# Yield to Maturity (YTM): What It Is, Why It Matters, Formula

## What Is Yield to Maturity (YTM)?

The term yield to maturity (YTM) refers to the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate.

### Key Takeaways

• Yield to maturity is the total rate of return that will have been earned by a bond when it makes all interest payments and repays the original principal.
• YTM is essentially a bond's internal rate of return if held to maturity.
• Calculating the yield to maturity can be a complicated process, and it assumes all coupon or interest payments can be reinvested at the same rate of return as the bond.
• A bond's YTM is different from its coupon rate, which is the total amount of income it pays for the length of time it's held.
• YTM calculations usually don't account for taxes paid on a bond.
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## Understanding Yield to Maturity (YTM)

Yield to maturity is also referred to as book yield or redemption yield. It is similar to current yield, which divides annual cash inflows from a bond by the market price of that bond to determine how much money one would make by buying a bond and holding it for one year.

Unlike current yield, YTM accounts for the present value of a bond's future coupon payments. In other words, it factors in the time value of money, whereas a simple current yield calculation does not. As such, it is often considered a more thorough means of calculating the return from a bond.

The YTM of a discount bond that does not pay a coupon is a good starting place in order to understand some of the more complex issues with coupon bonds.

## Formula and Calculation of Yield to Maturity (YTM)

The formula to calculate the YTM of a discount bond is as follows:

\begin{aligned} &YTM=\sqrt[n]{\frac{\textit{Face Value}}{\textit{Current Price}}}-1\\ &\textbf{where:}\\ &n=\text{number of years to maturity}\\ &\text{Face value}=\text{bond's maturity value or par value}\\ &\text{Current price}=\text{the bond's price today} \end{aligned}

Because YTM is the interest rate an investor would earn by reinvesting every coupon payment from the bond at a constant interest rate until the bond's maturity date, the present value of all the future cash flows equals the bond's market price.

An investor knows the current bond price, its coupon payments, and its maturity value, but the discount rate cannot be calculated directly. However, there is a trial-and-error method for finding YTM with the following present value formula:

\begin{aligned} \textit{Bond Price} &= \ \frac{\textit{Coupon }1}{(1+YTM)^1} +\ \frac{\textit{Coupon }2}{(1+YTM)^2}\\ &\quad +\ \cdots\ +\ \frac{\textit{Coupon }n}{(1+YTM)^n} \ +\ \frac{\textit{Face Value}}{(1+YTM)^n} \end{aligned}

Or this formula:

\begin{aligned} \textit{Bond Price} &=\ \left(\textit{Coupon }\ \times\ \frac{1-\frac{1}{(1+YTM)^n}}{YTM}\right)\\ &\quad+\left(\textit{Face Value }\ \times\ \frac{1}{(1+YTM)^n}\right) \end{aligned}

Each one of the future cash flows of the bond is known and because the bond's current price is also known, a trial-and-error process can be applied to the YTM variable in the equation until the present value of the stream of payments equals the bond's price.

Solving the equation by hand requires an understanding of the relationship between a bond's price and its yield, as well as the different types of bond prices. Bonds can be priced at a discount, at par, or at a premium. When the bond is priced at par, the bond's interest rate is equal to its coupon rate. A bond priced above par, called a premium bond, has a coupon rate higher than the realized interest rate, and a bond priced below par, called a discount bond, has a coupon rate lower than the realized interest rate.

If an investor were calculating YTM on a bond priced below par, they would solve the equation by plugging in various annual interest rates that were higher than the coupon rate until finding a bond price close to the price of the bond in question.

Calculations of yield to maturity assume that all coupon payments are reinvested at the same rate as the bond's current yield and take into account the bond's current market price, par value, coupon interest rate, and term to maturity. The YTM is merely a snapshot of the return on a bond because coupon payments cannot always be reinvested at the same interest rate. As interest rates rise, the YTM will increase; as interest rates fall, the YTM will decrease.

The complex process of determining yield to maturity means it is often difficult to calculate a precise YTM value. Instead, one can approximate YTM by using a bond yield table, financial calculator, or online YTM calculator.

## Yield to Maturity vs. Coupon Rate

Buying bonds is a relatively low-risk way to invest your money. That's because, unlike stocks, bond issuers promise to pay the holder the full face value once it matures. Having said that, investors should ensure that they do their research before making any investment decisions, including purchasing any bonds.

Bonds come with two very important metrics: YTM and their coupon rate. Remember that the YTM is the total return that's expected on a bond if it's held until it matures. The coupon rate, on the other hand, is the total amount that a bond pays in income to the bondholder for as long as they hold it. The coupon rate, which is also called the coupon yield, is the amount of interest paid on the bond's face value on an annual basis.

A bond's YTM fluctuates over time. The coupon rate, though, remains fixed. If you buy a bond at face value, both the YTM and the coupon rate are the same. A bond purchased at a discount means that the YTM is higher. But if you purchase a bond at a premium (higher than its face value), the coupon rate will be higher.

Investors typically look for bonds with higher coupon rates.

## Example: Calculating YTM Through Trial and Error

Let's say an investor currently holds a bond whose par value is $100. The bond is currently priced at a discount of$95.92, matures in 30 months, and pays a semi-annual coupon of 5%. Therefore, the current yield of the bond is (5% coupon x $100 par value) /$95.92 market price = 5.21%.

