Perpetual Bonds and Consols

A perpetual bond, or perpetuity, never matures and never repays principal, the issuer simply pays a fixed coupon forever. The best-known historical example is the UK's Consols ("consolidated annuities"), first issued in the 18th century and only fully redeemed in 2015. Because there's no principal repayment to discount, a perpetual bond's fair price collapses to a simple formula: price = annual coupon ÷ required yield. There's no maturity date to plug into a present-value calculation, just an infinite stream of identical payments.

For example, a perpetual bond paying a $4 annual coupon, priced to yield 5%, is worth $4 / 0.05 = $80. If yields fall to 4%, matching the coupon rate exactly, the price rises to $4 / 0.04 = $100, i.e. par. This is the same math used to value preferred stock with a fixed dividend and no maturity, and it's a useful mental shortcut for estimating the price sensitivity of very long-dated bonds, whose behavior approaches a perpetuity's as maturity gets far enough away.