Updated for the 2026-2027 CFA® Level I curriculum.
The Gordon growth model values a stock as the present value of dividends that grow at one constant rate forever. The two-stage dividend discount model (DDM) handles companies whose growth rate changes over time. Both models appear in Equity Investments and both rely on the same core idea: a stock's intrinsic value equals the present value of its future dividends.
After this note, you should be able to apply each formula correctly and identify which model fits a given company profile.
Quick Answer
The Gordon growth model values a share as:
where is next year's dividend, is the required return, and is constant growth. It requires . A two-stage DDM adds the present value of near-term dividends to a discounted terminal value based on stable growth.
Key Takeaways About Gordon Growth and Two-Stage Dividend Discount Models
The Gordon growth model assumes one constant dividend growth rate forever.
The formula uses , next year's expected dividend, not .
The model requires . If equals or exceeds , the formula breaks down.
The two-stage DDM splits valuation into a high-growth period and a stable-growth period.
The stable-growth period is valued with the Gordon growth formula at the point growth becomes constant, producing a terminal value.
That terminal value must be discounted back to time zero along with the interim dividends.
Company maturity and growth stability determine which model applies.
What You Need to Know for CFA Level I
Apply the Gordon growth model formula and correctly identify versus .
Build a two-stage DDM valuation from dividend forecasts, a terminal value, and discounting.
State and apply the condition for the constant-growth stage.
Match company characteristics (mature versus high-growth) to the correct model.
Avoid applying constant growth to a company with a clearly changing growth pattern.
Gordon Constant-Growth DDM
The Gordon growth model prices a stock using one dividend growth rate that holds forever. It fits mature, stable companies with a long history of steady dividend increases, such as regulated utilities or established consumer staples firms.
The model states:
Where:
= intrinsic value today
= expected dividend next year =
= required return on equity
= constant, sustainable dividend growth rate
The model only holds when is greater than . If is equal to or larger than , the denominator becomes zero or negative, and the formula produces a nonsensical or infinite value. This condition matters because it defines when the model can be used at all, not just when it gives a "good" answer.
Two-Stage DDM
The two-stage DDM values a company that will not grow at one rate forever. It assumes a period of higher, often unsustainable growth, followed by a permanent shift to stable growth.
The valuation has two parts:
High-growth stage. Forecast dividends for each year of the high-growth period and discount each one back to today at the required return.
Stable-growth stage. At the point growth becomes constant, apply the Gordon growth model to find a terminal value. Then discount that terminal value back to today using the same required return, over the same number of periods as the high-growth stage.
Where:
= dividend expected in year during the high-growth stage
= number of years in the high-growth stage
= terminal value at the end of year
= required return
= stable long-term growth rate
The terminal value calculation still requires in the stable stage. That condition never disappears just because a company had faster growth earlier.
Required Return, Growth, and Dividend Inputs
Both models depend on three inputs, and errors in any one changes the result significantly.
Input | Definition | Common Source |
|---|---|---|
Required return () | Minimum return an investor demands for the stock's risk | CAPM or another cost of equity estimate |
Growth rate () | Expected long-run dividend growth rate | Historical dividend growth, earnings retention and ROE, or analyst forecasts |
Dividend ( or ) | Dollar dividend expected in a specific future year | Prior dividend grown forward by the expected rate |
A small change in has a large effect on value because sits in the denominator alongside . A one percentage point increase in , holding constant, can raise intrinsic value by 20% or more depending on the size of the () spread. This sensitivity is why analysts stress-test growth assumptions rather than relying on a single point estimate.
Characteristics of Companies Suited to Each Model
Company Profile | Better Model | Why |
|---|---|---|
Mature, stable earnings and dividends | Gordon growth | Growth rate has settled near a sustainable, long-run pace |
Regulated or slow-cycle industry | Gordon growth | Limited reinvestment opportunities support steady, predictable growth |
High current growth expected to slow | Two-stage DDM | Captures the transition from an unsustainable rate to a stable one |
Recently profitable or early dividend payer | Two-stage DDM | Early growth is rarely constant, so a single rate misrepresents value |
The core question is whether one growth rate can realistically describe the company forever. If the answer is no, a two-stage or multistage approach is required.
Worked Example
Case 1: Stable Utility Co. (Gordon growth model)
Stable Utility Co. just paid a dividend of $2.00 per share. Dividends are expected to grow at a constant 3% per year. The required return on equity is 8%.
Step 1: Find
Step 2: Apply the Gordon growth formula.
Because Stable Utility Co. has a long, predictable growth pattern and exceeds , the Gordon growth model produces a clean, single-step valuation of $41.20 per share.
Case 2: TechRise Inc. (two-stage DDM)
TechRise Inc. just paid a dividend of $1.00 per share. Analysts expect 20% annual dividend growth for the next three years, followed by a permanent shift to 4% growth. The required return is 10%.
Step 1: Forecast high-growth dividends.
Step 2: Find the terminal value at the end of year 3.
Step 3: Discount everything back to today at 10%.
TechRise's early growth is too fast to hold forever, so treating it as a Gordon growth stock would overstate value. The two-stage model captures the temporary high-growth phase separately from the permanent stable-growth phase.
Common Exam Traps
Using instead of
The Gordon growth formula needs next year's dividend, not the dividend just paid. Forgetting to grow forward by one period is one of the most common calculation errors on this topic.
Allowing to equal or exceed
If growth equals or exceeds the required return, the constant-growth formula is invalid. Exam questions sometimes embed this condition to test whether candidates check it before calculating.
Applying constant growth to a changing-growth company
A company transitioning from high growth to maturity cannot be valued accurately with a single growth rate. Questions describing a young, fast-growing firm are a signal to use a two-stage approach, not the Gordon growth model directly.
Forgetting to discount the terminal value
The terminal value is calculated as of the end of the high-growth period, not today. It must be discounted back the same number of periods as the last high-growth dividend before it can be added to the other present values.
Practice Question
A company just paid a dividend of $3.00 per share. Dividends are expected to grow at a constant rate of 4% per year indefinitely. The required return on the company's equity is 9%. Using the Gordon growth model, the stock's intrinsic value per share is closest to:
$60.00
$62.40
$78.00
Correct Answer: B
Option A: Uses ($3.00) instead of in the numerator, a common data-entry error.
Option C: Divides by (0.04) instead of by (), confusing the growth rate with the discount spread.
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FAQs About Gordon Growth and Two-Stage Dividend Discount Models
Why does the Gordon growth model require to be greater than ?
If , the denominator in is zero or negative, so the constant-growth model is not valid.
How do I know when to use a two-stage model instead of the Gordon growth model?
Use the two-stage model when a company's current growth rate is clearly unsustainable long term, such as a young company reinvesting heavily. Use the Gordon growth model once growth has settled into a steady, mature pace.
Can the two-stage model use more than two growth rates?
The core LOS here covers two stages. Multistage models with three or more growth phases follow the same logic, just with additional forecast periods before the terminal value.