How much is a dividend-paying stock really worth? One of the most classic ways to answer is the Dividend Discount Model (DDM), and in particular its constant-growth version, the Gordon Growth Model. The idea is elegant: the value of a stock is the sum of all the future dividends it will pay, discounted to today. If dividends are assumed to grow at a constant rate, this infinite sum condenses into a simple formula. It is a fundamental tool for dividend investing and stock valuation. The Dividend Discount Model calculator gives you the intrinsic value of a stock from the current dividend, the expected growth rate and the required return, also showing the dividend yield and the sensitivity of the result.

What the Dividend Discount Model (Gordon model) is

The Dividend Discount Model values a stock as the present value of all its future dividends. The most used version, the Gordon Growth Model, assumes dividends grow at a constant rate forever. Under this assumption, the intrinsic value of the stock is simply the dividend expected next year divided by the difference between the required return and the growth rate. It is one of the most famous formulas in finance, used to estimate how much a stock "should" be worth based on its dividend fundamentals, regardless of the market price. The model applies well to mature, stable companies that pay growing dividends predictably — utilities, consumer goods, established companies — and is a pillar of dividend-oriented fundamental analysis.

How it is calculated: the Gordon formula

The formula is: intrinsic value = dividend expected next year / (required return − growth rate). In symbols: P = D1 / (r − g), where D1 = D0 × (1 + g), that is the current dividend grown by one year. Example: a stock pays a dividend of 2 today (D0), expected to grow 4% a year (g), and a return of 9% is required (r). Next year's dividend is 2 × 1.04 = 2.08 (D1). The intrinsic value is 2.08 / (0.09 − 0.04) = 2.08 / 0.05 = 41.60. The calculator shows the intrinsic value, the expected dividend D1, the dividend yield at intrinsic value (which equals r − g) and the price-to-dividend multiple, as well as an assessment of the sensitivity of the result.

The dividend and its growth

The starting point of the model is the dividend. The DDM distinguishes between the current dividend (D0), the one recently paid, and the dividend expected next year (D1), which is D0 grown by the growth rate: D1 = D0 × (1 + g). The Gordon formula uses D1 in the numerator. The growth rate (g) is the most delicate assumption: it represents how much the dividend is expected to grow each year, forever. It is estimated from the company's dividend history, from earnings growth, or from the formula "retention rate × return on equity". Since the model projects this growth to infinity, g must be a prudent and sustainable estimate: no company can grow faster than the economy forever. A too-optimistic g enormously inflates the intrinsic value.

The required return (r)

The required return (r) is the discount rate: the return the investor demands to hold the stock, given its risk. It represents the opportunity cost of capital and the compensation for risk. The higher r, the lower the intrinsic value (future dividends are worth less today). Where does r come from? Typically from the CAPM (Capital Asset Pricing Model): r = risk-free rate + beta × equity risk premium. The CAPM and the DDM combine naturally: the CAPM provides the required return based on the stock's risk, the DDM uses it to discount the dividends and obtain the value. An accurate estimate of r is crucial: together with the growth rate, it determines the denominator (r − g) on which the entire result depends.

The r > g condition: why it is fundamental

The Gordon model has an inescapable mathematical condition: the required return must be greater than the growth rate (r > g). If r were equal to or less than g, the denominator (r − g) would become zero or negative, and the formula would give an infinite or meaningless value. This is not just a technical rule: it reflects an economic reality. If a company grew at a rate equal to or higher than the required return forever, its value would be infinite — impossible. This is why the long-term growth rate must be lower than the required return, and in practice cannot exceed the growth of the economy as a whole. The calculator checks this condition: if you enter a growth rate greater than or equal to the required return, it signals the error, because the model is not applicable in that case.

