What Is the Yield of a Zero-Coupon Bond at Maturity?
Corporations, municipalities and even the U.S. Treasury issue zero-coupon bonds, which releases them from the requirement of having to pay periodic interest to investors. The yield on these types of bonds is a product of the rate at which the security sells. However, this increases the volatility associated with the bond, as the investor does not have the option to reinvest a coupon payment when interest rates rise or fall.
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Characteristics
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Zero-coupon bonds do not come with coupon, or interest, payments. Instead, these bonds sell at a deep discount. For example, a 10-year, $1,000 zero-coupon bond may sell for $286 in the market. Over time, the value of the bond will increase, which is the primary means for determining yield. As a result, the yield on a zero-coupon bond is almost guaranteed for an investor.
Determining Yield
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To calculate the yield-to-maturity on a zero-coupon bond, it is easiest to use a financial calculator. However, there is a specific formula. Dividing the face value of the bond by the purchase price and raising it to the power of one divided by the number of years to maturity, then subtracting one, gives the yield. For example, a 10-year, $1,000 zero-coupon bond that sells for $380 in the market equals would yield 10.16 percent. This is derived from the equation ($1,000/$380)^(1/10) - 1 = 10.16 percent.
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Semi-Annual Compounding
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If the interest on a zero-coupon bond compounds semi-annually, rather than annually, this affects the rate of return. Rather than calculating for 10 years, or periods, it must be determined for 20 periods. Multiplying the original result by two then gives the yield. Using the previous example, the new equation would be ($1,000/$380)^(1/20) - 1 = 4.96 percent. Multiplying this by two gives a yield of 9.92 percent.
Effects of Compounding
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Reinvesting accrued interest reduces yield because the new amount reduces the necessary earnings to produce a certain amount of capital. By more frequently adding money to the initial amount, the investment does not have to produce as much in earnings. For example, it takes less earnings for $450 to reach $1,000 than for $380 to reach $1,000. With compounding, the interest adds to the amount already invested.
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