Module II· Cost of Equity & CAPMIntermediate
Question
How does beta change when a company increases its leverage?
Answer
Mechanics
The Hamada formula links levered and unlevered beta:
```
β_L = β_U × (1 + (1 − t) × D/E)
```
Example — beta sensitivity by capital structure
Inputs:
- β_U (asset beta): 0.8
- Tax rate t: 30%
Calculation:
```
D/E 0.5: β_L = 0.8 × (1 + 0.7 × 0.5) = 0.8 × 1.35 = 1.08
D/E 1.0: β_L = 0.8 × (1 + 0.7 × 1.0) = 0.8 × 1.70 = 1.36
D/E 2.0 (typical LBO): β_L = 0.8 × (1 + 0.7 × 2.0) = 0.8 × 2.40 = 1.92
```
Observation
Higher leverage raises equity risk more than proportionally — in an LBO setup, β_L is typically 1.5–2.0+.