# When are a bond’s coupon rate and yield to maturity the same?

By Mark Holland / a few days ago The coupon rate of a bond equals its yield to maturity if its purchase price equals its face value. The face value of a bond is its face value, or the declared value of the bond at the time of issue, as determined by the issuing entity. Most bonds have a face value of \$ 100 or \$ 1,000.

However, the face value of a bond does not determine its market price. Instead, the market or selling price of a bond is influenced by a number of factors in addition to its peer. These factors include the bond’s coupon rate, maturity date, prevailing interest rates, and the availability of more lucrative bonds.

## Defining the coupon rate, maturity date and market value of the bonds

The coupon rate of a bond is its interest rate, or the amount of money it pays to the bondholder each year, expressed as a percentage of its face value. A bond with a face value of \$ 1,000 and a coupon rate of 5% pays \$ 50 in interest each year until maturity.

Suppose you purchase an IBM Corp. bond with a face value of \$ 1,000 and it is issued with semiannual payments of \$ 10. To calculate the bond’s coupon rate, divide the total annual interest payments by the face value. In this case, the total annual interest payment equals \$ 10 x 2 = \$ 20. Therefore, the annual coupon rate for IBM bonds is equal to \$ 20 ÷ \$ 1000 = 2%.

Coupons are fixed; Regardless of the price the bond is trading for, the interest payments always equal \$ 20 per year. So if interest rates went up, lowering the price of the IBM bond to \$ 980, the 2% coupon on the bond will remain unchanged.

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The maturity date of a bond is simply the date on which the bondholder receives a refund of their investment. Upon maturity, the issuing entity must pay the bondholder the nominal value of the bond, regardless of its current market value. This means that if an investor purchases a \$ 1,000 five-year bond for \$ 800, he will collect \$ 1,000 at the end of the five years, in addition to any coupon payments he received during that time.

The market value of bonds has a negative correlation with prevailing interest rates. As interest rates go up, the price of pre-existing bonds goes down. As rates drop, today’s higher-rate bonds become more valuable.

For example, if a company issues a \$ 1,000 bond with an interest rate of 4%, but the government subsequently raises the minimum interest rate to 5%, then any new bonds that are issued will have higher coupon payments than the 4% initial bonus from the company. To entice investors to buy the bond despite its lower coupon payments, the company has to sell the bond for less than its face value, which is called a discount. If interest rates fall to 3%, the pre-existing 4% bond sells for more than its face value, which is called a premium.

Since the market price of bonds is so variable, it is possible to make a profit in addition to that generated by coupon payments by buying discount bonds. The yield to maturity of a bond is the rate of return generated by a bond after accounting for its market price, expressed as a percentage of its face value. Considered a more accurate estimate of the yield of a bond than other yield calculations, the yield to maturity of a bond incorporates the profit or loss created by the difference between the bond’s purchase price and its face value.

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## Comparison of bond coupon rates and yields

The coupon rate is often different from the yield. The yield on a bond is more accurately viewed as the effective rate of return based on the bond’s actual market value. At face value, the coupon rate and the yield are equal. If you sell your IBM Corp. bond with a premium of \$ 100, the yield on the bond is now equal to \$ 20 / \$ 1,100 = 1.82%. Assuming interest rates increased and the price of your bond fell to \$ 980, your return on selling the bond at a discount will be \$ 20 / \$ 980 = 2.04%. Therefore, performance and price are inversely related.

Because coupon payments are not the only source of earnings on bonds, the yield to maturity calculation incorporates the potential gains or losses generated by changes in market price. If an investor buys a bond at face value, the yield to maturity equals the coupon rate. If the investor buys the bond at a discount, his yield to maturity is always greater than his coupon rate. In contrast, a bond purchased at a premium always has a yield to maturity lower than its coupon rate.

The yield to maturity approximates the average yield on the bond over the remaining term. A single discount rate is applied to all future interest payments to create a present value roughly equivalent to the price of the bond. The entire calculation takes into account the coupon rate, the current price of the bond, the difference between the price and the face value, and the time to maturity. Along with the spot rate, the yield to maturity is one of the most important figures in bond valuation.