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

Most investors buy bonds for income and for preservation of capital. In addition to getting semi-annual interest payments, bond issuers promise to repay the face value of bonds to investors at maturity. Depending on the particulars of a bond, you might pay more or less than its face value when you buy it, known as buying bonds at a premium or at a discount. The price you "should" pay is based on the required rate of return, which is a technical term that discounts the semiannual and face-value payments to present-day values.

## Required Rate of Return

The required rate of return, financially speaking, is the rate you should "require" from your bond based on comparable investments that are available. 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. For example, if there are bonds available in the marketplace that pay 5 percent, and they carry they same safety and return characteristics that you require, a bond you invest in should have at least a 5 percent return to be attractive. Therefore, you would use 5 percent as your required rate of return.

## Converting Payment Periods

Because semiannual coupon payments are paid twice per year, your required rate of return, mathematically speaking, must be cut in half. Therefore, the example's required rate of return would be 2.5 percent per semiannual period. To convert this to a coupon payment, or the amount of money you'd actually receive each period, multiply the face amount of the bond by the required rate of return.

Continuing with the example, if the face value was \$1,000, you'd multiply it by 0.025. This results in a semiannual payment of \$25.

## Discounting Future Payment to Present Values

Future payments must be discounted to present values to determine how much you should pay for your bond, but you're best off using a bond calculator – or a financial adviser – to do the heavy lifting. If you want to run through the equation on your own, 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.

In the example of a 5 percent bond – which has two 2.5 percent payments annually – with a four-year term, raise 1.025 to the power of negative 1 to calculate the discount factor for the first period. For the eighth period, raise 1.025 to the power of negative 8. Multiplying the results by the eight coupon payments and the one final face-value payment 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 have to pay a higher price, you're better off opting for the alternative investment.