Dividend discount model (DDM): the Gordon growth formula explained

The dividend discount model (DDM) values a share as the present value of all the dividends it will ever pay. For a long-term holder who never sells, dividends are the only cash the stock delivers, so in principle a share is worth exactly what that stream of payments is worth today. The best-known version, the Gordon growth model, compresses the idea into a one-line formula that every finance student learns.

It is also one of the easiest models to misuse. The formula is extremely sensitive to the gap between the required return and the growth rate, and it only makes sense for companies whose dividends reflect most of what they could pay out. This guide works the formula on Apple Inc., whose fiscal 2025 dividend (the year ended September 27, 2025) was small relative to its profits, to show both how the arithmetic works and why the model gives a misleading answer for a company like Apple. It then covers multi-stage DDMs and the kinds of company where the model does fit.

The idea behind the model

A dividend discount model treats a share like a bond with no maturity date and a coupon that grows. Each future dividend is discounted at the investor's required return k, the return demanded for holding a stock with this level of risk. If you sell the share someday, the price you receive is itself the value of the dividends that follow, so selling does not change the logic: the value still rests on dividends.

The Gordon form follows when dividends grow at a constant rate g forever. The infinite sum collapses to a single fraction, provided k is greater than g. If growth equals or exceeds the required return, the formula breaks down, because a payment growing as fast as you discount it would be worth an infinite amount.

A worked example on Apple

Apple declared a quarterly dividend of $0.26 a share with its fourth-quarter fiscal 2025 results on October 30, 2025, after raising it from $0.25 in May 2025. Annualized, that is D0 = 0.26 × 4 = $1.04. Its shares closed at $255.46 on September 26, 2025, the last trading day of fiscal 2025, for a dividend yield of 1.04 ÷ 255.46 = 0.41%.

Now run it backward. Using the implied-return form, the market price says that if dividends grow 4% a year forever, investors must require only 1.0816 ÷ 255.46 + 0.04 = 4.42% a year, barely above the growth rate. Few analysts would accept a required return that low for a stock, which is a sign that the inputs, not the market, are the problem.

Why the DDM fails for Apple

The model's answer is about a tenth of the market price because Apple's dividend is a small slice of what Apple distributes and what it could distribute. In fiscal 2025:

• Dividends paid: $15,421 million, or 13.8% of net income of $112,010 million (13.7% on a per-share basis, $1.02 declared against $7.46 diluted EPS).
• Share repurchases: $90,711 million, almost six times the dividend.
• Free cash flow: $98,767 million, of which dividends took only 15.6%.

A DDM that values only the dividend stream ignores roughly 85% of the cash Apple returned and the retained earnings that fund future growth. Buybacks matter here: they shrink the share count, so each remaining share's future dividends grow faster than the total dividend bill, but a single growth assumption struggles to capture that. The standard fixes are either to model a total payout (dividends plus net buybacks) in place of dividends, or to switch to a Discounted cash flow (DCF): a step-by-step valuation on Apple model that values free cash flow regardless of how it is paid out. The Dividend payout ratio: formula, examples and sustainability page explains how to measure payout in the first place.

The general rule: a DDM works when dividends approximate the free cash flow to equity. When a company retains most of its earnings or returns cash mainly through buybacks, the model understates value. When a company pays out more than it can sustain, it overstates it.

Explosive near k equals g

The figure plots the Gordon value of Apple's dividend, with growth fixed at 4%, against the spread k − g.

Because the spread sits in the denominator, the curve is a hyperbola. Going from an 8-point spread to a 4-point spread doubles the value. Going from 4 to 2 doubles it again, to about $54.08 with g at 4%. At a 1-point spread (k 5%, g 4%) it would be $108.16. Small disagreements about long-run growth or the required return, well within normal estimation error, produce enormous swings in the output. The same mathematics drives the terminal value in a DCF, which is why both models need a sensitivity table.

