Dividend Discount Model (DDM)

From Dividends to Value: Exploring the Dividend Discount Model

The concept of time value of money is fundamental to Dividend Discount Models. In everyday life, we often try to determine the present value of an asset. For example, if we expect to receive a bonus of $10,000 from our employer in one year, we might ask ourselves what its present value is.

With an inflation rate of 10%, its present value would be $10,000 / 1.1 = $9,090. Conversely, looking from the present to the future, $9,090 today would buy the same as $10,000 in a year. Thus, the value of money changes over time.

The Dividend Discount Model is one of the most prominent representatives of present value models. Since dividends are a form of payments from a company to its shareholders, the DDM aims to determine the present value of future dividend payments.

For example:

• Dividend in one year (D1): $10
• Required rate of return (r): 10%
• Present value of the dividend (V0): $9.09

In this example, a dividend of $10 to be paid in one year has a present value of $9.09.

It is evident that determining the present value of dividends presents some challenges. One must forecast the value of future dividends and the rate at which they should be discounted (r). Therefore, additional methods are needed to address the problem of determining these variables, which will be discussed further.

Single-Period Dividend Discount Model

If you purchase a stock today with the intention of selling it in one year, you will be interested in its theoretical current price – that is, the present value of the expected benefits.

Let’s add some additional information to the example. Besides the expected dividend payment of $10 in one year, you predict that the market price of the stock will be $100 at that time (the stock price at the end of the investment horizon is also known as the terminal stock value).

• Dividend in one year (D1): $10
• Stock Price in one year (P1): $100
• Required rate of return (r): 10%
• Present value of the share today (V0): $100

Substituting into the equation, the present price should be:

Multi-Period Dividend Discount Model

The logic of discounting for more than one period is identical to that for one period – the present values of the dividends are sought. Let’s assume you want to sell your stock after 2 years. Besides the $10 dividend at the end of the first year, it is expected to pay another $10 dividend and be worth $110 at the end of the second year.

• Dividend in one year (D1): $10
• Dividend in two years (D2): $10
• Stock Price in two years (P2): $110
• Required rate of return (r): 10%
• Present value of the share today (V0): $108.26

The present value of the dividend from the first year is:

The present value of the dividend and the stock from the second year is:

Therefore, the present value of the stock is: $9.09 + $99.17 = $108.26.

The discount factor for the second year is squared because it finds the present value for two periods.

Similarly, the model can be extended to three, four, or more periods.

In the example, a dividend of $10 is used for each year, but in practice, it often varies over time (e.g., $10 for year 1, $12 for year 2). Sometimes dividends follow a certain growth rate over time.

The Gordon Growth Model

The Gordon Growth Model (GGM) assumes that dividends grow at a constant rate indefinitely. This model is most effectively applied to companies that are in their mature stage, relatively insensitive to the business cycle, and have a stable and predictable dividend policy. Typically, these are companies with a stable market share.

The present fair value of a stock can be calculated using the formula:

Where:

• Most recent dividend (D0): $10
• Dividend in one year (D1) = D0 *(1 + g)
• Required rate of return (r): 10%
• Constant growth rate (g): 5%

If the most recent dividend (D0) is $10, the required rate of return is 10%, and the expected growth rate is 5%, then substituting into the formula:

The GGM can only be applied when the required rate of return (cost of equity) is higher than the dividend growth rate.

Multi-Stage Dividend Discount Model

The Gordon Growth Model assumes that dividends grow at a constant rate indefinitely. However, a business goes through different stages of development – rapid growth, a transitional period, and maturity. Depending on the stage of development, a company’s dividend policy varies. To account for these changes, multi-stage dividend discount models have been developed.

Two-Stage Dividend Discount Model

This model involves a short initial stage with an unsustainably high growth rate (e.g., 20% for the first 5 years), followed by an infinite second stage with a lower, sustainable growth rate (e.g., 8%).

H-Model

The H-Model assumes that the dividend growth rate in the first period (e.g., 20%) decreases linearly until it reaches the long-term growth rate of the second period (e.g., 8%).

Three-Stage Dividend Discount Model

This model considers three distinct stages of dividend growth:

1. First Stage: High growth rate (e.g., 20%).
2. Second Stage: Transitional period with a lower growth rate (e.g., 10%).
3. Third Stage: Long-term stage with a constant growth rate (e.g., 8%).

