How do I implement a three-stage DDM with declining growth in the middle period?
CFA Level II has the three-stage dividend discount model where there is a high-growth phase, a transition phase where growth linearly declines, and a mature phase. I'm having trouble calculating dividends during the transition. Can someone walk through the entire calculation with numbers?
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:
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:
- 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.
- Terminal value uses g_3, not the last transition rate. D_7 grows at 5%, not the Phase 2 rate.
- The terminal value captures all dividends from Year 7 to infinity — do not add separate dividends after Year 6.
- 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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