Your firm has $500 million of investor-supplied capital, its return on investors' capital (ROIC) is 15%, and it currently has no debt in its capital structure (i.e., wd = 0). The CFO is contemplating a recapitalization where it would issue debt at an after-tax cost of 10% and use the proceeds to buy back some of its common stock, such that the percentage of common equity in the capital structure (wc) is 1 - wd. If the company goes ahead with the recapitalization, its operating income, the size of the firm (i.e., total assets), total investor-supplied capital, and tax rate would remain unchanged. Which of the following is most likely to occur as a result of the recapitalization? The ROA would increase. The ROA would remain unchanged. The return on investors' capital would decline. The return on investors' capital would increase. The ROE would increase.

Return on Assets (ROA) is calculated as Net Income divided by Total Assets. In this scenario, since the operating income and total assets remain unchanged, introducing debt into the capital structure will not alter the ROA. Therefore, the ROA would remain unchanged.

Return on Investors' Capital (ROIC) is similar to ROA but focuses on the capital invested by shareholders and creditors. Since the firm's operating income and total investor-supplied capital remain unchanged and the firm will replace some of this investor-supplied capital with cheaper debt, the returns to the remaining investors' capital would go up. Therefore, the ROIC would increase.

The cost of debt is lower than the current ROIC (10% vs. 15%), so using debt to replace equity will reduce the weighted average cost of capital (WACC). The saving on the cost of capital could then translate into a higher return on the remaining equity capital.

Return on Equity (ROE) measures the profitability relative to shareholders' equity. Using debt to buy back some of its common stock means that the shareholder's equity will be reduced. Since the net income remains the same because the operating income is not changing, and the equity decreases, the ROE would increase because the same amount of income is being generated with less equity.

In conclusion, as a result of the recapitalization, the most likely outcomes are that the ROA would remain unchanged, the return on investors' capital would increase, and the ROE would increase.

Extra: When discussing recapitalization, it’s important to understand a few key concepts:

1. **Capital Structure:** This is the mix of debt and equity that a company uses to finance its operations. The mix can have implications for risk and return – generally, more debt means more risk, but also potential for more return on equity.

2. **Debt vs Equity Financing:** Debt is borrowed money that a company has to pay back with interest. Equity involves selling a stake in the company. Debt payments are obligations that must be met, while equity does not have to be repaid and dividends are paid at the discretion of the company.

3. **Return on Assets (ROA):** This is a measure of how effectively a company uses its assets to generate net income. It's calculated by dividing net income by total assets.

4. **Return on Investors' Capital (ROIC):** Similar to ROA, this measures how well a company generates net income from its total capital, which includes both debt and equity.

5. **Return on Equity (ROE):** This measures profitability from the shareholders' perspective, calculating how much net income is generated for each dollar of shareholders' equity.

6. **Cost of Debt:** This is the effective rate that a company pays on its borrowed funds. The after-tax cost of debt is usually considered because interest payments are tax-deductible, reducing the effective rate.

7. **Weighted Average Cost of Capital (WACC):** This measures a firm's cost of capital from all sources, including common shares, preferred shares, bonds, and other forms of debt. It weights each type of capital by its proportion in the firm’s structure.

In finance, a general principle is that cost savings or improvements in efficiency should benefit the company's return metrics, assuming the overall operating performance doesn't change negatively. When a company uses debt responsibly and the cost of debt is less than the return generated on that debt, it can have a leveraging effect, improving returns for equity holders. However, it's also important to consider the risks of leverage, as increased debt also means increased fixed financial obligations, which can make a company more susceptible to economic downturns.