# What Is Yield to Maturity (YTM)?

The yield to maturity represents the comprehensive rate of return acquired from a bond upon receipt of all interest payments and the principal repayment. Essentially, YTM signifies the bond's internal rate of return if it is retained until maturity. The calculation of YTM can be intricate, assuming reinvestment of all coupon or interest payments at an equal rate to the bond. It's important to distinguish YTM from the bond's coupon rate, which denotes the total income provided during the bond's tenure. YTM computations typically neglect the consideration of taxes applicable to bond earnings.

## Basics

Yield to maturity (YTM) is an expression of the total return expected from a bond held until maturity. It signifies the internal rate of return (IRR) on an investment in the bond, assuming it is held until maturity, with timely payments and reinvestments at a consistent rate. This long-term bond yield is presented as an annual rate.

## Exploring Yield to Maturity (YTM)

Yield to maturity, alternatively known as book yield or redemption yield, differs from current yield, which calculates annual bond cash inflows divided by its market price for a one-year holding gain assessment. YTM, however, incorporates the present value of future coupon payments, acknowledging the time value of money, thus offering a more comprehensive return calculation for bonds. Examining the YTM of a non-coupon discount bond provides valuable insights into the complexities of coupon bonds.

## Yield to Maturity Calculation and Formula

Here is the formula for computing the YTM of a discount bond:

- "n" represents the number of periods to maturity
- "Face Value" denotes the bond's maturity value or par value
- "Current Price" signifies the bond's present market price

Given that YTM represents the interest rate achievable through reinvesting each bond coupon payment at a consistent rate until maturity, the market price of the bond aligns with the present value of all future cash flows. Although an investor possesses information about the bond's current price, coupon payments, and maturity value, determining the discount rate requires an indirect approach. To compute YTM, a trial-and-error method is employed, employing the subsequent present value formula:

Or this:

The YTM calculation involves knowledge of each future cash flow from the bond and the known current bond price. To determine YTM, a trial-and-error approach is applied to the equation until the present value of payments aligns with the bond's price.

The manual solution of this equation necessitates an understanding of the bond's price-yield relationship, considering bond pricing variations: discount, par, and premium. When a bond is priced at par, its interest rate equals the coupon rate. Premium bonds, priced above par, possess a coupon rate surpassing the actual interest rate, while discount bonds, priced below par, have a coupon rate lower than the realized interest rate.

For a bond priced below par, investors find YTM by testing various annual interest rates higher than the coupon rate until the bond's price approximates the desired value. YTM computations assume reinvestment of coupon payments at the bond's current yield rate, factoring in the bond's market price, par value, coupon rate, and maturity period. YTM serves as a momentary representation of a bond's return since reinvesting coupon payments at a consistent interest rate isn't always feasible. With rising interest rates, YTM increases, while it decreases with falling rates. The intricate YTM determination process often challenges the precise calculation of YTM, prompting the use of bond yield tables, financial calculators, or online YTM calculators for approximate values.

## Comparing Yield to Maturity and Coupon Rate

Investing in bonds offers a comparatively low-risk approach. Unlike stocks, bond issuers commit to repaying the full face value upon maturity. Nonetheless, investors must conduct thorough research before any investment decision, including bond purchases. Bonds are characterized by two crucial metrics: YTM and coupon rate. YTM represents the expected total return when holding the bond until maturity, while the coupon rate, also known as coupon yield, signifies the annual interest payment based on the bond's face value.

A bond's YTM fluctuates, while the coupon rate remains constant. Purchasing a bond at face value results in an equal YTM and coupon rate. Buying a discount bond yields a higher YTM, while a premium bond (above face value) provides a higher coupon rate.

## Illustration: Deriving YTM Through Trial and Iteration

Consider an investor in possession of a $100 par value bond currently trading at a discount of $95.92. This bond matures in 30 months and offers a semi-annual coupon rate of 5%. Thus, the bond's present yield stands at 5.21%, calculated as (5% coupon x $100 par value) / $95.92 market price.

