The Two Stage Dividend Growth Model Evaluates

The two-stage dividend growth model evaluates the present value of a stock based on the premise that dividends will grow at different rates over two distinct periods. This model is particularly useful for companies experiencing a period of high growth that is expected to moderate over time. It provides a more realistic valuation than models that assume a constant growth rate indefinitely.

Understanding the Two-Stage Dividend Growth Model

The dividend discount model (DDM) is a family of models that values a stock based on the present value of its expected future dividends. The simplest form of the DDM, the Gordon Growth Model, assumes a constant dividend growth rate. However, this assumption often doesn't hold true in the real world. Companies, especially young, rapidly growing ones, often experience high dividend growth rates initially, followed by a slowdown as they mature.

The two-stage dividend growth model addresses this limitation by dividing the future into two periods:

• Stage 1: A period of high, often unsustainable, dividend growth. This stage typically reflects a company's early years of rapid expansion and market penetration.
• Stage 2: A period of stable, sustainable dividend growth. This stage represents the company's mature phase, where growth aligns more closely with the overall economy or industry average.

Key Components

The two-stage dividend growth model relies on several key components:

• D0: The most recent dividend paid. This is the starting point for projecting future dividends.
• g1: The dividend growth rate in Stage 1. This is the high-growth rate expected for the initial period.
• n: The number of years in Stage 1. This defines the duration of the high-growth period.
• g2: The dividend growth rate in Stage 2. This is the stable, sustainable growth rate expected for the long-term.
• r: The required rate of return (or discount rate). This reflects the investor's minimum acceptable return, considering the risk associated with the stock.

The Formula

The formula for the two-stage dividend growth model is as follows:

P0 = ∑ [D0 * (1 + g1)^t / (1 + r)^t] + [Dn * (1 + g2) / (r - g2)] / (1 + r)^n

Where:

• P0 = The current stock price
• D0 = The most recent dividend paid
• g1 = The dividend growth rate in Stage 1
• n = The number of years in Stage 1
• g2 = The dividend growth rate in Stage 2
• r = The required rate of return
• t = Year (from 1 to n)
• Dn = Dividend at the end of Stage 1 (D0 * (1 + g1)^n)

This formula can be broken down into two main parts:

1. Present Value of Dividends in Stage 1: This part calculates the present value of each dividend expected to be paid during the high-growth period (Stage 1). It sums the discounted values of these dividends.

   ∑ [D0 * (1 + g1)^t / (1 + r)^t]

2. Present Value of the Terminal Value: This part calculates the present value of the stock's price at the end of Stage 1 (also known as the terminal value). The terminal value is estimated using the Gordon Growth Model, assuming that dividends will grow at a constant rate (g2) from that point forward. The terminal value is then discounted back to the present.

   [Dn * (1 + g2) / (r - g2)] / (1 + r)^n

Step-by-Step Calculation

To effectively utilize the two-stage dividend growth model, follow these steps:

1. Gather the Necessary Data: Obtain the values for D0, g1, n, g2, and r. Estimating g1 and g2 can be challenging and often requires careful analysis of the company and its industry. The required rate of return (r) can be estimated using models like the Capital Asset Pricing Model (CAPM).

2. Calculate Dividends for Stage 1: Project the expected dividends for each year in Stage 1 by applying the growth rate g1 to the initial dividend D0.

   • D1 = D0 * (1 + g1)
   • D2 = D1 * (1 + g1) = D0 * (1 + g1)^2
   • ...
   • Dn = D0 * (1 + g1)^n

3. Calculate the Present Value of Dividends for Stage 1: Discount each of the projected dividends from Stage 1 back to the present using the required rate of return (r).

   • PV(D1) = D1 / (1 + r)
   • PV(D2) = D2 / (1 + r)^2
   • ...
   • PV(Dn) = Dn / (1 + r)^n

4. Sum the Present Values of Stage 1 Dividends: Add up all the present values calculated in the previous step. This gives you the present value of the dividends expected during the high-growth period.

   PV of Stage 1 Dividends = PV(D1) + PV(D2) + ... + PV(Dn)

5. Calculate the Terminal Value: Estimate the stock's price at the end of Stage 1 (the terminal value) using the Gordon Growth Model with the stable growth rate (g2). Remember that Dn is the dividend expected at the end of Stage 1.

