To answer the question, we need to compare the total cash flow to Louis under two scenarios: when the firm remains unlevered and when the firm converts $4 million of equity into debt at a cost of 10%.
- EBIT (Earnings Before Interest and Taxes): $2,000,000
- Tax rate: 34%
Since the firm is unlevered, there is no interest expense. Therefore, the taxable income is equal to EBIT.
Taxable Income = EBIT = $2,000,000
Taxes = Taxable Income * Tax Rate = $2,000,000 * 34% = $680,000
Net Income = Taxable Income - Taxes = $2,000,000 - $680,000 = $1,320,000
Since Louis is the lone shareholder, the total cash flow to Louis is the net income.
Total Cash Flow to Louis (Unlevered) = $1,320,000
- Debt: $4,000,000
- Interest rate on debt: 10%
- EBIT: $2,000,000
- Tax rate: 34%
First, we need to calculate the interest expense on the debt.
Interest Expense = Debt * Interest Rate = $4,000,000 * 10% = $400,000
The taxable income is now reduced by the interest expense.
Taxable Income = EBIT - Interest Expense = $2,000,000 - $400,000 = $1,600,000
Taxes = Taxable Income * Tax Rate = $1,600,000 * 34% = $544,000
Net Income = Taxable Income - Taxes = $1,600,000 - $544,000 = $1,056,000
Now, we need to add the interest income that Louis would receive from holding the debt.
Interest Income = Interest Expense = $400,000
Total Cash Flow to Louis (Levered) = Net Income + Interest Income = $1,056,000 + $400,000 = $1,456,000
- Total Cash Flow to Louis (Unlevered): $1,320,000
- Total Cash Flow to Louis (Levered): $1,456,000
Conclusion:
The total cash flow to Louis if the firm remains unlevered is $1,320,000. If the firm converts $4 million of equity into debt and Louis holds all the debt, the total cash flow to Louis would be $1,456,000. Therefore, Louis would have a higher total cash flow by $136,000 if the firm leverages by converting $4 million of equity into debt.