The WACC for ABC is 9.85%, and the WACC for XYZ is approximately 9.855%.
Let's break down each part of this problem step by step:
owns $41,500 worth of XYZ's stock. To calculate the rate of return he is expecting, we need to find the dividend yield and the capital gains yield for XYZ. Since we are told that XYZ expects EBIT of $67,000 and we ignore taxes, the entire EBIT will be available to the shareholders.
1. Calculate the dividend for XYZ:
- Dividend = EBIT - Interest on debt
- Dividend = $67,000 - (7% of $340,000)
- Dividend = $67,000 - $23,800
- Dividend = $43,200
2. Calculate the dividend yield:
- Dividend Yield = Dividend / Stock Price
- Dividend Yield = $43,200 / $340,000
- Dividend Yield = 0.1271 or 12.71%
3. Calculate the capital gains yield (rate of return):
- Rate of Return = Dividend Yield + Capital Gains Yield
- Capital Gains Yield = Rate of Return - Dividend Yield
- Capital Gains Yield = Rate of Return - 12.71%
Rico's expected rate of return on XYZ's stock is a combination of the dividend yield and capital gains yield. You'll need to provide the rate of return for the answer.
b. To generate the same cash flows and rate of return by investing in ABC and using homemade leverage, Rico would need to create a similar capital structure as XYZ. In this case, Rico can use homemade leverage by borrowing an amount equal to XYZ's debt, which is 7% of $340,000. Then, he can invest the borrowed money in ABC's stock.
1. Borrowed amount = 7% of $340,000
- Borrowed amount = $23,800
2. Invest the borrowed amount in ABC's stock:
- ABC's stock = $680,000
- Rico borrows $23,800 and invests it in ABC's stock.
Now, Rico's investment in ABC is identical in terms of capital structure to XYZ. He can expect the same cash flows and rate of return as he would from XYZ.
c. To find the cost of equity for ABC and XYZ, we can use the dividend discount model (DDM):
Cost of Equity = Dividend / Stock Price
For ABC:
- Dividend for ABC = EBIT (since ABC is all-equity financed and we ignore taxes)
- Dividend for ABC = $67,000
- Stock Price for ABC = $680,000
Cost of Equity for ABC = $67,000 / $680,000 = 9.85%
For XYZ:
- Dividend for XYZ = $43,200 (calculated in part a)
- Stock Price for XYZ = $340,000
Cost of Equity for XYZ = $43,200 / $340,000 = 12.71% (calculated in part a)
d. To calculate the weighted average cost of capital (WACC) for ABC and XYZ, we need to consider their respective capital structures.
For ABC (all-equity financed), WACC = Cost of Equity (since there's no debt):
WACC for ABC = Cost of Equity = 9.85%
For XYZ (uses both stock and perpetual debt), we need to consider both equity and debt in the WACC calculation. The weight of equity and debt in XYZ's capital structure is as follows:
- Weight of Equity = Stock Price / (Stock Price + Debt) = $340,000 / ($340,000 + $340,000) = 0.5 or 50%
- Weight of Debt = Debt / (Stock Price + Debt) = $340,000 / ($340,000 + $340,000) = 0.5 or 50%
WACC for XYZ = (Weight of Equity * Cost of Equity) + (Weight of Debt * Cost of Debt)
Since Cost of Equity for XYZ is 12.71%, and the interest rate on its debt is 7%, we can calculate the WACC:
WACC for XYZ = (0.5 * 12.71%) + (0.5 * 7%) = 6.355% + 3.5% = 9.855%