# Assumptions of Yield to Maturity Calculations

by Cam Merritt, studioD

The yield to maturity of a bond tells you the rate you will earn on your investment based on the price you pay for the bond, the regular interest payments you will receive while you own the bond and the payment you will receive when the bond matures. The calculations of yield to maturity rest on a couple of assumptions.

## Bond Basics

The typical bond has a face value and a stated interest rate, commonly called the coupon rate. A bondholder receives interest payments based on the coupon rate. A five-year, \$1,000 bond with an annual coupon rate of 7 percent, for example, will receive \$70 each year in interest -- 7 percent of \$1,000. If the bondholder actually paid \$1,000 for the bond, her annual return is 7 percent. But bonds commonly sell for more or less than their face values. The price you pay for the bond determines the interest rate you really earn, known as the yield to maturity or just "yield." If you pay less than face value, your return will be higher than the coupon rate. (If you paid \$900 for the bond, for example, a \$70 coupon payment is more like a 7.8 percent return that year.) If you pay more than face value, your return will be lower than the coupon rate.

## Holding Period

The first major assumption in yield-to-maturity calculations is evident in the name itself. Yield to maturity assumes that the bondholder will actually hold onto the bond until it matures, collecting all the coupon payments as well as the maturity payment. Unless the bond was purchased for face value -- "at par" -- the bondholder won't earn the rate implied by the yield unless she also collects the maturity payment. That's because the difference between the price paid for the bond and the face value received at maturity factors into the yield.

## Calculations

Bond prices follow a formula, in which "P" is the price, "CPN" is the coupon payment each period, "Y" is the yield per period, "N" is the number of periods in the bond term and "FV" is the face value of the bond. The formula is this: P = (CPN / Y) * [1 - 1/(1+Y)^N] + FV/(1+Y)^N In the formula, "FV/(1+Y)^N" represents the maturity payment. This portion of the price also takes into account the yield rate. Thus, the assumption built into the yield is that the buyer will hold the bond to maturity. Even if the buyer doesn't plan to do so, however, the price remains the same. At some point, someone is going to collect the maturity payment, so the value of that future cash flow will be included in the bond's price all along.

## Default Risk

The second big assumption made in calculating yield to maturity is that the issuer of the bond will actually make all the payments. With the exception of U.S. Treasury securities, which the financial world generally assumes to be risk free, any bond carries a risk of default, even if that risk is very small. Some bonds have to offer a higher interest rate than others because they have a greater default risk. If the bond issuer winds up not making some or all of the promised payments, the investor won't realize anything like the yield-to-maturity rate.

#### References (2)

• "Corporare Finance: The Core," Second Edition; Jonathan Berk and Peter DeMarzo
• "Financial Accounting for MBAs," Fourth Edition; Peter D. Easton, et al

#### About the Author

Cam Merritt is a writer and editor specializing in business, personal finance and home design. He has contributed to USA Today, The Des Moines Register and Better Homes and Gardens"publications. Merritt has a journalism degree from Drake University and is pursuing an MBA from the University of Iowa.

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