# Annual coupon yield to maturity

So in simplest terms, the coupon is the amount of fixed interest the bond will earn each year. Yield to maturity is the expected return if the bond is held until maturity. This yield is known as the yield to maturity , which is effectively a guesstimate of the average return over the bond during its remaining lifespan.

### Bond Maturity Date

As such, yield to maturity can be a critical component of bond valuation. A single discount rate applies to all as-yet-unearned interest payments. It works the other way, too. The financial markets serve as conduits through which funds are distributed from borrowers to lenders. The allocation of funds is determined by the relative rates paid on bonds, loans, and other financial securities, with the differences in rates among claims being determined by risk, maturity, and other factors that serve to differentiate the claims.

There are a number of different measures of the rates of return on bonds and loans. Some measures, for example, determine annual rates based on cash flows received over days, whereas others use days; some measures determine rates that include the compounding of cash flows, whereas some do not; and some measures include capital gains and losses, whereas others exclude price changes.

In this section, we examine some of the measures of rates of return, including the most common measureâ€”the yield to maturity. When the term rate of return is used it can mean a number of different rates, including the interest rate, coupon rate, current yield, or discount yield. The term interest rate sometimes refers to the price a borrower pays a lender for a loan. Unlike other prices, this price of credit is expressed as the ratio of the cost or fee for borrowing and the amount borrowed. This price is typically expressed as an annual percentage of the loan even if the loan is for less than one year.

Today, financial economists often refer to the yield to maturity on a bond as the interest rate. In this article, the term interest rate will mean yield to maturity.

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## Bond Yield-to-Maturity

Another measure of rate of return is a bond's coupon rate. As noted in the last section, the coupon rate , C R , is the contractual rate the issuer agrees to pay each period. It is usually expressed as a proportion of the annual coupon payment to the bond's face value:. Unless the bond is purchased at par, the coupon rate is not a good measure of the bond's rate of return because it fails to take into account the price paid for the bond.

In examining corporate bond quotes, the current yield on a bond is often provided. As noted, this rate is computed as the ratio of the bond's annual coupon to its current price. This measure provides a quick estimate of a bond's rate of return, but in many cases not an accurate one because it does not capture price changes. The current yield is a good approximation of the bond's yield, if the bond is selling at or near its face value or if it has a long maturity. That is, we noted earlier that if a bond is selling at par, its coupon rate is equal to the discount rate. In this case, the current yield is equal to the bond's yield to maturity.

Thus, the closer the bond's price is to its face value, the closer the current yield is to the bond's yield to maturity. As for maturity, note that a coupon bond with no maturity or repayment of principal, known as a perpetuity or consul , pays a fixed amount of coupons forever. The value of such a bond is:. Thus, when a coupon bond has a long-term maturity e.

Finally, the discount yield is the bond's return expressed as a proportion of its face value.

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The discount yield used to be the rate frequently quoted by financial institutions on their loans because the discount rate is lower than a rate quoted on the borrowed amount. The difficulty with this rate measure is that it does not capture the conceptual notion of the rate of return being the rate at which the investment grows. Because of tradition, the rates on Treasury bills are quoted by dealers in terms of the bills' discount yields.

Whereas Treasury bills have maturities less than one year, the discount yields are quoted on an annualized basis. As we noted in the last section, dealers quoting the annualized rates use a day count convention of actual days to maturity but with a day year:. But, when the asset sells for more than their face value it sells at a premium. Likewise, when they sell for less than the face value they sell at a discount. To an individual bond investor, the coupon payment is the source of bond profit. To the bond trader, there is the potential gain or loss generated by variations in market price.

The yield to maturity calculation incorporates the potential gains or losses generated by those market price changes. If an investor purchases a bond at par value or face value , the yield to maturity is equal to its coupon rate.

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If the investor purchases the bond at a discount, its yield to maturity will be higher than its coupon rate. YTM represents the average return of the bond over its remaining lifetime. Calculations apply a single discount rate to future payments creating a present value that will be about equivalent to the bond's price. In this way, the time until maturity, coupon rate, current price, and the difference between price and face value all are considered.

### A Guide for Beginning Bond Investors: Coupon vs. Yield to Maturity

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## Bond Yield to Maturity (YTM) Formula

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