What Is the Gordon Growth Model? Formula and Stock Valuation Example

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The Gordon growth model (GGM) values a stock as the present value of all its future dividends, assuming those dividends grow at one constant rate forever. Under that assumption, an infinite stream of payments collapses into a single short formula: next year’s dividend divided by the difference between the required rate of return and the dividend growth rate. The model is named after economist Myron J. Gordon, who developed it with Eli Shapiro in the 1950s. You will also see it called the constant growth model, the Gordon dividend growth model or the dividend capitalization model. It is the simplest form of the dividend discount model (DDM).

The Gordon Growth Model Formula

The formula is:

P₀ = D₁ / (r − g)

where:

• P₀ is the intrinsic value of one share today. This is the model’s estimate of what the share is worth, not the price it trades at.
• D₁ is the dividend per share expected over the next 12 months.
• r is the required rate of return on the stock, also called the cost of equity.
• g is the dividend growth rate, assumed constant in perpetuity.

The variable that causes the most mistakes is D₁. The formula needs next year’s dividend, not the one just paid. If you start from the most recent annual dividend (D₀), you first grow it by one year: D₁ = D₀ × (1 + g). Plugging D₀ straight into the numerator understates the value by a factor of (1 + g).

Each input is a rate per period, usually per year, and r and g must be measured on the same basis. Both are normally nominal rates. If one is real (inflation-adjusted) and the other nominal, the result is inconsistent.

Derivation of the Gordon Growth Model

The general dividend discount model says a share is worth the sum of every future dividend, each discounted back to today:

P₀ = D₁/(1 + r) + D₂/(1 + r)² + D₃/(1 + r)³ + …

If dividends grow at a constant rate g, then D₂ = D₁(1 + g), D₃ = D₁(1 + g)², and so on. The sum becomes:

P₀ = D₁/(1 + r) × [1 + (1 + g)/(1 + r) + ((1 + g)/(1 + r))² + …]

The bracket is a geometric series with common ratio (1 + g)/(1 + r). A geometric series converges only when that ratio is below 1, which is the same as saying g is less than r. When it converges, the bracket equals (1 + r)/(r − g). Multiplying through:

P₀ = D₁/(1 + r) × (1 + r)/(r − g) = D₁ / (r − g)

The Inputs and How to Estimate Them

Next Year’s Dividend (D₁)

For a company with a stable payout, D₁ is usually the current annual dividend grown by g, or a declared or forecast dividend for the coming year. Use the regular dividend. Special one-time payouts distort the base that the model compounds forever.

The Dividend Growth Rate (g)

The growth rate does the most work in the formula and is the hardest input to pin down. Common approaches:

• Historical growth: the compound annual growth rate of dividends over a past period. This assumes the past pattern continues indefinitely.
• Analyst or management forecasts: useful for the near term, though rarely meant to apply forever.
• Sustainable growth: g = b × ROE, where b is the retention ratio (1 minus the payout ratio) and ROE is return on equity. It is roughly the rate at which a company can grow earnings and dividends by reinvesting retained earnings, without outside financing. For example, a firm that pays out 40% of earnings (b = 0.60) with an ROE of 12% has a sustainable growth rate of 0.60 × 12% = 7.2%.

The sustainable growth approach is the usual way to estimate g for banks and other financial institutions. Their retained profit feeds the capital base that supports future lending, and capital requirements limit how much they can pay out, so the retention ratio and ROE carry real information about future dividend capacity.

Because g applies in perpetuity, it should be modest. A company cannot grow faster than the overall economy forever, so analysts often cap perpetual growth near long-run nominal economic growth: expected inflation plus real growth.

The Required Rate of Return (r)

The required return is the minimum annual return an investor demands for holding the stock, given its risk. It is often estimated with the capital asset pricing model:

r = risk-free rate + beta × (expected market return − risk-free rate)

Because dividends belong only to shareholders, r should be the cost of equity, not the weighted average cost of capital (WACC). WACC blends in the cost of debt and is the right rate for cash flows available to all capital providers, which is a different calculation.

Gordon Growth Model Example

Hypothetical example for illustration only. A utility just paid an annual dividend of $2.00 per share. You expect dividends to grow 4% a year indefinitely, and you require a 9% return given the stock’s risk.

1. Next year’s dividend: D₁ = $2.00 × 1.04 = $2.08
2. Spread between required return and growth: r − g = 0.09 − 0.04 = 0.05
3. Intrinsic value: P₀ = $2.08 / 0.05 = $41.60

If the shares trade at $48, the model says the market is pricing in either a lower required return or faster growth than you assumed, and the stock looks overvalued on your inputs. At $36, it would look undervalued.

