Question

Declan Ross wants to sell his business. The firm has no debt and earns an 9% return (ROE) on equity of $110,000. 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 (9%) than the after-tax loan rate (5%), borrowing money to reduce equity will increase ROE. 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 $30,000, reducing equity by the same amount. Recalculate net income and ROE. Repeat with different debt amounts until ROE is close to 11%.) Round the answer to the nearest thousand dollars.

Answer 1

Return on Equity (ROE) =  Net income / Shareholders Equity

9% = Net income / $110,000

Net income = 9% * $110,000 = $9,900

As asked in the question ROE needs to raised to be 11% keeping the Net income constant.

Currently, Total Capital in the Declan Ross which will remain constant = $110,000 (Equity)

Now, assume Declan borrows $30,000

A debt of $30,000 will reduce equity by $30,000 and reduce net income by 0.05 * $30,000 (Interest Payment needed to be done) taking into consideration after-tax rate of 5%.

Then, Equity + Debt = $110,000

New Equity Capital = $110,000 - $30,000 = $80,000

Net Income = Old Net Income - Interest Expenses due to new Debt

Net Income = $9,900 - (0.05 * $30,000) = $9,900 - $1,500 = $8,400

New ROE = Net income / New Equity Capital = $8,400 / $80,000 =10.5%

but we need ROE to be 11%.

11% = Net income - 0.05 * (New Debt) / (Earlier Equity - New Debt) [Denominator gives the value of New Equity Capital ]

11% = $9,900 - 0.05 D / ($110,000 - D)

11% * ($110,000 - D) = $9,900 - 0.05 D

$12100 - 0.11D = $9,900 - 0.05 D

$12100 - $9,900 = 0.11D - 0.05 D

D = $2200 / 0.06 = 36666.666 = $37,000

ROE = Net Income / New Equity Capital = ($9,900 - 0.05 * $37,000) / ( $110,000 - $37,000)

ROE = ($9,900 - $1,850) / $73,000 = $8050/$73,000 = 11.027% =11.03%

Declan have to borrow to raise $37,000 for his firm’s to make ROE to 11%.