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Dividend Growth Model

Stock price based on growing dividends.

Understand the formulaSee the free derivationOpen the full walkthrough

P_{0} = \frac{D _{1}}{r - g}

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Core idea

Overview

The Dividend Growth Model, also known as the Gordon Growth Model, determines the intrinsic value of a stock by summing its future dividend payments discounted to their present value. It assumes dividends grow at a constant rate indefinitely, providing a simplified valuation tool for stable, dividend-paying companies.

When to use: This model is ideal for valuing mature companies with stable, predictable dividend payout histories and constant growth rates. It is most effective when the firm's required rate of return is higher than the dividend growth rate, ensuring a finite valuation.

Why it matters: It enables investors to estimate whether a stock is fairly priced, overvalued, or undervalued relative to its expected cash flows. Additionally, by rearranging the formula, analysts can determine the implied cost of equity capital for a corporation.

Symbols

Variables

P_0 = Stock Price, D_1 = Next Dividend, r = Req. Return, g = Growth Rate

P_{0}

Stock Price

D_{1}

Next Dividend

r

Req. Return

V a r iab l e

g

Growth Rate

V a r iab l e

Walkthrough

Derivation

Derivation of the Gordon Growth Model

The Gordon growth model values a share by discounting a perpetually growing dividend stream at a required return r.

Dividends grow at a constant rate g forever.
Required return r is constant and r>g (so the series converges).
Dividends are paid at regular intervals (end of period).

Write the Discounted Dividend Series:

The price today equals the present value of all future dividends, where each dividend grows by factor $(1 + g)$ .

P_{0} = \frac{D _{1}}{1 + r} + \frac{D _{1} ( 1 + g )}{( 1 + r ) ^{2}} + \frac{D _{1} ( 1 + g ) ^{2}}{( 1 + r ) ^{3}} + \dots

Sum the Infinite Geometric Series:

This is an infinite geometric series with ratio $\frac{1 + g}{1 + r}$ . Summing gives the Gordon growth formula.

P_{0} = \frac{D _{1}}{r - g}

Note: D1 is the dividend expected next period (not the most recent dividend D0).

Result

P_{0} = \frac{D _{1}}{r - g}

Source: Standard curriculum — A-Level Accounting / Finance

Free formulas

Rearrangements

Solve for $P_{0}$

Make P0 the subject

P_{0} = \frac{D _{1}}{r - g}

P0 is already the subject of the formula.

Difficulty: 1/5

Solve for $D_{1}$

Make D1 the subject

D_{1} = P_{0} (r - g)

Start from the Dividend Growth Model. Multiply both sides by the denominator $(r - g)$ to eliminate the fraction, then express $D_{1}$ as the subject by symmetry.

Difficulty: 2/5

Solve for $r$

Make r the subject

r = \frac{D _{1}}{P _{0}} + g

To make `r` (Required Return) the subject of the Dividend Growth Model, first clear the denominator `(r - g)`, then isolate `(r - g)`, and finally add `g` to both sides.

Difficulty: 2/5

Solve for $g$

Make g the subject of the Dividend Growth Model

g = r - \frac{D _{1}}{P _{0}}

Rearrange the Dividend Growth Model to make `g` (the growth rate) the subject. This involves clearing the denominator, isolating the term `(r - g)`, and then solving for `g`.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a hyperbola because the required return appears in the denominator of the price formula. As the required return increases, the stock price drops rapidly, approaching zero as the return gets very large, with a vertical asymptote at the growth rate where the price becomes undefined. For a finance student, this shape illustrates that investors demand lower prices for stocks with higher risk, as a higher required return significantly reduces the present value of future dividends. The most important feature

Graph type: hyperbolic

Why it behaves this way

Intuition

The stock's value is like a present-day lump sum equivalent to an infinite series of future dividend payments, each growing steadily, but diminishing in present value due to the investor's required return.

