Growing Perpetuity (Gordon Growth Model)

Time Value of Money

Updated Apr 2026 • Has calculator

The present value of a cash flow that grows at a constant rate forever.

What is Growing Perpetuity?

A growing perpetuity pays a cash flow that increases by a fixed percentage each period indefinitely. The present value formula — payment divided by the spread between discount rate and growth rate — is the foundation of the Gordon Growth Model (dividend discount model). Equity analysts use it to estimate a stock's intrinsic value when dividends are expected to grow at a steady long-term rate. It also appears as the terminal value in multi-stage DCF models, where the business eventually matures to a constant growth phase.

Formula

PV = PMT ÷ (r − g)

Worked Example

FY2024 — Gordon Growth Model Estimate

Step 1 Expected next-year dividend (D₁): $1.97 (annualized, FY2024 Q4 rate × 4)

Step 2 Required return (r): 9.0% (CAPM estimate)

Step 3 Long-term dividend growth rate (g): 4.0% (10-year trailing average)

Step 4 PV = $1.97 ÷ (0.09 − 0.04) = $1.97 ÷ 0.05 = $39.40

Step 5 → Gordon Growth Model implies a fair value of ~$39.40/share under these assumptions

Source: Coca-Cola 2024 Annual Report — Investor Relations (2024-12-31)

Calculate Growing Perpetuity

Next Period's Payment (D₁)

Expected next-year dividend or cash flow

Required Return (r)

Cost of equity or required rate of return

Growth Rate (g)

Constant long-term growth rate; must be < r

Intrinsic Value

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Not investment advice.

How to Interpret Growing Perpetuity

< 0

Undefined — growth rate may exceed required return

> 0

Positive — implied fair value under constant-growth assumption

📚 Time Value of Money — Complete the path

Sources