Multistage Growth Models

• [b] Calculate and explain the meaning of the value of a common stock using the dividend discount model (DDM) for single or multiple holding periods.
• [l] Describe and justify the selection of different valuation models for common shares of a company, such as the two-stage DDM, H-model, three-stage DDM, or spreadsheet modeling, based on their assumptions.
• [k] Describe the growth stage, transitional stage, and maturity stage of a company.
• [m] Explain the concept of the terminal value and describe the different methods that can be used to calculate it in a DDM.
• [n] Compute and explain the value of common shares using the H-model, two-stage DDM, and three-stage DDM.

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• 00:00 – Introduction to Multistage Growth Models
• 00:41 – 1. Phases of the Business Cycle
• 01:50 – 2. Overview of Multistage Growth Models
• 04:00 – 3. Terminal Value Calculation
• 06:35 – 4. Valuation using Multistage Models (Examples & Practice)
• 15:01 – Summary

Introduction to Multistage Growth Models

This lesson expands on the single-stage Gordon Growth Model (GGM) to incorporate more realistic valuation scenarios where a company’s growth rate changes over time. Multistage models align a company’s dividend growth with its position in the business life cycle.

Lesson Agenda:

• Phases of the Business Cycle
• Overview of various multistage models
• Calculating Terminal Value
• Applying multistage models to value equity

1. Phases of the Business Cycle

A company’s dividend policy and growth potential are heavily influenced by its stage in the business cycle. Understanding these phases is crucial for selecting the appropriate valuation model.

Phase	Earnings Growth	Dividends	Capex	Description
Initial Growth	Very High	Low or None	Heavy	The firm is rapidly expanding, reinvesting most earnings back into the business. Little cash is available for dividends.
Transition	High but Falling	Increasing	Decreasing	Competition increases, slowing the growth rate. As capital needs decrease, the company has more cash to start or increase dividend payments.
Maturity	Stable (Slower)	Stable Payout Ratio	Stable	The company’s growth stabilizes at a long-term, sustainable rate. Capex is primarily for maintenance. Dividend growth matches earnings growth. This is the phase where the Gordon Growth Model (GGM) is most applicable.

2. Overview of Multistage Growth Models

Different models are suited for different phases of the business cycle. The core idea is to forecast dividends explicitly during high-growth and transition phases and then use a perpetual growth model to calculate a terminal value once the company reaches maturity.

• Constant Growth (GGM): A single-stage model suitable for mature companies with a stable growth rate in perpetuity.
• Two-Stage DDM: Suitable for companies moving from a high-growth phase to a mature phase.
  • Stage 1: A period of high, stable growth.
  • Stage 2: A perpetual period of lower, stable growth.
  • Limitation: The transition between the two growth rates is abrupt and often unrealistic.
• H-Model: A type of two-stage model that provides a more realistic transition.
  • It assumes the growth rate declines linearly from a high initial rate to a stable long-term rate over a specified period.
• Three-Stage DDM: Suitable for young companies in their initial growth phase.
  • Stage 1: A period of high, constant growth (e.g., a startup’s initial years).
  • Stage 2: A transition period where growth declines (can be modeled with H-Model assumptions).
  • Stage 3: A perpetual period of stable, lower growth.
• Spreadsheet Model: Offers the most flexibility by allowing for year-by-year forecasts of dividend growth rates before a final, perpetual growth stage is assumed.

3. Calculating the Terminal Value (V_T)

The foundation of any multistage model is the calculation of the stock’s value at the point where it enters the final, stable growth phase. This is known as the terminal value.

Gordon Growth Model (GGM) Approach

The most common method to calculate terminal value is using the GGM. The value of the stock at the beginning of the final stage (Time T) is calculated as:

\[ V_T = \frac{D_{T+1}}{r – g_L} = \frac{D_T(1+g_L)}{r – g_L} \]

• \(V_T\): Terminal value at time T (the beginning of the perpetual growth phase).
• \(D_T\): Dividend at the end of the last year of the explicit forecast period.
• \(g_L\): The long-term, constant perpetual growth rate.
• \(r\): The required rate of return on the stock.

Market Multiple Approach

An alternative, though less common in DDM, is to estimate the terminal value using a price multiple, such as the P/E ratio.

\[ V_T = (\text{Benchmark Trailing P/E}) \times (\text{Forecasted EPS}_T) \]

This is useful when estimating a long-term growth rate is difficult, but a justifiable benchmark P/E can be determined.

4. Valuation using Multistage Models (Examples & Practice)

The total value of the stock today (\(V_0\)) is the sum of the present values of all explicitly forecasted dividends plus the present value of the terminal value.

Two-Stage DDM Valuation Formula

\[ V_0 = \sum_{t=1}^{n} \frac{D_0(1+g_S)^t}{(1+r)^t} + \frac{V_n}{(1+r)^n} \]

Where \(V_n\) is the terminal value calculated at the end of the initial high-growth period (year n).

H-Model Valuation Formula

The H-model captures both the value from perpetual growth and the extra value from the supernormal growth during the linear decline period.

\[ V_0 = \frac{D_0 \times (1+g_L)}{r – g_L} + \frac{D_0 \times H \times (g_S – g_L)}{r – g_L} \]

• \(g_S\): The initial short-term high growth rate.
• \(g_L\): The final long-term constant growth rate.
• \(H\): The half-life of the high-growth period (i.e., half the number of years in the transition period).

Valuation for Companies with Delayed Dividends

If a company is not currently paying dividends but is expected to in the future, the valuation process is similar.

1. Calculate the value of the stock at the point in time when the first dividend is paid (e.g., at T=2). This value will encompass all subsequent dividend payments.
2. Treat the value calculated in step 1 as a single future cash flow.
3. Discount this single future value back to today (T=0) to find the current stock price.

Example: If Matchly was expected to pay its first dividend of $2 in 2 years (D₂), and the growth profile was the same, the value of the stock at T=0 would be the value calculated previously ($126.64), discounted back an additional two years (assuming the $126.64 represents the value at T=2). \[ V_0 = \frac{V_2}{(1+r)^2} = \frac{126.64}{1.09^2} = \$106.59 \] Note: This is a simplification. The precise method would re-calculate the entire timeline starting with D₂=$2, but the principle of discounting a future valuation is the key takeaway.

Summary

• Multistage DDM provides a more realistic valuation than the single-stage GGM by allowing for changing growth rates that correspond to a firm’s life cycle.
• Model Selection: Choose the model (Constant Growth, 2-Stage, H-Model, 3-Stage) that best fits the company’s expected growth trajectory.
• Valuation Process:
  1. Define the growth stages and their durations/rates.
  2. Calculate the terminal value (\(V_T\)) at the beginning of the final, perpetual growth stage, typically using the GGM.
  3. Forecast the explicit dividends for all years leading up to the terminal stage.
  4. Discount all explicit dividends and the terminal value back to the present day using the required rate of return (\(r\)).
• Key Formulas: It is crucial to know the GGM formula for terminal value and the H-Model formula for valuing periods of linear decline in growth.