The Hamada formula is the fundamental tool for adjusting the systematic risk (the Beta – ß) of a company according to its financial structure. It makes it possible to neutralize the impact of debt to isolate pure economic risk, or, on the contrary, to integrate the impact of new debt on the risk perceived by shareholders.
Here is how this mechanism of “deleveraging” and “re-leveraging” works:

1. The principle: Distinguish between economic and financial risk

The observed Beta of a listed company (${\mathrm{ß}}_{\mathrm{L}}$ for Levered Beta) reflects two types of risks borne by the shareholder:
Economic risk (Business Risk): Linked to the company’s activity (sector, fixed costs, market). This is the ${\mathrm{ß}}_{\mathrm{U}}$ (Unlevered Beta).
Financial risk: Linked to debt. Debt makes the flows back to shareholders more volatile (leverage).
Hamada’s formula establishes the mathematical link:

${\mathrm{ß}}_{\mathrm{L}}={\mathrm{ß}}_{\mathrm{U}}\times [1+(1–\mathrm{T})\mathrm{D}/\mathrm{EQ}]$

T: Corporate tax rate (debt provides a tax shield).
D/EQ: Debt ratio (Net debt / Equity).

2. Step 1: Deleverage the Beta (Calculation of ${\mathrm{ß}}_{\mathrm{U}}$)

This step is crucial for comparing companies with different financial structures or for valuing an unlisted company. Since the ${\mathrm{ß}}_{\mathrm{L}}$ observed in the market is “polluted” by the specific debt structure of the company, we use the inverse formula to find the Beta of the economic asset alone:

${\mathbf{ß}}_{\mathbf{U}}\mathbf{=}{\mathbf{ß}}_{\mathbf{L}}\mathbf{/}\mathbf{[}\mathbf{1}\mathbf{+}\mathbf{(}\mathbf{1}\mathbf{–}\mathbf{T}\mathbf{)}\mathbf{\times }\mathbf{D}\mathbf{/}\mathit{E}\mathit{Q}\mathbf{]}$

Example: If Corporation A has an ${\mathrm{ß}}_{\mathrm{L}}$ of 1.5, a D/EQ ratio of 0.8 and a tax rate of 25%:

${\mathrm{ß}}_{\mathrm{U}}=1.5/[1+(1–0.25)\times 0.8]=1.5/1.6=0.94$

This figure of 0.94 represents the intrinsic risk of Company A’s industrial activity, regardless of how it is financed.

3. Step 2: Re-leverage the Beta (Calculation of the target ${\mathrm{ß}}_{\mathrm{U}}$)

Once a representative ${\mathrm{ß}}_{\mathrm{U}}$ is available (often the average of the ${\mathrm{ß}}_{\mathrm{U}}$ of a sample of comparable companies), the relevant beta for the company or project you want to evaluate can be calculated. The beta is “re-leveraged” using the target financial structure (the projected D/EQ ratio) of the company to be evaluated.
Example: If we estimate that the ${\mathrm{ß}}_{\mathrm{U}}$ of the sector is 0.94 and that our target company will have a D/EQ ratio of 0.5 (with T=25%):
target ${\mathrm{ß}}_{\mathrm{L}}=0.94\times [1+(1–0.25)\times 0.5] =0.94\times 1.375=1.29$= 0.94 [1 + (1 – 0.25) 0.5] = 0.94 1.375 = 1.29

4. Why is it important?

This process determines the appropriate Cost of Equity (${\mathrm{K}}_{\mathrm{E}}$) to calculate the WACC (Weighted Average Cost of Capital).

• The more the company takes on debt, the more its D/EQ ratio increases.
• Mechanically, via Hamada’s formula, its ${\mathrm{ß}}_{\mathrm{L}}$ increases.
• As a result, shareholders perceive a higher risk and demand higher profitability.

This explains why debt does not reduce the cost of capital indefinitely: the savings made on the cost of debt (cheaper) are largely cancelled out by the increase in the shareholder profitability requirement due to the increase in Beta.
It is shown that the only financial advantage of debt over equity lies in the tax deductibility of financial expenses (Modigliani and Miller).