First find the firm’s current net income — Declan Ross wants sell his business has debt and earns return ROE — Equity — 150 000

Declan Ross wants to sell his business. The firm has no debt and earns an 8% return (ROE) on equity of $150,000. 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 (8%) 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 12%?

SOLUTION

First find the firm’s current net income

ROE = Net Income / Equity .08 = Net Income / $150,000 Net Income = $12,000

A debt of D will reduce equity by D and reduce net income by .05D. Begin by evaluating the effect of borrowing $50,000.

Equity = $150,000 - $50,000 = $100,000 Net Income = $12,000 - .05D = $12,000 - .05($50,000) = $12,000 - $2,500 = $9,500 Then ROE = $9,500 / $100,000 = .095 = 9.5%

So borrowing $50,000 has raised ROE but not enough.

We try other values of D searching for a 12% return until we arrive at approximately $86,000 at which

Equity = $150,000 - $86,000 = $64,000 and Net Income = $12,000 - .05($86,000) = $7,700 So ROE = $7,700 / $64,000 = .1203 = 12.0%