Sub-topic 4: Dividend Discount Models (DDM)

Dividend Discount Models (DDMs) are a cornerstone of equity valuation, particularly for mature companies that pay regular dividends. These models operate on the fundamental principle that the value of a stock is the present value of all its future expected dividends. By forecasting future dividend payments and discounting them back to the present using an appropriate required rate of return, investors can estimate the intrinsic value of a stock.

The Core Concept: Present Value of Future Dividends

The basic idea behind DDMs is simple: investors buy stocks for the cash flows they expect to receive. For dividend-paying stocks, these cash flows are the dividends. Therefore, the value of a stock today should reflect the sum of all future dividends, adjusted for the time value of money and risk. The formula for the most basic DDM is:

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

Where:

$V_0$ = Value of the stock today
$D_t$ = Expected dividend per share in period $t$
$r$ = Required rate of return (discount rate)

Types of Dividend Discount Models

Different assumptions about dividend growth lead to various DDM formulations. The most common ones are:

Model	Key Assumption	Formula (Simplified)
Zero-Growth DDM	Dividends remain constant forever.	$V_0 = \frac{D}{r}$
Constant-Growth DDM (Gordon Growth Model)	Dividends grow at a constant rate ( $g$ ) forever, where $g < r$ .	$V_0 = \frac{D_1}{r-g}$
Multi-Stage DDM	Dividends grow at different rates over different periods (e.g., high growth for a few years, then constant growth).	Sum of present values of dividends during each stage.

The Gordon Growth Model (Constant-Growth DDM)

The Gordon Growth Model is widely used for valuing mature, stable companies with a history of consistent dividend growth. It assumes that dividends will grow at a constant rate ( $g$ ) indefinitely. The formula is derived from the perpetuity formula and is a special case of the general DDM.

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

Where:

$D_1$ = Expected dividend per share next year ( $D_0 \times (1+g)$ )
$r$ = Required rate of return
$g$ = Constant dividend growth rate

A critical condition for the Gordon Growth Model is that the required rate of return ( $r$ ) must be greater than the dividend growth rate ( $g$ ). If $g \ge r$ , the model yields an infinite or negative value, which is nonsensical.

Multi-Stage Dividend Discount Models

In reality, many companies do not grow at a constant rate forever. They might experience a period of high growth followed by a more stable, slower growth phase. Multi-stage DDMs account for these different growth phases. The most common is the two-stage model, but three-stage and even more complex models can be used.

The process involves:

Forecasting dividends during the initial high-growth phase.
Calculating the present value of these dividends.
Estimating the terminal value of the stock at the end of the high-growth phase, typically using the Gordon Growth Model, assuming constant growth thereafter.
Discounting the terminal value back to the present.
Summing the present values from steps 2 and 4 to arrive at the stock's intrinsic value.

The multi-stage DDM visually represents different growth phases. Imagine a timeline: Phase 1 shows rapidly increasing dividend bars, followed by Phase 2 where the bars grow at a slower, steady pace. The calculation involves discounting each individual dividend in Phase 1 and then discounting a single large 'terminal value' lump sum at the end of Phase 1, which represents all future dividends from Phase 2 onwards.

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Key Inputs and Considerations

Accurate valuation using DDMs hinges on the quality of the inputs:

Dividend Forecasts ( $D_t$ ): This is often the most challenging input. Analysts must consider the company's earnings, payout ratio, reinvestment opportunities, and industry trends. Historical dividend growth is a starting point, but future prospects are paramount.
Required Rate of Return ( $r$ ): This reflects the riskiness of the investment. It's typically estimated using the Capital Asset Pricing Model (CAPM) or other asset pricing models, incorporating the risk-free rate, the stock's beta, and the market risk premium.
Growth Rate ( $g$ ): For the Gordon Growth Model, $g$ is assumed constant. For multi-stage models, different growth rates are estimated for each stage. Sustainable growth rate is often calculated as $(1 - ext{payout ratio}) \times \text{Return on Equity (ROE)}$ .

Advantages and Disadvantages of DDMs

DDMs offer a theoretically sound approach to valuation, but they are not without limitations.

Advantages	Disadvantages
Theoretically sound: Based on the present value of expected cash flows.	Highly sensitive to inputs: Small changes in $r$ or $g$ can lead to large changes in valuation.
Useful for mature, stable companies with predictable dividends.	Not suitable for non-dividend-paying stocks or companies with erratic dividend policies.
Provides an intrinsic value estimate, useful for comparing with market price.	Assumptions about future growth can be difficult to make accurately.
Relatively simple to understand and implement for basic models.	The Gordon Growth Model requires $r > g$ , which may not always hold.

Active Recall

What is the fundamental principle behind Dividend Discount Models?

The value of a stock is the present value of all its future expected dividends.

What is the key condition for the Gordon Growth Model to be valid?

The required rate of return ( $r$ ) must be greater than the dividend growth rate ( $g$ ).

What are the three main inputs required for a DDM calculation?

Dividend forecasts ( $D_t$ ), required rate of return ( $r$ ), and dividend growth rate ( $g$ ).

Learning Resources

CFA Program Curriculum - Equity Valuation: Concepts and Basic Tools(documentation)

The official CFA Institute curriculum provides in-depth coverage of Dividend Discount Models, essential for exam preparation. Accessing the relevant sections will offer comprehensive explanations and examples.

Investopedia: Dividend Discount Model (DDM)(wikipedia)

A clear and concise explanation of the Dividend Discount Model, its variations, and its applications in stock valuation. It's a great starting point for understanding the core concepts.

CFI - Dividend Discount Model (DDM)(blog)

Corporate Finance Institute offers a practical guide to the DDM, including the Gordon Growth Model and multi-stage models, with examples and formulas.

Khan Academy: Dividend Discount Model(video)

A video tutorial explaining the Dividend Discount Model, focusing on the Gordon Growth Model and its components. Ideal for visual learners.

Morningstar: How to Use the Dividend Discount Model(blog)

This article from Morningstar discusses the practical application and limitations of the DDM, offering insights from a leading investment research firm.

Valuation Tutorial: Dividend Discount Models(tutorial)

Wall Street Prep provides a detailed tutorial on DDMs, including step-by-step instructions for building valuation models in Excel.

The Gordon Growth Model Explained(wikipedia)

A focused explanation of the Gordon Growth Model, a key component of DDM, detailing its formula, assumptions, and limitations.

Multi-Stage Dividend Discount Model - CFA Level I(video)

A video specifically covering multi-stage dividend discount models, which is crucial for understanding more complex valuation scenarios.

Financial Modeling & Valuation Analyst (FMVA) - DDM(tutorial)

While a broader course, the FMVA program by Wall Street Prep includes comprehensive modules on valuation techniques, including detailed DDM applications.

Academic Paper: The Dividend Discount Model: A Review(paper)

A more academic perspective on the Dividend Discount Model, exploring its theoretical underpinnings and empirical evidence. Suitable for deeper dives.