What the Gordon growth model says a share is worth
A share entitles you to a stream of dividends and nothing else. Even a capital gain is only someone else paying you for the dividends they expect after you sell. The Gordon growth model takes that seriously: it says the value of a share today is the present value of every dividend it will ever pay, and if you assume those dividends grow at a constant rate forever, the infinite sum collapses into one line of arithmetic.
That collapse is the point. Discounting an infinite series of dividends D₀(1+g)/(1+r) + D₀(1+g)²/(1+r)² + … is a geometric series with ratio (1+g)/(1+r). Whenever that ratio is below one — that is, whenever g is less than r — the series converges to D₁ ÷ (r − g). When g reaches r the ratio hits one, the series diverges, and there is no finite answer. The calculator reports nothing rather than a large number in that case, because a large number would be misleading.
The model is at its most useful in three places: valuing mature dividend payers such as utilities, consumer staples and regulated infrastructure; computing the terminal value inside a larger discounted cash flow model, where the same algebra reappears under a different name in the terminal value calculator; and running backwards to extract what the market is already assuming.
The formula, term by term
D₁, not D₀, sits in the numerator. This is the most common error in the model. The value today is the present value of dividends still to come, so the first one you count is next year's. If you took the dividend from a filing you have D₀, the dividend just paid, and you must grow it once: D₁ = D₀(1 + g). Selecting the wrong basis with a 5% growth rate understates the value by 5% straight away.
r is your required return, not the company's cost of debt or its WACC. Dividends are paid to shareholders, so they are discounted at the cost of equity. Most analysts build it from the capital asset pricing model: the risk-free rate plus beta times the equity risk premium.
g is a perpetual rate, and it is not a free parameter. Dividends can only grow forever as fast as the equity base that funds them, which gives the sustainable growth identity g = retention ratio × return on equity. A company paying out 60% of earnings and earning 15% on equity supports 0.40 × 15% = 6% growth. Assuming a rate far above that is assuming growth from nowhere.
The denominator does all the work. Because r − g is a small difference between two large numbers, its proportional error is much larger than the error in either input. Moving the required return from 9% to 8.5% with growth at 5% narrows the spread from 4.0 to 3.5 points and raises the value by 14.3%. That is not a defect in the calculator; it is the actual sensitivity of any perpetuity, and it is the reason a single-point Gordon value should always be reported alongside a range.
Read the formula backwards and it becomes a return decomposition. Rearranging gives r = D₁/P₀ + g: your expected return equals the forward dividend yield plus the growth rate. That is the same identity behind the classic building-block estimate of long-run equity returns, and it is often the most defensible thing the model produces.
Worked example: a $2.00 dividend growing 5% against a 9% required return
A utility paid $2.00 per share over the last twelve months. You expect the dividend to grow 5% a year indefinitely, you require 9% on the equity, and the shares trade at $48.00.
- Grow the dividend one year. D₁ = $2.00 × 1.05 = $2.10.
- Compute the spread. r − g = 9% − 5% = 4.00 percentage points, or 0.04 as a decimal.
- Divide. P₀ = $2.10 ÷ 0.04 = $52.50 per share.
- Compare with the market. ($52.50 − $48.00) ÷ $48.00 = +9.4%. Your assumptions value the share above where it trades.
- Solve for the implied return. At $48.00 the forward yield is $2.10 ÷ $48.00 = 4.375%. Add the 5% growth: the market price offers 9.375% if your growth assumption is right.
- Solve for the implied growth. Setting $48.00 = $2.00(1 + g) ÷ (0.09 − g) and rearranging gives g = (48.00 × 0.09 − 2.00) ÷ (48.00 + 2.00) = $2.32 ÷ $50.00 = 4.64%. The market is assuming a little over four and a half percent; you are assuming five.
Framed that way the gap is far less dramatic than a 9.4% upside figure suggests. Thirty-six basis points of perpetual dividend growth is well inside the noise of any forecast, which is exactly the check the reverse calculation is for.
How to read the result
Treat the intrinsic value as a hypothesis and the implied numbers as the finding. The forward calculation tells you what the share is worth if your two rates are right. The reverse calculation tells you what rates the market is using, and that is a far more robust output because it involves no forecast of your own beyond the dividend.
A useful test: work out the implied growth rate, then compare it with the company's sustainable growth rate from retention and return on equity. If the market implies 7% and the company can only fund 4%, the price depends on something outside the dividend stream — a buyback programme, an asset revaluation, an expected takeover — and the model is not capturing it.
Check the payout is sustainable before you trust the growth rate. A payout ratio above 100% of earnings, or a dividend not covered by free cash flow, means the current dividend is being funded from the balance sheet. A constant-growth model applied to an unsustainable dividend produces a confident, wrong answer.
