Final answer:
According to Modigliani and Miller's theorem with taxes, a firm will minimize its cost of capital and maximize value by using debt financing, as it provides a tax shield by reducing taxable income. This contrasts with equity financing, which dilutes control and creates shareholder obligations.
Step-by-step explanation:
When looking at how a firm subject to a positive corporate tax rate should approach its capital structure with no other market imperfections, according to Modigliani and Miller's (M&M) theorem with taxes, the correct statement among the options provided is b) The firm will minimize the cost of capital by using only debt financing. M&M’s proposition with tax implies that debt financing provides a tax shield, since interest payments are tax-deductible, thus reducing the taxable income and corporate taxes paid by the firm. This increases the overall value of the firm. Furthermore, issuing equity involves selling company ownership, which can dilute control and introduce new obligations to shareholders. Meanwhile, borrowing through debt enables a firm to maintain control but comes with the obligation of making scheduled interest payments, regardless of income levels.