Gordon Growth Model Explained: Formula, Assumptions, Intrinsic Value Calculation, and Limitations

May 9, 2026 · guides · 12 min read

Gordon Growth Model Explained: Formula, Assumptions, Intrinsic Value Calculation, and Limitations

The Gordon Growth Model reduces the intrinsic value of a dividend-paying stock to a single formula built on three inputs: the next expected dividend, the investor's required rate of return, and the stock's long-run dividend growth rate.

That simplicity is both its greatest strength and its most significant limitation. In the right context, the model produces a defensible, transparent fair value estimate in seconds. In the wrong context, the same formula produces a number that is misleading.

This guide covers the model's origin, the full formula, how to derive each input, a step-by-step worked example, a sensitivity analysis showing how fragile the output is, the connection to DCF terminal value, and the conditions under which the model is and is not appropriate.

Origin: Myron Gordon and the 1956 Dividend Model

The Gordon Growth Model is named after Myron J. Gordon, who formalized it in a 1956 paper co-authored with Eli Shapiro titled 'Capital Equipment Analysis: The Required Rate of Profit.' Gordon extended the work in his 1962 book 'The Investment, Financing, and Valuation of the Corporation.'

The model builds on dividend discount theory, which holds that the fair value of a stock equals the present value of all future dividends it will pay. The conceptual foundation traces to John Burr Williams, whose 1938 book 'The Theory of Investment Value' introduced that framework. Gordon's contribution was to assume dividends grow at a single constant rate forever, converting an infinite series into a clean closed-form equation.

The Gordon Growth Model Formula

The core equation is:

P = D1 / (r - g)

Where:

This formula is derived by solving for the present value of an infinite geometric series of dividends, each growing at rate g, discounted at rate r. The simplification works only because g is less than r, which makes the series converge.

Understanding Each Input

D1: The Next Expected Dividend

D1 is the dividend the company is expected to pay in the next period, usually the next full year.

If the company just paid a dividend (called D0), you can estimate D1 by applying the recent growth rate:

D1 = D0 x (1 + g)

For example, if a company paid a dividend of $2.00 per share this year and dividends are growing at 4% per year, then D1 = $2.00 x 1.04 = $2.08.

This is the only input that comes directly from the company's dividend history. The other two inputs require judgment.

r: The Required Rate of Return

The required rate of return is the minimum annual return an investor needs to justify holding the stock, given its risk level. This is not what the stock is currently yielding; it is what the investor demands given the uncertainty of future cash flows.

The most common way to estimate r is with the Capital Asset Pricing Model (CAPM):

r = Rf + Beta x (Rm - Rf)

Where:

For example, if the risk-free rate is 4.5%, the stock's beta is 0.85, and the equity risk premium is 5.5%:

r = 4.5% + 0.85 x 5.5% = 4.5% + 4.675% = 9.175%, or roughly 9.2%

The equity risk premium is an estimate that varies by source and time period. Analysts typically use a figure between 4.5% and 6% for U.S. equities; Aswath Damodaran at NYU Stern publishes widely cited monthly estimates.

g: The Perpetual Growth Rate

The growth rate is the single most influential and most debated input in the model. It represents the rate at which dividends grow forever. That word, forever, carries enormous weight. A growth rate of 5% applied forever means the company's dividends compound infinitely at that pace, which is unrealistic for most firms.

One principled way to estimate a sustainable long-run growth rate is the sustainable growth rate formula:

g = ROE x Retention Ratio

Where:

For example, if a company earns an ROE of 12% and pays out 60% of earnings as dividends, the retention ratio is 40%, and the sustainable growth rate is:

g = 12% x 0.40 = 4.8%

This formula derives from the internal funding model: a company can only grow its earnings by reinvesting retained earnings, and the rate of return on those reinvested earnings is ROE. A company paying out all of its earnings has no retained capital to reinvest, so its sustainable growth rate is zero unless it borrows or issues equity.

In practice, the long-run growth rate for the Gordon Growth Model should not exceed the expected long-run nominal GDP growth rate for the economy. If a company's assumed perpetual growth rate is above the economy's long-run growth rate, the company would eventually become larger than the entire economy, which is arithmetically impossible. For U.S. companies, analysts typically cap g at 3% to 4% for the Gordon Growth Model.

