# Calculate a Zero Coupon Bond

Most bonds make periodic interest payments to their owners as a return on investment and a reward for taking the risk inherent in the bond. These payments are known as coupons, because many years ago bonds would actually come with coupons that you could mail in to prompt the payment of interest. A "zero-coupon" bond, however, does not make interest payments. Instead, the bond holder is rewarded with an increase in the value of the bond over time. You can calculate the present value of a zero coupon bond using a formula involving the stated yield (return), the par or face value, and the time until maturity (when the bond's par or face value will be paid out to the bond holder).

## Steps

1. Add 1 to the required interest rate on the bond.
• The required interest rate or "yield-to-maturity" is the rate of return that a bond is presumed to require in order to entice investors to purchase the bond. Generally, bonds that are riskier will require a higher rate of return in order to attract buyers. Risks can include the potential for default (the bond issuer being unable to pay back the bond holder) or the risk of a future increase in the interest rate of new bonds, which will decrease the attractiveness (relative value) of the present bond. Also the longer the remaining time until the bond matures and pays out its final value, the riskier the bond is (simply because of the increased potential for payout problems inherent in longer periods of time).
• For example, in analyzing a zero coupon bond, if a comparable bond (one with the same time-to-maturity and issued by an equally viable company or government) sells at face value and pays an annual interest rate of 6%, then the required rate on the zero coupon bond being considered will also be 6%. Thus, for purposes of this formula, you would add 1 to 0.06 (6%) and the result is 1.06.
2. Determine the number of time periods (years in this case) remaining until the bond matures.
• For example, if the bond issuer will pay the bond holder the face value of the bond in five years, then the time-to-maturity is five.
3. Take the sum calculated in Step 1 above and raise it to the power of the remaining time period.
• Thus, 1.06 raised to the power of 5 equals 1.338.
• On a calculator, you would multiply 1.06 by itself four times in succession in order to raise it to the fifth power.
4. Divide the par (face) value of the bond by the result of the previous step.
• The par value of the bond is the amount that the bond issuer will pay to the bond holder when the bond matures. The par value is typically \$1,000.
• Thus, in this example, \$1,000 divided by 1.338 equals 747.26. This means that the present value of a zero coupon bond providing a 6% rate of return by paying out \$1,000 at maturity is \$747.26.

## Warnings

• Make sure that the required rate of return and the number of time periods remaining until maturity are measured in the same units of time. In the above example, the stated interest rate was an annual one, and the number of time periods until maturity was measured in years.

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