Last year Chart Corp. had sales of $300,000, operating costs of $265,000, and year-end assets of $200,000. The debt-to-total assets ratio was 25%, the interest rate on the debt was 10%, and the firm's tax rate was 35%. The new CFO wants to see how the ROE would have been affected if the firm had used a 60% debt ratio. Assume that sales and total assets would not be affected, and that the interest rate and tax rate would both remain constant. By how much would the ROE change in response to the change in the capital structure?
To calculate the change in Return on Equity (ROE) resulting from a change in capital structure, we need to compare the original ROE with the ROE under the new capital structure.
First, let's calculate the original ROE using the given information:
ROE = Net Income / Shareholders' Equity
We need to calculate the net income and shareholders' equity.
Net Income = Sales - Operating Costs - Interest Expense - Tax Expense
Interest Expense = Debt × Interest Rate
Tax Expense = Net Income × Tax Rate
Now, let's calculate the original ROE:
Original Debt = Total Assets × Debt-to-total assets ratio
= $200,000 × 0.25 (25%)
= $50,000
Original Interest Expense = Original Debt × Interest Rate
= $50,000 × 0.10 (10%)
= $5,000
Original Tax Expense = Net Income × Tax Rate
= (Sales - Operating Costs - Original Interest Expense) × Tax Rate
= ($300,000 - $265,000 - $5,000) × 0.35 (35%)
= $30,750
Original Net Income = Sales - Operating Costs - Original Interest Expense - Original Tax Expense
= $300,000 - $265,000 - $5,000 - $30,750
= $-9750 (Loss)
Original Shareholders' Equity = Total Assets - Original Debt
= $200,000 - $50,000
= $150,000
Original ROE = Original Net Income / Original Shareholders' Equity
= $-9,750 / $150,000
= -0.065 or -6.5% (Loss)
Now, let's calculate the ROE under the new capital structure with a 60% debt ratio:
New Debt = Total Assets × New Debt ratio
= $200,000 × 0.6 (60%)
= $120,000
New Interest Expense = New Debt × Interest Rate
= $120,000 × 0.10 (10%)
= $12,000
New Tax Expense = (Sales - Operating Costs - New Interest Expense) × Tax Rate
= ($300,000 - $265,000 - $12,000) × 0.35 (35%)
= $23,625
New Net Income = Sales - Operating Costs - New Interest Expense - New Tax Expense
= $300,000 - $265,000 - $12,000 - $23,625
= $-675
New Shareholders' Equity = Total Assets - New Debt
= $200,000 - $120,000
= $80,000
New ROE = New Net Income / New Shareholders' Equity
= $-675 / $80,000
= -0.0084 or -0.84% (Loss)
The change in ROE resulting from the change in the capital structure is calculated as follows:
Change in ROE = New ROE - Original ROE
= -0.84% - (-6.5%)
= 5.66%
Therefore, the ROE would change by 5.66% in response to the change in the capital structure.