PastPaperHero | Equity valuation basics - Dividend discount and Gordon growth

Learning Outcomes

After reading this article, you will be able to: apply the dividend discount model (DDM) and Gordon growth formula for valuing equities, identify required assumptions, distinguish between constant and variable dividend growth, and interpret how growth and required return affect the value of a share. You will also analyze limitations and typical exam applications for CFA Level 1.

CFA Level 1 Syllabus

For CFA Level 1, you are required to understand the fundamental concepts and applications related to dividend valuation models for equities. This article covers key exam areas, including:

Explain the rationale and formula for valuing equities using the dividend discount model (DDM)
Apply the Gordon growth (constant growth) model and variable/dividend growth approaches
Calculate fundamental value given required return, dividend, and expected growth
Analyze the sensitivity of valuation to required return and growth rate
Identify assumptions, limitations, and appropriate use cases of dividend discount models

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

What key assumption must hold for the Gordon growth model to be valid?
If a stock pays a $3 dividend next year, is expected to grow dividends at 4% forever, and your required return is 10%, what is its value using the Gordon growth model?
True or false? If the expected growth rate exceeds the required return, the standard Gordon growth formula gives a negative value.
Briefly describe one situation where the dividend discount model may be inappropriate for equity valuation.

Introduction

Dividend-based valuation models are commonly tested on CFA Level 1. The dividend discount model (DDM) provides a framework for valuing a common share as the present value of its future dividends, discounted at the required rate of return. The Gordon growth (constant growth) model is a popular DDM variation, using the assumption of dividends growing at a constant rate in perpetuity. CFA exam questions often require careful attention to correct inputs, valid model selection, and the implications of growth assumptions.

Key Term: dividend discount model (DDM)
The valuation approach that estimates the fundamental value of a share as the present value of all expected future dividends, discounted at the required rate of return.

Key Term: Gordon growth model
A form of the DDM in which future dividends are assumed to grow at a constant rate forever, producing a simplified valuation formula.

THE DIVIDEND DISCOUNT MODEL (DDM)

The DDM states that the fundamental value of a share (V₀) equals the sum of all expected future dividends (D₁, D₂, D₃, ...) discounted back to present value at the required rate of return for equity (r):

V_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r)^t}

This model simply applies the time value of money principle to equity cash flows. In practice, calculation depends on assumptions about the pattern of future dividends and the appropriate required return.

Dividends — the actual cash distributed to shareholders — are used because they represent a tangible return to investors. In DDM, the future price at which you might sell the share is also a function of expected future dividends.

Constant vs. Variable Growth

If dividends are expected to grow at a constant annual rate (g), the formula can be simplified using the Gordon growth model. When dividend growth is not constant, an analyst typically forecasts dividends for a finite high-growth period, and assumes constant growth thereafter (a two-stage or multi-stage model).

THE GORDON GROWTH (CONSTANT GROWTH) MODEL

The Gordon growth model values a share as the present value of a perpetual, constantly growing stream of dividends:

V_0 = \frac{D_1}{r - g}

Where:

$V_0$ = fundamental value of the share today
$D_1$ = expected dividend next year
$r$ = required rate of return for equity
$g$ = expected constant annual growth rate of dividends

Key Term: required rate of return (r)
The return equity investors demand given the risks of the share, calculated by models such as CAPM.

Key Term: perpetual growth
The assumption that cash flows (dividends) will continue to grow indefinitely at a constant rate.

This model requires $r > g$ for a valid (positive) value.

Worked Example 1.1

Suppose a company will pay a dividend of $2.00 per share next year. Dividends are expected to grow at 5% per year indefinitely. The required return is 9%. What is the fair value of the share?

Answer:
Using the Gordon growth model:

$V_0 = \frac{2.00}{0.09 - 0.05} = \frac{2.00}{0.04} = \$ 50.00$

If the share trades below $50, it may be undervalued given these assumptions.

Model Assumptions

Dividends grow at a constant rate forever.
The required return (r) and growth (g) are both constant, and r > g.
The company pays dividends — DDM cannot be used for firms that do not and will not pay dividends.

