# Yield to Maturity: A Bond

Published 17 Oct 2017

A bond is a debt security that is usually issued by parties like companies or governments in order to raise funds to be used for particular purposes. A company borrows money from a certain group and in return gives assurance that it will pay the amount it borrowed plus interest on an earlier agreed time. In general then, a bond functions like an “IOU.”

In order to have a simple understanding of how a bond works, one only need remember these three terms: face or par value, coupon or interest rate and maturity. The par value is the amount that the borrower pays when the bond becomes due. Coupon is simply another term for interest payment. Maturity is the date wherein the borrower will pay the lender the par value of the bond. The date of maturity is agreed upon earlier by both the borrower and lender when the bond is issued.

In the problem, all we know is that my coworker has purchased a bond that has a 10% coupon. Let us assume that the bond my coworker bought has a par value of \$10,000 and matures in 5 years. What this means is that my coworker will receive a total of \$1,000 of interest per year up to 5 years. Once the 5 years is up, my coworker gets back the original \$10,000 used to pay for the bond.

Now we talk about yield. Yield is defined as the return a lender gets for a bond issued. The easiest way to compute this is to divide the coupon amount with the price. So in the problem stated, the yield on the bond that my coworker bought is equal to \$1,000/\$10,000 or 10%. Take note that yield is not the same as coupon. Coupon is a fixed amount while yield changes with respect to the price. Meaning, if prior to maturity, the price of the bond drops to \$5,000 then the coupon is still 10% but the yield is now \$1,000/\$5,000 or 20%. What this shows is that my coworker would still be receiving \$1,000 of interest per year on a bond that is now worth just \$5,000.

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The bond market however is not as simple and this is where confusion begins. While we know what it means, in the market when people say yield, they typically refer to yield to maturity. Before moving on, let us go back to our original definition of yield. We know that when the price decreases, the yield increases or vice-versa.

So if you’re planning to invest on bonds, you would probably prefer to buy it at a lower price since it gives a higher yield. However, if you have already invested in a bond, you would prefer that the price increase so that if you sell it before it matures, then you stand to gain a certain amount of profit. As seen here, bonds work like stocks since they can be bought or sold anytime prior to the maturity date.

This is where the idea of yield to maturity comes in. Yield to maturity or YTM, is rate of return that is obtained from a bond when a lender holds on it until it matures. While the computation is not easy, it takes into account four factors namely: the current price of the bond on the market, the par value of the bond, the coupon and the number of years it takes for the bond to mature.

By considering these four factors, we can have three possible conclusions. If the coupon is greater than the current yield which in turn is greater than the YTM, then the bond is selling at a premium. If it is the opposite, that is the YTM is greater than the current yield which is greater than the coupon, then the bond is selling at a discount. If all the values are equal then the bond is said to be selling at par.

So my coworker says that the bond carries 10% coupon but the broker says that the YTM is 9%. Even with only these two bits of information, I know that the bond my coworker bought is currently selling at premium. Simply put, the bond is currently selling at a price higher than the par value.

### References

• Block, S.B. & Hirt, G. (2005). Foundations of Financial Management (11th ed.). New York: McGaw-Hill.
• Thau, Annette. (2000). The Bond Book: Everything Investors Need to Know About Treasuries,Municipals, GNMAs, Corporates, Zeros, Bond Funds, Money Market Funds, and More. McGraw-Hill.
• Moneychimp. Bond Yield-to-Maturity. Retrived April 28, 2008.