Step-by-Step Worked Example

Consider a hypothetical utility company with the following characteristics:

Step 1: Calculate D1

D1 = D0 x (1 + g) = $3.00 x 1.04 = $3.12

Step 2: Derive the required return using CAPM

r = Rf + Beta x (Rm - Rf) r = 4.5% + 0.70 x 5.5% r = 4.5% + 3.85% r = 8.35%

Step 3: Confirm g is less than r

g = 4.0%, r = 8.35%. The spread (r - g) = 4.35%. This is positive, so the formula is valid.

Step 4: Apply the Gordon Growth Model

P = D1 / (r - g) P = $3.12 / (0.0835 - 0.04) P = $3.12 / 0.0435 P = $71.72

The model estimates an intrinsic value of approximately $71.72 per share. If the stock is currently trading at $65.00, the model suggests a potential margin of safety of about 10%.

Sensitivity Analysis: Why Small Changes Matter Enormously

The Gordon Growth Model is highly sensitive to its inputs. Because (r - g) appears in the denominator, small changes in either variable produce large swings in estimated value.

Using the base case above (D1 = $3.12, r = 8.35%, g = 4.00%, P = $71.72), consider what happens when g or r shifts by half a percentage point:

Varying the growth rate (g), holding r constant at 8.35%:

Growth Rate (g) r - g Estimated Value (P)
3.0% 5.35% $58.32
3.5% 4.85% $64.33
4.0% (base) 4.35% $71.72
4.5% 3.85% $81.04
5.0% 3.35% $93.13

Varying the required return (r), holding g constant at 4.0%:

Required Return (r) r - g Estimated Value (P)
7.35% 3.35% $93.13
7.85% 3.85% $81.04
8.35% (base) 4.35% $71.72
8.85% 4.85% $64.33
9.35% 5.35% $58.32

A growth rate assumption just 1 percentage point above the base case pushes the estimated value from $71.72 to $93.13, an increase of 30%. A required return 1 percentage point below the base case produces the same result.

This sensitivity illustrates the core risk in the model: the output is only as reliable as the assumptions. Small differences in input estimates produce drastically different valuations. Always run at least three scenarios (conservative, base, optimistic) and report a range rather than a single point estimate.

The Gordon Growth Model and Terminal Value in DCF Analysis

The Gordon Growth Model has a second major application beyond standalone stock valuation: it is the standard formula used to calculate terminal value at the end of a discounted cash flow (DCF) model.

A full DCF model projects free cash flows (or dividends) for a finite period, typically five to ten years, and then needs to estimate what the business is worth at the end of that projection window. Because a business is expected to continue operating beyond the projection period, some assumption must be made about the value of all cash flows occurring after year N.

The terminal value using the Gordon Growth Model (also called the Gordon Growth terminal value or the perpetuity growth method) is:

Terminal Value = Cash Flow in Year N+1 / (r - g)

Where:

The terminal value is then discounted back to the present using the same discount rate as the rest of the model:

Present Value of Terminal Value = Terminal Value / (1 + r)^N

In practice, the terminal value often accounts for 60% to 80% of the total estimated enterprise value in a DCF model, which means the Gordon Growth terminal value assumption is often the single most important driver of the final valuation. This reinforces the sensitivity point above: the terminal growth rate must be selected with care.

When the Gordon Growth Model Is Appropriate

The Gordon Growth Model produces meaningful results under a specific and narrow set of conditions.

The model is most appropriate when:

Classic candidate industries include electric and gas utilities, water utilities, established consumer staples companies, mature real estate investment trusts (REITs), and large-cap telecommunications firms in stable markets. These businesses pay consistent, growing dividends at rates well below their cost of equity.

Key Assumptions and Their Fragility

Every model rests on assumptions. The Gordon Growth Model has four that deserve scrutiny.

1. Dividends grow at a constant rate forever. No business grows at a constant rate in perpetuity. Industries mature, competition intensifies, and regulatory environments shift. The constant growth assumption is a simplification that works well enough when the assumed rate is low and the company is genuinely mature, but it becomes unrealistic for any company with meaningful competitive dynamics.

2. The required rate of return is constant. The CAPM-derived discount rate shifts over time as interest rates and the company's risk profile change. The Gordon Growth Model treats r as fixed.

