How sensitive is the H-model to changes in the initial high-growth rate assumption?
I'm working through DDM variants for CFA Level II and I find the H-model tricky. It assumes linear decline from a high growth rate to a stable rate over a specified half-life. But how much does the valuation change if I adjust the initial growth rate? Can someone show the sensitivity?
The H-model is a dividend discount model that approximates a gradual linear decline in the growth rate from an initial high rate (gS) to a long-term sustainable rate (gL) over 2H years, where H is the half-life.
H-Model Formula:
> V0 = D0(1 + gL) / (r - gL) + D0 x H x (gS - gL) / (r - gL)
The first term is the stable-growth Gordon model value. The second term is the premium for the above-normal growth that fades linearly.
Worked Example — Redcliffe Biotech (fictional):
| Parameter | Value |
|---|---|
| D0 (current dividend) | $2.00 |
| gL (long-term growth) | 4% |
| r (required return) | 10% |
| H (half-life) | 5 years (full fade = 10 years) |
Scenario 1: gS = 18%
- Stable value = 2.00(1.04) / (0.10 - 0.04) = $34.67
- Growth premium = 2.00 x 5 x (0.18 - 0.04) / (0.10 - 0.04) = $23.33
- V0 = $58.00
Scenario 2: gS = 14%
- Stable value = $34.67 (same)
- Growth premium = 2.00 x 5 x (0.14 - 0.04) / (0.10 - 0.04) = $16.67
- V0 = $51.33
Scenario 3: gS = 10%
- Stable value = $34.67 (same)
- Growth premium = 2.00 x 5 x (0.10 - 0.04) / (0.10 - 0.04) = $10.00
- V0 = $44.67
Sensitivity: A 4 percentage point change in gS (from 14% to 18%) changes value by $6.67, or about 13%. The model is moderately sensitive to gS because the growth premium is linear in (gS - gL). Doubling the spread between gS and gL doubles the premium.
Key Insight: The H-model is less sensitive to gS than a two-stage DDM because the H-model assumes linear decay rather than a sustained high-growth phase. The half-life (H) acts as a multiplier — a longer H amplifies the sensitivity to gS.
Exam Tip: Be ready to compute V0 under different gS assumptions and explain why the H-model is preferred when you expect a gradual (not abrupt) transition in growth.
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