Intrinsic value and market value

The DDM produces the intrinsic value: how much the stock is worth based on its dividend fundamentals, regardless of the price at which it trades on the market. The comparison between intrinsic value and market price is the heart of the analysis: if the intrinsic value is greater than the price, the stock is potentially undervalued (a bargain, according to the model); if lower, potentially overvalued. Value investors use the DDM precisely to identify stocks that the market prices below their "true" value. Beware though: the intrinsic value is only as good as the assumptions. If the market prices the stock differently from the DDM, the market might be right (with better information) or the model might be (if the market is irrational). The DDM is an input to judgment, not an absolute verdict.

Dividend yield and growth

There is an elegant relationship in the Gordon model: the required return is the sum of the dividend yield and the growth rate. In formula: r = (D1/P) + g. The total return the investor gets is composed of two parts: the dividend yield (the dividends collected relative to the price) and the capital growth (the appreciation due to the growth of dividends). At intrinsic value, the dividend yield is exactly r − g. In the example, with r 9% and g 4%, the dividend yield at intrinsic value is 5%. This breakdown helps understand where the return of a dividend stock comes from: part from the coupon, part from growth. High-growth companies have a low dividend yield (most of the return is growth); mature companies have a high dividend yield and low growth.

Why the model is so sensitive to assumptions

The Gordon model is powerful but extremely sensitive to assumptions, because of the denominator (r − g). When r and g are close, the denominator is small, and small variations in the assumptions produce enormous variations in the value. Example: with r 8% and g 7%, the denominator is 1% and the value is very high; if g drops to 6%, the denominator doubles (2%) and the value halves. A change of a single percentage point in growth can change the intrinsic value by 50% or more. This sensitivity is the main practical limit of the model: it makes results fragile when r − g is small. This is why it is wise to use prudent assumptions, test multiple scenarios (sensitivity analysis) and be wary of very high intrinsic values derived from a minimal r − g margin. The calculator signals when the margin is too narrow.

Intrinsic value by growth and return

Here is how the intrinsic value of a stock with dividend D0 of 2 changes as the growth rate varies, with a required return fixed at 9%:

Note the acceleration: going from 2% to 7% growth, the value almost quadruples, and the last point (from 6% to 7%) alone adds more value than the first ones. It is the effect of the shrinking denominator: sensitivity grows as g approaches r.

When to use the DDM

The DDM works best for mature and stable companies that pay regular and predictably growing dividends: utilities, established banks, consumer goods, telecoms, "dividend aristocrat" companies. In these cases the constant-growth assumption is reasonable and the model gives sensible estimates. The DDM does not work well for companies that don't pay dividends (startups, many growing tech), for companies with irregular or unpredictable dividends, or for rapidly growing companies where the constant-growth assumption is unrealistic (in those cases multi-stage or cash-flow-based models are used). Before applying the DDM, ask yourself: does this company pay stable and predictably growing dividends? If so, the model is appropriate; if not, different approaches are needed.

The multi-stage DDM

The basic Gordon version assumes constant growth forever, which is unrealistic for high-growth companies. For these, the multi-stage DDM is used: a first phase of high growth is modeled (for a defined number of years) and then a stable and sustainable growth phase (the "terminal" growth), to which the Gordon formula is applied. The total value is the sum of the discounted dividends of the high-growth phase plus the discounted terminal value. This approach is more realistic for companies that grow fast but will slow with maturity. The calculator implements the single-stage (Gordon) model, the most direct and used for stable companies; for high-growth companies, consider that the value should be estimated with a multi-stage model, applying Gordon only to the terminal phase.

DDM and CAPM: how they combine

The DDM and the CAPM are complementary and often used together. The CAPM answers the question "what return should I require for this stock, given its risk?" and provides r = risk-free rate + beta × equity premium. The DDM answers the question "how much is this stock worth, given its dividends and the required return?" and uses r as the discount rate. In practice: first you calculate r with the CAPM (based on the stock's beta), then you enter it into the DDM to obtain the intrinsic value. A higher beta (riskier stock) raises r, which lowers the intrinsic value: consistently, a riskier company is worth less at equal dividends. This combination — CAPM for risk, DDM for valuation — is a pillar of the fundamental analysis of dividend stocks.