3. The company will pay dividends forever. Companies cut dividends, get acquired, or fail. The model assumes a perpetual payment stream.

4. Growth can be captured in a single number. Real dividend growth is lumpy. Companies raise dividends in strong years and hold them flat in downturns. A single constant rate smooths over that reality.

None of these assumptions invalidate the model for the right use cases, but they do require the analyst to be explicit about what the model is not capturing.

Key Limitations

g Must Be Less Than r

This is not optional. If g equals or exceeds r, the denominator (r - g) becomes zero or negative, and the formula breaks down entirely. An estimated value of negative $200 per share, produced when g exceeds r, is not meaningful.

This mathematical constraint is also economically sensible. A company growing faster than the discount rate forever would eventually be worth an infinite amount, which is not consistent with any real-world business. When g approaches r, the estimated value grows without bound, which is the model's way of telling you that its assumptions are not realistic for that company.

Not Suitable for High-Growth or Non-Dividend Companies

The Gordon Growth Model cannot be applied to companies that do not pay dividends. For a growth-stage company reinvesting all of its cash flows, there are no dividends to model. Attempting to proxy dividends with free cash flow is possible but converts the model into something different.

For companies that do pay dividends but are growing quickly, the constant growth assumption will produce an overestimate of value if the assumed growth rate is unsustainably high. A technology company growing dividends at 15% per year may not sustain that rate for more than a few years. Applying that rate as a perpetual growth assumption will dramatically inflate the output.

Single-Stage vs. Multi-Stage Dividend Discount Models

The Gordon Growth Model is a single-stage model: one growth rate applies for all time. When a company's growth is expected to change over time, a multi-stage dividend discount model (DDM) is more appropriate.

A two-stage DDM, for example, applies a higher growth rate during a finite high-growth phase (say, 10% for five years) and then switches to a lower, sustainable terminal growth rate (say, 3.5%) for all periods beyond that. The intrinsic value is the sum of the present value of dividends during the high-growth stage plus the present value of the terminal Gordon Growth value at the end of that stage.

The multi-stage approach is more realistic for companies transitioning from growth to maturity, but it requires additional assumptions about the length and magnitude of each phase, which introduces more estimation error. The Gordon Growth Model's advantage is transparency and parsimony; the multi-stage model's advantage is flexibility.

Using the Gordon Growth Model Within a Broader Framework

Because of its sensitivity to input assumptions, the Gordon Growth Model works best as one input in a multi-method valuation rather than a standalone verdict.

A practical approach: run the model under conservative, base-case, and optimistic growth rate assumptions to produce a fair value range. Cross-check that range against a full DCF model using the Gordon Growth terminal value, and against comparable-company multiples such as EV/EBITDA or forward P/E. Require a meaningful discount to the model estimate before treating a stock as potentially undervalued, to account for the inevitable estimation error in g and r.

The model's unique contribution relative to ratio-based methods is that it ties intrinsic value directly to the investor's required return and the company's dividend trajectory. It is forward-looking by construction. A P/E ratio tells you what the market is paying relative to last year's earnings; the Gordon Growth Model tells you what the stock is worth if the assumed dividend path and discount rate hold.

Equity Rank applies multi-method logic across more than eight valuation frameworks simultaneously, including dividend discount approaches, to produce the SAVE score, a composite measure of how consistently a stock appears undervalued or overvalued across independent methods. When multiple models converge on a similar estimate, model confidence is higher. When they diverge, that divergence is itself informative.

Summary

The Gordon Growth Model (P = D1 / (r - g)) was formalized by Myron Gordon in 1956. Its three inputs are next year's expected dividend, the required rate of return derived from CAPM, and the perpetual dividend growth rate grounded in the sustainable growth formula (ROE multiplied by the retention ratio).

The model is most reliable for mature, dividend-paying businesses in stable industries. It does not apply to non-dividend payers or high-growth companies whose near-term growth rates cannot be sustained in perpetuity. Because g and r both appear in the denominator, small changes in either produce large swings in estimated value; always report a range, not a single number.

Within DCF analysis, the Gordon Growth Model is the standard terminal value formula, which makes it one of the most widely applied valuation tools in professional finance regardless of whether dividends are the primary analytical focus.

Understanding the model's assumptions, not just its formula, is what separates investors who use it well from those who misapply it.

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