Gordon Growth Model

In one sentence: The Gordon growth model says a share is worth its next dividend divided by the gap between the return you want and the rate the dividend grows.

$P_0 = \frac{D_1}{r - g}$

Read it out loud: “P zero equals D one divided by r minus g. P zero is the price of one share today. D one is the dividend we expect next year. The letter r is the return investors want each year, and g is the steady yearly growth rate of the dividend.”

Before you start

The ideas and signs this page uses, explained from zero. For powers of ten, Greek letters and other notation in general, see Math basics.

Subscripts like $D_0$ , $D_1$ and $P_0$: A small number written below a letter is a subscript, and it says when the quantity happens. $D_0$ is the dividend paid most recently, at time zero, which means now. $D_1$ is the dividend one year later, and $P_0$ is the price today. The letter is the same kind of thing in each case, and only the subscript changes the time.
Shares and dividends: A share is one small piece of ownership in a company. Some companies pay a dividend, a cash payment to each share’s owner, usually once a year. Dividends are measured in dollars per share, so 2 dollars per share means each share receives 2 dollars in cash.
Percent written as a decimal: Rates in formulas are decimals. To turn a percent into a decimal, move the decimal point two places to the left: 4% becomes 0.04 and 9% becomes 0.09. Writing 9 instead of 0.09 is one of the most common slips in this formula.
Growth by a rate: To make a number grow by a rate, multiply it by 1 plus the rate. If a dividend of 2 dollars grows by 4%, the next dividend is $2 \times (1 + 0.04) = 2.08$ dollars. The 1 keeps the original amount, and the rate adds the growth on top.
Present value and the required return: Money promised for later is worth less than the same money today, because money in hand can be invested to earn a return. The required return $r$ is the yearly return an investor wants. Future payments are shrunk, or discounted, by $1 + r$ for each year they wait.
Fractions and the gap $r - g$: A fraction $\frac{a}{b}$ means $a$ divided by $b$ . The top is the numerator and the bottom is the denominator. Here the bottom is $r - g$ , the gap between two rates, found by subtracting the smaller rate $g$ from the larger one $r$ .

What each symbol means

Symbol	Meaning
$P_0$	The price today of one share, measured in dollars per share. The small 0 means time zero, which is now. The formula gives a value built from the dividends, so it is an estimate of what the share should be worth under the model’s assumptions.
$D_1$	The dividend one year from now, the cash one share is expected to pay next year, in dollars per share. The 1 means one year ahead. It is found from the dividend paid most recently, $D_0$ , using $D_1 = D_0(1 + g)$ .
$r$	The required return, the yearly return an investor wants for owning the share, written as a decimal per year. For example, 9% per year is written 0.09. It must be bigger than $g$ .
$g$	The growth rate of the dividend, the steady share by which the dividend rises each year, written as a decimal per year. For example, 4% per year is written 0.04. It must be smaller than $r$ for the model to work.

The formula piece by piece

$D_1$: Start with the dividend the investor expects one year from now, in dollars per share. It is the cash one share pays next year, and the whole price is built from it.
$r - g$: The gap. $r$ is the return the investor requires and $g$ is the steady growth rate. Subtracting gives the yearly difference, which the model divides by. For the model to work, this gap must be a positive number.
$\frac{D_1}{r - g}$: Divide the next dividend by the gap. A small gap makes the price large and a large gap makes it small, so the price reacts strongly to the required return and to the growth rate.
$P_0 = \frac{D_1}{r - g}$: The whole formula in one sentence: the price of a share today equals its dividend for next year divided by the required return minus the growth rate.

What the formula is doing, and why

A share of a company is worth the cash its owners can expect to receive from it. Many companies pay a dividend, a cash payment for each share, usually once a year. The Gordon growth model is the simplest way to turn a stream of future dividends into one price today. It assumes the dividend grows at one steady rate, $g$ , forever. The formula $P_0 = \frac{D_1}{r - g}$ says the price is next year’s dividend divided by the gap between $r$ and $g$ .

Why divide by the gap? Money promised for later is worth less now, because money in hand can earn the return $r$ . Each future dividend is therefore shrunk, or discounted, by $(1 + r)$ for every year it waits. The dividends also grow by $(1 + g)$ each year. Adding all of these shrinking, growing payments forever gives a total that collapses to one neat fraction, $\frac{D_1}{r - g}$ . The geometric series page shows how a sum like this settles down to a single number.

Why $r$ must be bigger than $g$ . The payments are shrunk by $(1 + r)$ each year but grow by $(1 + g)$ . If $g$ is at least as big as $r$ , the shrinking does not win, so the total keeps growing without limit and has no finite value. The formula would then give a zero or negative denominator, and a zero or negative price, which makes no sense. That is why the model is used only when $r$ is larger than $g$ .

