principal repayment is approximately $747.26.

Bond Price ≈ $957.88.

Below shows us the results:

Bond Detail

Value

Face Value

$1,000.00

Annual Coupons

$50.00

Market Yield

6%

Years Until Maturity

5

Bond Price

$957.88

Difference from Face Value

-$42.12

The bond is selling below the face value as the coupon rate is less than the market yield.

This is just an example and actual bond prices in the market can vary due to the timing of payments, credit risk, accruals, liquidity and other factors.

Understanding Your Results

A Bond Price Calculator will typically tell you how much the bond is worth based on its remaining cashflows and the market yield you have chosen.

Bond Price – This tells you how much the bond is worth now based on the remaining cashflows.

Discounted – If the price of the bond is lower than the face value it means it is selling at a discount. This is typically due to it having a lower coupon rate than the market yield.

Premium – If the price of the bond is higher than face value it means it is selling at a premium. This is typically due to it having a higher coupon rate than market yield.

Par Value – If the price equals the face value it is selling at par. This will happen if the coupon rate and market yield requirement are the same, assuming standard assumptions.

The bond price and yield are typically inversely related. As the market yield increases the present value of the future fixed payments will typically decrease. If the market yield decreases the bond price will typically increase.

Keep in mind the bond price isn’t the same as the total return. The total return will also depend on the coupon payments, reinvestment, costs and price changes.

What Affects the Results?

There are several factors that will affect a bond’s price:

Coupon Rate – Bonds with higher coupon payments can be more attractive if the comparable bonds have a lower yield.

Market Rates – If interest rates change this can greatly affect bond prices. Bonds with a longer term can be affected more.

Term – Bonds with longer terms tend to be more sensitive to changes in the market yield.

Credit Risk – The bond issuer’s financial position and ability to make payments will effect the market yield they will need. If there is a higher level of perceived credit risk you will typically require a higher yield, meaning the bond price will decrease.

Coupon Frequency – Bonds can pay out annually, semi-annually or other variations.

Inflation Expectations – If there is an expectation of higher inflation this can lead to higher yields being required. Existing fixed rate bonds will be worth less.

Liquidity – If the bond is less liquid or has low demand it may need adjusting.

Callable – Some bonds can be paid back before their maturity date. This can affect the valuation of the bond as you may not expect to receive the same cashflows.

Advantages & Uses of the Bond Price Calculator

A Bond Price Calculator can be useful to understand how bonds are valued and compare fixed income.

Investment – Work out what the theoretical price of the bond is.

Treasuries – Work out what the US Treasuries are worth based on their coupons, term and market yield.

Compare Corporate Bonds – Compare bonds with different coupons, terms and market yields.

Municipal Bonds – Work out what the bonds are worth based on their specifics.

Interest Rate Sensitivity – See how sensitive the bond is to changes in the market yield.

Managing Portfolio – See how your bonds may be affected by interest rate movements.

Education – See how the bond price is related to the coupon and yield.

For example, you can compare two bonds with the same face value but different coupons. This will show you how they would be worth differently if they have the same market yield. This can give you an understanding of why a bond with a higher coupon may not be a good investment.

Accuracy, Assumptions & Limitations

A Bond Price Calculator can give accurate results based on the correct cashflows, timing and discount rate. However the price may not be the same as the actual trading price.

Often the basic bond price calculation will assume that the yield is fixed, coupons are paid on time, the face value is returned at maturity and there is no default. This may not consider other factors such as accruals, costs, taxes, varying market yields, callable and other bond specifics.

Many bonds in the United States are quoted as a clean price, meaning they do not include any accruals. The invoice price (dirty price) typically includes any accruals to be paid to the seller. Basic calculators may not consider this.

Make sure you are using the correct yield based on the bond’s payment frequency. If the bond is callable, mortgage backed or has uncertain cashflows more specialised methods may be needed.

Bonds can be volatile and you could lose money if you sell it before maturity. Even though the bond states it will return your principal, it will only do so if the bond issuer fulfils their obligations.

Use this as an analytical tool.

FAQs

1. What is a bond price?

A bond price is how much an investor will pay to buy a bond. It depends on the present value of the expected coupons and principal to be returned discounted at the correct market yield.

2. Why do bond prices drop when interest rates increase?

When the market yield increases new bonds may offer better returns than current bonds with lower fixed coupon rates. This will cause the price of current bonds to typically drop.

3. What is the difference between face value and market price?

Face value is the principal stated on the bond. Typically it will be returned to you at maturity if the bond issuer fulfils their obligations. The market price is how much investors are willing to pay for the bond.

4. What is a bond at a premium or discount?

A bond at a premium is one where the market price is higher than the face value. A bond at a discount is when the market price is lower than the face value. This depends largely on the coupon rate and market yield requirements.

5. How are US Treasury bonds priced?

US Treasury bonds are valued by discounting the expected coupons and principal to be returned at the correct market yield. Actual prices depend on market conditions, term, timing and other trading factors.

6. Does a bond price calculator include accruals?

Not necessarily. Many basic calculators will give a theoretical value that does not include accruals. Check if the bond you are looking at is a clean price or a dirty price.

7. Is a bond with a higher coupon a better investment?

No. Although they offer more income they may be more expensive, have a higher level of credit risk or other unfavourable terms. Compare the price, yield to maturity, credit quality, costs, tax and your investment goals.