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Declan Ross wants to sell his business. The firm has no debt and earns an 7% return (ROE) on equity of $160,000. The business can borrow at an after-tax rate of 5%. A consultant has advised that the business will be worth more if its financial statements show a higher return on equity (ROE = net income/equity). Unfortunately an increase in profitability isn't feasible. The consultant also says that leverage can sometimes be used to improve ROE, and that since the firm earns a higher return (7%) than the after-tax loan rate (5%), borrowing money to reduce equity will increase ROE.
Problem 1: How much will Declan have to borrow to raise his firm's ROE to 11%? (Hint: First calculate net income using the definition of ROE. Then assume Declan borrows $60,000, reducing equity by the same amount. Recalculate net income and ROE. Repeat with different debt amounts until ROE is close to 11%.)
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