Basic bond valuation

A bonds value is the present value of the payments the issuer is contractually obligated to make — from the present until maturity. The discount rate depends on the prevailing interest rate for debt obligations with similar risks and maturities.

Look at the example to the right to see the formula in action.

If you know the bonds par value, coupon rate, time to maturity and current yield, you can compute its price. Seeattached spreadsheetfor computing prices and yields for bonds paying semi-annual interest.

Suppose Play Now, Inc. issues ten-year bonds (par $1,000) with an annual coupon of 8.6%. Similar ten-year bonds are paying 8.0% interest. What is the value of one of Play Nows new bonds — that is, what should be its price?

Answer (using tables).You can usepresent valueandpresent value annuitytables:

Answer (using spreadsheet).You can also use a spreadsheet:

Most bonds, although the coupon rate is stated as an annual interest rate, actually pay interest semiannually. Valuing bonds that pay interest semiannually involves three steps:

Convert bonds annual interest (I) to semiannual interest — divide I by 2

Convert the years to maturity (n) to semiannual periods — multiply n by 2

Convert annual required return (i) to semiannual discount rate — divide i by 2

The bond valuation formula for a bond paying interest semiannually is:

B0= I/2 *[(1+i/2)2n- 1] / [(1+i/2)2n* i/2]

Computing bond price.If you know the bonds par value, coupon rate, time to maturity and current yield, you can compute its price. Seeattached spreadsheetfor computing prices and yields for bonds paying semi-annual interest.

Continuous compounding.[Example of continuous compounding]

Returning to our example, suppose Play Now issues ten-year bonds (par $1,000) with an annual coupon rate of 8.6% that pay interestsemiannually. Similar ten-year bonds are paying 8.0% interest. What is the value of one of Play Nows new bonds — that is, what should be its price?

Answer.You can usepresent valueandpresent value annuitytables:

Notice that this bond is identical to the bond in the previous example with the exception that it pays interest semiannually. The effect of the semiannual payments is to increase the price of the bond — from $1,040.26 to $1,040.77.