Yield To Maturity

The yield to maturity is a fancy way of saying the rate of return that a bond delivers if held from the current date to the date the bond matures.  In order to expand on this definition, there are some terms that a person should know.  

Par Value - The is the original value that a bond is issued at and is predetermined by the company or organization issuing the bond.  This does not mean that a bond won't sell for more or less than the par value at issuance, as the market will determine what the bond sells for.  

Maturity - This is the date that a bond matures or in other words, is redeemed.  The maturity date is also predetermined by the organization that issued the bond.   When redemption of a bond occurs, the par value of the bond is returned to the person owning the bond and in exchange, the organization that issued the bond no longer has an obligation to the former bond owner.  

Market Value - While a bond is issued and until maturity, it will have a market value.  This is the price that "the market" is willing to pay for the bond.  This price may be higher or lower than the par value depending on several factors including but not limited to the organization's financial strength and performance, and interest rates.  

Coupon Rate - The rate of interest that the organization that issued the bond will pay to the bondholder in regular increments.  The coupon rate is stated as a rate relative to the par value.  The coupon rate can be paid at different time periods depending on how the bond was issued...or the organization issuing the bond can pay no coupon at all.  

Why Yield To Maturity Is Important

If it isn't clear yet, the yield to maturity is important because it is that rate of return that a bond purchaser gets when they purchase a bond and if they hold the bond until maturity.  And if that isn't important to someone, they aren't going to make a very good bond investor.  You see, a person can't just look at the coupon rate and decide that that is the rate of return that they will get.  

A Bond's Rate of Return Come From Two Places

When speaking about basic bonds, the rate of return a bond will yield is derived from two sources.  First, and most obvious is the coupon.   The coupon provides a rate of return relative to the par value in incremental "coupon" payments.  The second, is the premium or discount that a bond is purchased for relative to the par value.  For example, if a bond is purchased for more than par value, this means the bond was purchased at a premium.  Therefore, the bond's yield to maturity will be less than the coupon rate as the premium will slowly decrease over time until at maturity, the market value will equal the par value.  We will look at an example more in depth later.

If a bond is purchased at a discount, this means the bond was purchased for less than the par value.  As a result, the bonds market value will slowly increase over time until at maturity, the market value equals the par value.  This change in the market value over time, is where the second source of an investor's yield comes from.  As you'll remember, the first source is the coupon rate.  

Yield To Maturity Formula

The yield to maturity formula is very simple if the par value equals the market value.  At that point, the yield to maturity is simply the coupon rate.  However, this is rarely the case.  Therefore, for the many times the market value doesn't equal the par value, the yield to maturity is the same as calculating the IRR(Internal Rate of Return) on any investment.  It is a calculation measuring the cash flows starting with the purchase of the bond, the coupon payments while holding the bond, and ending with the bond issuer returning the bond's principal to the bondholder at redemption or maturity.  

The IRR formula is not a simple formula nor one that can be done with pen and paper so it's hardly worth mentioning.  If a person understands how IRR is calculated using a financial calculator or excel, then you will understand how to calculate the YTM(Yield to Maturity).

Yield to Maturity Example

Let's say Peggy is evaluating the purchase of a bond and wants to know the yield to maturity...afterall, she wants to hold it until maturity.  She knows that the par value is $1,000 and the coupon payment is 5% with the coupon payment being paid annually.  That is to say, the bond will pay an annual coupon payment of $50 every year.  The market value of the bond is $900 at the moment because the interest rates have risen sharply since the bond was issued.  The bond is set to mature in 10 years from now...what is the yield to maturity?

For this problem, we need to identify the important parts and filter out the noise.  The important parts are the cash flows so let's identify those for our YTM calculation.  The initial cash flow will be the $900 purchase of the bond.  The cash flow for 10 years while the bond is held will be $50 per year.  The final cash flow at maturity is the par value or $1,000.  

If we plug that into a yield to maturity calculator, or IRR calculator, we get the yield to maturity equals 6.38 percent.  By understanding how yield to maturity works, we could have guessed that the YTM would be higher than the coupon rate of 5 percent...because we bought the bond at a discount to par.

Some Bond Basics

Inverse Relationship Between Interest Rates and Bond Prices

When discussing yield to maturity, it is also helpful to understand some basic information about bonds.   And by this, it's meant that it is important to understand that there is always an inverse relationship between a bond's price or market value and interest rates.  If interest rates go up, with all else staying equal, the market price of the bond will go down.  If interest rates go down, with all else staying equal, the market price of the bond will go up.  As you can see from the example laid out above, a lower market price means a higher yield to maturity.  

Putting this together, if interest rates go up, it means that investors are going to demand relatively higher interest rates and so in order to compensate investor demand, bond prices decrease in value.  And the vice versa is true when interest rates decrease. 

Debt Versus Equity 

It is also important to understand the difference between bonds and stocks.  Bonds and stocks are also sometimes referred to as debt and equity.  When a person buys a bond, they are lending a company money and that company offers to pay interest in return for borrowing the money.  When a person buys stock, they are receiving ownership in the company and they are compensated or rewarded when the company's income grows and their stock becomes more valuable.  

The main thing to understand between debt and equity is the risk differences between the two.  Let's ay that the company or organization in question falls on hard times and files for bankruptcy.  At this point, it is very likely that the equity in the company will be completely worthless.  That is because when a company goes bankrupt, they have to sell their assets in order to pay back creditors or debtholders first.  After creditors are paid from the proceeds from selling company assets, the equity holders can be paid.  This fact makes debt less risky relative to equity.  

Conclusion

Yield to maturity is a very important concept for any investor to understand so that when buying bonds, they know their YTM isn't just dependent on the coupon rate that is paid.  But rather, its dependent on the coupon rate AND the premium or discount that is paid for the bond relative to the par value.  This knowledge can help investors more accurately evaluate their bond purchases.  We hope you found this article from IQ Calculators useful.  Please leave a comment in the comment section.