# Bond Price Calculator

Created by Wei Bin Loo
Reviewed by Dominik Czernia, PhD and Jack Bowater
Based on research by
Garrett, S. An Introduction to the Mathematics of Finance: A Deterministic Approach, 2nd Edition (2013)
Last updated: Mar 28, 2023

With this bond price calculator, we aim to help you calculate the bond price issued by a government or a corporation. Finding out the current bond price is one of the most critical procedures for bond investors, as miscalculating can lead to huge losses. But worry not. This calculator is built to make the process easier for you.

We have written this article to help you understand what a bond price is and how to price a bond using the bond price formula. We will also demonstrate some examples to help you understand the concept.

## What is a bond price? Understanding the dynamic of the bond price equation

Before we dive into calculating the current bond price with our bond valuation calculator, let's take some time to talk about what a bond is. A bond is one of the most prevalent fixed-income securities. When an entity issues bonds, it is considered as acquiring funding from investors through issuing debt. The bond market may not be as famous as the stock market, but believe it or not, the global bond market is more than double the stock market.

When you purchase a bond from the bond issuer, you are essentially making a loan to the bond issuer. As the bond price is the amount of money investors pay for acquiring the bond, it is one of the most important, if not the most important, metrics in valuing the bond.

Now, let's look at some examples to understand how to calculate bond prices.

## How to calculate the bond price? The bond price formula

Bond price is calculated as the present value of the cash flow generated by the bond, namely the coupon payment throughout the life of the bond and the principal payment, or the balloon payment, at the end of the bond's life. You can see how it changes over time in the bond price chart in our calculator.

To use the bond price equation, you need to input the following data into our current bond price calculator:

• Face value – The coupon's face value;
• Coupon rate – The annual coupon rate;
• Frequency – The coupon frequency, i.e., the number of times the coupon is distributed in a year;
• n – The years to maturity; and
• YTM – The yield to maturity.

Let's take Bond A, issued by Company Alpha, as an example. It has the following data:

• Face value: $1,000 • Annual coupon rate: 5% • Coupon Frequency: Annual • Years to maturity: 10 years • Yield to maturity (YTM): 8% The bond valuation calculator follows the steps below: 1. Determine the face value. The face value is the balloon payment a bond investor will receive when the bond matures. For our example, it is face =$1,000.

2. Calculate the coupon per period.

To calculate the coupon per period, you will need two inputs, namely the coupon rate and frequency.

It can be calculated using the following formula:

coupon per period = face value × coupon rate / frequency

As this is an annual bond, the frequency = 1. And the coupon for Bond A is:

($1,000 × 5%) / 1 =$50.

3. Determine the years to maturity.

The n is the number of years it takes from the current moment to when the bond matures. The n for Bond A is 10 years.

4. Determine the yield to maturity (YTM).

The YTM is the annual rate of return that the bond investor will get if they hold the bond from now to when it matures. In this example, YTM = 8%.

5. Calculate the bond price

As mentioned above, the bond price is the net present value of the cash flow generated by the bond and can be calculated using the bond price equation below:

${\rm bond\ price} = \sum_{k=1}^{n} \frac{\rm cf}{(1 + r)^k}$

where:

• $\rm cf$ – Cash flows;

• $r$YTM; and

• $n$ – Years to maturity.

Hence, the price for Bond A will be:

$\footnotesize {\rm bond\ price} = \frac{\50}{(1 + 8\%)^1} + \frac{\50}{(1 + 8\%)^2}\\[1em]\qquad +\ \frac{\50}{(1 + 8\%)^3} + ... + \frac{\50}{(1 + 8\%)^9}\\[1em]\qquad +\ \frac{\1,050}{(1 + 8\%)^{10}}$

Eventually, the final result is:

bond price = $798.70 In our bond price calculator, you can follow the present values of payments on the bond price chart for a given period. ## Bond price calculator's results - some more insights Now that you understand the meaning of bond price and how to find bond price. Here are a few insights we wish to share with you: • Bond prices are massively affected by the macroeconomic environment, especially interest rates. When the central banks, such as the Federal Reserve and the Bank of England, change their interest rate policies, the bond prices fluctuate. Specifically, the bond price increases when the interest rates go down and vice versa. • Bond prices can be either higher than or lower than their face value. This depends on the coupon rates and the risks of the bond. The higher the coupon rate, the higher the price, holding all else constant. The higher the risks of the bond, the lower the price, holding all else constant. • Corporate bonds tend to be riskier than otherwise similar government bonds. This is because corporate bonds are associated with credit risks since they can default. Most government bonds are less sensitive to credit risks as most of them can print more money to repay their debt. ## Here a few bond calculator that you might interested in: ## FAQ ### What is a bond? A bond is a debt security, usually issued by a government or a corporation, sold to investors. The investors will lend the money to the bond issuer by buying the bond. The investors will get the returns by receiving coupons throughout the life of the bond and the face value when the bond matures. ### What is a coupon? A coupon is the interest payment of a bond. Typically, it is distributed annually or semi-annually depending on the bond. It is normally calculated as the product of the coupon rate and the face value of the bond. ### What is the YTM? YTM stands for the yield to maturity of a bond. It is the rate of return bond investors will get if they hold the bond to maturity. ### What is face value? The face value of a bond can also be called the principal. It is the amount of money the bond investor will receive at the maturity date if the bond issuer does not default. It is the last payment a bond investor will receive if the bond is held to maturity. ### If interest rates rise what happens to bond prices? If interest rates rise, so will the YTM of the bond. When the YTM increases: • The cash flows generated are discounted more heavily; and • Hence the bond price will go down. Similarly, when interest rates decrease, and the YTM decrease, the bond price will increase. Wei Bin Loo Coupon per period Face value$
Annual coupon rate
%
Coupon frequency
Annually
Coupon per period
$Annual Coupon$
Bond price
Years to maturity
year(s)
Yield to maturity (YTM)
%
Bond price
\$
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