# How to Calculate the Price of a Bond With Semiannual Coupon Interest Payments

Most bonds make simple-interest coupon payments twice a year until the bond matures, at which point it also pays the bond's face value. You can purchase these bonds at a discount or premium, depending on the expected return. However, knowing what is an acceptable price can be tricky without having a required rate of return that discounts the semiannual and face-value payments to present day values.

## Required Rate of Return

The required rate of return is usually a comparable investment that offers a certain interest rate with similar investment time and risk. The assumption is that it's pointless to invest in a bond if you can achieve an equivalent or better return with an alternative investment. As an example, if you could invest in another opportunity that guaranteed 6 percent interest per year, the bond would have to offer at least that to be attractive. Therefore, you would use 6 percent as the required rate of return to discount future bond payments.

## Converting Periods

Because semiannual coupon payments happen twice per year, your interest rates must similarly be converted by cutting them in half. Therefore, the example's required rate of return would be 3 percent per semiannual period. Likewise, the bond's advertised coupon rate of, for example, 5 percent would drop to 2.5 percent per period. If the face value of the bond is \$1,000, multiply 0.025 times \$1,000 to calculate the periodic coupon payment of \$25.

## Discounting Future Payment to Present Values

Individually multiply each future payment by the discount factor to convert it to present day value. You can calculate the discount factor by adding 1 to the semiannual required rate of return and raising the result to the nth value, where "n" is the period number expressed as a negative figure. To use a four-year bond as an example, raise 1.025 to the power of negative 1 to calculate the discount factor for the first period or negative 8 to calculate it for the eighth period. Multiplying the results by the eight coupon and one final face-value payments discounts them to \$24.27, \$23.56, \$22.88, \$22.21, \$21.57, \$20.94, \$20.33, \$19.74 and \$789.41, respectively

## Summing and Pricing

Add the results of the previous calculations to achieve a total present value. Concluding the example, adding the present values of each payment results in a total present value of \$964.91. This means the bond's price needs to be \$964.91 to achieve an equivalent return. If you can get a lower price, you'll enjoy a higher return, but if you get a higher price, you're better off opting for the alternative investment.

#### Photo Credits

• Thinkstock/Stockbyte/Getty Images