The price-to-dividend multiple

The Gordon model implies a price-to-dividend multiple: how many times the dividend the stock should be worth. From the formula, this multiple is 1 / (r − g). In the example (r 9%, g 4%), the multiple is 1 / 0.05 = 20: the stock should be worth 20 times its expected dividend. This multiple is the inverse of the dividend yield (r − g): a 5% dividend yield corresponds to a 20× multiple. When r − g is small (growth close to the return), the multiple explodes: with a 1% margin the multiple is 100×, with a 0.5% margin it is 200×. It is the same sensitivity phenomenon seen before, expressed as a multiple. Comparing the multiple implied by the DDM with the actual market one is another way to judge whether a stock is expensive or cheap.

The sensitivity to the r − g margin

Here is how the margin (r − g) determines the price-to-dividend multiple and the fragility of the estimate:

The narrower the margin, the higher the multiple and the more fragile the estimate. Intrinsic values derived from very small margins must be treated with great caution: small revisions of the assumptions are enough to overturn them.

The limits of the model

The Gordon DDM has important limits. It applies only to companies that pay dividends, excluding much of the market (many companies don't pay them). It assumes constant growth forever, unrealistic for most companies. It is extremely sensitive to the assumptions of r and g, as seen. It ignores share buybacks, an increasingly common alternative way of returning capital to shareholders, which the dividend-only model doesn't capture. And it depends on the quality of the estimates: g and r are forecasts, not certainties. Nonetheless, the DDM remains a valuable educational and practical tool for stable-dividend companies, and its logic (value as the sum of discounted future flows) is at the base of all valuation. It must be used with judgment, prudent assumptions and sensitivity analysis, not as absolute truth.

The breakdown of the return

The total return expected from a dividend stock, according to the model, breaks down as follows:

This breakdown (r = dividend yield + growth) is one of the most useful insights of the model: it shows that the return of a dividend stock comes both from the coupon and from growth, and that the two components offset each other (high growth = low dividend yield, and vice versa).

How the calculator works

Enter the current annual dividend per share (D0), the expected growth rate of the dividend (g) and the required return (r, typically from the CAPM). The calculator applies the Gordon model and gives you the intrinsic value of the stock, the dividend expected next year (D1), the dividend yield at intrinsic value, the implied price-to-dividend multiple and an assessment of the sensitivity based on the r − g margin. If you enter a growth rate greater than or equal to the required return, the calculator signals that the model is not applicable.

The data you need

You need three data. The current annual dividend per share (D0): the last annual dividend paid, from the company's data. The expected growth rate of the dividend (g): estimated from the dividend history, from earnings growth or from the formula retention × return on equity — use a prudent and long-term sustainable value. The required return (r): the discount rate, often calculated with the CAPM based on the stock's risk, or the return you demand for that level of risk. Remember that r must be greater than g. The quality of your estimates of g and r entirely determines the reliability of the intrinsic value: small differences matter a lot, especially when r and g are close.

Common mistakes

• Using a growth rate that is too high or unsustainable, which enormously inflates the value.
• Entering a growth greater than or equal to the required return (the model is not applicable).
• Applying the DDM to a company that doesn't pay stable and growing dividends.
• Trusting an intrinsic value derived from a minimal r − g margin, without sensitivity analysis.
• Ignoring share buybacks, which the dividend-only model doesn't capture.

How to use the calculator

Calculate the intrinsic value of a dividend stock and compare it with its market price: if the intrinsic value is higher, the stock is potentially undervalued (according to the model); if lower, potentially expensive. Always do sensitivity analysis: try different growth rates and required returns to see how much the value changes, especially if the r − g margin is narrow. Use the required return from the CAPM for consistency. Look at the price-to-dividend multiple for a quick comparison. Remember that the model applies only to companies with stable and growing dividends, that it is very sensitive to assumptions, and that the intrinsic value is only as good as the estimates you enter. It is an informational tool for financial analysis, not advice nor an investment recommendation.

