a) To find the rate of return on operations, we need to use the formula for Return on Common Equity (ROCE), which is: ROCE = Return on Operations + (Return on Operations - After-tax net borrowing cost) * Financial Leverage Given that ROCE is 40%, Financial Leverage is 40% and After-tax net borrowing cost is 5%, we can rearrange the formula to solve for Return on Operations: Return on Operations = ROCE - (Return on Operations - After-tax net borrowing cost) * Financial Leverage Substituting the given values: 0.40 = Return on Operations - (Return on Operations - 0.05) * 0.40 Solving for Return on Operations, we get approximately 0.29 or 29%. b) If the firm repurchases $125 million of its stock and finances the repurchase with further borrowing at a 5% after-tax borrowing cost, the financial leverage of the firm will increase. This is because financial leverage is the ratio of the firm's debt to its equity, and by borrowing more money, the firm is increasing its debt. The effect on the firm's return on common equity will depend on the return on operations. If the return on operations remains the same, the increase in financial leverage will result in a higher return on common equity. This is because the firm is using more borrowed money to generate profits, which increases the return on the equity invested by the shareholders. However, this also means that the firm is taking on more risk, as it now has more debt to repay. If the return on operations were to decrease, the higher financial leverage could result in a lower return on common equity. ####