Cost of Equity Estimation: Hamada's Equation, Unlevered Peer Betas & Private Company Risk Premia

## Deleveraging Betas: The Hamada Equation

The Capital Asset Pricing Model (CAPM) estimates the Cost of Equity ($K_e$):

$$K_e = R_f + \beta_L \times (R_m - R_f) + \text{Size Premium} + \text{Specific Company Risk}$$

Because private middle-market firms lack traded equity shares, analysts calculate $\beta_L$ by identifying comparable public peers, stripping out their capital structure debt, and relevering the asset beta.

### 1. The Hamada Mathematical Formulations

**Step 1: Unlever Peer Public Betas**:
$$\beta_U = \frac{\beta_L}{1 + (1 - T) \times (D / E)}$$

**Step 2: Relever at Target Private Firm Capital Structure**:
$$\beta_{L,\text{target}} = \beta_U \times \left[ 1 + (1 - T_{\text{target}}) \times \left( \frac{D_{\text{target}}}{E_{\text{target}}} \right) \right]$$