Which of the following is a false statement about the theoretical work of Modigliani and Miller $($MM$)?$

Group of answer choices

According to MM Proposition II$,$ the impact of leverage on the required return on equity is stronger when taxes are excluded from the formula

In a world with taxes, Modigliani and Miller predict that an increase in a firm$$s debt$-$to$-$equity ratio should cause its WACC to fall

Based on the theoretical predictions of Modigliani and Miller, replacing equity with debt should cause a firm$$s stock price to rise when tax effects are considered

Modigliani and Miller argue that in the absence of corporate taxation, capital structure decisions should have no impact on a firm$$s total value, WACC, or stock price

According to MM Proposition I, a reduction in a company$$s debt$-$to$-$equity ratio will cause the value of the firm to rise in a world with corporate taxes