# Yield to Maturity (YTM)

Yield to maturity (YTM) is the general return expected to be received from a bond if this debt instrument is kept to its maturity. Yield to maturity refers to income on long-term bonds, however, it is expressed in the form of an annual rate. Yield to maturity is the internal rate of return (IRR) of a debt instrument, provided that the investor keeps the bond in his portfolio until it matures, all payments are made strictly on schedule, and reinvestment is carried out at the same rate. Book and redemption yield are other equally well-known names for yield to maturity.

## What is Yield to Maturity

Yield to maturity is like the current yield that is calculated by dividing the cash inflow from bonds in a year by the market value of these investments. Through this action, an investor can find out the income received from the purchase and retention of bonds in the portfolio for a whole year.

In contrast to the current yield, the yield to maturity considers the present value of anticipated coming bond coupon payouts. This calculation uses the time value of money, which is not taken into account in a simple calculation of current yield, and therefore is the most accurate method for figuring out bond return.

The discount bond yield to maturity, coupon payments on which are not paid, can be taken as a starting point for clarifying more complicated problems connected with coupon bonds.

Yield to maturity is subject to temporary fluctuations, whereas the rate of coupon does not change, and it is the main difference between these two concepts. Bond price and interest rates affect yield to maturity. It is believed if the coupon rate is below the yield to maturity, the bond is sold at a discount to its par value, and when the yield to maturity is greater than the coupon rate, the bond selling is at a premium.

Sometimes calculating the yield to maturity is a rather complicated procedure, that suggests all received coupons will be reinvested at the similar rate of return as the bond. A higher yield to maturity can give a signal about an ability of a bargain opportunity, because the current bond is accessible for less than its par value. The yield to maturity of a bond will be greater when the bond price is smaller.

## How to calculate Yield to Maturity

To figure out the yield to maturity of a discount bond:

The present value of all upcoming money flows corresponds to the bond value in the market, since the yield to maturity is considered to be the interest rate that would be ultimately received by an investor if he reinvests each bond coupon at a fixed rate until the maturity.

It is impossible to calculate the discount rate directly, even if an investor knows such parameters as the bond price at the current moment, its coupon size and redemption value.

A trial-and-error technique is applied to figure out the yield to maturity. To calculate it, the present value formula is used:

In such a situation, the bond price at the current moment and anticipated cash flows of the bond are known, and trial and error is applied to the yield to maturity variable in the equation until the present value of the payment stream equal to the bond price.

## Example of Yield to Maturity

Assume that some investor owns a bond with a par value of $100. At the current moment, the bond price in the market is $90.5, it priced at a discount, maturity date is 30 months, and its semi-annual coupon equal to 7%. As a result, the bond current yield = (7% x $100) / $90.5 = 7.73%.

In order to figure out the yield to maturity, the first step is to identify the cash flows. The holder of the bond would get a coupon equal to (7% x $100)/2 = $3.50 every half a year.

This investor would get 5 payments of $3.50 besides the bond face value of $100 at maturity.

After that, this data is used in the formula:

Again, if a bond is valued at a discount from face value, the rate on it will be above the coupon rate. In the example above, the bond that has a par value of $100, but it is currently priced lower than par value at the price of $90.5, meaning the bond is valued at a discount. As a result, the annual interest rate should be above the coupon rate, that is, 7%.

Applying several various interest rates above 7% by the technique of trial and error, an investor can assume the bond yield to maturity, assuming that there is an inverse connection between the bond price and the interest. Since the current price of the bond is known and equal to $90.5, the yield to maturity must be about a value of 9%.

The present value is at the level of $90.5 when the yield to maturity is at 9.4%. 9.4% equal to the price of the bond, so no other calculations are needed. If we found that using a yield to maturity of 9.4% in the presented calculations did not give the exact price of the bond, it would be necessary to continue testing in order to test interest rates increasing in increments of 0.01%.

Many investors use special programs to calculate the yield to maturity without using the trial and error method, as the calculations required to determine the yield to maturity can be quite lengthy and time-consuming.

## How to use Yield to Maturity

Yield to maturity is necessary to understand whether buying a bond is a profitable investment. The first step for an investor is to figure out a required yield, that is, a bond return that makes the debt instrument worthwhile. Then the yield to maturity of this bond should be calculated by the investor. After that, these two indicators may be compared, determining the benefit of current acquisition.

As mentioned above, the yield to maturity is reflected in the form of an annual rate without reference to bond maturity. That is why yield to maturity can be applied as a comparative measure for bonds with different maturities and coupon payments, because yield to maturity represents different bond prices using the same annual expression.

## Restrictions of Yield to Maturity

Taxes paid by investors on bonds are usually not included in the yield to maturity calculation. Then, the yield to maturity is called the gross redemption yield. Purchasing or selling costs are also not taken into account in yield to maturity calculations.

In addition, yield to maturity allows the investor to form hypotheses about the future, unknown in advance. Thus, all coupons may not be reinvested by the investor, or the issuer of a bond can be in the state of default.

## Versions of Yield to Maturity

There are several widespread versions of yield to maturity that take into account bonds with embedded options:

**Yield to call (YTC)**. Yield to call means that the issuer will repurchase the bond before it matures, and the bond will be called. As a result, the cash flow period of this debt investment will be shorter than expected. The calculation of YTC is carried out taking into account the expected situation when the bond will be called in the nearest future at the first financial opportunity and the conditions created for this.

**Yield to put (YTP). **Yield to put differs from yield to call in that a put bond can be sold back by its holder to the issuer at a set constant price, depending on the terms of the bond. YTP calculation is made taking into account the fact that the bond will be returned to the issuer in the nearest future at the first financial opportunity.

**Yield to worst (YTW). **Yield to worst is a method to calculate a bond with numerous options. For instance, when investors were evaluating bonds with both calls and put provisions, they would calculate the yield to worst based on the option terms that demonstrate the minimum yield.