   Terminal Value = Dn * (1 + g2) / (r - g2)

6. Calculate the Present Value of the Terminal Value: Discount the terminal value back to the present using the required rate of return (r) and the number of years in Stage 1 (n).

   PV of Terminal Value = Terminal Value / (1 + r)^n

7. Calculate the Current Stock Price (P0): Add the present value of the Stage 1 dividends and the present value of the terminal value. This result is the estimated current stock price based on the two-stage dividend growth model.

   P0 = PV of Stage 1 Dividends + PV of Terminal Value

Example

Let's consider a hypothetical company, "TechGrowth Inc.," to illustrate the application of the two-stage dividend growth model.

• D0 = $1.00 (Most recent dividend paid)
• g1 = 20% (Dividend growth rate in Stage 1)
• n = 5 years (Number of years in Stage 1)
• g2 = 5% (Dividend growth rate in Stage 2)
• r = 12% (Required rate of return)

Step 1: Gather the Necessary Data

We already have all the necessary data.

Step 2: Calculate Dividends for Stage 1

• D1 = $1.00 * (1 + 0.20) = $1.20
• D2 = $1.20 * (1 + 0.20) = $1.44
• D3 = $1.44 * (1 + 0.20) = $1.728
• D4 = $1.728 * (1 + 0.20) = $2.0736
• D5 = $2.0736 * (1 + 0.20) = $2.48832

Step 3: Calculate the Present Value of Dividends for Stage 1

• PV(D1) = $1.20 / (1 + 0.12) = $1.0714
• PV(D2) = $1.44 / (1 + 0.12)^2 = $1.1466
• PV(D3) = $1.728 / (1 + 0.12)^3 = $1.2251
• PV(D4) = $2.0736 / (1 + 0.12)^4 = $1.3071
• PV(D5) = $2.48832 / (1 + 0.12)^5 = $1.3927

Step 4: Sum the Present Values of Stage 1 Dividends

PV of Stage 1 Dividends = $1.0714 + $1.1466 + $1.2251 + $1.3071 + $1.3927 = $6.1429

Step 5: Calculate the Terminal Value

Terminal Value = $2.48832 * (1 + 0.05) / (0.12 - 0.05) = $37.3248

Step 6: Calculate the Present Value of the Terminal Value

PV of Terminal Value = $37.3248 / (1 + 0.12)^5 = $21.1788

Step 7: Calculate the Current Stock Price (P0)

P0 = $6.1429 + $21.1788 = $27.32

Therefore, according to the two-stage dividend growth model, the estimated current stock price for TechGrowth Inc. is $27.32.

Advantages of the Two-Stage Model

The two-stage dividend growth model offers several advantages over simpler valuation models:

• More Realistic Assumptions: It acknowledges that growth rates are unlikely to remain constant indefinitely, providing a more realistic representation of a company's lifecycle.
• Suitable for High-Growth Companies: It's particularly well-suited for valuing companies experiencing a period of rapid growth followed by a period of more stable growth.
• Flexibility: The model allows for different growth rates and time periods, providing flexibility in adapting to various company scenarios.
• Improved Accuracy: Compared to the Gordon Growth Model, the two-stage model often provides a more accurate valuation for companies with non-constant growth.

Disadvantages and Limitations

Despite its advantages, the two-stage dividend growth model also has limitations:

• Complexity: It's more complex than simpler models like the Gordon Growth Model, requiring more data and calculations.
• Sensitivity to Inputs: The model is highly sensitive to the inputs, particularly the growth rates (g1 and g2) and the required rate of return (r). Small changes in these inputs can significantly impact the estimated stock price.
• Difficulty Estimating Growth Rates: Accurately estimating future growth rates, especially for Stage 1, can be challenging and subjective. Analysts must rely on historical data, industry trends, and management guidance, all of which are subject to error.
• Terminal Value Dependence: The model's valuation is heavily influenced by the terminal value, which is calculated using the Gordon Growth Model. This means that the accuracy of the terminal value depends on the assumption of constant growth in Stage 2. If the growth rate in Stage 2 is not constant, the terminal value may be inaccurate.
• Ignores Other Valuation Factors: The model focuses solely on dividends and ignores other factors that can influence stock prices, such as earnings, cash flow, and market sentiment.
• Assumes Dividends are Paid: The model is only applicable to companies that pay dividends. It cannot be used to value companies that do not distribute dividends.

