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Answer: Leverage = 2.6 and ROE = 17.0%.
## Calculation Explanation **Initial Situation:** - Assets = $20.0 million - Debt = $10.0 million - Equity = Assets - Debt = $20.0M - $10.0M = $10.0 million - Leverage = Assets/Equity = $20.0M/$10.0M = 2.0 - ROA = 9.0% - Cost of debt = 4.0% - ROE = 14.0% (given) **After Additional Borrowing:** - Additional debt = $6.0 million - New debt = $10.0M + $6.0M = $16.0 million - Assets increase by $6.0 million (since borrowed money is invested) - New assets = $20.0M + $6.0M = $26.0 million - New equity remains $10.0 million (no new equity issued) **New Leverage:** - Leverage = Assets/Equity = $26.0M/$10.0M = 2.6 **New ROE Calculation:** - Operating income = Assets × ROA = $26.0M × 9.0% = $2.34 million - Interest expense = Debt × Cost of debt = $16.0M × 4.0% = $0.64 million - Net income = Operating income - Interest expense = $2.34M - $0.64M = $1.70 million - New ROE = Net income/Equity = $1.70M/$10.0M = 17.0% Therefore, the correct answer is **Leverage = 2.6 and ROE = 17.0%**.
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Suppose a firm with a simple capital structure has assets of $20.0 million and debt of $10.0 million. Return on assets (ROA) is 9.0% and cost of debt is 4.0%, such that the firm's leverage is 2.0 and its return on equity (ROE) is 14.0%. If the firm borrows an additional $6.0 million at the same cost of 4.0%, and asset returns are fixed, what is the firm's new leverage and return on equity (ROE)?
A
Leverage = 1.7 and ROE = 13.3%.
B
Leverage = 2.0 and ROE = 15.7%.
C
Leverage = 2.3 and ROE = 23.5%.
D
Leverage = 2.6 and ROE = 17.0%.