Dividend Discount Model: The Gordon Growth Formula, a Worked Example and When It Works

The Gordon growth formula

Value per share = D1 ÷ (r − g)
D1 = next year's dividend = this year's dividend × (1 + g)

where r is the return you require and g is the rate at which the dividend grows, forever. The formula is the sum of an infinite series of growing payments, each discounted a year further, and it needs r to be greater than g; as the two approach each other the value heads to infinity, and above it the formula returns nonsense. It is the same mathematics as the terminal value in a DCF, which the terminal value formula article covers, applied to the whole life of the company rather than to the years after a forecast.

Worked example: Harbor Foods (illustrative)

Harbor Foods, the fictional packaged-food company used across these guides, pays $0.90 a share and trades at $30. Suppose you require 9% and expect the dividend to grow 5% a year:

• D1 = 0.90 × 1.05 = $0.945
• Value = 0.945 ÷ (0.09 − 0.05) = $23.63

The model says the shares are worth less than their $30 price on those assumptions. That is a useful disagreement rather than a verdict, because it means the market expects either faster growth or accepts a lower return, and the next section reads which.

One point on the required return moves the value by about a third, because the denominator is the small gap between two percentages. The WACC formula article covers how to choose the rate, and the lesson here is that the model is only as good as that choice.

The growth the price implies

Implied growth g = (price × r − D0) ÷ (price + D0)

Rearranging the formula turns it into a reverse valuation. At $30, a $0.90 dividend and a 9% required return, Harbor's price implies dividend growth of about 5.8% a year forever. The question for the research is then whether Harbor can grow its dividend at nearly 6% indefinitely, which depends on earnings growth and on the payout ratio having room to rise. The dividend yield formula article covers the cover ratios behind that judgment, and the implied growth rate article applies the same reversal to cash flows rather than dividends.

Where dividend growth comes from

Sustainable growth = return on equity × (1 − payout ratio)

A dividend can only grow as fast as the profit behind it, and profit grows from the earnings the company keeps and reinvests. A business earning 15% on its equity and paying out 37.5% of profit retains 62.5%, so it can grow its earnings and its dividend by about 15% × 0.625 = 9.4% a year without raising the payout ratio, provided the retained money keeps earning 15%. That last condition is the one that usually fails: returns on new capital are often lower than returns on the old, which is why a 5% growth assumption for a company with that arithmetic is conservative rather than timid. Growth above the sustainable rate must come from a rising payout ratio, which has a ceiling, or from borrowing, which the return on equity formula article shows is a different kind of growth. Checking the assumed g against this formula is the quickest way to notice a dividend model that has quietly assumed a payout the business cannot afford.

Two stages, and counting buybacks

Few companies grow at one rate forever, so the usual refinement forecasts a few years explicitly and applies the formula afterwards. Suppose Harbor grows its dividend 8% a year for five years, then 5%:

The second refinement counts buybacks. A company that returns cash by repurchasing shares pays part of its "dividend" by raising each remaining holder's stake, so the model understates it. Harbor returns $45 million in dividends and $15 million in buybacks, $1.20 a share in total; growing that at 5% and discounting at 9% gives $31.50, close to the $30 price. The stock buybacks explained article covers when that cash counts as a return and when it does not.

When the model works, and when it does not

The dividend discount model is exact for a company whose dividend is a stable, growing share of a stable, growing profit, which describes regulated utilities, consumer staples, many banks and insurers, and mature industrials. It is the natural model for a dividend investor, because it values the thing the investor actually receives. It fails, or needs heavy adaptation, for:

• Non-payers. A company that pays nothing has no D1, and assuming a future dividend policy is a forecast about management rather than the business.
• Buyback-heavy companies, unless total payout is used, as above.
• Fast growers, whose growth exceeds any sensible required return for years; use a multi-stage model or a cash-flow DCF.
• Companies whose payout ratio is changing, since dividend growth then differs from earnings growth for a period and the long-run g is the earnings figure.

For everything else, the cash-flow methods in the stock valuation guide value what the business generates rather than what it chooses to pay, and the intrinsic value article shows the two approaches on the same company.