How does the H-model work for valuation, and how is it different from a two-stage DDM?

Question

AcadiFi · Accepted Answer

The H-model is a simplified approximation of a two-stage DDM where the growth rate declines linearly from a high rate to a long-term stable rate, rather than dropping abruptly.

**The H-Model Formula:**

$$
V_0 = \frac{D_0 	imes (1 + g_L)}{r - g_L} + \frac{D_0 	imes H 	imes (g_S - g_L)}{r - g_L}
$$

Where:
- **H** = half-life of the high-growth period (years of supernormal growth / 2)
- **gS** = initial short-term growth rate
- **gL** = long-term sustainable growth rate
- **r** = required rate of return

**Intuition:** The first term is the standard GGM value (what the stock would be worth at stable growth). The second term adds the extra value from the above-normal growth during the transition period.

**Worked Example: Solara Consumer Brands**

- D0 = $2.40
- Current growth rate (gS) = 16%
- Long-term growth rate (gL) = 4%
- High-growth period = 8 years, so H = 4
- Required return (r) = 11%

**Step 1: Stable Growth Value**
$$\frac{2.40 	imes 1.04}{0.11 - 0.04} = \frac{2.496}{0.07} = \$35.66$$

**Step 2: Extra Growth Premium**
$$\frac{2.40 	imes 4 	imes (0.16 - 0.04)}{0.11 - 0.04} = \frac{2.40 	imes 4 	imes 0.12}{0.07} = \frac{1.152}{0.07} = \$16.46$$

**V0 = $35.66 + $16.46 = $52.11**

```mermaid
flowchart TD
    V["V0 = $52.11"] --> SG["Stable Growth Value
$35.66"]
    V --> EP["Extra Growth Premium
$16.46"]
    SG --> SGF["D0 × (1+gL) / (r-gL)
GGM at stable growth"]
    EP --> EPF["D0 × H × (gS-gL) / (r-gL)
Premium for above-normal growth"]
    style V fill:#c9a84c,color:#0a0a0f,stroke:#c9a84c
    style SG fill:#1a1a2e,color:#fff,stroke:#c9a84c
    style EP fill:#1a1a2e,color:#fff,stroke:#c9a84c
```

**H-Model vs. Two-Stage DDM:**

| Feature | Two-Stage DDM | H-Model |
|---|---|---|
| Growth transition | Abrupt drop | Linear decline |
| Complexity | Higher (discount each dividend) | Lower (closed-form) |
| Realism | Less realistic | More realistic for most firms |
| Best for | Patent expiries, regulatory changes | Natural competitive fade |

**Key Limitations:**
- The H-model is an approximation — it assumes a perfectly linear decline
- It doesn't handle cases where growth might increase before declining
- The formula assumes dividends are paid (doesn't work for non-dividend payers)

**Exam Tip:** If the CFA Level II vignette describes a company whose competitive advantage is gradually eroding, the H-model is likely the intended approach. If growth drops at a specific point (e.g., patent expiry in 3 years), use the standard two-stage DDM.

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How does the H-model work for valuation, and how is it different from a two-stage DDM?

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