If the coupon rate of a bond coincides with the market rate of interest when the bonds are actually sold to investors, then the bonds will sell at par value or face value. The price at which a bond is trading is usually quoted as a percentage of the bond’s par value, so that a bond that sells at par has a price of 100. To illustrate the sale of bonds at par, assume Marley Company issues bonds on January 1, 2000, with a principal amount of $100 million, to be repaid in 10 years and a 12% coupon rate of interest payable semiannually. The bond contract obligates Marley to make the following payments:
Principal: $100,000,000 due in 10 years (after 20 six-month periods),
Interest: $6,000,000 due at the end of each six-month period, for 10 years ($100,000,000 * 12% * 6/12 = $6,000,000).
Because the market rate and the coupon rate of interest are the same, the bonds sell at their face value of $100 million. The quoted annual interest rate of 12% is actually 6% each six-month period because the bonds pay interest each six months. When interest is paid each six months, the interest rate is said to be compounded semiannually. To use the present value tables, bonds with a 12% semiannual interest coupon are regarded as outstanding for a number of six-month periods (20 in this case), and the interest rate is 6% per period. In general, when interest is compounded n times each year, the periodic interest rate is i/n, and the number of periods is n years. In the present case, the periodic interest rate is 6% (i / n or 12% / 2 = 6%), and the number of periods is 20 (n * years or 2 * 10 = 20).