What Is the Dividend Discount Model (DDM)? Formula and Examples

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The dividend discount model (DDM) is a valuation method that sets the intrinsic value of a share equal to the present value of all the dividends it is expected to pay in the future. Each expected dividend is discounted back to today at the shareholder’s required rate of return, and the discounted amounts are added together. If the resulting value is above the current market price, the model says the stock is undervalued. If it is below, the model says the stock is overvalued.

The method is also called the discounted dividend model or the dividend discount method. Its best-known version, the constant-growth model, is usually called the Gordon growth model.

How the Dividend Discount Model Works

A shareholder who buys a stock and holds it forever receives only one thing from the company: dividends. A shareholder who sells receives dividends up to the sale and then a price from the buyer. That price, in turn, depends on the dividends the buyer expects to collect. Follow that chain far enough and the value of a share comes back to the stream of dividends the company will pay. The DDM formalizes this idea.

The time value of money behind the DDM

The model rests on the principle that a dollar received today is worth more than a dollar received later, because today’s dollar can be invested and earn a return.

The relationship works in both directions:

• Future value = Present value × (1 + r)
• Present value = Future value ÷ (1 + r)

For cash received t years from now, the divisor becomes (1 + r)^t. The DDM applies the present value side of this relationship to every expected dividend, using the required return on equity as r. It is the same discounting logic used in net present value (NPV), applied to dividends per share.

The general DDM formula

In its most general form, the dividend discount model formula is:

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

where:

• P₀ = intrinsic value of the stock today
• Dₜ = expected dividend per share in year t
• r = required rate of return on equity (the cost of equity)

Because the series runs forever, it cannot be computed directly without some assumption about how dividends behave. Each DDM variant is a different assumption about that pattern.

Estimating future dividends

Forecasting dividends is where most of the judgment sits. Analysts typically start from the current dividend and the company’s payout history, then apply a growth assumption.

The simplest approach is a fixed growth rate. If a company paid $1.00 per share this year and dividends are expected to grow 5% a year, next year’s dividend is expected to be $1.05.

Another approach extrapolates a visible trend. A hypothetical company that paid $2.00, $2.50, $3.00 and $3.50 over four years is raising its dividend by $0.50 a year, which suggests $4.00 next. A pattern like this rises by a constant dollar amount, so its percentage growth rate falls each year. Converting it into a single percentage for a constant-growth model requires a choice about which rate to use.

A third approach ties growth to the business that funds the dividend. The sustainable growth rate is estimated as:

g = ROE × retention ratio

The retention ratio is the share of earnings the company keeps rather than pays out (1 minus the dividend payout ratio). A company earning a 12% return on equity that retains 40% of its earnings has an implied growth rate of 12% × 0.40 = 4.8%, assuming ROE and the payout policy stay the same. The logic is that dividends come from earnings, and earnings can only grow from the capital the company reinvests.

Choosing the discount rate

The discount rate in the DDM is the cost of equity: the return shareholders require for bearing the risk of owning the stock. Shareholders are not promised anything. Dividends can be cut and the share price can fall, so they demand compensation above what a risk-free asset pays.

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

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

Some investors use a personal hurdle rate instead, the minimum return they would accept from the investment. The required rate of return is therefore partly a matter of investor discretion, and two people analyzing the same company can reach different values simply because they demand different returns.

Note that the DDM uses the cost of equity, not the weighted average cost of capital (WACC). Dividends belong only to shareholders, so they are discounted at the shareholders’ required return. WACC blends in the cost of debt and is used to discount cash flows available to all capital providers.

The Constant-Growth DDM (Gordon Growth Model)

If dividends are assumed to grow at a constant rate g forever, the infinite series above collapses into a single expression:

P₀ = D₁ / (r − g)

where:

• D₁ = expected dividend per share over the next year
• r = required rate of return (cost of equity)
• g = constant dividend growth rate, in perpetuity

The model is named after economist Myron J. Gordon, who published it in the early 1960s, including in his 1962 book The Investment, Financing, and Valuation of the Corporation. It is the most widely taught form of the DDM.

Why infinite growth produces a finite value

Each future dividend grows by (1 + g) a year but is discounted by (1 + r) a year. As long as g is smaller than r, each successive discounted dividend is smaller than the one before it, and the sum of the infinite series converges to D₁ / (r − g). The term (r − g) is effectively the net discount rate applied to the dividend stream.

If g equals r, the denominator is zero and the value is undefined. If g exceeds r, the formula returns a negative price, which is meaningless. No company can grow its dividend faster than the required return forever. A growth rate that high can only be a temporary stage, which is why multi-stage models exist.