Why small changes matter so much. Because the price divides by $r - g$ , a small change in that gap moves the price a lot, as long as the next dividend is held fixed. Halving the gap doubles the price. A higher required return lowers the price, and faster expected growth raises it. This sensitivity is one reason the model works best for steady companies that pay a regular dividend and grow slowly.

An everyday picture

Think of a small apartment that you rent out. The rent comes in every year, and the landlord raises it by a steady share each year. The price a buyer should pay for the apartment depends on next year’s rent, on the return the buyer wants from the money, and on how fast the rent is expected to rise. If the buyer wants a higher return, the price falls. If the rent is expected to rise faster, the price rises. The Gordon model works the same way for a share and its dividend.

Worked example: What is one share of a bakery worth today?

Imagine a small bakery company that has paid a dividend of 2 dollars per share, so $D_0 = 2$ dollars per share. The dividend is expected to grow by 4% each year, so $g = 0.04$ . An investor wants a return of 9% per year for owning the share, so $r = 0.09$ . What is one share worth today?

Find next year’s dividend. The model needs the dividend one year from now, not the one already paid. The dividend grows by the rate $g$ each year, so we multiply today’s dividend by $1 + g$ : $D_1 = D_0(1 + g) = 2 \times 1.04 = 2.08$ dollars per share.
Find the gap between the return and the growth. The bottom of the formula is $r - g$ . We subtract the growth rate from the required return, which measures how far the wanted return sits above the dividend’s growth: $r - g = 0.09 - 0.04 = 0.05$ per year.
Divide the next dividend by the gap. Now we put both numbers into the formula: $P_0 = \frac{2.08}{0.05} = 41.6$ . Dividing by 0.05 is the same as multiplying by 20, because 1 divided by 0.05 is 20, and $2.08 \times 20 = 41.6$ . So one share is worth about 41.6 dollars today.
Check the answer with a sense test. A price should be a clear multiple of the next dividend, and here that multiple is $\frac{1}{r - g}$ , which is 20. Dividing the price by the next dividend, $41.6 \div 2.08 = 20$ , gives the same multiple, so the arithmetic is consistent.
Test a higher required return. Suppose the investor now wants 11% per year instead of 9%. The next dividend stays at 2.08 dollars, but the gap grows to $0.11 - 0.04 = 0.07$ , so the price falls to $\frac{2.08}{0.07} \approx 29.71$ dollars. A more demanding investor pays less for the same dividend.

Answer: With a 9% required return and 4% growth, one share is worth about 41.6 dollars today under the model’s assumptions. This is an estimate of value from the dividends, not a forecast of the market price.

The numbers in this example are recomputed by script every time the site is built.

Common mistakes

Using today’s dividend $D_0$ instead of next year’s $D_1$ . The formula needs the dividend one year ahead, so multiply $D_0$ by $1 + g$ before you divide.
Letting $g$ equal or exceed $r$ . Then the gap $r - g$ is zero or negative, the division breaks down, and the model does not apply to that share.
Typing a percent as a whole number. Write 9% as 0.09 and 4% as 0.04. Using 9 and 4 gives a gap of 5, and the price comes out 100 times too small.
Using the model for a company that pays no dividend, or whose dividend is irregular. The model needs a steady stream of dividends that grows at one rate.

Where you will meet it

Stock valuation in finance courses and equity research, where it is usually the first model taught for dividend-paying shares.
Estimating the return investors expect from a share: rearranging the formula gives $r = \frac{D_1}{P_0} + g$ .
Valuing mature companies with long dividend records, where growth is slow and fairly predictable.
Quick checks on whether a share price is high or low compared with the dividends it pays, by working out the growth rate the price implies.

Questions people ask

What is the difference between $D_0$ and $D_1$ ?

$D_0$ is the dividend that was paid most recently, a fact about the past. $D_1$ is the dividend expected one year from now, so $D_1 = D_0(1 + g)$ . The price depends on what is still to come, which is why the formula uses $D_1$ .

Why must $r$ be bigger than $g$ ?

If growth is at least as large as the required return, the discounted future dividends do not shrink, so their total never settles on a finite number. The formula would give a zero or negative price, which makes no sense, so the model does not apply.

Can I use this model for a company that pays no dividend?

Not directly. The model values a share by its dividends, so a company that pays none gives no cash stream to discount. Analysts use other methods for such companies.

Does the formula predict the future share price?

No. It gives a value that matches the assumptions you put in: the next dividend, the required return and one steady growth rate. If those inputs change, the value changes too, so the result is only as good as the inputs.

Net Present Value (NPV): Net present value says whether a plan is worth its cost: it adds every future cash flow, shrunk back to today’s money, and the total is the plan’s value in dollars today.
Internal Rate of Return (IRR): The internal rate of return is the yearly rate a plan earns on its money: the single rate at which all of its cash flows exactly balance in today’s money.
Geometric Series: A geometric series adds up a list where each term is the one before it times a fixed number, and this formula finds the whole sum in one step.