• 6 min read (EN)
Gordon Growth Model: Three Inputs, One Fair Price
The Gordon Growth Model values a dividend stock as the sum of every future dividend, discounted to today and growing at one steady rate forever. Three inputs decide the fair price: next year's dividend, the required return, and the long-run growth rate. Nothing else.
Myron Gordon and Eli Shapiro published the shortcut in 1956, and it still sits inside most dividend valuations and nearly every DCF terminal value.
The Formula in Plain English
The formula is one line:
V₀ is the fair value per share today. D₁ is the expected dividend one year from now. r is the required rate of return. g is the constant rate at which dividends grow forever.
The intuition is an infinite geometric series collapsed into a fraction. Dividends grow at g each year and get discounted back at r, so a single subtraction in the denominator does all the work.
One rule cannot bend: r must exceed g. When g catches up to r, the denominator hits zero and the valuation explodes toward infinity, which is the model's way of saying the assumption is wrong.
The Three Inputs That Decide the Answer
D₁: Next year's expected dividend. Most analysts start from the last dividend paid and grow it by one year: D₁ = D₀ × (1 + g). A $2.00 dividend with 5% growth gives D₁ = $2.10.
r: The required return. In theory this is the cost of equity, built from a risk-free rate plus beta times the equity risk premium. In practice many investors use a hurdle rate in the 8% to 12% range.
g: The long-run dividend growth rate. The standard derivation is g = ROE × retention ratio, where retention ratio equals one minus the payout ratio. A company earning a 15% return on equity and keeping 40% of profits has an implied sustainable growth rate of 6%. Aswath Damodaran adds a ceiling: g cannot exceed long-run nominal GDP growth.
The interaction between r and g matters more than either input alone. A 5-point spread between them produces stable valuations. A 1-point spread produces numbers that swing wildly on any input change.
A Worked Example and the Sensitivity That Bites
Take a mature consumer staples firm. Next year's dividend is $2.00, the required return is 8%, and dividends have grown at 4% for the last decade.
At $45 the model calls it undervalued. At $58, overvalued.
Now move one input. Push g from 4% to 5%:
A single percentage point on growth added 33% to the fair value. Push r to 9% instead and the answer drops to $40. The sensitivity table for a $2.00 dividend across different r minus g spreads:
| r − g spread | Fair value |
|---|---|
| 5% | $40.00 |
| 4% | $50.00 |
| 3% | $66.67 |
| 2% | $100.00 |
| 1% | $200.00 |
Every point the spread narrows roughly doubles the valuation. Most analysts run a sensitivity grid rather than report a single number. The math is clean. The output is only as stable as the weakest input.
Beyond Dividends: The Terminal Value Engine
Most professionals never value a whole stock with pure Gordon Growth. They use it for the tail of something bigger. Inside a discounted cash flow model, analysts project free cash flows explicitly for 5 or 10 years, then switch to a terminal value for everything after. The standard terminal value formula is Gordon Growth dressed up for cash flow:
That single line often represents 60% to 80% of the DCF total, so the Gordon assumption does most of the work in cash-flow-based models.
The same structure values the broad market: plug the S&P 500 forward dividend into D₁, the equity risk premium plus the risk-free rate into r, and long-run GDP growth into g.
Where the Model Breaks
The model fails quietly for most of the modern equity market. Growth companies that pay no dividend have no D₁, so there is nothing to discount. Firms that return cash through share buybacks are invisible to the formula. Cyclicals have real earnings but no steady g to plug in.
Other failure modes are subtler.
g approaching r: As the denominator shrinks, the valuation becomes theater. Any firm with expected growth close to its cost of equity needs a multi-stage model or a reverse DCF that solves for the growth the market is already pricing in.
Payout changes: A company that cuts its dividend in a recession breaks every Gordon projection retroactively, no matter how defensible the prior inputs looked.
Ignored optionality: Brand value, reinvestment returns, and buyback capacity sit outside the equation.
Use the formula where its assumptions hold. Mature dividend payers, regulated utilities, and index-level valuations are its home territory. Screen candidates on the dividend yield heatmap, check the r minus g spread sits comfortably wide, and pair the answer with a second method before trusting it. The WACC calculator gives a defensible starting point for r.
Frequently Asked Questions
Is the Gordon Growth Model the same as the dividend discount model?
Gordon Growth is the simplest version of the dividend discount model, and the version most people mean when they say DDM. It assumes a single constant growth rate forever. Multi-stage DDMs let growth shift over time at the cost of extra inputs and more assumptions to defend.
How do I estimate the growth rate g without a long dividend history?
The standard fallback is g = ROE × retention ratio, which infers sustainable growth from profitability and reinvestment. Cap the result at long-run nominal GDP growth, since no company outgrows its own economy indefinitely. For most developed markets that ceiling sits near 4% to 5%.
Can the Gordon Growth Model value preferred stocks?
Yes, and the formula gets simpler. Preferred dividends do not grow, so g is zero and the equation reduces to V = D / r, where D is the fixed preferred dividend and r is the required yield for that class of security.
Why is the Gordon Growth Model still taught if it is so fragile?
Because nothing else is as clean. It forces explicit assumptions about return and growth, slots directly into DCF terminal values, and works for mature dividend payers and broad indices where those assumptions hold. The fragility becomes useful when the formula is used as a sensitivity tool, not a point estimate.