There are other multi-stage dividend discount models, but their logic is always the same – finding the present value of future dividend payments.

Determining the dividend growth rate and the required rate of return is crucial for the dividend discount models. Changes in these variables can lead to significant changes in the present value assessment.

Dividend Growth Rate

There are various methods to determine the dividend growth rate in both the short term and long term.

Short-Term Growth Rate

In the short term, financial statements can reveal certain patterns regarding dividend payments. For example, the dividend might be constant (e.g., $10 annually), or each subsequent dividend might increase by a dollar or a certain percentage. Management usually communicates their dividend policy to investors, providing insights into expected short-term growth.

Long-Term Growth Rate

Determining the long-term growth rate (sustainable growth rate) is more challenging because it involves predicting the distant future. One approach is to use the average growth rate for the specific industry in which the company operates. This method provides a benchmark that reflects broader market conditions and trends.

Mathematical Determination

Mathematically, the growth rate can be determined using the formula from the Gordon Growth Model (or another dividend discount model):

Constant Growth Rate (g):

Where:

• Present value of share today (V0): $210
• Cost of capital (r): 5%
• Dividend in one year (D1): $10.50

Substituting the values:

In many cases, investors assume that the dividend growth rate will be identical to the growth rate achieved by reinvested earnings in the business. This can be calculated using the formula:

Dividend Growth Rate (g):

Where:

• b = earnings retention rate (1 – dividend payout ratio)
• ROE (Return on Equity) = Net Income / Shareholders’ Equity

Required Rate of Return

The required rate of return, often referred to as the cost of equity, is a critical financial metric used to discount future cash flows to their present value. This rate represents the compensation investors expect for taking on the risk of investing in a particular stock. Analysts frequently use the cost of equity as the required rate of return to evaluate investment opportunities.

Importance of the Required Rate of Return

Accurately determining the required rate of return is essential, much like estimating the dividend growth rate, for the effectiveness of the DDM. The DDM is a valuation method used to estimate the value of a company’s stock based on the theory that its worth is equal to the sum of all its future dividend payments, discounted back to their present value. Several methods exist to calculate the required rate of return, with the Capital Asset Pricing Model (CAPM) being one of the most widely used.

Capital Asset Pricing Model (CAPM)

The CAPM is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. The formula for CAPM is:

Where:

• r: Required rate of return
• Β (beta): Measures the sensitivity of the stock to the overall market.
• Risk-free rate: The yield on government notes or bonds, representing the return expected from a risk-free investment.
• Risk premium: The difference between the expected market rate of return and the risk-free rate of return.

Gordon Growth Model (GGM)

Another method to determine the required rate of return is the Gordon Growth Model, which is particularly useful for valuing dividend-paying stocks. The GGM formula is:

Where:

• r: Required rate of return
• V0​: Present value of the share today, which is $210 in this example.
• g: Constant growth rate of dividends, assumed to be 5%.
• D0​: Most recent dividend, which is $10.
• D1​: Dividend in one year, calculated as D0​×(1+g) = $10.50.

Substituting into the formula, r = 10%.

In future discussions, other methods for calculating the required rate of return will be explored.

Challenges and Considerations of DDM

1. Forecasting Future Dividends: Accurately predicting future dividends can be difficult, as it requires a deep understanding of the company’s financial health, growth prospects, and dividend policy.
2. Determining the Discount Rate: The required rate of return (r) is subjective and can vary based on the investor’s risk tolerance and market conditions. It usually is calculated by adding a risk premium to the risk-free rate.
3. Growth Rate Assumptions: For companies expected to increase their dividends, the growth rate must be estimated. This can add complexity, especially for firms with volatile earnings.

Conclusion

In conclusion, the Dividend Discount Model offers a valuable approach for estimating the intrinsic value of a stock based on the present value of its future dividends. By incorporating factors like expected dividend growth rates and required rates of return, investors can assess whether a stock is undervalued or overvalued. While the DDM is particularly useful for valuing dividend-paying companies, it has limitations, especially for firms with irregular or no dividend payments. Nonetheless, it remains a fundamental tool for long-term investors seeking to evaluate the potential returns from dividend-yielding stocks.

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