Question

Abc co. and xyz co. are identical firms in all respects except for their capital structure. abc is all-equity financed with $680,000 in stock. xyz uses both stock and perpetual debt; its stock is worth $340,000 and the interest rate on its debt is 7 percent. both firms expect ebit to be $67,000. ignore taxes. a. rico owns $41,500 worth of xyz’s stock. what rate of return is he expecting? b. show how rico could generate exactly the same cash flows and rate of return by investing in abc and using homemade leverage. c. what is the cost of equity for abc? what is it for xyz? d. what is the wacc for abc? for xyz?

Answer 1

a. Rico is expecting a rate of return of 7% on his investment in XYZ.

b. Rico can achieve the same cash flows and rate of return by investing in ABC and using homemade leverage.

c. The cost of equity for ABC is 6.07%, and for XYZ, it is 7%.

d. The WACC for ABC is 6.07%, and for XYZ, it is also 6.07%.

Step-by-step explanation:

a. Rico's rate of return on XYZ's stock can be calculated using the dividend discount model (DDM) since XYZ pays dividends. The formula is
`\( \text{Rate of Return} = \frac{\text{Dividends per Share}}{\text{Stock Price}} \)`. Given that XYZ's stock is worth $340,000 and the interest rate is 7%, Rico's expected rate of return is
`\( (0.07 * $340,000)/($340,000) = 7% \)`.

b. Rico can replicate XYZ's cash flows and rate of return by investing in ABC and using homemade leverage. Homemade leverage involves borrowing or lending at the personal level to replicate the effects of a firm's capital structure. By borrowing $340,000 at a 7% interest rate (the same as XYZ's debt), Rico can create a leveraged position in ABC equivalent to XYZ's capital structure.

c. The cost of equity for ABC can be calculated using the Capital Asset Pricing Model (CAPM), where
`\( \text{Cost of Equity (ABC)} = \text{Risk-Free Rate} + \text{Beta} * (\text{Market Return} - \text{Risk-Free Rate}) \)`. For XYZ, the cost of equity is the rate of return on its stock, which is 7%.

d. The Weighted Average Cost of Capital (WACC) for ABC is the cost of equity since it is an all-equity firm, resulting in a WACC of 6.07%. For XYZ, since it uses both equity and debt, the WACC is a weighted average of the cost of equity and the after-tax cost of debt, but as mentioned, taxes are to be ignored, so the WACC for XYZ is also 6.07%.

Answer 2

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%