Answer: increases

## Explanation According to Modigliani-Miller Proposition II without taxes, the cost of equity increases as the debt-to-equity ratio increases. This relationship is expressed by the formula: $$r_e = r_0 + (r_0 - r_d) \times \frac{D}{E}$$ Where: - $r_e$ = cost of equity - $r_0$ = unlevered cost of equity (cost of equity for an all-equity firm) - $r_d$ = cost of debt - $D/E$ = debt-to-equity ratio **Key points:** 1. As D/E increases, the term $(r_0 - r_d) \times \frac{D}{E}$ increases (assuming $r_0 > r_d$, which is typically true) 2. This means $r_e$ increases linearly with D/E 3. The increase in cost of equity exactly offsets the benefit of using cheaper debt, keeping the weighted average cost of capital (WACC) constant **Why this happens:** - As a firm takes on more debt, equity becomes riskier because debt holders have priority claim on assets and cash flows - Equity investors require higher returns to compensate for this increased financial risk - In a world without taxes, the benefit of cheaper debt is exactly offset by the higher cost of equity Therefore, when D/E ratio increases, the cost of equity increases.

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