How Do I Price Bonds?

Bond Pricing

Prices for bonds traded on an organized exchange are often published in newspapers and through online services. This information normally includes the bond price (called quote), its contract rate, and its current market (called yield) rate. However, only a fraction of bonds are traded on organized exchanges. To compute the price of a bond, we apply present value concepts. This section explains how to use present value concepts to price the Fila discount bond and the Adidas premium bond described earlier.

Point: InvestingInBonds.com is a bond research and learning source.

Present Value of a Discount Bond The issue price of bonds is found by computing the present value of the bonds’ cash payments, discounted at the bonds’ market rate. When computing the present value of the Fila bonds, we work with semiannual compounding periods because this is the time between interest payments; the annual market rate of 10% is considered a semiannual rate of 5%. Also, the two-year bond life is viewed as four semiannual periods. The price computation is twofold: (1) Find the present value of the $100,000 par value paid at maturity and (2) find the present value of the series of four semiannual payments of $4,000 each; see Exhibit 14.4. These present values can be found by using present value tables. Appendix B at the end of this book shows present value tables and describes their use. Table B.1 at the end of Appendix B is used for the single $100,000 maturity payment, and Table B.3 in Appendix B is used for the $4,000 series of interest payments. Specifically, we go to Table B.1, row 4, and across to the 5% column to identify the present value factor of 0.8227 for the maturity payment. Next, we go to Table B.3, row 4, and across to the 5% column, where the present value factor is 3.5460 for the series of interest payments. We compute bond price by multiplying the cash flow payments by their corresponding present value factors and adding them together; see Exhibit 14.12.

EXHIBIT 14.12 Computing Issue Price for the Fila Discount Bonds

Point: A bond’s market value (price) at issuance equals the present value of its future cash payments, where the interest (discount) rate used is the bond’s market rate.

Point: Many calculators have present value functions for computing bond prices.

Present Value of a Premium Bond We find the issue price of the Adidas bonds by using the market rate to compute the present value of the bonds’ future cash flows. When computing the present value of these bonds, we again work with semiannual compounding periods because this is the time between interest payments. The annual 10% market rate is applied as a semiannual rate of 5%, and the two-year bond life is viewed as four semiannual periods. The computation is twofold: (1) Find the present value of the $100,000 par value paid at maturity and (2) find the present value of the series of four payments of $6,000 each; see Exhibit 14.8. These present values can be found by using present value tables. First, go to Table B.1, row 4, and across to the 5% column where the present value factor is 0.8227 for the maturity payment. Second, go to Table B.3, row 4, and across to the 5% column, where the present value factor is 3.5460 for the series of interest payments. The bonds’ price is computed by multiplying the cash flow payments by their corresponding present value factors and adding them together; see Exhibit 14.13.

Point: There are nearly 5 million individual U.S. bond issues, ranging from huge treasuries to tiny municipalities. This compares to about 12,000 individual U.S. stocks that are traded.

EXHIBIT 14.13	Computing Issue Price for the Adidas Premium Bonds