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Numerical Example

Three-Stage Dividend Discount Model

Problem:

We want to value a stock, "EvolvingTech," using a three-stage DDM.

  • Stage 1 (High Growth - Years 1-3): The company is expected to grow its dividends at a rate of 20% per year for the next 3 years. The current dividend (D0) is $0.80 per share.
  • Stage 2 (Transition - Years 4-6): The dividend growth rate is expected to decline linearly from 20% in Year 3 to 8% in Year 6.
  • Stage 3 (Stable Growth - Beyond Year 6): The company is expected to grow its dividends at a constant rate of 8% per year indefinitely.
  • Required Rate of Return (Ke): 12%

Solution:

  1. Calculate Dividends During the High-Growth Phase (Years 1-3):

    • Year 1 (D1): $0.80 * (1 + 0.20) = $0.96
    • Year 2 (D2): $0.96 * (1 + 0.20) = $1.152
    • Year 3 (D3): $1.152 * (1 + 0.20) = $1.3824

  2. Calculate Dividends During the Transition Phase (Years 4-6):

    The growth rate declines linearly from 20% to 8% over 3 years, meaning it declines by (20%-8%)/3 = 4% each year.

    • Year 4 (Growth Rate = 16%): D4 = $1.3824 * (1 + 0.16) = $1.6036
    • Year 5 (Growth Rate = 12%): D5 = $1.6036 * (1 + 0.12) = $1.7960
    • Year 6 (Growth Rate = 8%): D6 = $1.7960 * (1 + 0.08) = $1.9397

  3. Calculate the Terminal Value at the End of Year 6:

    Using the Gordon Growth Model:

    • Terminal Value (TV6) = D7 / (Ke - g)
    • First calculate D7 = $1.9397 * (1 + 0.08) = $2.095
    • Terminal Value (TV6) = $2.095 / (0.12 - 0.08) = $2.095 / 0.04 = $52.375

  4. Discount the Dividends and Terminal Value Back to the Present:

    Year Dividend Discount Factor (1.12)^-t Present Value
    1 $0.96 0.8929 $0.857
    2 $1.152 0.7972 $0.918
    3 $1.3824 0.7118 $0.984
    4 $1.6036 0.6355 $1.019
    5 $1.7960 0.5674 $1.019
    6 $1.9397 0.5066 $0.983
    6 $52.375 0.5066 $26.535
    Total: $32.315

  5. Calculate the Intrinsic Value of the Stock:

    The intrinsic value of the stock is the sum of the present values of the dividends and the terminal value:

    • Intrinsic Value (P0) = $0.857 + $0.918 + $0.984 + $1.019 + $1.019 + $0.983 + $26.535 = $32.315

Therefore:

  • The estimated intrinsic value of EvolvingTech's stock using the three-stage DDM is $32.315 per share.

This example illustrates how the three-stage DDM can be used to value companies with more complex growth patterns. The key is to carefully estimate the dividends during each stage and to use realistic assumptions about the growth rates and required rate of return.

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