How a forever-stream of dividends becomes one number
If you owned a share forever, the only cash it would ever hand you is its dividends. So a share ought to be worth the present value of that entire future stream — and that is exactly what the dividend discount model computes. The trick is the infinity: discounting an unending series of cash flows sounds impossible until you assume each dividend grows at the same constant rate g. With that single assumption the sum becomes a geometric series that converges to D₁ / (r − g), turning an infinite calculation into one division. It is the same discounting logic behind a fullDCF calculator; the Gordon Growth model is just the special case where the cash flows are dividends that grow forever at one rate.
The Gordon Growth formula
P = D₁ / ( r − g )
D₁ = D₀ · (1 + g)
where P = fair price today, D₀ = the dividend most recently paid, D₁ = next year’s expected dividend,r = the required rate of return, and g = the constant perpetual growth rate of dividends. The model only holds whenr > g: if growth meets or exceeds the discount rate the perpetuity diverges and the price becomes undefined or negative.
What makes this calculator different
- It handles r ≤ g honestly. When growth meets or beats the discount rate the formula has no finite answer — instead of printing a misleading negative number, the calculator tells you the model breaks down and why.
- It shows D₁ and the (r − g) spread. Next year’s dividend and the all-important denominator are displayed explicitly, so you can see precisely what is driving the price rather than just reading a final figure.
- It makes the sensitivity visible. Because price hinges on the spread, nudging r or g by a fraction can move the valuation dramatically — the tool surfaces that fragility so you treat the output as a range, not a precise target.
Frequently asked questions
What is the dividend discount model and the Gordon Growth model?+
The dividend discount model (DDM) values a stock as the present value of all the dividends it will ever pay — discount each future dividend back to today and add them up. The Gordon Growth model is the simplest closed form of the DDM: it assumes dividends grow at a single constant rate g forever. Under that assumption the infinite stream of discounted dividends collapses to a tidy formula, P = D₁ / (r − g), where D₁ is next year’s dividend, r is the required return, and g is the perpetual growth rate. It is a teaching tool first — a way to see how growth, discount rate, and price are mathematically linked.
What is the difference between D₁ and D₀?+
D₀ is the dividend just paid — the most recent, known dividend. D₁ is next year’s expected dividend, the first cash flow you actually discount in the model. Because dividends are assumed to grow at rate g, the two are linked by D₁ = D₀ × (1 + g). A common mistake is to plug D₀ straight into the formula; using D₀ instead of D₁ understates the price by exactly one year of growth. This calculator computes D₁ from your D₀ and g so the distinction is explicit.
Why must r be greater than g?+
The Gordon Growth formula is the sum of an infinite geometric series, and that series only converges when the discount rate r exceeds the growth rate g. If g equals r, you divide by zero and the value is undefined; if g exceeds r, the denominator (r − g) goes negative and the formula spits out a negative price — economic nonsense for a growing dividend. Intuitively, if dividends grew faster than you discounted them forever, their present value would be infinite. So r > g is not a suggestion, it is a hard mathematical requirement for the model to mean anything.
What is a reasonable long-run growth rate?+
The key constraint is that no company can grow its dividends faster than the overall economy forever — if it did, it would eventually become larger than the economy itself, which is impossible. So a sensible perpetual g is anchored to something like long-run nominal economic growth and must stay below your required return r. Analysts often keep g modest and well under r precisely to respect this ceiling. Short bursts of rapid growth are fine in reality, but they belong in a multi-stage model, not in the single perpetual rate this formula assumes.
What are the limitations of the model?+
The Gordon Growth model only fits companies that pay a stable, predictably growing dividend — it says little about firms that pay nothing or whose payouts are erratic. It is also famously sensitive: because price depends on the spread (r − g), small changes in either input can swing the valuation enormously, especially when r and g are close. The single-stage constant-growth assumption is a simplification of messy reality, so the output is a rough, illustrative anchor rather than a precise target price. Treat it as a lens for understanding the drivers of value, not a definitive valuation.
Disclaimer: This calculator is foreducation and illustration only. The Gordon Growth model rests on simplifying assumptions (a single constant growth rate forever, a stable dividend, and r > g) and is extremely sensitive to its inputs; its output is an illustrative estimate, not a target price or a market quote. Nothing here is investment, tax, or financial advice.