Perpetuity Value Calculator

V = C / r — present value of an infinite stream of equal cash flows.

Inputs

Use 0 for simple perpetuity, >0 for growing.

Result

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General calculation reads

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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter the periodic cash flow C.
  • Enter discount rate r.
  • For growing perpetuity, enter growth rate g (must be less than r).

About this calculator

A perpetuity is an infinite stream of equal cash flows. PV = C / r. For a "growing perpetuity" with growth rate g < r, PV = C / (r − g) — this is the Gordon growth model used to value stocks. The smaller the gap (r − g), the higher the value, which is why high-growth companies sell at high multiples.

Frequently asked

Why does r need to exceed g?+
Mathematically: if g ≥ r, the geometric series diverges — value would be infinite. Economically: no finite-rate cash flow can grow faster than its required return forever.
Real-world examples of perpetuities?+
British "consols" (Government bonds with no maturity), perpetual preferred stock, dividend-paying mature companies (approximately).
How does the Gordon model relate?+
Same formula: P = D₁ / (r − g). Used for stock valuation where dividends grow at constant rate.
Does this account for varying cash flows?+
No — perpetuity assumes constant (or constantly growing) C. For uneven cash flows, use NPV.
When is the formula a poor fit?+
Companies in declining industries, those with capex needs, or in mature markets where g approaches 0 — then approximation is fine. Tech firms with shifting profitability — not a great fit.

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