Guide

How the Gordon growth model works

Published August 17, 2026

Gordon growth says a stock is worth next year's dividend divided by required return minus growth. A $2.00 dividend just paid, growing at 4 percent, with a 9 percent required return, is worth $41.60, because next year's $2.08 over 5 percent is $41.60.

Gordon growth price

$41.60

Next year's dividend $2.08 over 9 percent minus 4 percent. The implied yield is 5.00%, which equals the gap between those two rates.

Next year's dividend: $2.08
Required return minus growth: 5.00%
Price: $41.60
Implied dividend yield: 5.00%

Dividend just paid

The dividend that has already gone out. Next year's is this times one plus growth.

Perpetual growth

Required return

Must stay above growth, or a growing perpetuity has no finite price.

In short

Price is $D_1 / (k - g)$ . A $2.00 dividend just paid, growing at 4 percent, is a $2.08 dividend next year. At a 9 percent required return, $k - g$ is 5 percent and the price is $41.60.
The implied yield $D_1 / P$ equals $k - g$ . On that sheet, $2.08 / 41.60$ is 5 percent, the same 5 percent that sat in the denominator.
A $3.50 dividend just paid, growing at 3 percent, with an 8 percent required return, is a $3.605 next dividend and a $72.10 price. The implied yield is 5 percent again, because $k - g$ is 5 percent again.
Zero growth is just next year's dividend over $k$ . Keep $2.00 and 9 percent, set growth to 0, and the price is $22.22. The implied yield is 9 percent, equal to $k$ .
Growth has to stay below the required return or the growing perpetuity has no finite price. This page will not print one in that case.

Next year's dividend, over a spread

The Gordon growth model is a growing perpetuity. A dividend just paid, growing at a constant rate forever, is worth

$P = \frac{D_0(1+g)}{k-g} = \frac{D_1}{k-g}$

$D_0$ is the dividend just paid. $D_1$ is next year's. $k$ is the required return. $g$ is perpetual growth. $k$ must stay above $g$ .

A $2.00 dividend just paid, growing at 4 percent, is $2.08 next year. At 9 percent required return, the spread $k - g$ is 5 percent, and $2.08 / 0.05$ is $41.60.

The implied yield is $D_1 / P$ . On this sheet that is $2.08 / 41.60$ , which is 5 percent, equal to $k - g$ by construction. The dividend discount calculator on this page is that identity.

How DCF works is the model that does not assume a single growth rate forever. Gordon is the special case that does. How stocks work is the claim being priced.

The same 5 percent spread on a different dividend

A $3.50 dividend just paid, growing at 3 percent, with an 8 percent required return. Next year's dividend is $3.605. The spread $k - g$ is 5 percent again. The price is $72.10. The implied yield is 5 percent again.

The dividend is larger. The growth is slower. The required return is lower. The spread in the denominator matched the first sheet, so the implied yield matched. The price did not: $72.10 is not $41.60, because $3.605 is not $2.08.

Zero growth is a level perpetuity

Keep the $2.00 dividend and the 9 percent required return. Set growth to 0. Next year's dividend is $2.00, the same as this year's. The price is $2.00 / 0.09$ , which is $22.22. The implied yield is 9 percent, equal to $k$ .

With no growth, you are not paying for a rising coupon. You are paying for a level one, and the whole required return shows up as yield. That is why $22.22 sits well below $41.60: the 4 percent growth was most of the first price.

What this page is not doing

It is not a two-stage DCF, not a buy or sell, and not a claim that 4 percent growth will last. Growth at or above $k$ has no finite price, and this calculator will not print one. The three sheets are $2.00 growing at 4 percent with $k$ of 9 percent ($41.60), $3.50 growing at 3 percent with $k$ of 8 percent ($72.10), and $2.00 with no growth at 9 percent ($22.22). This is educational material, not financial advice.

Worked examples

A \$2.00 dividend growing at 4 percent, required return 9 percent

The dividend just paid is $2.00. Growth is 4 percent forever. Required return is 9 percent. Price, next dividend, implied yield?

Next year's dividend: $2.00 \times 1.04 = 2.08$ , so $2.08.
Price: $2.08 / (0.09 - 0.04) = 2.08 / 0.05 = 41.60$ , so $41.60.
Implied yield: $2.08 / 41.60 = 0.05$ , 5 percent, which equals $9 - 4$ .

The price is $41.60. Next year's dividend is $2.08 and the implied yield is 5 percent, equal to the 5-point gap between 9 percent and 4 percent.

A \$3.50 dividend growing at 3 percent, required return 8 percent

Dividend just paid $3.50, growth 3 percent, required return 8 percent.

Next year's dividend: $3.50 \times 1.03 = 3.605$ , so $3.61 to the cent.
Price: $3.605 / (0.08 - 0.03) = 3.605 / 0.05 = 72.10$ .
Implied yield: $3.605 / 72.10 = 0.05$ , 5 percent again, because $8 - 3 = 5$ .

The price is $72.10. Next year's dividend is $3.605 and the implied yield is 5 percent. Same yield as the first example, different price, because the gap $k-g$ is the same 5 percent and the dividend is larger.

Zero growth is just next year's dividend over k

A $2.00 dividend that never grows, required return 9 percent. What is the price?

Next year's dividend is still $2.00, because growth is 0.
Price: $2.00 / (0.09 - 0) = 22.22$ .
Implied yield: $2.00 / 22.22 = 0.09$ , 9 percent, equal to $k$ itself when $g = 0$ .

The price is $22.22. With no growth, Gordon growth collapses to a level perpetuity, $D/k$ , and the implied yield equals the required return. Next year's dividend is $2.00.

Common questions

Why does the implied yield equal k minus g?

Because the price is D1 / (k - g), so D1 / P is k - g. On the first sheet, $2.08 over $41.60 is 5 percent, and 9 percent minus 4 percent is 5 percent. It is the same identity, read backwards.

What if growth is above the required return?

Then the growing perpetuity has no finite price. A firm cannot grow faster than the discount rate forever. This page will not print a number in that case. A two-stage DCF is the model that lets growth be high for a while and then fade.

Is this the same algebra as a cap rate?

Close. A cap rate on a level property income is income over price, which is the zero-growth case: $22.22 is $2.00 over 9 percent. A growing rent would need the same k - g spread the Gordon formula uses. The cap-rate page is the property version of the level case.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.