Addressing the Limitations

While the limitations of the two-stage dividend growth model are significant, several strategies can be employed to mitigate their impact:

• Sensitivity Analysis: Conduct sensitivity analysis to assess how the estimated stock price changes with variations in the input variables. This can help identify the key drivers of the valuation and highlight the potential range of outcomes.
• Scenario Planning: Develop multiple scenarios with different growth rate assumptions to account for uncertainty. This can provide a more comprehensive view of the potential range of values.
• Peer Group Analysis: Compare the estimated growth rates and required rate of return to those of comparable companies in the same industry. This can help ensure that the inputs are reasonable and consistent with market expectations.
• Fundamental Analysis: Conduct thorough fundamental analysis to gain a deeper understanding of the company's business, financial performance, and competitive position. This can improve the accuracy of the growth rate estimates.
• Consider Alternative Valuation Methods: Use other valuation methods, such as discounted cash flow (DCF) analysis or relative valuation, to cross-check the results obtained from the two-stage dividend growth model.
• Be Conservative: When estimating growth rates, err on the side of caution and use conservative estimates. This can help avoid overvaluing the stock.
• Continuously Monitor and Update: Regularly monitor the company's performance and update the model's inputs as new information becomes available. This can help ensure that the valuation remains accurate and relevant.

When to Use the Two-Stage Dividend Growth Model

The two-stage dividend growth model is most appropriate in the following situations:

• Companies with High Initial Growth: When valuing companies that are currently experiencing high growth but are expected to transition to a more sustainable growth rate in the future.
• Companies with a Clear Two-Stage Lifecycle: When a company's lifecycle can be clearly divided into two distinct stages: a high-growth phase and a stable-growth phase.
• Companies with a History of Dividend Payments: The model is best suited for companies with a consistent history of dividend payments and a clear dividend policy.
• Companies in Mature Industries: While applicable to high-growth companies initially, the model is particularly useful when those companies transition into more mature industries with predictable, albeit lower, growth rates.
• As a Complement to Other Valuation Methods: The two-stage model is often best used in conjunction with other valuation techniques to provide a more robust and comprehensive assessment of a company's value.

Alternatives to the Two-Stage Model

While the two-stage dividend growth model offers advantages, other valuation models may be more appropriate in certain circumstances:

• Gordon Growth Model (Constant Growth Model): This model is suitable for companies with a stable dividend growth rate that is expected to continue indefinitely. It's simpler to use but less accurate for companies with non-constant growth.
• H-Model: This model is a variation of the two-stage model that assumes a linear decline in the growth rate from the initial high growth rate to the stable growth rate. It's useful for companies where the transition from high growth to stable growth is gradual.
• Three-Stage Dividend Growth Model: This model divides the future into three periods: an initial high-growth phase, a transition phase, and a stable-growth phase. It provides even greater flexibility but requires more data and more complex calculations.
• Discounted Cash Flow (DCF) Model: This model values a company based on the present value of its expected future free cash flows. It's more flexible than the dividend discount model and can be used to value companies that do not pay dividends.
• Relative Valuation: This approach compares a company's valuation multiples (e.g., price-to-earnings ratio, price-to-book ratio) to those of its peers. It's a quick and easy way to assess a company's value relative to the market.

Conclusion

The two-stage dividend growth model provides a valuable framework for valuing companies with non-constant dividend growth. By explicitly modeling two distinct growth phases, it offers a more realistic and accurate valuation than models that assume constant growth indefinitely. However, it's crucial to understand the model's limitations and to use it in conjunction with other valuation techniques and thorough fundamental analysis. Accurate estimation of growth rates and the required rate of return is paramount to achieving reliable results. By carefully considering these factors, investors can leverage the two-stage dividend growth model to make more informed investment decisions.