Explanation
According to Modigliani and Miller's Proposition I without taxes, the value of a firm is independent of its capital structure. This means that changing the proportion of debt in the capital structure does not affect the overall value of the company.
Key points of MM Proposition I (without taxes):
- Capital structure irrelevance: The market value of a firm is determined by its operating income and the risk of its underlying assets, not by how it is financed.
- WACC remains constant: As a firm increases its debt, the cost of equity rises exactly enough to offset the benefit of using cheaper debt, keeping the weighted average cost of capital (WACC) unchanged.
- No arbitrage opportunity: Investors can create homemade leverage to achieve any desired capital structure, so firm-level leverage doesn't create value.
Why the other options are incorrect:
- Option B (a lower cost of equity): Actually, according to MM Proposition II without taxes, as debt increases, the cost of equity rises linearly with the debt-to-equity ratio due to increased financial risk.
- Option C (a greater company value): Without taxes, there is no tax shield benefit from debt, so company value remains unchanged regardless of capital structure.
Mathematical representation:
- Proposition I: Vᴜ = Vʟ (Value of unlevered firm = Value of levered firm)
- Proposition II: rᴇ = r₀ + (r₀ - rᴅ) × (D/E)
Where: rᴇ = cost of equity, r₀ = cost of capital for unlevered firm, rᴅ = cost of debt, D/E = debt-to-equity ratio
Therefore, the correct answer is A - the same WACC.
