How sensitive is the H-model to changes in the initial high-growth rate assumption?

Question

AcadiFi · Accepted Answer

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.

```mermaid
graph LR
    subgraph "Sensitivity Analysis"
    A["gS = 18%"] -->|"V0 = $54.67"| D["High Valuation"]
    B["gS = 14%"] -->|"V0 = $48.00"| E["Mid Valuation"]
    C["gS = 10%"] -->|"V0 = $41.33"| F["Lower Valuation"]
    end
    style A fill:#ef4444,color:#fff
    style B fill:#f59e0b,color:#000
    style C fill:#10b981,color:#fff
```

**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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How sensitive is the H-model to changes in the initial high-growth rate assumption?

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Practice Questions

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)