The example also shows how sensitive the result is to small changes:

A one-point change in either input moves the value by roughly 17% to 26% in this case. The narrower the spread between r and g, the larger the swings, because the spread sits in the denominator.

Interpreting the Result

The GGM value is an estimate of intrinsic value under your assumptions, and the signal it gives is only as good as the inputs. Two analysts using different growth or return estimates can reach opposite conclusions about the same stock.

The model has a few built-in implications worth knowing:

• The share price grows at g. If all assumptions hold, next year’s value is P₁ = D₂/(r − g), which is P₀ × (1 + g).
• Total return splits into yield and growth. An investor who buys at the model value earns the dividend yield (D₁/P₀) plus price appreciation at g, and the two add up to r.
• It implies a justified P/E ratio. Dividing both sides by next year’s earnings gives P₀/E₁ = payout ratio / (r − g). This links the multiple a stock deserves to its payout policy, risk and growth.

Using the Formula in Reverse

Rearranging the Gordon equation solves for the return the market is implying:

r = D₁ / P₀ + g

Suppose a stock trades at $50, is expected to pay $2.00 next year, and grows its dividend at 5%. The implied return is 4% + 5% = 9%. This version is a common way to estimate a company’s cost of equity (sometimes written as ke = D₁/P₀ + g) and, applied to a broad index’s dividend yield and expected dividend growth, to estimate the expected return on the market as a whole.

How the Gordon Growth Model Is Used

Valuing Mature Dividend Payers

The model suits businesses whose dividends grow in a slow, predictable way, such as regulated utilities, consumer staples companies and established banks. It is also used as a quick check on whether a market price makes sense for a stock with a long dividend history.

Terminal Value in DCF Models

The most common professional use of Gordon growth math is the terminal value in a discounted cash flow (DCF) model. An analyst forecasts cash flows for an explicit period, say five or ten years, then assumes cash flows grow at a constant rate afterward. The value of everything after the forecast period is:

Terminal value at year n = cash flow in year n+1 / (discount rate − g)

That terminal value is then discounted back to today along with the explicit cash flows. In this setting the cash flow is often free cash flow and the discount rate is often WACC, but the structure is the same constant-growth perpetuity.

Two-Stage Models

A single constant rate is unrealistic for a company growing quickly today. A two-stage dividend discount model discounts each dividend individually during a high-growth phase, then applies the Gordon growth formula once growth is expected to settle to a stable long-run rate. That GGM value is discounted back to today and added to the present value of the stage-one dividends. The second-stage growth rate must still be below r.

Limitations of the Gordon Growth Model

• Constant growth is an assumption, not an observation. Dividends respond to recessions, booms, acquisitions and changes in strategy. A single rate applied forever smooths all of that away.
• The r > g condition. The formula divides by zero when g equals r and turns negative when g exceeds r, which rules out any firm whose expected growth is near or above its cost of equity.
• High sensitivity. Because the spread r − g is usually small, minor changes in estimates produce large changes in value.
• No dividend, no value. A company that pays nothing, or pays a token amount while reinvesting heavily, gets a value of zero or close to it. That makes the model unsuitable for most early-stage and growth companies.
• Share buybacks are ignored. Many companies return cash through repurchases instead of, or alongside, dividends. A dividend-only model understates what shareholders receive from such firms unless the analyst adjusts the inputs.
• Value outside dividends is left out. Assets, brand strength or a cash pile that has not yet been paid out matter to the model only through their effect on expected dividends.

Gordon Growth Model vs. Related Concepts

Dividend discount model (DDM). The DDM is the general framework: value equals the present value of all future dividends, with any growth pattern. The GGM is the special case where growth is constant forever.

Zero-growth perpetuity. If g is 0, the formula reduces to P = D / r, the value of a fixed payment received forever. This is how a non-growing preferred stock dividend is typically valued.

Discounted cash flow. DCF discounts cash flows, usually free cash flow to the firm, rather than dividends, and can value companies that pay nothing. It often uses the Gordon growth formula only for its terminal value.

The Bottom Line

The Gordon growth model is most useful to investors and analysts valuing mature, steady dividend payers such as utilities, consumer staples companies and established banks, and to anyone building terminal values in DCF models. Its output depends heavily on the spread between required return and growth, so small input changes move the value sharply. Treat the result as an estimate under stated assumptions, and use other methods for firms that pay little or no dividend.