# Yield to Maturity (YTM): What It Is and How It Works

> **Definition**
>
> Yield to Maturity is expressed as an annual rate and is the estimated total return a bond will generate if it is held to maturity.

## What Is Yield to Maturity (YTM)?

Yield to maturity (YTM) is the [internal rate of return](https://www.investopedia.com/terms/i/irr.asp) (IRR) that equates all future cash flows of a bond to its current price. YTM assumes the bond is held until maturity and that an investor can reinvest at the same yield.

### Key Takeaways

*   Yield to maturity is also referred to as book yield or redemption yield.
*   YTM may fluctuate, while a bond's coupon rate or the interest paid annually on the bond's face value remains fixed.
*   As interest rates rise, YTM increases; as interest rates fall, YTM decreases.

![Yield to Maturity (YTM)](https://www.investopedia.com/thmb/nFUHd0ndusQvPu5aDd2XjdBVzps=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Term-Definitions_yieldtomaturity-5bf078bc6f6147d4ae99e549fe87611b.jpg)

*Investors use YTM to compare bonds with different coupon rates and maturity dates. — Investopedia / Jessica Olah*

## YTM Formula

A bond's YTM can be calculated using the formula:

> YTM = \[ C+ (FV - PV) ÷ t \] ÷ \[ (FV + PV) ÷ 2 \]

Where:

*   C = Coupon Payment
*   FV = Face Value
*   PV = Present Value/Current Price
*   t = Years to Maturity  
    

> **Fast Fact**
>
> Bonds are priced at a discount, par, or a premium. At par, the bond's interest rate equals its coupon rate. Above par, the bond is called a premium bond with a coupon rate higher than the realized interest rate. A bond priced below par, called a discount bond, has a coupon rate lower than the realized interest rate.

## YTM vs. Coupon Rate

Unlike stock investments, bond issuers promise to pay the holder the full face value once it matures. Bonds come with two metrics: YTM and coupon rate. YTM is the total return expected on a bond if it's held until maturity.

The coupon rate is the total amount the bond pays in income to the bondholder for as long as they hold it. The coupon rate is the interest paid annually on the bond's face value. A bond's YTM fluctuates over time while the coupon rate remains fixed.

## Calculating YTM

To calculate YTM on a bond priced below par, investors plug in various annual interest rates higher than the coupon rate to find a bond price close to the researched bond price. Calculations of yield to maturity assume that all coupon payments are reinvested at the same rate as the bond's current yield and account for the bond's current market price, par value, coupon interest rate, and [term to maturity](https://www.investopedia.com/terms/t/termtomaturity.asp).

The YTM is 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. Investors can approximate YTM by hand or by using a bond yield table, financial calculator, or online YTM calculator.

The annual rate of a bond must be calculated via trial and error. Imagine an investor holds a bond whose par value is $100. The bond:

*   It is priced at a discount of $95.92
*   Matures in 30 months (2.5 years)
*   Pays a semi-annual coupon of 5%

The current yield is calculated using the formula:

> Annual Cash Flow ÷ Market price

Therefore, the current yield is (5% coupon x $100 par value) / $95.92 market price = 5.21%. This is the value to which investors compare the next calculations.

To calculate YTM, the cash flows must be determined first. Every six months (semi-annually), the bondholder receives a coupon payment of ( 5% x $100 ) / 2 = $2.50. Next, we incorporate this data into the formula (30 months = 2.5 years):

> YTM = \[ C+ (FV - PV) ÷ t \] ÷ \[ (FV + PV) ÷ 2 \]

*   YTM = \[ $2.50 + ($100 - $95.92) ÷ 2.5 \] ÷ \[ ($100 + $95.92) ÷ 2 \]
*   YTM = \[ $2.50 + $4.08 ÷ 2.5\] ÷ \[$195.92 ÷ 2 \]
*   YTM = \[ $2.50 + $1.632 \] ÷ \[ $97.96 \]
*   YTM = \[$4.132 \] ÷ \[ $97.96 \]
*   YTM = .0422, or 4.22%  
    

This bond's YTM is less than its coupon rate, so the next step is to estimate rates to learn what its YTM is. Here, we'll use 6%, so the coupon payment would be ( 6% x $100 ) / 2 = $3.00.  

