Last year Charter 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) in response to a change in capital structure, you need to follow these steps:
Step 1: Calculate the current and new debt levels.
To calculate the current debt level, multiply the total assets by the current debt-to-total-assets ratio:
Current debt = Debt-to-total-assets ratio * Current total assets
Given that the debt-to-total-assets ratio is 25% and the total assets are $200,000, the current debt can be calculated as follows:
Current debt = 0.25 * $200,000 = $50,000
To calculate the new debt level based on a 60% debt ratio, multiply the total assets by the new debt-to-total-assets ratio:
New debt = Debt-to-total-assets ratio * Current total assets
Given that the new debt-to-total-assets ratio is 60% and the total assets remain the same at $200,000, the new debt can be calculated as follows:
New debt = 0.6 * $200,000 = $120,000
Step 2: Calculate the current and new interest expense.
To calculate the current interest expense, multiply the current debt by the interest rate:
Current interest expense = Current debt * Interest rate
Given that the interest rate on the current debt is 10% and the current debt is $50,000, the current interest expense can be calculated as follows:
Current interest expense = $50,000 * 0.10 = $5,000
To calculate the new interest expense based on the new debt, multiply the new debt by the same interest rate:
New interest expense = New debt * Interest rate
Given that the interest rate remains constant at 10% and the new debt is $120,000, the new interest expense can be calculated as follows:
New interest expense = $120,000 * 0.10 = $12,000
Step 3: Calculate the current and new net income.
To calculate the current net income, subtract the current operating costs and the current interest expense from the sales revenue:
Current net income = Sales revenue - Operating costs - Current interest expense
Given that the sales revenue is $300,000, the operating costs are $265,000, and the current interest expense is $5,000, the current net income can be calculated as follows:
Current net income = $300,000 - $265,000 - $5,000 = $30,000
To calculate the new net income, subtract the same operating costs and the new interest expense from the sales revenue:
New net income = Sales revenue - Operating costs - New interest expense
Given that the new interest expense is $12,000 and all other values remain the same, the new net income can be calculated as follows:
New net income = $300,000 - $265,000 - $12,000 = $23,000
Step 4: Calculate the current and new equity.
To calculate the current equity, subtract the current debt from the current assets:
Current equity = Current total assets - Current debt
Given that the current total assets are $200,000 and the current debt is $50,000, the current equity can be calculated as follows:
Current equity = $200,000 - $50,000 = $150,000
To calculate the new equity, subtract the new debt from the current assets:
New equity = Current total assets - New debt
Given that the current total assets remain the same at $200,000 and the new debt is $120,000, the new equity can be calculated as follows:
New equity = $200,000 - $120,000 = $80,000
Step 5: Calculate the current and new ROE.
To calculate the current ROE, divide the current net income by the current equity and multiply by 100 to express it as a percentage:
Current ROE = (Current net income / Current equity) * 100
Given that the current net income is $30,000 and the current equity is $150,000, the current ROE can be calculated as follows:
Current ROE = ($30,000 / $150,000) * 100 = 20%
To calculate the new ROE, divide the new net income by the new equity and multiply by 100:
New ROE = (New net income / New equity) * 100
Given that the new net income is $23,000 and the new equity is $80,000, the new ROE can be calculated as follows:
New ROE = ($23,000 / $80,000) * 100 = 28.75%
Step 6: Calculate the change in ROE.
To calculate the change in ROE, subtract the current ROE from the new ROE:
Change in ROE = New ROE - Current ROE
Given that the new ROE is 28.75% and the current ROE is 20%, the change in ROE can be calculated as follows:
Change in ROE = 28.75% - 20% = 8.75%
Therefore, the ROE would change by 8.75% in response to the change in the capital structure.