Multi-stage dividend discount models

Constant growth forever is rarely realistic. A multi-stage DDM forecasts dividends explicitly through one or more growth phases, then applies the Gordon formula once growth has settled.

Three-stage models add a transition period in which growth fades gradually from the high rate to the stable one, which avoids an abrupt drop. The H-model is a shortcut for that linear fade. More stages make the model look more realistic, but each stage adds assumptions that are just as uncertain.

Where the DDM fits

The model is most useful when three conditions hold:

1. The company pays out most of its earnings as dividends, so dividends are a good proxy for what owners receive.
2. Dividend growth is steady and modest, tied to a predictable business.
3. The payout policy is stable, with no frequent switches between dividends and buybacks.

As general patterns, these conditions are more often met by regulated utilities, some consumer-staples companies, real estate investment trusts (which must distribute most of their taxable income under US tax rules) and mature banks and insurers. Even there, check the payout ratio and the balance sheet: a dividend funded by borrowing is not a sound base for a model that assumes it lasts forever. The DDM is a poor fit for fast-growing companies, companies that pay no dividend, and companies like Apple whose cash returns run mainly through buybacks.

Pitfalls

• Treating the dividend as the company's whole cash return. Buybacks and retained earnings carry value too.
• Growth at or above the required return. The formula then produces nonsense or a negative number. Long-run growth must stay below long-run nominal economic growth.
• Using the current yield as the expected return without checking growth. k = yield + g only holds under constant growth forever.
• Ignoring dividend safety. A high current dividend with a payout above 100% of earnings may be cut, which the formula does not anticipate.
• False precision. A two-point change in the spread can double or halve the output.

The DDM compared with other methods

See Valuation methods: intrinsic, relative and asset-based compared for the wider landscape.

How Finabase does it

Finabase does not run a dividend discount model, but it shows the inputs. The Dividends & splits tab lists each dividend's ex-dividend date and amount, which is where you read D0 and check how steadily it has grown. The Valuation tab charts ten fiscal years of dividend yield and payout ratio, so you can see at a glance whether dividends are a large or small share of earnings, the first test of whether a DDM is the right tool. The summary page shows the current dividend, dividend yield, payout ratio and ex-dividend date from the data provider. Across the market, the ex-dividend calendar lists upcoming payers with amount, frequency, indicated yield (amount × payments per year ÷ price), record and pay dates.

Frequently asked questions

What is the Gordon growth model formula?

The Gordon growth model values a share as P = D1 ÷ (k − g), where D1 is next year's dividend, k the required return and g the constant dividend growth rate. It only works when k is greater than g.

Why does the dividend discount model undervalue some stocks?

It undervalues companies that pay out a small share of earnings as dividends, because it counts only dividends. Apple paid 13.8% of fiscal 2025 net income as dividends and spent far more on buybacks, so a DDM on its $1.04 dividend gives about $27 against a $255.46 price.

What is a two-stage dividend discount model?

It forecasts dividends year by year through a high-growth phase, then applies the Gordon formula to the stable phase that follows and discounts both back to today. It suits payers expected to grow faster for a few years before settling down.

What kinds of companies suit a DDM?

Companies with high, stable payout ratios and modest, steady growth suit it best; as a general pattern that includes many regulated utilities and other mature dividend payers. It suits growth companies and heavy buyback users poorly.

Summary

The dividend discount model values a share as the present value of its future dividends, and the Gordon growth version reduces that to D1 ÷ (k − g). Worked on Apple's annualized $1.04 dividend from fiscal 2025, sensible-looking inputs give about $27, a tenth of the market price, because dividends were only 13.8% of Apple's net income and buybacks were almost six times larger. Halving the spread between required return and growth doubles the answer, which shows how fragile the formula is near k ≈ g. Multi-stage versions handle a growth phase, but the model remains best suited to steady, high-payout payers, and for companies like Apple a free-cash-flow DCF or a total-payout model is the better tool.