### Yield to maturity equal coupon rate

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.

## How are bond yields different from coupon rate? - The Financial Express

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. 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:. The most widely used measure of a bond's rate of return is the yield to maturity YTM.

As noted earlier, the YTM, or simply the yield, is the rate that equates the purchase price of the bond with the present value of its future cash flows. Mathematically, the YTM y is found by solving the following equation:.

Calculating the Yield of a Coupon Bond using Excel

The YTM is analogous to the internal rate of return used in capital budgeting. It is a measure of the rate at which the investment grows. It also assumes the bond is held to maturity and that all CFs from the bond are reinvested to maturity at the calculated YTM.

If the cash flows on the bond coupons and principal are not equal, then Equation 1 cannot be solved directly for the YTM.

## The yield to maturity and bond equivalent yield

Alternatively, one must use an iterative trial and error procedure, substituting different y values into Equation 1 until a y is found that equates the present value of the bond's cash flows to the market price. An estimate of the YTM, however, can be found using the bond's average rate to maturity, ARTM also referred to as the yield approximation formula.

This measure determines the rate as the average return per year as a proportion of the average price of the bond per year. For a coupon bond with a principal paid at maturity, the average return per year on the bond is its annual coupon plus its average annual capital gain. Thus the ARTM is:.

The YTM calculated above represents the yield for the period in the above example this was an annual rate, given annual coupons. If a bond's CFs were semiannual, then solving Equation 1 for y would yield a 6-month rate; if the CFs were monthly, then solving 1 for y would yield a monthly rate.

### What is Bond Pricing Formula?

To obtain a simple annualized rate with no compounding , y A , one needs to multiply the periodic rate, y , by the number of periods in the year. In this example, the simple annualized rate is obtained by determining the periodic rate on a bond paying coupons semiannually and then multiplying by 2.

Because Treasury bonds and many corporate bonds pay coupons semiannually, the rate obtained by multiplying the semiannual periodic rate by 2 is called the bond-equivalent yield. Bonds with different payment frequencies often have their rates expressed in terms of their bond-equivalent yields so that their rates can be compared to each other on a common basis.

This bond-equivalent yield, though, does not take into account the reinvestment of the bond's cash flows during the year. Therefore, it underestimates the actual rate of return earned. As noted earlier, the In general, the bond market is volatile, and fixed income securities carry interest rate risk. As interest rates rise, bond prices usually fall, and vice versa. This effect is usually more pronounced for longer-term securities.

## How are bond yields different from coupon rate?

Fixed income securities also carry inflation risk, liquidity risk, call risk, and credit and default risks for both issuers and counterparties. Any fixed income security sold or redeemed prior to maturity may be subject to loss. Skip to Main Content. Search fidelity. Investment Products. The yield to maturity and the interest rate used to discount cash flows to be received by a bondholder are two terms representing the same number in the bond pricing formula, but they have different economic meanings.

While yield to maturity is a measure of the total return a bond offers, an interest rate is simply the percentage return offered on an annual basis. Discounting refers to reducing the future cash flow by an amount that reflects the interest earned over time: The higher the interest rate, the lower the present value of the future cash flows and the lower the bond price, which is the sum of the discounted future cash flows. Cash flows consist of coupon payments — the interest paid by the corporation each year, plus the final return to the bondholder of the principal borrowed by the corporation.

When a coupon-paying bond is first issued by a corporation, the coupon rate is often set very close to the return required by investors for a security possessing risk characteristics of the bond being issued. Assume that investors require a 5 percent rate of return. Bonds are also called fixed-income securities because the coupons paid by the corporation issuing a bond do not change over time.

However, the economy and interest rate environment do change, and then the return that investors require changes. This is because it still pays the same fixed coupon of each year 5 percent of the par value. To earn 6 percent, a smaller investment — a lower bond price -- is necessary, because bond prices and interest rates are inversely related. The yield to maturity is the yield that you would earn if you held the bond to maturity and were able to reinvest the coupon payments at that same rate.

It is the same number used in the bond pricing formula to discount future cash flows.

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Kathryn Christopher has been writing about investments for more than 20 years. Her work has appeared in the "Journal of Alternative Investments" and numerous other academic and industry publications.