P_{0}

The calculated intrinsic value of a company's stock today

Represents the fair price an investor should pay for the stock, based on its future dividend-paying potential

D_{1}

The expected dividend per share to be paid in the next period (year 1)

The immediate cash benefit an investor anticipates receiving from owning the stock

The minimum annual rate of return an investor requires from the stock, reflecting its risk

A higher required return (due to higher perceived risk or better alternative investments) reduces the present value of future dividends, thus lowering the stock's calculated value

The constant annual rate at which the company's dividends are expected to grow indefinitely

A higher sustainable growth rate for dividends increases the value of future payouts, thus raising the stock's calculated value

Signs and relationships

r - g: This term represents the net discount rate applied to the growing stream of dividends. The subtraction indicates that the dividend growth rate (g) partially offsets the required rate of return (r).

Free study cues

Insight

Canonical usage

All monetary values must be in the same currency, and rates (r and g) must be expressed as decimals and correspond to the same time period as the dividend (e.g., annual).

Common confusion

The most common mistake is using 'r' and 'g' as percentages (e.g., 10 for 10%) instead of their decimal equivalents (0.10), which leads to significantly incorrect valuations.

Dimension note

The rates 'r' and 'g' are dimensionless quantities representing fractions or percentages per period. Their difference (r - g) is also dimensionless.

Unit systems

$P_{0}$ currency/share · The resulting stock price will be in the same currency unit as D_1.

$D_{1}$ currency/share · Expected dividend per share in the next period. Must be in the same currency as P_0 and consistent with the time period of r and g (e.g., annual dividend for annual rates).

$r$ decimal · Required rate of return (cost of equity). Must be expressed as a decimal (e.g., 0.10 for 10%) and consistent with the time period of D_1 and g. The denominator (r - g) must be positive.

$g$ decimal · Constant growth rate of dividends. Must be expressed as a decimal (e.g., 0.05 for 5%) and consistent with the time period of D_1 and r. It must be strictly less than r for the model to yield a finite, positive value.

One free problem

Practice Problem

A utility company is expected to pay a dividend of $2.50 per share next year. If the required rate of return for equity investors is 8% and the dividends are projected to grow at a constant rate of 3% per year, what is the intrinsic value of the stock?

Next Dividend2.5 $

Req. Return0.08

Growth Rate0.03

Solve for: $P 0$

Hint: Subtract the growth rate from the required return and divide the dividend by that result.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Valuing a utility company stock.

Study smarter

Tips

Always ensure that the required return (r) is strictly greater than the growth rate (g) to avoid a negative price.
Convert all percentages (e.g., 5%) to decimal form (0.05) before entering them into the equation.
Use D1 (the dividend expected in the next period), not D0 (the dividend just paid); if only D0 is known, calculate D1 as D0 × (1 + g).

Avoid these traps

Common Mistakes

Using D0 instead of D1.
Using if g > r (model breaks).

Common questions

Frequently Asked Questions

The Gordon growth model values a share by discounting a perpetually growing dividend stream at a required return r.

This model is ideal for valuing mature companies with stable, predictable dividend payout histories and constant growth rates. It is most effective when the firm's required rate of return is higher than the dividend growth rate, ensuring a finite valuation.

It enables investors to estimate whether a stock is fairly priced, overvalued, or undervalued relative to its expected cash flows. Additionally, by rearranging the formula, analysts can determine the implied cost of equity capital for a corporation.

Using D0 instead of D1. Using if g > r (model breaks).

Valuing a utility company stock.

Always ensure that the required return (r) is strictly greater than the growth rate (g) to avoid a negative price. Convert all percentages (e.g., 5%) to decimal form (0.05) before entering them into the equation. Use D1 (the dividend expected in the next period), not D0 (the dividend just paid); if only D0 is known, calculate D1 as D0 × (1 + g).

References

Sources

Brealey, Myers, and Allen, Principles of Corporate Finance
Ross, Westerfield, and Jaffe, Corporate Finance
Wikipedia: Gordon Growth Model
CFA Institute, CFA Program Curriculum, Level I
Brealey, Myers, Allen Principles of Corporate Finance
Ross, Westerfield, Jaffe Corporate Finance
Berk, DeMarzo Corporate Finance
Damodaran Investment Valuation

Dividend Growth Model

Overview

Variables

Derivation

Write the Discounted Dividend Series:

Sum the Infinite Geometric Series:

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Perpetuity Present Value

Frequently Asked Questions

Sources