Question

ABC Company and XYZ Company are identical firms in all respects except for their capital structure. ABC is all-equity financed with $550,000 in stock. XYZ uses both stock and perpetual debt; its stock is worth $275,000 and the interest rate on its debt is 10 percent. Both firms expect EBIT to be $59,000. Ignore taxes.

a. Rico owns $33,000 worth of XYZ’s stock. What rate of return is he expecting? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. Suppose Rico invests in ABC Company and uses homemade leverage to match his cash flow in part (a). Calculate his total cash flow and rate of return. (Do not round intermediate calculations and enter your return answer as a percent rounded to 2 decimal places, e.g., 32.16.)
c. What is the cost of equity for ABC and XYZ? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
d. What is the WACC for ABC and XYZ? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a. Rico's rate of return on XYZ is 166.67%. b. Rico's rate of return on ABC using homemade leverage is also 166.67%. c. The cost of equity for ABC is 0% and for XYZ is 10%. d. The WACC for ABC is 0% and for XYZ is 10%.

Step-by-step explanation:

a. To calculate Rico's rate of return, we need to find the total cash flow he expects from XYZ, which includes the dividends received from the stock and the interest paid on the debt. The dividends can be calculated as the stock value multiplied by the expected return on equity: $275,000 * 0.10 = $27,500. The interest paid on the debt can be calculated as the debt value multiplied by the interest rate: $275,000 * 0.10 = $27,500. The total cash flow is the sum of these two amounts: $27,500 + $27,500 = $55,000. The rate of return can be calculated as the total cash flow divided by the initial investment: $55,000 / $33,000 = 166.67%.

b. If Rico invests in ABC Company and uses homemade leverage to match his cash flow from XYZ, he would need to borrow an amount equal to the initial investment in XYZ, which is $33,000. The total cash flow from ABC can be calculated as the expected return on equity multiplied by the stock value: $550,000 * 0.10 = $55,000. The rate of return can be calculated as the total cash flow divided by the initial investment: $55,000 / $33,000 = 166.67%.

c. The cost of equity for ABC can be calculated using the dividend discount model: Cost of Equity = Dividends / Stock Price. In this case, the dividends are zero because ABC does not have any debt, and the stock price is $550,000. Therefore, the cost of equity for ABC is 0 / $550,000 = 0%. The cost of equity for XYZ can be calculated as the expected return on equity, which is 10%.

d. The weighted average cost of capital (WACC) is calculated as the weighted average of the cost of equity and the cost of debt, using the proportions of equity and debt in the capital structure. In the case of ABC, since it is all-equity financed, the WACC is equal to the cost of equity, which is 0%. In the case of XYZ, the proportions of equity and debt can be calculated as the stock value divided by the total capital value and the debt value divided by the total capital value, respectively. The total capital value is the sum of the stock value and the debt value: $275,000 + $275,000 = $550,000. Therefore, the proportions of equity and debt are: Equity Proportion = $275,000 / $550,000 = 0.5 and Debt Proportion = $275,000 / $550,000 = 0.5. The WACC can then be calculated as the weighted average of the cost of equity and the cost of debt, using the proportions of equity and debt: WACC = (0.5 * 10%) + (0.5 * 10%) = 10%.