The dividend discount model (DDM) says a share of stock is worth the present value of every dividend it will ever pay, discounted at the return you require for holding it. Every version of the model — zero-growth, constant-growth, multi-stage — starts from that same sum; the versions differ only in the pattern the future dividends are assumed to follow. Choose the pattern that matches the company, and an infinite sum collapses into something you can compute by hand.
You will meet the DDM in intro finance courses, in the CFA equity curriculum, and in practice wherever a stable dividend payer needs a value that does not depend on what the market happens to think today. The logic is the same as any present-value problem: a dividend paid years from now is worth less than one paid tomorrow, so each expected payment gets discounted back to today and the discounted pieces are added up.
P0 = Σ Dt / (1 + r)^t, summed for t = 1 to infinity
P0 — Value of the stock today, per share
Dt — Expected dividend per share in year t — the first one counted is D1, next year's
r — Required rate of return on the stock (cost of equity), as a decimal
t — Years from today; each dividend is discounted for the number of years until it arrives
Dt — the expected dividends. The model counts every dividend from next year forward. The dividend the company just paid, D0, is already in shareholders' pockets and never enters the sum — it only matters as the base you grow future dividends from. Since no one can forecast an infinite list of payments one by one, every usable version of the model replaces the list with a growth assumption.
r — the required rate of return. The annual return investors demand for holding this stock, also called the cost of equity. In coursework it is either given or estimated with CAPM: the risk-free rate plus the stock's beta times the equity risk premium. The worked example below uses 8.6 percent.
The discounting itself. Each year's dividend is divided by (1 + r) raised to the number of years until it arrives. In the example below, the year-2 discount factor at 8.6 percent is 1 ÷ 1.086² = 0.8479, so a dividend of $1.8728 arriving in two years is worth $1.5879 today.
Zero-growth: the dividend never changes. If the payment is fixed forever, the infinite sum is a perpetuity, and dividing one payment by the required return prices the whole stream:
P0 = D / r
D — The fixed dividend per share, paid every year forever
r — Required rate of return, as a decimal
A preferred stock paying a fixed $3.15 a year against an 8.4 percent required return is worth $3.15 ÷ 0.084 = $37.50. This version fits preferred shares and the rare common stock with a genuinely flat payout; almost no growing company qualifies.
Constant-growth: the dividend grows at one rate forever. Assume a single growth rate g that holds permanently, and the sum collapses to next year's dividend divided by the gap between the required return and that growth rate. This is the Gordon growth model, and it deserves its own treatment — that article works a full example, shows why the answer swings hard with g, and covers the traps in choosing the inputs. It fits mature, steady payers: utilities, consumer staples, big banks.
Multi-stage: growth changes over time. Most real companies grow fast now and slower later, so analysts split the future into stages — most commonly two. Forecast each dividend individually through a short high-growth stage, then apply the constant-growth formula once growth settles to a sustainable rate, producing a terminal value that stands in for every dividend beyond the forecast. Discount all of it back to today. This is the version to reach for when the current growth rate could not last forever — and it is the only honest option when near-term growth exceeds r, which breaks the constant-growth formula outright.
| Year | Cash flow | Discount factor at 8.6% | Present value |
|---|---|---|---|
| 1 | D1 = $1.52 × 1.11 = $1.6872 | 1 ÷ 1.086 = 0.9208 | $1.5536 |
| 2 | D2 = $1.6872 × 1.11 = $1.8728 | 1 ÷ 1.086² = 0.8479 | $1.5879 |
| 3 | D3 = $1.8728 × 1.11 = $2.0788 | 1 ÷ 1.086³ = 0.7807 | $1.6229 |
| 3 (terminal value) | D4 = $2.0788 × 1.032 = $2.1453; TV = $2.1453 ÷ (0.086 − 0.032) = $39.7278 | 1 ÷ 1.086³ = 0.7807 | $31.0155 |
| Value per share (P0) | sum of the four present values | — | $35.78 |
Walk the logic once and the table reads itself. Stage one grows the just-paid $1.52 dividend at 11 percent for three years and discounts each payment individually: those three dividends are worth $4.76 today. Stage two handles everything after year 3 with the constant-growth formula: grow D3 one more period at the stable 3.2 percent rate to get D4 = $2.1453, divide by the 5.4-point gap between 8.6 percent and 3.2 percent, and the result — $39.7278 — is the value at the end of year 3 of every dividend from year 4 to forever. Because that terminal value sits three years away, it gets the same 0.7807 discount factor as D3.
Notice where the value lives: $31.02 of the $35.78 — about 87 percent — comes from the terminal value. That is typical for two-stage models, and it means the stable-stage growth assumption matters far more than the flashy stage-one rate. Test the answer at 2.7 and 3.7 percent terminal growth before trusting it.
Discounting D0. The dividend the company just paid is not a future cash flow. Students see "the stock just paid $1.52" and put $1.52 in year 1; year 1's dividend is $1.52 grown one period, $1.6872. Including D0 in the sum, or forgetting to grow it, shifts every number in the table.
Forgetting to discount the terminal value. The $39.7278 is a year-3 value, not a today value. Adding it to the stage-one present values without discounting gives $4.7644 + $39.7278 = $44.49 — about 24 percent too high. A related trap is discounting it four years instead of three: the terminal value is dated to the last explicit forecast year because it is built from D4, the first dividend after it.
Letting g reach r in the terminal stage. The terminal value divides by r minus g, so a stable growth rate at or above the required return produces an infinite or negative answer. High growth belongs in stage one, where each dividend is discounted individually and no such limit applies; the terminal rate must be modest — below r, and defensibly below long-run economic growth.
Every dividend discount model is the same statement — price equals the present value of all future dividends — with a different assumption about the dividend path. Use the perpetuity for fixed payers, constant growth for mature ones, and a two-stage model when today's growth cannot last; then discount every piece back to today, terminal value included.
It is the idea that a stock is worth all the cash it will ever hand you, counted at what each payment is worth today. For a shareholder that cash is the dividends, so the model forecasts them, discounts each one back to today at the return you require, and adds them up.
Pick the dividend pattern first. If dividends are flat, divide one payment by the required return. If they grow at one constant rate, use the Gordon growth model. If growth changes, forecast each early dividend and discount it individually, compute a terminal value at the point growth stabilizes, discount that back too, and sum everything — the two-stage example above shows each step.
The DDM is the general principle: price equals the present value of all future dividends, whatever pattern they follow. The Gordon growth model is its most-used special case, which assumes one constant growth rate forever so the infinite sum collapses into a single division.
Not directly — with no expected dividends the model prices the stock at zero, which is wrong for a company reinvesting all its earnings. Analysts either substitute free cash flow for dividends in the same discounting framework or value the company with market multiples instead.
Run the constant-growth version backward. Instead of solving for price, take the market price as given and solve for r: next year's expected dividend divided by today's price, plus the growth rate. The result is the return the market implicitly requires — a common alternative to CAPM for estimating the cost of equity of a dividend payer.
The terminal value is built from D4 using the constant-growth formula, and that formula always prices a stream as of one period before its first payment. A value built from the year-4 dividend is therefore a year-3 value, so it rides the same three-year discount factor as the year-3 dividend.
By the FinanceBrain Team · Last verified July 10, 2026 · How we produce and verify articles