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.