D₀ versus D₁

The formula uses next year’s dividend, not the one just paid. If you start from the most recent annual dividend (D₀), convert it first:

D₁ = D₀ × (1 + g)

Using D₀ directly in the numerator understates the value by a factor of (1 + g). It is one of the most common DDM errors.

Rearranging for the required return

The same equation can be solved for r:

r = D₁ / P₀ + g

The expected return on a stock under the constant-growth model is the forward dividend yield plus the dividend growth rate. Plugging in the current market price gives the return the market is implicitly pricing in, which you can compare with your own required return. This rearranged form is also one way practitioners estimate the cost of equity for dividend-paying companies, as an alternative to CAPM.

Capital gains are already included

The constant-growth DDM appears to count only dividends, but it also captures price appreciation. Under its assumptions, the share price grows at the same rate g as the dividend, so an investor who holds for a few years and sells collects dividends plus a sale price that has risen by g a year. The sale price is itself the present value of the dividends that come after it. The model is normally applied before taxes, so it does not separate the tax treatment of dividends from that of capital gains.

Worked Examples

All examples below are hypothetical and chosen to show the mechanics.

Constant-growth example

Company X paid a dividend of $1.80 per share this year. Dividends are expected to grow at 5% a year in perpetuity, and the cost of equity is 7%.

1. Next year’s dividend: D₁ = $1.80 × 1.05 = $1.89
2. Value per share: P₀ = $1.89 / (0.07 − 0.05) = $1.89 / 0.02 = $94.50

If Company X trades at $80, the model suggests it is undervalued by about $14.50 per share. If it trades at $110, the model suggests it is overvalued.

How sensitive the result is

Keep everything the same but lower the growth rate to 4.5%:

1. D₁ = $1.80 × 1.045 = $1.881
2. P₀ = $1.881 / (0.07 − 0.045) = $1.881 / 0.025 = $75.24

A half-point change in g cut the value by about 20%. Now restore g to 5% and raise the required return to 8%:

• P₀ = $1.89 / (0.08 − 0.05) = $1.89 / 0.03 = $63.00

One percentage point on the discount rate removed a third of the value. The narrower the gap between r and g, the more violently the output reacts, because a small denominator magnifies every change. This is why analysts often run a sensitivity table across a range of growth and discount rates instead of relying on a single number.

Zero-growth example

If dividends are expected to stay flat forever, g is zero and the formula becomes:

P₀ = D / r

This is the valuation of a perpetuity. It suits instruments with a fixed payout, such as a preferred share. A hypothetical preferred share paying $4.00 a year, with a required return of 8%, is worth $4.00 / 0.08 = $50.00. For common stock the zero-growth model is usually unrealistic, since most companies aim to raise payouts over time, but it can serve as a conservative floor.

Multi-Stage Dividend Discount Models

Many companies do not fit a single growth rate. A business may be raising its dividend quickly now and slow down as it matures. Multi-stage models split the forecast into periods with different growth assumptions.

Two-stage model

The two-stage model (also called the supernormal growth model) assumes a period of high growth followed by constant, lower growth forever. The steps are:

1. Forecast each dividend during the high-growth period and discount each one back to today.
2. At the end of the high-growth period, use the Gordon growth model to calculate the value of all remaining dividends (the terminal value).
3. Discount the terminal value back to today.
4. Add the results.

The formula structure is:

P₀ = Σ Dₜ / (1 + r)^t for t = 1 to n, + [Dₙ₊₁ / (r − g_L)] / (1 + r)^n

where n is the number of high-growth years and g_L is the long-term growth rate.

Hypothetical example: a company just paid $2.00 per share. Dividends grow 10% a year for three years, then 4% forever. The required return is 9%.

Year 4 dividend: $2.662 × 1.04 = $2.768. Terminal value at the end of year 3: $2.768 / (0.09 − 0.04) = $55.37. Discounted to today: $55.37 / 1.2950 = $42.76.

Value per share: $2.018 + $2.037 + $2.056 + $42.76 = about $48.87.

The terminal value accounts for roughly 87% of the total. That share is typical of how the arithmetic works whenever the explicit forecast period is short: the long-term growth assumption ends up driving most of the answer.

Three-stage model

The three-stage model adds a transition period between high growth and stable growth, during which the growth rate steps down gradually. It is built the same way: discount each dividend through the first two stages individually, then apply the Gordon growth model at the start of the final stage. It produces a smoother and often more realistic path, at the cost of more inputs to estimate.

H-model

The H-model, developed by Russell Fuller and Chi-Cheng Hsia in 1984, approximates a growth rate that declines in a straight line from a high initial rate to a long-term rate, without forecasting each year separately:

P₀ = [D₀ × (1 + g_L)] / (r − g_L) + [D₀ × H × (g_S − g_L)] / (r − g_L)

where:

• g_S = initial (short-term) growth rate
• g_L = long-term growth rate
• H = half the length of the period over which growth declines, in years

The H in the formula is the half-life of the high-growth period. If growth fades from the high rate to the long-term rate over 10 years, H = 5.

