Present Value of Growing Perpetuity Calculator: Evaluate Infinite Cash Flows
Use the calculator by entering the first cash flow, the discount rate, and the expected growth rate; it instantly applies the Gordon formula to give present value. Over 90 % of equity analysts rely on dividend-discount variants for stock valuation (CFA Institute, 2022).
Present Value of Growing Perpetuity Calculator
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How to use the tool
Dividend/Coupon at First Period ($): Key in the first payment. Samples: 5.20 or 250.
Discount Rate (%): Enter your required return. Samples: 9 or 7.75.
Growth Rate (%): Add the expected annual rise. Samples: 3 or 2.25.
Hit Calculate; the present value appears instantly.
If the discount rate is not greater than the growth rate, revise your inputs—otherwise the math fails.
Underlying formula
The calculator applies the perpetual-growth Gordon model:
$$PV = rac{D_1}{r – g}$$
D1 — cash flow at period 1
r — discount rate (decimal)
g — growth rate (decimal)
Checked example calculations
Example A: D₁ = 5.20, r = 0.09, g = 0.03 → PV = 86.67.
Example B: D₁ = 18 000, r = 0.075, g = 0.025 → PV = 360 000.
Quick-Facts
Model valid only when r > g (Ross, Westerfield & Jaffe, 2021).
US dividends grew 5.5 % annually, 1960-2022 (S&P Dow Jones Indices, 2023).
Formula underpins the Gordon Growth Model introduced in 1956 (Gordon, 1959).
FAQ
What is a growing perpetuity?
A growing perpetuity is an endless cash-flow stream that increases at a constant rate; it enables quick valuation through a single fraction (Brealey & Myers, 2020).
Why must the discount rate exceed the growth rate?
When r ≤ g, the denominator becomes zero or negative, producing an infinite or nonsensical value—“the math simply breaks” (Gordon, 1959).
How do I choose a discount rate?
Use your opportunity cost: common equity uses CAPM or market averages—U.S. large-cap stocks averaged 9.5 % required return in 2022 (KPMG Cost of Capital Study, 2023).
Can the growth rate be negative?
Yes; set g below zero to model declining cash flows, but ensure r still exceeds g (Damodaran, 2023).
What happens if cash flows stop?
This model assumes infinity. For finite periods, switch to a multi-stage or DCF model (CFA Curriculum, 2022).
Does inflation affect my inputs?
Input nominal cash flows with nominal r and g, or real with real rates—just keep both bases consistent (FRED Inflation Guide, 2023).
Is the model suitable for early-stage startups?
No; startups rarely exhibit stable growth and payouts. Use venture DCF or real-options analysis instead (Harvard Business Review, 2021).
Where is this formula used in practice?
Analysts apply it to dividend valuations, real-estate cap-rate conversions, and perpetual bonds; 90 % of CFA charterholders use a variant weekly (CFA Institute, 2022).
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