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FinanceGordon Growth Model
By Sitraka Forler · Lecturer, Durham Business SchoolUpdated 13 September 2026 About this site
Values a stock as next dividend over (required return − growth).
The dividend discount model assumes dividends grow at a constant rate g forever. It is intuitive and widely taught, but extremely sensitive to the spread between r and g - small changes swing the valuation wildly.
Where a share price comes from - dividends, discounted forever
Each bar is the present value of one future dividend. Their sum is the price.
P₀ = €2.00 / (9.0% − 4.0%) = €40.00
The intuition
The Gordon growth model prices a share as the sum of every future dividend, discounted back to today, assuming those dividends grow at a single constant rate forever. That infinite stream sounds impossible to add up, but because each dividend grows by g while being discounted by r, the sum collapses to one clean formula: P₀ = D₁ / (r - g). In the chart above, each bar is the present value of one year's dividend; the gold running total climbs bar by bar and levels off exactly on the dashed price line. The whole valuation lives in that convergence.
Why does the sum converge at all? Each bar equals the previous bar multiplied by (1 + g) / (1 + r). As long as r is greater than g, that ratio is below one, so the bars shrink geometrically: distant dividends may be huge in nominal terms, but discounting shrinks them faster than growth inflates them. It is the same trick that makes 1/2 + 1/4 + 1/8 + ... equal exactly 1. The moment g reaches r, the ratio hits one, the bars stop shrinking, and the price becomes an infinite sum of equal pieces: undefined.
This also explains the model's famous fragility. The price depends on the gap r - g, and when that gap is small, tiny changes in either input produce enormous swings in value. Drag g toward r in the chart above and watch the bars refuse to shrink while the price line rockets upward. Practitioners respect this by keeping g conservative, usually at or below long-run nominal GDP growth, and by reading the formula backwards: given a market price, it reveals the growth rate investors are implicitly paying for, which is often the more honest use.
Formula / theory
P₀ = D₁ / (r − g) (requires r > g)
In Python
price = d1 / (r - g)
Pricing a €2.00 dividend stream, then stress-testing it
- Start with next year's expected dividend D₁ = €2.00, a required return r = 9%, and dividend growth g = 4%.
- Compute the denominator: r - g = 0.09 - 0.04 = 0.05.
- Apply the formula: P₀ = D₁ / (r - g) = 2.00 / 0.05 = €40.00.
- Stress-test the growth assumption: raise g to 6%, so r - g = 0.09 - 0.06 = 0.03 and P₀ = 2.00 / 0.03 = €66.67.
- Measure the sensitivity: the value moved from €40.00 to €66.67, a rise of 26.67 / 40.00 = 66.7%, from a change of just 2 percentage points in g.
- Invert the model: if the share actually trades at €50.00, the implied growth is g = r - D₁/P = 0.09 - 2.00/50.00 = 0.09 - 0.04 = 0.05, so the market is pricing in 5% growth.
A 2-point change in one assumption moved the valuation by two thirds, so quote a range, and use the inversion to read what growth the market already believes.
Common pitfalls
- Setting g at or above r: the formula returns a negative or infinite price, which is mathematical nonsense. No company can outgrow the discount rate forever, so a candidate g that close to r is a sign the single-stage model does not apply.
- Applying it to non-dividend payers or high-growth firms: with no stable payout there is no D₁ to grow, so the formula has nothing to price. Use a free-cash-flow DCF or a multi-stage dividend model instead.
- Treating the point estimate as precise when r - g is small: with a 1-point spread, a 0.25-point rise in g lifts the value by a third. Always present a sensitivity range rather than a single number.
- Discounting this year's dividend instead of next year's: the numerator must be D₁ = D₀ × (1 + g). Forgetting to grow the current dividend one year understates the value by a factor of (1 + g).
Frequently asked questions
What is the Gordon growth model formula?
The Gordon growth model formula is P₀ = D₁ / (r - g), where D₁ is the dividend expected next year, r is the investor's required rate of return, and g is the constant annual growth rate of dividends. For example, a €2.00 dividend, a 9% required return and 4% growth give a value of 2 / 0.05 = €40.00. The formula is the closed-form sum of an infinite discounted dividend stream.
Why must r be greater than g in the Gordon growth model?
r must exceed g because the model sums an infinite geometric series that only converges when each discounted dividend is smaller than the last. Each term is the previous one multiplied by (1 + g) / (1 + r); if g is at or above r that ratio is one or more, the terms never shrink, and the sum is infinite. Economically, no company can grow faster than investors' required return forever, or it would outgrow the economy itself.
What growth rate should I use in the Gordon growth model?
Use a growth rate at or below the long-run nominal growth of the economy, often 2% to 4% for developed markets, since no firm can outgrow GDP forever. In practice the Gordon model is most often used for the terminal value in a DCF, where analysts deliberately pick a conservative g and check the implied exit multiple. If your candidate g sits close to r, the model is telling you it is the wrong tool for that company.
When is the Gordon growth model appropriate?
The Gordon growth model suits mature companies with a long record of stable, steadily growing dividends: think utilities, consumer staples and large banks in steady state. It is inappropriate for firms that pay no dividend, reinvest heavily, or are growing fast, because their payouts are neither stable nor predictable. For those, use a multi-stage dividend model or a free-cash-flow DCF, and reserve the Gordon formula for the terminal, steady-state stage.
Test yourself
Further reading
Where to go deeper. Free means a full, legal copy is online.
Damodaran's freely posted valuation material sets the Gordon model inside the wider dividend-discount and DCF toolkit.