To derive the YTM, one must first establish the cash flows. Every six months, the bondholder receives a $2.50 coupon payment (5% x $100) divided by 2. Over the bond's duration, they receive five such payments of $2.50 each, along with the $100 face value at maturity. This data is then integrated into the following formula:

Now, our objective is to determine the interest rate, YTM, which can be a challenging task. However, there's no need to resort to random guessing if we pause to consider the bond price-yield relationship. As previously mentioned, when a bond is below its par value, its interest rate exceeds the coupon rate. In this instance, the bond's par value is $100, but its market price stands at $95.92, indicating it's priced at a discount. Consequently, the sought-after annual interest rate must surpass the 5% coupon rate. Armed with this insight, we can proceed to calculate and evaluate various bond prices by inputting diverse annual interest rates higher than 5% into the aforementioned formula.

Let's begin by increasing the interest rate by one and two percentage points to reach 6% and 7%, resulting in bond prices of $98 and $95, respectively. Given our bond's price of $95.92, it becomes evident that the interest rate we seek falls within the 6% to 7% range. With this rate range identified, we can delve deeper, constructing a new table that illustrates bond prices derived from YTM calculations at incremental interest rate increases of 0.1%, instead of 1.0%.

In this analysis, the bond's present value equals $95.92 precisely when the YTM stands at 6.8%. Thankfully, this rate aligns perfectly with our bond price, obviating the need for further computations. If, at this juncture, our calculations using a YTM of 6.8% did not yield an exact bond price match, we would have continued our iterative trials, testing interest rates in 0.01% increments. It becomes evident why many investors opt for specialized software to streamline YTM determination, as manual trial-and-error calculations can be protracted and time-intensive.

## Applications of YTM

Yield to maturity serves as a valuable tool for evaluating bond investments. Investors establish a necessary yield, the minimum return for a bond to be considered worthwhile. Once a bond's YTM is determined, it can be compared to the required yield, helping investors decide if the bond is a sound investment. YTM's expression as an annual rate, irrespective of a bond's maturity duration, enables the comparison of bonds with varying maturities and coupon rates on an equal annual basis.

## Different Forms of YTM

Yield to maturity exhibits various common variations tailored for bonds featuring embedded options:

- Yield to call (YTC) anticipates the bond's early redemption by the issuer, shortening the cash flow period. YTC assumes the bond's immediate call as soon as feasible and financially viable.
- Yield to put (YTP) resembles YTC but allows the bondholder to sell the bond back to the issuer at a fixed price, based on bond terms. YTP is calculated assuming the bond's prompt put back to the issuer as soon as possible and financially feasible.
- Yield to worst (YTW) applies to bonds with multiple options, such as both calls and put provisions. When assessing such a bond, investors compute YTW based on the option terms yielding the lowest yield.

## Constraints of YTM

YTM computations typically overlook investor taxes. The YTM is referred to as the gross redemption yield when taxes are factored in. Furthermore, YTM calculations exclude purchase and selling expenses. It's important to acknowledge that YTM relies on uncertain assumptions about the future, including the reinvestment of all coupons, the bond's maturity holding, and potential bond issuer defaults.

## Is a High YTM Good?

Now, the question arises: Is a higher YTM always preferable? The answer depends on the specific circumstances and investment objectives. While a higher YTM might signal a potential bargain, indicating that the bond is priced below its par value, it's crucial to conduct thorough due diligence. Consider factors such as the issuer's creditworthiness and alternative investment opportunities' interest rates. Evaluating these fundamentals is essential to make informed investment decisions in the complex world of bonds.

## Conclusion

Understanding a bond's yield to maturity involves determining the internal rate of return necessary for the present value of all future cash flows (including face value and coupon payments) to match the current bond price. YTM operates under the assumption that all coupon payments are reinvested at a yield identical to the YTM, and the bond is held until maturity.

Various bond investments are available, such as municipal, treasury, corporate, and foreign bonds. Municipal, treasury, and foreign bonds are typically obtained through local, state, or federal government channels, while corporate bonds are acquired through brokerage firms. If you are interested in corporate bonds, establishing a brokerage account is a requisite step in participating in this investment avenue.