Variable Growth Rate Dividend Discount Model

The Variable Growth Rate Dividend Discount Model (DDM) offers a more flexible and realistic approach to valuing stocks than the traditional constant growth model. This method recognizes that companies don't always grow at a constant rate and accounts for varying growth rates over different time periods. In this detailed exploration, we will uncover the intricacies of the variable growth rate DDM, how it can be applied, and why it is a powerful tool for investors looking to assess the true value of a stock.

Understanding the Basics of Dividend Discount Model (DDM)

At its core, the Dividend Discount Model values a stock based on the present value of its expected future dividends. The fundamental equation for a constant growth DDM is straightforward:

$P_0=\frac{D_0\times (1+g)}{r-g}$P0​=r−gD0​×(1+g)​

where $P_0$P0​ is the current stock price, $D_0$D0​ is the most recent dividend, $g$g is the growth rate of dividends, and $r$r is the required rate of return.

However, this model assumes a constant growth rate, which is often unrealistic. The variable growth rate DDM addresses this limitation by incorporating multiple stages of growth, making it a more dynamic and practical approach.

The Structure of the Variable Growth Rate DDM

The variable growth rate DDM involves multiple stages, typically categorized into three phases:

1. Initial High Growth Phase: This is the period during which the company is expected to grow at a higher rate than usual. This phase accounts for the rapid growth opportunities a company might have in its early stages or during specific expansion periods.

2. Transition Phase: As the company matures, the growth rate may stabilize. This phase reflects a transition from high growth to a more sustainable, moderate growth rate.

3. Stable Growth Phase: Eventually, the company reaches a stable growth rate, which is more consistent and predictable. This final phase assumes a constant growth rate similar to the traditional DDM.

Calculating the Stock Value with Variable Growth Rate DDM

Let's break down the steps to calculate the stock value using the variable growth rate DDM:

1. Estimate Dividends for the Initial High Growth Phase: Project the expected dividends for this period using the high growth rate.

2. Calculate the Present Value of Dividends During the High Growth Phase: Discount these dividends back to the present value using the required rate of return.

3. Estimate Dividends for the Transition Phase: Project the dividends for this phase using the transitional growth rate.

4. Calculate the Present Value of Dividends During the Transition Phase: Discount these dividends back to the present value.

5. Estimate the Dividends and Terminal Value for the Stable Growth Phase: Calculate the dividends and terminal value (the value of all future dividends growing at a constant rate).

6. Calculate the Present Value of the Terminal Value: Discount the terminal value back to the present value.

7. Sum Up All Present Values: Add the present values of dividends from all phases to get the stock's intrinsic value.

Example Calculation

Consider a company with the following assumptions:

• Initial high growth rate: 20% for 3 years
• Transition growth rate: 10% for 2 years
• Stable growth rate: 4% indefinitely
• Required rate of return: 8%
• Current dividend: $2 per share

1. High Growth Phase:

Projected dividends:

• Year 1: $2 × (1 + 0.20) = $2.40
• Year 2: $2.40 × (1 + 0.20) = $2.88
• Year 3: $2.88 × (1 + 0.20) = $3.46

Present values:

• PV Year 1: $2.40 / (1 + 0.08)^1 = $2.22
• PV Year 2: $2.88 / (1 + 0.08)^2 = $2.29
• PV Year 3: $3.46 / (1 + 0.08)^3 = $2.35

2. Transition Phase:

Projected dividends:

• Year 4: $3.46 × (1 + 0.10) = $3.81
• Year 5: $3.81 × (1 + 0.10) = $4.19

Present values:

• PV Year 4: $3.81 / (1 + 0.08)^4 = $2.77
• PV Year 5: $4.19 / (1 + 0.08)^5 = $2.57

3. Stable Growth Phase:

Terminal value at the end of Year 5:

• Terminal value = Dividend in Year 6 / (Required rate of return - Stable growth rate)
• Dividend in Year 6: $4.19 × (1 + 0.04) = $4.36
• Terminal value = $4.36 / (0.08 - 0.04) = $109.00

Present value of the terminal value:

• PV of Terminal Value: $109.00 / (1 + 0.08)^5 = $74.85

4. Sum of Present Values:

Total intrinsic value = PV of High Growth Phase + PV of Transition Phase + PV of Terminal Value

• Total intrinsic value = $2.22 + $2.29 + $2.35 + $2.77 + $2.57 + $74.85 = $87.95

Advantages of the Variable Growth Rate DDM

• Flexibility: Accommodates varying growth rates, making it suitable for companies with changing growth prospects.
• Realism: Reflects the real-life scenario of companies going through different growth phases.
• Comprehensive: Provides a more detailed valuation by considering different stages of growth.

Challenges and Considerations

• Complexity: Requires accurate estimates of multiple growth rates and future dividends, which can be challenging.
• Data Sensitivity: Small changes in growth rate assumptions or discount rates can significantly affect the valuation.

Conclusion

The Variable Growth Rate Dividend Discount Model is a sophisticated tool that provides a more nuanced approach to stock valuation by accounting for varying growth rates over different periods. It offers a more realistic perspective compared to the constant growth model, making it a valuable asset for investors seeking to understand the intrinsic value of stocks in a dynamic market environment.