Homemade Leverage and WACC ABC Co. and XYZ Co. are identical firms in all respects except for their capital structure. ABC is all equity financed with $540,000 in stock. XYZ uses both stock and perpetual debt; its stock is worth $270,000 and the interest rate on its debt is 8 percent. Both firms expect EBIT to be $61,000. Ignore taxes.
a. Richard owns $30,000 worth of XYZ’s stock. What rate of return is he expecting?
b. Show how Richard 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? What principle have you illustrated?
The correct answer and explanation is :
Solution:
(a) Richard’s Expected Rate of Return on XYZ Stock
The expected return on equity (RsR_s) for XYZ can be calculated as: Rs=EBIT−InterestEquity ValueR_s = \frac{\text{EBIT} – \text{Interest}}{\text{Equity Value}}
Interest Expense for XYZ: Debt=Total Value−Equity=540,000−270,000=270,000\text{Debt} = \text{Total Value} – \text{Equity} = 540,000 – 270,000 = 270,000 Interest Expense=270,000×0.08=21,600\text{Interest Expense} = 270,000 \times 0.08 = 21,600 Rs=61,000−21,600270,000=39,400270,000=0.1459 or 14.59%R_s = \frac{61,000 – 21,600}{270,000} = \frac{39,400}{270,000} = 0.1459 \text{ or } 14.59\%
Since Richard owns $30,000 of XYZ stock, his expected return is also 14.59%.
(b) Homemade Leverage using ABC
To replicate XYZ’s returns, Richard should borrow funds to create the same debt-equity ratio. Since XYZ has 50% debt, he borrows 50% of his investment ($15,000 at 8%) and invests $30,000 in ABC stock.
- Borrowing cost: 15,000×0.08=1,20015,000 \times 0.08 = 1,200
- Expected return from ABC stock: 61,000540,000×30,000=3,388.89\frac{61,000}{540,000} \times 30,000 = 3,388.89
- Net return: 3,388.89−1,200=2,188.893,388.89 – 1,200 = 2,188.89
- Effective return: 2,188.8915,000=14.59%\frac{2,188.89}{15,000} = 14.59\%
Thus, Richard replicates XYZ’s cash flow and return using ABC and personal borrowing.
(c) Cost of Equity for ABC and XYZ
- ABC: Rs=61,000540,000=11.30%R_s = \frac{61,000}{540,000} = 11.30\%
- XYZ: (Calculated earlier) 14.59%.
(d) WACC for ABC and XYZ
- ABC: (Since it’s all equity) WACC=Rs=11.30%WACC = R_s = 11.30\%
- XYZ: WACC=(270,000540,000×14.59%)+(270,000540,000×8%)WACC = \left( \frac{270,000}{540,000} \times 14.59\% \right) + \left( \frac{270,000}{540,000} \times 8\% \right) =7.295%+4.00%=11.30%= 7.295\% + 4.00\% = 11.30\%
Thus, WACC remains the same for both firms, illustrating Modigliani-Miller Proposition I: In a no-tax world, capital structure does not affect firm value or WACC.