Hypothetical example: D₀ = $2.00, g_S = 10%, g_L = 4%, growth fades over 10 years (H = 5), r = 9%.

• First term: $2.00 × 1.04 / 0.05 = $41.60
• Second term: $2.00 × 5 × 0.06 / 0.05 = $12.00
• Value: $53.60

The first term is the value if the company grew at the long-term rate from today. The second term is the extra value contributed by the above-normal growth period.

How the DDM Is Used

Spotting undervalued and overvalued stocks

The core use is a comparison: the model’s intrinsic value against the market price. A DDM value above the price points to a possible buying opportunity, and a value below the price points to a stock that may be overpriced. Because the calculation starts from the company’s own payouts and the investor’s required return, it does not depend on prevailing market sentiment the way relative valuation multiples do.

Reading the market’s assumptions

The model can also run backward. Using the current price, you can solve for the growth rate the market is implying (g = r − D₁ / P₀) or the return it is implying (r = D₁ / P₀ + g). If a stock’s price only makes sense with 8% dividend growth forever, and the company’s sustainable growth rate is closer to 4%, that gap is a finding in itself.

Comparing companies

Because every company is reduced to the same terms (dividends, growth, required return), the DDM allows direct comparisons between dividend payers, including those in different industries, provided each company’s discount rate reflects its own risk.

Companies the model suits

The DDM fits best where dividends are a large, stable share of what shareholders receive: mature companies with long records of regular payouts and moderate, predictable growth. Utilities and established consumer companies are typical examples. The model is also associated with valuing banks and other financial firms, because for these companies debt is part of the operating business, which makes the free cash flow used in other models hard to define, while dividends are directly observable.

Stocks that pay no dividend

A company that pays nothing today can still be valued with a DDM by assuming when it will start paying and how large the payout will be, typically using a multi-stage model. Every one of those assumptions lowers the precision of the result, so the output for a non-payer is far more speculative than for a long-time dividend payer.

Limitations of the Dividend Discount Model

Perpetual constant growth is a strong assumption. The Gordon growth model assumes the same growth rate forever. That can be a reasonable approximation for very mature companies with an established payout history, but it is a poor description of newer firms, cyclical businesses or companies whose dividends fluctuate.

Sensitivity to inputs. As the worked examples show, small changes in g or r can swing the result by 20% or more, and the constant-growth formula has no meaningful answer if g ≥ r. Since both rates are estimates, the model is less precise than the single number it produces suggests.

Dividends are a policy choice. A board decides how much to pay. A company can return cash through share buybacks instead, retain earnings for expansion, or keep paying a dividend while it is losing money. In each case, the dividend stream is a poor proxy for the economic value the business generates for shareholders.

It ignores everything outside the inputs. Balance sheet strength, competitive position and management quality affect value only through the forecasts you choose. The model does not flag a dividend that the company’s earnings cannot support.

Because of these limits, the DDM is usually treated as one tool among several, used alongside other valuation methods instead of as the sole basis for a decision.

DDM Compared With Related Concepts

DDM vs. discounted cash flow (DCF). The DDM is a specific type of discounted cash flow model. A general DCF discounts free cash flow, either to the whole firm (at WACC, producing enterprise value) or to equity holders (at the cost of equity). The DDM discounts only the cash the company actually distributes as dividends. For a company that pays out nearly all of its free cash flow to equity, the two approaches converge. For one that retains or buys back heavily, they can diverge widely.

DDM vs. dividend yield. Dividend yield is a single ratio, annual dividend divided by price. It says nothing about growth or risk. The DDM uses the dividend as one input and combines it with growth and the required return to produce a value.

Required return vs. growth rate. These are the two rates people mix up most often. r is what shareholders demand, and g is how fast the dividend is expected to rise. The model only works when r is greater than g.

DDM vs. IRR. The DDM takes the required return as given and solves for value. Solving the same cash flows for the discount rate that equates their present value with the current price is an internal rate of return (IRR) calculation, which the rearranged formula r = D₁ / P₀ + g performs under constant growth.

Nominal vs. real rates. Dividends are normally forecast in nominal dollars, so the discount rate should also be nominal. Mixing a real (inflation-adjusted) growth rate with a nominal required return understates value. Mixing the opposite way overstates it.

The Bottom Line

The DDM is most useful to investors valuing mature, steady dividend payers such as utilities, established consumer companies and banks. Because small changes in growth or required return can swing the result by 20% or more, a sensitivity table across several rates gives a more honest picture than a single value. Treat the output as one input alongside other valuation methods, especially for irregular payers or companies that favor buybacks.