To calculate YTM here, the cash flows must be determined first. Every six months (semi-annually), the bondholder would receive a coupon payment of (5% x $100)/2 =$2.50. In total, they would receive five payments of $2.50, in addition to the face value of the bond due at maturity, which is$100. Next, we incorporate this data into the formula, which would look like this:

$\95.92=\left(\2.5\ \times\ \frac{1-\frac{1}{(1+YTM)^5}}{YTM}\right) \ +\ \left(\100\ \times \ \frac{1}{(1+YTM)^5}\right)$

Now we must solve for the interest rate YTM, which is where things get tough. Yet, we do not have to start simply guessing random numbers if we stop for a moment to consider the relationship between bond price and yield. As mentioned earlier, when a bond is priced at a discount from par, its interest rate will be greater than the coupon rate. In this example, the par value of the bond is $100, but it is priced below the par value at$95.92, meaning the bond is priced at a discount. As such, the annual interest rate we are seeking must necessarily be greater than the coupon rate of 5%.

With this information, we can calculate and test several bond prices by plugging various annual interest rates that are higher than 5% into the formula above. Using a few different interest rates above 5%, one would come up with the following bond prices:

Taking the interest rate up by one and two percentage points to 6% and 7% yields bond prices of $98 and$95, respectively. Because the bond price in our example is $95.92, the list indicates that the interest rate we are solving for is between 6% and 7%. Having determined the range of rates within which our interest rate lies, we can take a closer look and make another table showing the prices that YTM calculations produce with a series of interest rates increasing in increments of 0.1% instead of 1.0%. Using interest rates with smaller increments, our calculated bond prices are as follows: Here, we see that the present value of our bond is equal to$95.92 when the YTM is at 6.8%. Fortunately, 6.8% corresponds precisely to our bond price, so no further calculations are required. At this point, if we found that using a YTM of 6.8% in our calculations did not yield the exact bond price, we would have to continue our trials and test interest rates increasing in 0.01% increments.

It should be clear why most investors prefer to use special programs to narrow down the possible YTMs rather than calculating through trial and error, as the calculations required to determine YTM can be quite lengthy and time-consuming.

## Uses of Yield to Maturity (YTM)

Yield to maturity can be quite useful for estimating whether buying a bond is a good investment. An investor will determine a required yield (the return on a bond that will make the bond worthwhile). Once an investor has determined the YTM of a bond they are considering buying, the investor can compare the YTM with the required yield to determine if the bond is a good buy.

Because YTM is expressed as an annual rate regardless of the bond's term to maturity, it can be used to compare bonds that have different maturities and coupons since YTM expresses the value of different bonds in the same annual terms.

## Variations of Yield to Maturity (YTM)

Yield to maturity has a few common variations that account for bonds that have embedded options:

• Yield to call (YTC) assumes that the bond will be called. That is, a bond is repurchased by the issuer before it reaches maturity and thus has a shorter cash flow period. YTC is calculated with the assumption that the bond will be called at soon as it is possible and financially feasible.
• Yield to put (YTP) is similar to YTC, except the holder of a put bond can choose to sell the bond back to the issuer at a fixed price based on the terms of the bond. YTP is calculated based on the assumption that the bond will be put back to the issuer as soon as it is possible and financially feasible.
• Yield to worst (YTW) is a calculation used when a bond has multiple options. For example, if an investor was evaluating a bond with both calls and put provisions, they would calculate the YTW based on the option terms that give the lowest yield.

## Limitations of Yield to Maturity (YTM)

YTM calculations usually do not account for taxes that an investor pays on the bond. In this case, YTM is known as the gross redemption yield. YTM calculations also do not account for purchasing or selling costs.

YTM also makes assumptions about the future that cannot be known in advance. An investor may not be able to reinvest all coupons, the bond may not be held to maturity, and the bond issuer may default on the bond.

## What Is a Bond’s Yield to Maturity?

The YTM of a bond is essentially the internal rate of return (IRR) associated with buying that bond and holding it until its maturity date. In other words, it is the return on investment associated with buying the bond and reinvesting its coupon payments at a constant interest rate. All else being equal, the YTM of a bond will be higher if the price paid for the bond is lower, and vice-versa.

## What Is the Difference Between a Bond’s YTM and Its Coupon Rate?

The main difference between the YTM of a bond and its coupon rate is that the coupon rate is fixed whereas the YTM fluctuates over time. The coupon rate is contractually fixed, whereas the YTM changes based on the price paid for the bond as well as the interest rates available elsewhere in the marketplace. If the YTM is higher than the coupon rate, this suggests that the bond is being sold at a discount to its par value. If, on the other hand, the YTM is lower than the coupon rate, then the bond is being sold at a premium.

## Is It Better to Have a Higher YTM?

Whether or not a higher YTM is positive depends on the specific circumstances. On the one hand, a higher YTM might indicate that a bargain opportunity is available since the bond in question is available for less than its par value. But the key question is whether or not this discount is justified by fundamentals such as the creditworthiness of the company issuing the bond, or the interest rates presented by alternative investments. As is often the case in investing, further due diligence would be required.

## The Bottom Line

A bond's yield to maturity is the internal rate of return required for the present value of all the future cash flows of the bond (face value and coupon payments) to equal the current bond price. YTM assumes that all coupon payments are reinvested at a yield equal to the YTM and that the bond is held to maturity.

Some of the more known bond investments include municipal, treasury, corporate, and foreign. While municipal, treasury, and foreign bonds are typically acquired through local, state, or federal governments, corporate bonds are purchased through brokerages. If you have an interest in corporate bonds then you will need a brokerage account.

Article Sources
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1. Financial Industry Regulatory Authority. "Bond Yield and Return."

2. U.S. Securities and Exchange Commission. "Bonds."

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