### If the market rate is greater than the coupon rate bonds will be sold at a premium

A bond's yield can be measured in a few different ways. Current yield compares the coupon rate to the current market price of the bond. A more comprehensive measure of a bond's rate of return is its yield to maturity. Since it is possible to generate profit or loss by purchasing bonds below or above par, this yield calculation takes into account the effect of the purchase price on the total rate of return.

If a bond's purchase price is equal to its par value, then the coupon rate, current yield, and yield to maturity are the same. Fixed Income Essentials. Treasury Bonds. Investopedia uses cookies to provide you with a great user experience. By using Investopedia, you accept our. Your Money.

## 6 ways bonds can bite you

Bond Yield Rate vs. Coupon Rate: An Overview A bond's coupon rate is the rate of interest it pays annually, while its yield is the rate of return it generates. Key Takeaways Coupon rates are influenced by government-set interest rates. In addition, a bond's designated credit rating will influence its price and it can happen that when looking at a bond's price, you will find it does not honestly show the relationship between other interest rates and the coupon rate at all. To understand the full measure of a rate of return on a bond, check its yield to maturity. Compare Investment Accounts.

The offers that appear in this table are from partnerships from which Investopedia receives compensation. T he yield concept provides a common bond metric that lets investors compare securities of different kinds and maturities, regarding the returns they offer. But what is the real, effective return rate? That is, what is the yield? What is the percent yield formula? Two primary approaches to yield calculations attempt to answer these questions: Firstly, Current yield and, secondly, Yield to maturity YTM.

T he Current yield for a bond is merely the annual interest payment, expressed as a percentage of the purchase price. For the investor who buys at face value par , the current yield and coupon rate are the same. A drop in the price below par would likely occur, for instance, if interest rates in the economy in general rise.

Now, only at the below-par cost does the bond offer investors return rates that compare favorably to new, higher rates available with other potential investments.

### Bond yields

An increase in price above par would likely occur if interest rates in the economy had fallen. Now, at the higher price, the bond offers investors return rates comparable to new, lower rates available on other potential investments. At this point, those with a background in finance may begin to suspect they have seen something like this definition before.

And, the sense of deja vu is appropriate because YTM is just the cash flow metric internal rate of return IRR under a different name. Internal return for the same bond investment is just a simple rearrangement of the above equation. IRR is the interest rate discount rate that equates both sides of this equation:. Each compares the timing and magnitude of investment gains to investment costs. And, each metric has its unique way of making this comparison. In any case, businesspeople should understand firstly, which conclusions about YTM numbers they can rely upon without further justification.

Investors may be tempted to draw still other kinds of conclusions about YTM numbers. Investors should understand, secondly, that these conclusions may or may not be justified. The answer to that question requires more analysis using a the investor's real cost of capital, b the actual return rate the investor achieves on re-invested funds, and c accurate estimates of future interest rates. The next two sections show the mathematical basis for this result, and another section further below, " Discount and Premium Pricing ," explains how the relationships between yields and coupon rates change when interest rates change.

To skip the next mathematics sections and go directly to the following topic on YTM for Zero Coupon securities, click here. F or the following example, yield to maturity is an interest rate that equates the purchase price with the present value of all future inflows from the investment. YTM is based on the same bond and transaction characteristics used above to calculate current yield, except that YTM also factors in the time remaining until maturity.

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Exhibit 1. Businesspeople often confuse the terms cost, expenditure, and expense. However, these, terms have different meanings and are not interchangeable.

Note that twelve interest-paying periods occur between purchase and maturity twice yearly payments for six years , and the interest rate for each is the annual rate i divided by 2. You can get a sense of how this works from Exhibit 2, which shows the NPV sum of present values of the cash inflows in the chart above, at different discount rates different i values. Exhibit 2 : "Net present value" of a bond's future returns, plotted as a function of discount rate.

Yield to Maturity is the discount rate that equates NPV of the investment with the bond purchase price. Exhibit 3. The same expression also serves to show the relationship between bond yield to maturity YTM and bond purchase price. The value of "i" that satisfies the equation, in this case, is This move creates an immediate cash outflow, the FV 0 in the equation. Given the same cash inflows and outflows, the same value of "i" solves both equations. One reason that people with financial backgrounds often turn to IRR, no doubt, when comparing potential business investments.

They do so even when the comparing investments of quite different kinds. The projected IRR for, say, an investment in a marketing program compares directly with the YTM of a potential bond investment. With zero-coupon bonds, however, the idea is more straightforward to apply. What is its yield to maturity? Now, what is its yield to maturity?

C urrent yield calculates as a ratio of two numbers, the periodic interest payment amount divided by the purchase price. However, Yield to maturity is "found" rather than "calculated," by trying different interest rates until a rate appears that equates purchase price with the present value of all future payments to the investor.

Finding YTM values could be a cumbersome, work-intensive exercise, except that today the internet provides an abundance of easy-to-use yield calculators. Most pre-programmed financial calculators also find YTM from a simple entry of data. The first example below re-uses data from above to show how Excel YIELD function finds yield to maturity for a bond transaction with the characteristics shown here.

YIELD settlement, maturity rate, pr, redemption, frequency, basis. Notice the following about the input parameters,. The only difference between the above example, for a coupon paying investment, and the next example for zero-coupon security, is the use of the rate parameter. Here again are similar data, but this time for zero coupon investment:. The spreadsheet user should see the YTM value of 2.

Notice that the YIELD function requires a non-zero coupon frequency, the final parameter entered here, even when the coupon rate is 0. Entering a frequency of 0 produces an error message.

## The Terminology of Bonds

E xamples above show that a single bond may have three different interest rates at any one time:. All three rates will be equal only when the bond is selling at par value. When its price is above or below par, these three rates will differ among themselves. Note that the relationships these rates give rise to the market terms "discount" and "premium. A bond is said to be selling at a discount when the coupon rate is less than the current yield, and the current yield is less than the yield to maturity.

They sell at a discount when interest rates in the economy, in general, are higher than they were on the security date of issue. By the same reasoning, a bond is said to be selling at a premium when the coupon rate exceeds current yield, and the current yield is greater than the yield to maturity. This bond is now selling at a premium, probably the result of falling interest rates since the bond's issue date. T he examples above show that as interest rates in the economy rise and fall, bond prices also fall and rise in response. As a result, investors have a keen interest in forecasting future interest rates and interest rate changes.

Some investors view the yield curve very much in the way that so-called "technical analysts" see stock price charts. The belief is that historical displays contain information that helps predict future price and interest changes. A characteristic yield curve for debt securities of a given class might have this form shown in Exhibit 4 below. Exhibit 4. A typical yield curve for debt securities. Bonds of approximately equal credit quality but different maturities are plotted between axes that represent yield and time to maturity, as shown in the example. To investors and analysts, the chart's message conveys in its shape.

In this example, for instance, longer maturity securities have a higher yield compared to shorter. Investors ordinarily expect this difference because it is reasonable to view longer maturities as riskier, and therefore having to pay higher yields. In any case, three main classes of yield curve shapes are:.

Yield curve "slope" also carries a message: A steep slope indicates a rapid change in interest rates, but a shallow slope suggests the opposite. All three yield curve shapes can be present in the same economy, at the same time, depending on the credit quality, issuing source, and nature of the payment schedule.

Why Bond Prices and Yields are Inversely Related

Yield curves, moreover, change daily for some securities. The US Treasury, for instance, publishes yield curves for its Treasury notes on a daily basis.