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Dividend Discount Models (DDM)

Two-Stage and Three-Stage

Dividend Discount Models (DDMs) are valuation models that estimate the intrinsic value of a stock based on the present value of its expected future dividends. The basic premise is that a stock is worth the sum of all future dividend payments, discounted back to the present.

1. Basic Dividend Discount Model (Single-Stage or Gordon Growth Model):

  • Formula: P0 = D1 / (Ke - g)
    • P0 = Current stock price (intrinsic value)
    • D1 = Expected dividend per share in the next period
    • Ke = Required rate of return on equity (cost of equity)
    • g = Constant dividend growth rate
  • Assumptions:
    • Dividends grow at a constant rate forever.
    • The growth rate (g) is less than the required rate of return (Ke).
  • Limitations:
    • Unrealistic assumption of constant growth forever.
    • Only suitable for mature, stable companies with a history of paying dividends.
    • Not applicable to companies that do not pay dividends.

2. Two-Stage Dividend Discount Model:

  • Concept: This model assumes two distinct growth phases: an initial high-growth phase followed by a stable, constant-growth phase.
  • Formula:
    • P0 = [ Σ (Dt / (1 + Ke)^t) ] + [ (Dn+1 / (Ke - gn)) / (1 + Ke)^n ]
    • Where:
      • Dt = Expected dividend per share in year t (during the high-growth phase)
      • Ke = Required rate of return on equity
      • n = Number of years in the high-growth phase
      • Dn+1 = Expected dividend per share in year n+1 (the first year of the stable growth phase)
      • gn = Constant dividend growth rate in the stable growth phase
  • Steps:
    1. Estimate dividends during the high-growth phase (Dt).
    2. Estimate the constant dividend growth rate in the stable growth phase (gn). This growth rate should be sustainable and realistic (e.g., close to the long-term GDP growth rate).
    3. Discount the dividends during the high-growth phase back to the present.
    4. Calculate the terminal value at the end of the high-growth phase using the Gordon Growth Model (Dn+1 / (Ke - gn)).
    5. Discount the terminal value back to the present.
    6. Sum the present values of the dividends during the high-growth phase and the present value of the terminal value to arrive at the intrinsic value of the stock.
  • Applicability: More realistic than the single-stage model. Suitable for companies that are expected to experience a period of high growth followed by a period of stable growth.
  • Advantages: Accounts for a more realistic growth pattern than the single-stage model.
  • Limitations: Still relies on the assumption of constant growth in the second stage.

3. Three-Stage Dividend Discount Model:

  • Concept: This model assumes three distinct growth phases: an initial high-growth phase, a transition phase, and a stable, constant-growth phase.
  • Justification: The three-stage model is useful when a company is currently experiencing high growth, will gradually transition to a more sustainable growth rate, and will eventually reach a stable growth rate.
  • Formula (Conceptual):
    • P0 = [ Σ (Dt / (1 + Ke)^t) ] (High Growth Stage)
      • [ Σ (Dt / (1 + Ke)^t) ] (Transition Stage)
      • [ (Dt / (Ke - g)) / (1 + Ke)^t ] (Stable Growth Stage)
    • Where:
      • Dt = Expected dividend per share in year t
      • Ke = Required rate of return on equity
      • g = Constant dividend growth rate in the stable growth phase.
  • Steps:
    1. Estimate dividends during the high-growth phase.
    2. Estimate dividends during the transition phase, where the growth rate gradually declines from the high-growth rate to the stable growth rate.
    3. Estimate the constant dividend growth rate in the stable growth phase.
    4. Discount the dividends during each phase back to the present.
    5. Sum the present values of the dividends during all three phases to arrive at the intrinsic value of the stock.
  • Applicability: Most realistic of the DDM models. Suitable for companies with complex growth patterns, such as young, rapidly growing companies.
  • Advantages: Allows for more flexibility in modeling growth patterns.
  • Limitations: Requires more assumptions and more data, making it more complex and potentially less reliable.

Choosing the Right DDM:

  • Single-Stage: Use for very stable, mature companies with predictable dividend growth.
  • Two-Stage: Use for companies expected to have a period of high growth followed by stable growth.
  • Three-Stage: Use for companies with complex growth patterns that include a transition phase.

The key to using DDMs effectively is to carefully consider the assumptions and limitations of each model and to use realistic estimates of future dividends, growth rates, and discount rates.

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