Watch the spread. Below about one percentage point between r and g, the value becomes arithmetically unstable: at a 1-point spread a further half-point narrowing raises the value by 100%, while at a 6-point spread the same half-point raises it by only 9%. Any company where you need a spread under a point is a company the constant-growth model cannot value; use a two-stage or three-stage model that lets growth fade, or move to a full discounted cash flow model built on free cash flow instead of dividends.
Value per $1.00 of next year's dividend, by spread
| Spread r − g | Value per $1 of D₁ | Value if the spread widens 0.5 pt | Change |
|---|---|---|---|
| 1.0% | $100.00 | $66.67 | −33.3% |
| 2.0% | $50.00 | $40.00 | −20.0% |
| 3.0% | $33.33 | $28.57 | −14.3% |
| 4.0% | $25.00 | $22.22 | −11.1% |
| 5.0% | $20.00 | $18.18 | −9.1% |
| 6.0% | $16.67 | $15.38 | −7.7% |
| 8.0% | $12.50 | $11.76 | −5.9% |
Each value is 1 ÷ spread; each change is spread ÷ (spread + 0.005) − 1. The narrower the spread, the more of your answer is an artefact of two rate assumptions rather than of the dividend itself.
Where the model goes wrong
- Using D₀ in the numerator. The formula needs next year's dividend. Using the trailing figure understates the value by exactly the growth rate.
- Applying it to a non-payer. A company that pays no dividend is not worthless, but this model will say it is worth zero. Value it on free cash flow instead.
- Assuming perpetual growth above the economy. No company grows faster than nominal GDP forever without eventually becoming the entire economy. A high-growth phase needs a multi-stage model that fades growth to a sustainable rate.
- Ignoring buybacks. Many companies now return more cash through repurchases than dividends. Where that is true, either use total shareholder yield in place of the dividend or switch to a cash-flow model, because a dividend-only view understates distributions.
- Confusing the required return with the expected return. The required return is what you demand for the risk; the implied return is what the price offers. The model compares them — it does not derive one from the other.
- Forcing the model onto a cyclical. A miner or a homebuilder whose dividend swings with the cycle has no constant growth rate, and picking a base year at the top or bottom of the cycle sets the whole valuation.
- Mixing real and nominal. A nominal required return from a nominal bond yield must be paired with a nominal dividend growth rate that includes inflation.
The same formula, three different jobs
Gordon growth arithmetic appears in three places in valuation practice and it is worth keeping them distinct. As a share valuation model it prices a dividend stream, which is what this calculator does by default. As a terminal value method it capitalises a company's final-year free cash flow inside a DCF, substituting free cash flow for the dividend and the WACC for the cost of equity. As a return-estimation tool it is rearranged into r = yield + growth to produce a forward-looking expected return for an index or a portfolio. Same algebra, different inputs, different meaning — and mixing the inputs across the three uses is a common source of wrong answers.
When to use a multi-stage model instead
Reach for a two-stage or three-stage dividend discount model whenever a single constant growth rate is not credible. The structure is straightforward: forecast dividends explicitly through the high-growth years, discount each one at the cost of equity, then apply the Gordon formula to the first sustainable-growth year and discount that terminal value back. The constant-growth model is not replaced, it is relegated to the tail where it belongs.
The H-model is a compact middle ground for a company whose growth declines linearly from an initial high rate to a stable rate over a set number of years, avoiding a year-by-year forecast while still fading growth. And where a company's distributions are dominated by buybacks or where dividends bear no stable relationship to earnings, the free cash flow to equity model substitutes the cash a firm could pay for what it does pay — the same logic as the FCFF build-up, one step further down the capital structure.
None of these removes the central difficulty, which is that any perpetuity method concentrates the answer in the gap between two estimated rates. The discipline that helps most is the reverse calculation: rather than defending a value, state the growth rate the current price implies and argue about whether the business can deliver it. That is a question about the company, and it can be researched. A required return is an opinion, and it cannot.
Key terms
- Dividend discount model (DDM)
- Any model that values equity as the present value of expected dividends. The Gordon growth model is its simplest form, assuming one constant growth rate forever.
- Sustainable growth rate
- Retention ratio times return on equity — the rate at which a company can grow its equity base, and therefore its dividend, without raising outside capital.
- Cost of equity
- The return shareholders require for bearing the risk of the equity, usually estimated by CAPM as the risk-free rate plus beta times the equity risk premium.
- Forward dividend yield
- Next year's expected dividend divided by the current share price. In the Gordon model, expected return equals this yield plus the growth rate.
- Payout ratio
- Dividends divided by earnings. One minus the payout ratio is the retention ratio that funds growth.