Setting price of a bond

When the market rate of interest is different from the contract rate, the bond will sell at a premium or discount. But precisely how much will the premium or discount be? How does one go about calculating this premium or discount? The answer is that the price is based upon the following formula:


Bond selling price = present value of the principal+ present value of the interest payments


Note: If you would like a quick review of present value concepts, please see in a Present Value Table


The interest payments are an annuity; the principal is not. Accordingly, both the Present Value of $1 table and the Present Value of an Annuity of $1 table (both appearing in the Appendix) must be used.

The Boston Corporation wishes to issue a $50,000, 4-year, 10% bond. The interest is payable annually. Unfortunately, the market rate has risen to 12%. Clearly, the bond must sell at a discount. But how much?
We must find the present value of the $50,000 principal and of the $5,000 ($50,000 × 10%) annuity. According to the tables:

Present value of $50,000, 4 periods, 12% = 0.63552
                                                                        × $50,000
                                                                                                      $31,776
Present value of $5,000 annuity, 4 periods, 12% = 3.03735
                                                                                   × $5,000
                                                                                                        15,187
The bond selling price is:                                                            $46,963

Notice that 12%, not 10%, was used in looking up the table. An important rule to remember is: Always look up the table at the market rate.