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?
Well, my financial friend, let's crunch some numbers to find out the answer.
First, let's calculate the ROE (Return on Equity) using the current capital structure. ROE is equal to the net income divided by total equity.
Net income can be found by subtracting operating costs and interest expense from sales and then multiplying it by (1 - tax rate):
Net income = (Sales - Operating costs - Interest expense) * (1 - Tax rate)
= ($300,000 - $265,000 - (0.10 * 0.25 * $200,000)) * (1 - 0.35)
= ($300,000 - $265,000 - $5,000) * 0.65
= $30,000
Total equity is calculated as the difference between total assets and total debt:
Total equity = Total assets - Total debt
= $200,000 - (0.25 * $200,000)
= $200,000 - $50,000
= $150,000
ROE = Net income / Total equity
= $30,000 / $150,000
= 0.2 or 20%
Now, let's calculate the new ROE using a 60% debt ratio. Since total assets and sales remain the same, the only change will be in the total debt and interest expense.
Total debt under the new capital structure would be:
Total debt = 0.6 * $200,000
= $120,000
Interest expense would be:
Interest expense = Interest rate * Debt
= 0.10 * $120,000
= $12,000
Net income would remain the same, as sales and operating costs are unchanged.
Total equity under the new capital structure would be:
Total equity = Total assets - Total debt
= $200,000 - $120,000
= $80,000
ROE = Net income / Total equity
= $30,000 / $80,000
= 0.375 or 37.5%
To find the change in ROE, subtract the new ROE from the old ROE:
Change in ROE = New ROE - Old ROE
= 37.5% - 20%
= 17.5%
Therefore, the ROE would increase by 17.5% in response to the change in the capital structure.
To determine the change in return on equity (ROE) in response to the change in the capital structure, we need to calculate both the before and after ROE.
Before the change in capital structure:
ROE = Net Income / Total Equity
1. Calculate net income:
Net Income = Sales - Operating Costs - Interest Expense - Taxes
Net Income = $300,000 - $265,000 - (Debt-to-Total-Assets Ratio * Year-End Assets * Interest Rate) - (Net Income * Tax Rate)
Given information:
Debt-to-Total-Assets Ratio = 25%
Year-End Assets = $200,000
Interest Rate = 10%
Tax Rate = 35%
Substitute the values into the equation:
Net Income = $300,000 - $265,000 - (0.25 * $200,000 * 0.10) - (Net Income * 0.35)
2. Rearrange the equation to solve for Net Income:
Net Income + Net Income * 0.35 = $300,000 - $265,000 - (0.25 * $200,000 * 0.10)
Net Income * (1 + 0.35) = $300,000 - $265,000 - (0.25 * $200,000 * 0.10)
Net Income * 1.35 = $300,000 - $265,000 - $5,000
Net Income * 1.35 = $30,000
Solve for Net Income:
Net Income = $30,000 / 1.35
Net Income = $22,222.22
3. Calculate Total Equity:
Total Equity = Year-End Assets - Total Debt
Total Debt = Debt-to-Total-Assets Ratio * Year-End Assets
Total Debt = 0.25 * $200,000
Total Debt = $50,000
Total Equity = $200,000 - $50,000
Total Equity = $150,000
Calculate the before Change in ROE:
ROE (before change) = Net Income / Total Equity
ROE (before change) = $22,222.22 / $150,000
ROE (before change) = 0.148 or 14.8%
After the change in capital structure:
Debt Ratio = 60%
Interest Rate = 10%
Tax Rate = 35%
4. Calculate the new Total Debt:
Total Debt (after change) = Debt Ratio * Year-End Assets
Total Debt (after change) = 0.60 * $200,000
Total Debt (after change) = $120,000
5. Calculate the new Total Equity:
Total Equity (after change) = Year-End Assets - Total Debt (after change)
Total Equity (after change) = $200,000 - $120,000
Total Equity (after change) = $80,000
6. Calculate the new Net Income:
Net Income (after change) = Sales - Operating Costs - Interest Expense - Taxes
Net Income (after change) = $300,000 - $265,000 - (Debt Ratio * Year-End Assets * Interest Rate) - (Net Income (after change) * Tax Rate)
Substitute the values into the equation:
Net Income (after change) = $300,000 - $265,000 - (0.60 * $200,000 * 0.10) - (Net Income (after change) * 0.35)
7. Rearrange the equation to solve for Net Income (after change):
Net Income (after change) + Net Income (after change) * 0.35 = $300,000 - $265,000 - (0.60 * $200,000 * 0.10)
Net Income (after change) * (1 + 0.35) = $300,000 - $265,000 - $12,000
Net Income (after change) * 1.35 = $23,000
Solve for Net Income (after change):
Net Income (after change) = $23,000 / 1.35
Net Income (after change) = $17,037.04
Calculate the after Change in ROE:
ROE (after change) = Net Income (after change) / Total Equity (after change)
ROE (after change) = $17,037.04 / $80,000
ROE (after change) = 0.213 or 21.3%
8. Calculate the change in ROE:
Change in ROE = ROE (after change) - ROE (before change)
Change in ROE = 0.213 - 0.148
Change in ROE = 0.065 or 6.5%
Therefore, the ROE would increase by 6.5% in response to the change in the capital structure.
