Answer: any increase in the cost of equity must exactly offset the greater use of lower cost debt.

## Explanation According to Modigliani-Miller Proposition I without taxes, the value of a firm is independent of its capital structure. This means that changing the capital structure (mix of debt and equity) does not affect the total value of the firm. **Key points of MM Proposition I without taxes:** 1. **Capital structure irrelevance**: The value of a firm is determined solely by its real assets and the cash flows they generate, not by how those cash flows are divided between debt and equity holders. 2. **Perfect capital markets assumption**: The proposition assumes perfect capital markets with no taxes, no bankruptcy costs, no transaction costs, and symmetric information. 3. **Offsetting effects**: While debt is typically cheaper than equity, the cost of equity increases with leverage to exactly offset the benefit of using cheaper debt. **Analysis of the options:** - **Option A**: Incorrect. According to MM Proposition I without taxes, firm value **cannot** be created by changing capital structure. The value remains constant regardless of the debt-equity mix. - **Option B**: **Correct**. This statement accurately captures the essence of MM Proposition I. The increase in the cost of equity (due to increased financial risk) exactly offsets the benefit of using lower-cost debt, leaving the weighted average cost of capital (WACC) unchanged. - **Option C**: While this statement is true in practice (equity holders do demand higher returns as leverage increases), it doesn't fully capture the MM Proposition I insight. The key insight is that this increase **exactly offsets** the benefit of cheaper debt, making capital structure irrelevant for firm value. **Mathematical representation:** According to MM Proposition I without taxes: $$V_L = V_U$$ Where: - $V_L$ = Value of levered firm - $V_U$ = Value of unlevered firm And according to MM Proposition II without taxes: $$r_e = r_0 + \frac{D}{E}(r_0 - r_d)$$ Where: - $r_e$ = Cost of equity - $r_0$ = Cost of capital for unlevered firm - $r_d$ = Cost of debt - $D/E$ = Debt-to-equity ratio This shows that as leverage ($D/E$) increases, the cost of equity ($r_e$) increases linearly to maintain the same overall cost of capital.

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