To determine Lear's earnings after taxes under the given financing plan, we need to calculate the interest expense for both short-term and long-term financing, and then deduct the taxes to get the net income.
1. Calculate the interest expense for long-term financing:
The total assets to be financed with long-term debt are $775,000 (half of working capital $175,000 + fixed assets $600,000). Multiply this by the interest rate of 10% to get the interest expense for long-term financing: $775,000 * 0.10 = $77,500.
2. Calculate the interest expense for short-term financing:
The other $175,000 (half of permanent current assets) will be financed at the short-term interest rate of 5%, as well as the $450,000 in variable current assets. Add these two amounts: $175,000 + $450,000 = $625,000. Multiply this by the short-term interest rate of 5% to get the interest expense: $625,000 * 0.05 = $31,250.
3. Calculate Earnings Before Taxes (EBT):
Subtract the long-term interest expense and the short-term interest expense from the earnings before interest and taxes (EBIT) of $200,000: $200,000 - $77,500 - $31,250 = $91,250.
4. Calculate Taxes (30%):
Multiply the EBT by the tax rate of 30% to calculate the tax amount: $91,250 * 0.30 = $27,375.
5. Calculate Earnings After Taxes (EAT):
Subtract the tax amount from the EBT: $91,250 - $27,375 = $63,875.
Therefore, Lear's earnings after taxes under this financing plan would be $63,875.