How do I implement a three-stage DDM with declining growth in the middle period?

The three-stage DDM extends the two-stage model by adding a transition period where growth declines linearly from the initial high rate to the stable rate. This is more realistic than an abrupt growth drop.

Structure:

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Worked Example — Evergreen Pharmaceuticals:

Parameter	Value
D_0 (current dividend)	$1.50
Phase 1 growth (g_1)	20% for years 1-3
Phase 2 transition	Years 4-6 (growth declines linearly from 20% to 5%)
Phase 3 stable growth (g_3)	5% from year 7 onward
Required return (r)	13%

Step 1: Phase 1 Dividends (constant 20% growth)

Year	Growth	Dividend
1	20%	$1.50 x 1.20 =$1.800
2	20%	$1.800 x 1.20 =$2.160
3	20%	$2.160 x 1.20 =$2.592

Step 2: Phase 2 — Linearly Declining Growth

Growth declines from 20% to 5% over 3 years. The annual decline = (20% - 5%) / 3 = 5% per year.

Year	Growth Rate	Dividend
4	20% - 5% = 15%	$2.592 x 1.15 =$2.981
5	15% - 5% = 10%	$2.981 x 1.10 =$3.279
6	10% - 5% = 5%	$3.279 x 1.05 =$3.443

Step 3: Terminal Value at End of Year 6

D_7 = $3.443 x 1.05 =$3.615

TV_6 = $3.615 / (0.13 - 0.05) =$3.615 / 0.08 = $45.19

Step 4: Discount All Cash Flows to Today

Year	Cash Flow	PV Factor (13%)	Present Value
1	$1.800	0.8850	$1.593
2	$2.160	0.7831	$1.692
3	$2.592	0.6931	$1.796
4	$2.981	0.6133	$1.829
5	$3.279	0.5428	$1.780
6	$3.443 +$45.19 = $48.633	0.4803	$23.368

V_0 = $1.593 +$1.692 + $1.796 +$1.829 + $1.780 +$23.368 = $32.06

Key Implementation Tips:

1. The transition growth rate formula: g_t = g_1 - [(g_1 - g_3) x (t - end of Phase 1) / length of Phase 2]. Make sure you index correctly.
2. Terminal value uses g_3, not the last transition rate. D_7 grows at 5%, not the Phase 2 rate.
3. The terminal value captures all dividends from Year 7 to infinity — do not add separate dividends after Year 6.
4. Check reasonableness: If your answer is wildly different from the current market price, re-examine the growth rates and discount rate.

When to use 3-stage vs. 2-stage:

• 3-stage: More realistic for companies with a clear growth trajectory that will slow gradually (biotech with patent cliff, tech gaining market share)
• 2-stage: Simpler and adequate when growth transition is expected to be abrupt

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