# Bond YTM Calculator

Created by Wei Bin Loo
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jan 15, 2023

The bond YTM calculator is a handy tool that you can use to calculate the bond yield to maturity and calculate the rate of return that an investor can expect from a bond. As this metric is one of the most significant factors that can impact the bond price, it is essential that an investor fully understands the calculation of bond yield to maturity.

We have written this article to help you understand the bond YTM meaning, how to calculate it using the bond YTM formula, and the factors that cause the bond YTM to rise and fall. We will also demonstrate some examples to help you calculate the bond yield to maturity formula.

## What is yield to maturity (YTM)? The bond YTM meaning

Before we talk about the bond YTM (yield to maturity) calculation, we must first understand what a bond is; only then you can understand what yield to maturity is. A bond is a financial instrument that governments and companies issue to get debt funding from the public.

If you invest in a bond, you are entitled to collect a fixed set of cash payments until the bond matures. The payments you receive can be seen as regular interest earnings, or coupon payments. When you arrive at the end of the bond's lifespan, or its maturity date, you get not only the last interest payment, but also recover the face value of the bond, that is, the bond's principal.

As bonds are a particular investment, their precise evaluation is crucial in the eyes of investors. The most apparent aspect of the assessment is whether money is made or lost on the investment, that is, what the return on the financial transaction is. And this is what the bond YTM definition represents.

The YTM can be thought of as the rate of return of a bond. If you hold the bond to maturity after buying it in the market and are able to reinvest the coupons at the YTM, the YTM will be the internal rate of return of your bond investment.

Now that we know the YTM definition, let's look at some examples to understand how to find the YTM of a bond.

## How to calculate yield to maturity. The bond yield to maturity formula

The bond yield to maturity formula needs five inputs, which you can find in our bond YTM calculator:

• face value - Face value of the bond;
• bond price - Price of the bond;
• coupon rate - Annual coupon rate;
• frequency - Number of times the coupon is distributed in a year; and
• n - Years to maturity.

Let's take Bond A issued by Company Alpha, which has the following data, as an example of how to calculate yield to maturity:

• Face value: $1,500; • Bond price:$1,350;
• Annual coupon rate: 6%;
• Coupon Frequency: Annual; and
• Years to maturity: 15 years.
1. Determine the face value

The face value is equivalent to the principal of the bond. In our example, face value = $1,500. 2. Calculate the bond price The bond price is the money an investor has to pay to acquire the bond. It can be found on most financial data websites. The bond price of Bond A is $1,350.

3. Determine the annual coupon rate and the coupon frequency

coupon rate is the annual interest you will receive by investing in the bond, and frequency is the number of times you will receive it in a year.

In our example, Bond A has a coupon rate of 6% and an annual frequency. This means that the bond will pay $1,500 * 5% =$75 as interest annually.

4. Determine the years to maturity

The n is the number of years from now until the bond matures. The n for Bond A is 15 years.

5. Calculate the bond YTM

The bond YTM can be seen as the internal rate of return of the bond investment if the investor holds it until it matures and reinvesting the coupons at the same interest rate. Hence, the bond YTM formula involves deducing the bond YTM $r$ in the equation below:

$\footnotesize\text{bond price} = \sum_{k=1}^n[cf / (1 + r)^k]$

where:

- $$cf$$ - Cash flows, i.e., coupons or the principal;
- $$r$$ - Bond YTM; and
- $$n$$ - Years to maturity.

This calculation involves a complex iteration, and it is nearly impossible to do it by hand in a reasonable time. That's why we have built this bond YTM calculator for you!

For Bond A, the equation looks like:

$\begin{split} \footnotesize\1350& = \\ \text{ }& \footnotesize\75 / (1 + r)^1\text{ }+ \\ & \footnotesize\75 / (1 + r)^2\text{ }+ \\ & \footnotesize\75 / (1 + r)^3\text{ }+ \\ & ...\text{ }+ \\ & \footnotesize\75 / (1 + r)^{14}\text{ }+ \\ & \footnotesize\1575 / (1 + r)^{15}\text{ } \end{split}$

After the estimation, our bond YTM calculator gives bond YTM of $r = 7.11\%$.

## Why is bond YTM important?

Now that you understand the bond YTM meaning and how to calculate the bond YTM, let's explore its importance in analyzing bonds:

• Bond dynamics are complex. A bond with a higher coupon rate does not mean that it gives you a better return. The magnitude of the face value means little to investors in terms of the returns that they can get as well. And this is where bond YTM comes in.

• As the bond YTM represents the internal rate of return of a bond investment, calculating the bond YTM allows you to compare the returns of different bonds. Using the bond YTM, you can find which bond will bring the highest returns, regardless of their face value, coupon rate, etc.

## Understanding the yield curve

The yield curve is one of the best instruments to analyze the evolution of YTM. The bond yield curve plots the YTM against time.

For instance, if the yield curve is upward-sloping, the long-term YTM, such as the 10-year YTM, is higher than the short-term YTM, such as the 2-year YTM. On the other hand, if the yield curve is trending downwards, the 10-year YTM will be lower than the 2-year YTM.

## FAQ

### Does bond yield equal to bond YTM?

Technically, yes. Bond yield will equal bond YTM if you hold to the bond until its maturity and reinvest at the same rate as the bond YTM.

### How do I calculate the yield to maturity of a bond?

You can calculate the yield to maturity of a bond in three steps:

1. Check the face value, bond price, annual coupon rate, and years to maturity of your bond.

2. Find the cash flows for each year.

3. Calculate the bond YTM from the below formula. Note that it involves complex iteration:

bond price = Σk=1n[cash flows / (1 + YTM)k]

### What causes bond YTM to fall?

There are several factors that can make bond YTM fall. For instance, the lower the inflation, the lower the bond YTM. The less volatile the market condition, the lower the bond YTM.

### Can bond YTM be negative?

Yes, bond YTM can be negative. It happens every now and then, even though it is not common. This situation normally happens when inflation is out of control and the market is unstable.

In such a situation, even a negative bond YTM is still better than storing cash since hyperinflation might happen.

Wei Bin Loo
Face value
$Bond price$
Annual coupon rate
%
Coupon frequency
Annually
Years to maturity
year(s)
Yield to maturity (YTM)
%
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