Numericals

Numerical Example: Two-Stage Dividend Discount Model

Problem:

We want to value a stock, "GrowthCo," using a two-stage DDM.

• Stage 1 (High Growth): The company is expected to grow its dividends at a rate of 15% per year for the next 5 years. The current dividend (D0) is $1.00 per share.
• Stage 2 (Stable Growth): After Year 5, the company is expected to grow its dividends at a constant rate of 5% per year indefinitely.
• Required Rate of Return (Ke): 12%

Solution:

1. Calculate Dividends During the High-Growth Phase (Years 1-5):

   • Year 1 (D1): $1.00 * (1 + 0.15) = $1.15
   • Year 2 (D2): $1.15 * (1 + 0.15) = $1.3225
   • Year 3 (D3): $1.3225 * (1 + 0.15) = $1.5209
   • Year 4 (D4): $1.5209 * (1 + 0.15) = $1.7490
   • Year 5 (D5): $1.7490 * (1 + 0.15) = $2.0114

2. Calculate the Terminal Value at the End of Year 5:

   First, calculate the dividend in Year 6 (D6):

   • D6 = D5 * (1 + Stable Growth Rate) = $2.0114 * (1 + 0.05) = $2.1120

   Then, calculate the Terminal Value:

   • Terminal Value (TV5) = D6 / (Ke - gn) = $2.1120 / (0.12 - 0.05) = $2.1120 / 0.07 = $30.17

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

   Year	Dividend	Discount Factor (1.12)^-t	Present Value
   1	$1.15	0.8929	$1.027
   2	$1.3225	0.7972	$1.054
   3	$1.5209	0.7118	$1.083
   4	$1.7490	0.6355	$1.111
   5	$2.0114	0.5674	$1.141
   5	$30.17	0.5674	$17.118
   			Total: $22.53

4. 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) = $1.027 + $1.054 + $1.083 + $1.111 + $1.141 + $17.118 = $22.53

Therefore:

• The estimated intrinsic value of GrowthCo's stock using the two-stage DDM is $22.53 per share.