04 // Interactive Formula Compendium // FINANCEP₀ = D₁ / (r − g) = [ D₀ · (1 + g) ] / (r − g)
Gordon Growth Model (Constant-Growth Dividend Discount Formula)
The Gordon Growth Model P₀ = D₁ / (r − g) values a stock or perpetual cash flow stream as next year's expected dividend D₁ = D₀(1 + g) divided by the spread between required return r and perpetual growth rate g (for r > g).
Formula Reference
Main Formula
P₀ = D₁ / (r − g) = [ D₀ · (1 + g) ] / (r − g)
Rearranged Forms
r = (D₁ / P₀) + g (Implied Cost of Equity = Dividend Yield + Growth)
g = ROE × b = ROE × (1 − Payout Ratio) (Sustainable Growth Rate)
P₀ / E₁ = Payout Ratio / (r − g) (Justified Forward P/E Multiple)
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| P₀ | Intrinsic Share Value (P₀) | USD |
| D1 | Next Year Expected Dividend (D₁) | USD |
| r | Required Cost of Equity (r, decimal) | 1/yr |
| g | Perpetual Growth Rate (g < r, decimal) | 1/yr |
Inputs & Parameters
[USD]
[1/yr]
[1/yr]
Calculated Result (Intrinsic Share Value (P₀))
P₀ =80USD
Formula Notes & Background
- Write intrinsic value as the infinite present value sum of growing dividends: P₀ = Σ_{t=1..∞} D₀(1 + g)ᵗ / (1 + r)ᵗ.
- Factor out D₁ / (1 + r) to recognize an infinite geometric series with common ratio q = (1 + g) / (1 + r).
- For g < r, |q| < 1 so the series converges to [D₁ / (1 + r)] / [1 − (1 + g)/(1 + r)] = D₁ / (r − g).
Step-by-Step Examples
#1: Value a utility stock paying an expected dividend D₁ = $4.00 next year with 4% perpetual growth and a 9% required return.
D₁ = $4.00r = 0.09g = 0.04
P₀ = 4.00 / (0.09 − 0.04) = 4.00 / 0.05
→ P₀ = $80.00 per share (implied dividend yield = 5.0%)
#2: Compute the DCF Terminal Value at Year 5 when Year 5 FCF = $100M, WACC = 10%, and terminal growth g = 2.5%.
FCF₆ = 100 × 1.025 = $102.5Mr = 0.10g = 0.025
TV₅ = 102.5 / (0.10 − 0.025) = 102.5 / 0.075
→ TV₅ = $1,366.67M
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Frequently Asked Questions
Why must the perpetual growth rate g be strictly less than the discount rate r?+
If g ≥ r, the geometric ratio (1 + g)/(1 + r) ≥ 1 and the infinite sum diverges; economically, no company can outgrow the overall economy forever.
What is the common mistake with D₀ vs D₁?+
The numerator must be next year's forward dividend D₁ = D₀(1 + g), not the trailing dividend D₀ just paid.
How is sustainable growth g linked to Return on Equity (ROE)?+
Without issuing new shares, a company's earnings and dividends grow at g = ROE × Retention Ratio = ROE × (1 − Dividend Payout Ratio).