Practical example

You want to value a stock of a utility that pays an annual dividend of 2 per share (D0), which you expect to grow 4% a year (g), and for which you require a return of 9% (r, consistent with its risk according to the CAPM). The calculation gives a dividend expected next year of 2.08 (D1), an intrinsic value of 41.60 (2.08 / 0.05), a dividend yield of 5% at intrinsic value and a price-to-dividend multiple of 20×. Verdict: balanced margin, reasonable estimate. If the stock trades at 35, the model suggests it is undervalued (worth 41.60 according to your assumptions); if at 55, overvalued. Then do sensitivity analysis: if growth were 5% instead of 4%, the value would rise to 52.50 — a notable change from a single point, which shows how much the assumptions matter. Enter your numbers. The calculation applies the Gordon model (constant growth), which is based on simplifying assumptions and on estimated and uncertain parameters (especially the growth rate and the required return). The model is very sensitive to assumptions, applies only to companies with stable and growing dividends, ignores share buybacks, and the intrinsic value is an estimate, not the "true" price nor a forecast. It is an informational tool for financial analysis, not advice nor an investment recommendation.

Frequently asked questions

What is the Dividend Discount Model (DDM)?

It is a model that values a stock as the present value of all its future dividends. The most used version, the Gordon model, assumes constant dividend growth and calculates the intrinsic value as D1 / (r − g).

How is the intrinsic value calculated with Gordon?

Value = dividend expected next year / (required return − growth rate), that is P = D1/(r−g) with D1 = D0×(1+g). With D0 2, g 4% and r 9%: D1 = 2.08, P = 2.08/0.05 = 41.60.

Why must r be greater than g?

Because the denominator (r − g) must be positive: if r ≤ g, the formula would give an infinite or negative value. Economically, a company cannot grow more than the required return forever. The calculator signals the error if g ≥ r.

What is the difference between D0 and D1?

D0 is the current dividend (just paid), D1 is the dividend expected next year: D1 = D0 × (1 + g). The Gordon formula uses D1 in the numerator, so the calculator grows D0 by one year before dividing it by (r − g).

Where does the required return (r) come from?

Typically from the CAPM: r = risk-free rate + beta × equity risk premium. CAPM and DDM combine: the CAPM gives r based on the stock's risk, the DDM uses it to discount the dividends and obtain the value.

Why is the model so sensitive?

Because of the denominator (r − g). When r and g are close, the denominator is small and small variations in the assumptions change the value enormously: from g 6% to g 7% (with r 9%) the value can almost double. With small margins, results are fragile.

Is the intrinsic value the fair price?

No, it is an estimate based on dividend fundamentals according to your assumptions. Compare it with the market price: intrinsic > price suggests undervaluation, intrinsic < price overvaluation. But the model is only as good as the assumptions (g and r).

What companies does the DDM apply to?

To mature and stable companies with regular and predictably growing dividends (utilities, consumer goods, established banks). NOT to those that don't pay dividends (startups, many techs) or have irregular dividends, where multi-stage or cash-flow models are needed.

What is the multi-stage model?

A version of the DDM that models a high-growth phase followed by stable (terminal) growth, to which Gordon is applied. It is more realistic for high-growth companies. The calculator uses the single-stage (Gordon) version, suitable for stable companies.

What is the price-to-dividend multiple?

It is how many times the dividend the stock should be worth: 1/(r−g). With r 9% and g 4%, the multiple is 20×. It is the inverse of the dividend yield. With small margins the multiple explodes (1% margin → 100×), signaling fragility.

What are the limits of the DDM?

It applies only to companies with dividends, assumes constant growth forever, is very sensitive to assumptions, ignores share buybacks, and depends on the quality of the g and r estimates. It must be used with prudent assumptions and sensitivity analysis.

Is it an investment recommendation?

No. The DDM is a tool for estimating intrinsic value based on simplifying assumptions and uncertain parameters (g and r). The value is an estimate, not the true price nor a forecast. It is an informational tool for financial analysis, not advice nor a recommendation.

Updated July 2026