There are several ways to calculate the yield on a bond such as a U.S. Treasury bond. The yield to maturity (YTM) most accurately represents the return you will earn from a bond, but the YTM calculation is also the most complicated. It requires a trial-and-error approach to get the answer to the yield-to-maturity question. Fortunately, in an era of computers and advanced calculators, getting the YTM of your bond is a plug-and-play operation.
Prices, Interest Rates and Yields
A Treasury bond is defined by its face or principal amount, the amount if interest paid annually by the bond, time until the bond matures, and the current or purchase price. Treasury bonds are marketable securities, and the market adjusts for changing interest rates by changing market prices. The price you pay for a bond may be higher (a premium bond) or lower (a discount bond) than the face amount of the bond. Yield to maturity, or YTM, includes the loss or gain from the price differential into the total return from the bond.
Calculating for Present Value
In math terms, the yield to maturity is the single interest rate that provides a total present value of all of the future interest and principal payments from the bond to equal the price of the bond. The present value of a future chunk of cash flow can be calculated using a rate and time. To get to a yield to maturity, the present value of a bond's cash flow pieces are calculated with different interest rates until a rate is found which gives a present value equal to the bond price. Calculating by hand, you must "back into" the yield-to-maturity rate through a trial-and-error process.
In the days before personal computers, bond dealers and investment reps used a dedicated desktop bond calculator to determine prices and yields. But spreadsheet programs turned every computer into a financial calculator, and the Internet put bond calculators on a wide range of financial websites. If you like to work with the numbers yourself, the RATE function on a spreadsheet calculates the yield to maturity if you are at an interest payment date, and the YIELD function gives the YTM for days between interest payment dates.
Different Yield Numbers
There are three yields associated with a U.S. Treasury bond (and most other types of bonds). Coupon rate is the rate of interest paid based on the face value. A $10,000 face value bond with a 6-percent coupon pays $600 per yield in interest. The current yield is the coupon rate or interest divided by the current price. If the bond paying $600 per year costs $10,500, the current yield is 5.71 percent. The yield to maturity amortizes a premium or discount over the remaining life of the bond. The YTM of a premium bond will be lower than the current yield, and the YTM will be higher than the other yields for a discount bond.
Tim Plaehn has been writing financial, investment and trading articles and blogs since 2007. His work has appeared online at Seeking Alpha, Marketwatch.com and various other websites. Plaehn has a bachelor's degree in mathematics from the U.S. Air Force Academy.