Perpetuity
A perpetuity is a series of identical cash flows that is paid at regular intervals forever, with no end date. Although the payments never stop, its value today is finite because each future payment is worth less when discounted. The present value of a perpetuity equals the periodic cash flow divided by the discount rate: PV = C ÷ r. It is a building block of bond and equity valuation.
Worked example
A preferred share pays a fixed 1,000 per year indefinitely, and the required rate of return is 5%. Its present value is PV = C ÷ r = 1,000 ÷ 0.05 = 20,000. If the discount rate rose to 8%, the value would fall to 1,000 ÷ 0.08 = 12,500 — showing how sensitive a perpetuity is to the rate.
Why it matters
Perpetuities matter because the same idea underpins the terminal value in a discounted cash flow model and the valuation of preferred shares and consols. A growing perpetuity uses PV = C ÷ (r − g). The pitfall is the denominator: if the discount rate is close to (or below) the growth rate, the formula explodes toward infinity and gives a meaningless value, so r must comfortably exceed g.
Frequently asked questions
How can something paid forever have a finite value?
Because of discounting: each future payment is worth progressively less in today's money. As payments stretch further into the future, their present value shrinks toward zero, so the infinite series adds up to a finite total — exactly C divided by r.
What is a growing perpetuity?
A growing perpetuity is one whose cash flow increases at a constant rate g each period. Its present value is C ÷ (r − g), where C is the next payment, r the discount rate and g the growth rate, valid only when r is greater than g.
Related terms: Terminal Value, Discounted Cash Flow (DCF)