Perpetual Bonds

A perpetual bond never matures. It pays a periodic coupon indefinitely. The price of a perpetual bond in terms of its yield to maturity can be expressed as follows:

By the rules of algebra, this simplifies to

Thus, if a perpetual bond has an annual coupon of $8 and a yield to maturity of 10 percent, its price is

Only a small number of perpetual bonds exist. However, perpetual bonds are interesting because they serve as a limiting case. Long-term bonds approach perpetual bonds as the maturity gets longer. As in the case of par bonds, the yield to maturity for a perpetual bond equals the coupon divided by the price (y = c/P). Since a long-term bond is similar to a perpetual bond, the yield to maturity for a long-term bond is close to the yield to maturity for a perpetual bond. As an illustration, look up the listings of Treasury bonds in the newspaper and compare the current yield (i.e., c/P) for the longest-maturity Treasury bond (often called the “long bond”) to the yield to maturity.