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.