If any of these assumptions is violated (e.g., dividends are irregular, or growth exceeds required return), model results are not valid.

Worked Example 1.2

A company pays $1.50 per share in expected dividends next year. Analysts forecast dividends will grow at 7% per year. If investors require a 12% return, what is the share's value?

Answer:
$V_0 = 1.50 / (0.12 - 0.07) = 1.50 / 0.05 = \$ 30.00.

When to Use DDM?

DDM is best suited for mature, stable companies with predictable dividend patterns and where dividend policy closely tracks earnings. It is not well suited for fast-growing companies that reinvest all earnings or for companies with irregular dividends.

Worked Example 1.3

ABC Corp. does not pay dividends and has no plans to initiate dividends for at least 5 years. Is the DDM appropriate for ABC Corp. valuation?

Answer:
No. The DDM assumes dividends drive valuation. For companies not paying dividends (and with no expectation to pay in the foreseeable future), alternative models (e.g., discounted free cash flow, earnings multiples) are more appropriate.

Multi-Stage Dividend Growth Models

Many companies experience an initial period of high (or unstable) growth before settling into long-term, sustainable growth. In this case, analysts use a multi-stage model: forecast dividends year-by-year for the high-growth period, then apply the Gordon growth formula to estimate the terminal value (present value of dividends from the point where growth becomes constant onwards).

Worked Example 1.4

Suppose Beta Inc. will pay dividends as follows: D₁ = $1.00, D₂ = $1.15, D₃ = $1.30, after which dividends will grow at 4% per year forever. The required return is 10%.

Answer:
Step 1: Discount year 1-3 dividends:

$PV_{D1} = 1.00/(1.10)^1 = 0.909$

$PV_{D2} = 1.15/(1.10)^2 = 0.950$

$PV_{D3} = 1.30/(1.10)^3 = 0.975$

Step 2: Terminal Value at t = 3:

$TV = D_4 / (r - g)$ ; $D_4 = 1.30 \times 1.04 = 1.352$

$TV = 1.352 / (0.10 - 0.04) = 22.53$

Discount TV to present: $PV_{TV} = 22.53 / (1.10^3) = 16.98$

Step 3: Value = $0.909 + 0.950 + 0.975 + 16.98 = $19.81$

Exam Warning

The Gordon growth model only applies if $r > g$ . If you are given values where $g \geq r$ , the model produces nonsensical or negative valuations — an easy exam trap.

Sensitivity to Growth and Required Return

The DDM, especially the Gordon model, is highly sensitive to small changes in $g$ and $r$ . If $g$ rises, holding $r$ fixed, the valuation increases sharply; if $r$ rises, value drops. Be careful to use consistent estimates.

Key Term: sensitivity analysis
The process of examining how model outputs (e.g., share value) change with variations in key assumptions (like $r$ or $g$ ).

Limitations of Dividend Discount Models

Only applicable if the company pays dividends that can be reliably forecast.
Not suitable for firms with irregular, zero, or unpredictable dividends.
Model outputs are very sensitive to assumptions regarding $g$ and $r$ .
Can undervalue companies which retain earnings for high-return reinvestment.

Summary

Dividend discount models value shares as the present value of future expected dividends, discounted at the required rate of return. The Gordon growth model is a widely used constant-growth version for mature companies. If growth is not constant, analysts apply multi-stage models, forecasting high-growth periods and using a simplified Gordon growth approach for the perpetual stage. The usefulness of these models rests on valid assumptions for future dividends and reasonable estimates for required return and growth.

Key Point Checklist

This article has covered the following key knowledge points:

Understand and apply the dividend discount model (DDM) to value equities
Use the Gordon growth (constant growth) model where appropriate and know its formula
Recognize key assumptions behind DDM and Gordon models (dividends, growth, required return)
Apply multi-stage DDM for variable dividend growth
Calculate fundamental value given expected dividend, growth rate, and required return
Recognize limitations and common exam pitfalls, including misuse of the model when $r \leq g$

Key Terms and Concepts

dividend discount model (DDM)
Gordon growth model
required rate of return (r)
perpetual growth
sensitivity analysis

Equity valuation basics - Dividend discount and Gordon growt...