To calculate the change in the return on equity (ROE) in response to the change in the capital structure, we need to compute the ROE for the original debt ratio and the new debt ratio, and compare the two.
Here's the step-by-step process to calculate the ROE for each scenario:
1. Calculate the original ROE:
ROE = Net Income / Total Equity
2. Calculate Net Income:
Net Income = Sales - Operating Costs - Interest Expense - Taxes
3. Calculate Interest Expense:
Interest Expense = Debt * Interest Rate
4. Calculate Taxes:
Taxes = Net Income * Tax Rate
5. Calculate Total Equity:
Total Equity = Total Assets - Debt
Once we have computed the original ROE, we can repeat the process for the new debt ratio. However, since sales and total assets remain constant, the only changes will occur in the interest expense and total equity calculations.
Let's compute the original ROE first:
Net Income = $300,000 - $265,000 - (Debt * Interest Rate) - (Net Income * Tax Rate)
We know that the debt-to-total-assets ratio was 25%, and we can calculate the debt value as follows:
Debt = Debt Ratio * Total Assets
Debt = 0.25 * $200,000
Debt = $50,000
Let's substitute this value into the equation:
Net Income = $300,000 - $265,000 - ($50,000 * 0.10) - (Net Income * 0.35)
Now, let's solve for Net Income:
Net Income + 0.35 * Net Income = $300,000 - $265,000 - $5,000
1.35 * Net Income = $30,000
Net Income = $30,000 / 1.35
Net Income ≈ $22,222.22
Next, we can calculate the original Total Equity:
Total Equity = $200,000 - $50,000
Total Equity = $150,000
Finally, we can compute the original ROE:
ROE = Net Income / Total Equity
ROE = $22,222.22 / $150,000
ROE ≈ 0.1481 or 14.81%
Now that we have the original ROE, we can repeat the steps above for the new debt ratio of 60%.
New Debt = 0.60 * $200,000
New Debt = $120,000
Net Income = $300,000 - $265,000 - ($120,000 * 0.10) - (Net Income * 0.35)
Solving for Net Income:
Net Income + 0.35 * Net Income = $300,000 - $265,000 - $12,000
1.35 * Net Income = $23,000
Net Income = $23,000 / 1.35
Net Income ≈ $17,037.04
Total Equity remains the same in this case:
Total Equity = $200,000 - $120,000
Total Equity = $80,000
Finally, we calculate the new ROE:
ROE = Net Income / Total Equity
ROE = $17,037.04 / $80,000
ROE ≈ 0.2129 or 21.29%
To find the change in ROE, subtract the original ROE from the new ROE:
Change in ROE = New ROE - Original ROE
Change in ROE = 0.2129 - 0.1481
Change in ROE ≈ 0.0648 or 6.48%
Therefore, the change in the return on equity (ROE) in response to the change in the capital structure would be approximately 6.48%.