*   YTM = \[ $3.00 + ($100 - $95.92) ÷ 2.5 \] ÷ \[ ($100 + $95.92) ÷ 2 \]
*   YTM = \[ $3.00 + $4.08 ÷ 2.5\] ÷ \[$195.92 ÷ 2 \]
*   YTM = \[ $3.00 + $1.632 \] ÷ \[ $97.96 \]
*   YTM = \[ $4.632\] ÷ \[$97.96\]
*   YTM = .0473. or 4.73%

Next, we'll try 7%, with a YTM of ( 7% x $100 ) / 2 = $3.50

*   YTM = \[ $3.50 + ($100 - $95.92) ÷ 2.5 \] ÷ \[ ($100 + $95.92) ÷ 2 \]
*   YTM = \[ $3.50 + $4.08 ÷ 2.5\] ÷ \[$195.92 ÷ 2 \]
*   YTM = \[ $3.50 + $1.632 \] ÷ \[ $97.96 \]
*   YTM = \[ $5.132\] ÷ \[$97.96\]
*   YTM = 0.0524, or 5.24%

Because 7% has a YTM of more than the [current yield](https://www.investopedia.com/terms/c/currentyield.asp) and 6% results in less than the current yield of 5.21%, we know the rate is between 6% and 7%. This is how investors calculate and test several bond prices by plugging various annual interest rates that are higher than the bond's coupon rate:

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 the example is $95.92, the chart indicates that the interest rate is between 6% and 7%.

Having determined the range of rates, investors can take a closer look and make another table showing the prices where YTM calculations produce a series of interest rates increasing in increments of 0.1% instead of 1.0%. Using interest rates with smaller increments, calculated bond prices are as follows:

The present value of this bond is equal to $95.92 when the YTM is at 6.8%. Fortunately, 6.8% corresponds precisely to the bond price, so no further calculations are required. If the investor found that using a YTM of 6.8% in their calculations did not yield the exact bond price, they would continue trials and test interest rates increasing in 0.01% increments.

## Variations of YTM

Yield to maturity has variations that account for bonds with embedded options:

*   **Yield to Call (YTC)**: Assumes the bond will be called and repurchased by the issuer before it reaches maturity and thus has a shorter cash flow period. [Yield to Call](https://www.investopedia.com/terms/y/yieldtocall.asp) is calculated, assuming the bond will be called as soon as possible and financially feasible.
*   **Yield to Put (YTP)**: Similar to YTC; However, the holder of a [put bond](https://www.investopedia.com/terms/p/putbond.asp) can 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 returned to the issuer as soon as possible and financially feasible.
*   **Yield to Worst (YTW)**: A calculation used when a bond has multiple options. If an investor evaluates a bond with both call and put provisions, they would calculate the [Yield to Worst](https://www.investopedia.com/terms/y/yieldtoworst.asp) based on the option terms that give the lowest yield.  
    

## Explain Like I'm 5

A bond's maturity date is the date the issuer is required to pay back the bondholder. Yield to maturity is the estimated total return you get from a bond if you hold it until it matures.

Yield to maturity is calculated using different interest rates to find a bond that offers the best estimated total return at current prices.

## What Is Meant By Yield to Maturity?

Yield to maturity is the total return you should expect from a bond if you hold it until it matures.

## Is Higher or Lower YTM Better?

It depends on market conditions. If the YTM is higher than the current yield, it might be undervalued, indicating a possible buy opportunity. If the YTM is lower than the current yield, it might indicate the bond is overvalued and could be sold.

## How Is YTM Calculated?

Yield to maturity is calculated using its current value, coupon payment, years to maturity, and face (par) value.

## The Bottom Line

A bond's yield to maturity is the internal rate of return required for the present value of all future cash flows, including 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.