Final answer:
Modigliani and Miller's no-tax model assumes no personal tax on interest or financial distress costs, implying no optimal debt-equity ratio. In their corporate tax model, they assume corporate taxes exist but personal tax on interest and financial distress costs do not, suggesting an optimal debt-equity ratio would be infinitely high.
Step-by-step explanation:
When considering the value of a levered firm in a world with personal taxes on interest income but no taxes on equity distributions, Modigliani and Miller made specific assumptions in their models. In their no-tax model, they assumed that both the personal tax rate on interest income, tint, and the present value (PV) of financial distress costs are equal to zero. These assumptions imply that there would be no optimal debt-equity ratio since the value of a levered firm would be the same as an unlevered firm, as debt would neither provide a tax shield benefit nor have bankruptcy cost implications.
In their model with corporate taxes, Modigliani and Miller assumed that the corporate tax rate, t, is positive, providing a tax shield benefit to the firm, while keeping the personal tax rate tint and the PV of financial distress costs at zero. This leads to the implication that in a world of corporate taxes only, the optimal debt-equity ratio would be as high as possible, as debt would provide a tax shield while incurring no personal tax or bankruptcy costs.