What Is a Perpetuity?
A perpetuity is a cash flow stream with a fixed payment that never ends. It may seem like an infinite series of payments should be infinitely valuable, but discounting resolves the paradox: cash flows far in the future are worth almost nothing today, so the sum converges to a finite number. The classic historical example is the British consol, a government bond that paid interest indefinitely with its principal never scheduled for repayment.
Perpetuities come in two flavors. A level perpetuity pays the same amount every period forever, which is roughly how a traditional preferred stock with a fixed dividend behaves. A growing perpetuity pays a stream that increases at a constant rate each year, which is the standard assumption for a mature company's cash flows beyond the explicit forecast horizon.
How to Value a Perpetuity
The present value of a level perpetuity is PV = C / r, where C is the payment received one period from now and r is the discount rate. For a growing perpetuity, the formula becomes PV = C / (r − g), where g is the constant growth rate — often called the Gordon growth formula. The math only works when g is less than r; otherwise the series never converges.
A payment of $50 per year forever, discounted at 5%, is worth $50 / 0.05 = $1,000 today. Now suppose a cash flow of $100 arrives next year and grows 3% annually forever, with a 10% discount rate: the value is $100 / (0.10 − 0.03) = $1,429. Notice how sensitive the answer is to the denominator — nudging growth to 4% lifts the value to $1,667.
Why Perpetuities Matter in Valuation
The growing perpetuity is the workhorse behind terminal value in a DCF. After projecting cash flows explicitly for five or ten years, analysts capture everything beyond the forecast with TV = FCF in the first post-forecast year / (WACC − g), where g is a long-run growth rate near GDP or inflation. That single number routinely accounts for well over half of a company's total DCF value. The dividend discount model applies the same formula directly to a stock's dividends.
Because so much value hangs on the perpetuity assumption, small input changes swing valuations dramatically, which is why analysts sanity-check terminal values against exit multiples and present sensitivity tables. Interviewers exploit this too — a favorite question asks for the value of a perpetual cash flow stream, and a strong candidate can answer instantly with C / r and explain what happens as growth approaches the discount rate.
