Given the following information: current assets = $400; fixed assets = $500; accounts payable = $100; notes payable = $45; long-term debt = $455; equity = $300; sales = $450; costs = $400; tax rate = 34%. Suppose that current assets, costs, and accounts payable maintain a constant ratio to sales. If the firm is producing at 80% capacity, what is the total external financing needed if sales increase 25%? Assume the firm pays no dividends.

Please show the steps

To calculate the total external financing needed, we need to determine the changes in both current assets and accounts payable due to the increase in sales.

1. Calculate the increase in sales:
- Sales increased by 25%, so the new sales can be calculated as follows:
New Sales = Current Sales + (Current Sales * 25%)
New Sales = $450 + ($450 * 0.25)
New Sales = $450 + $112.50
New Sales = $562.50

2. Calculate the new levels of current assets and accounts payable using the constant ratio assumption:
- Since the levels of current assets, costs, and accounts payable maintain a constant ratio to sales, we can calculate the new levels as follows:
New Current Assets = Current Assets * (New Sales / Current Sales)
New Current Assets = $400 * ($562.50 / $450)
New Current Assets = $500

New Accounts Payable = Accounts Payable * (New Sales / Current Sales)
New Accounts Payable = $100 * ($562.50 / $450)
New Accounts Payable = $125

3. Calculate the change in current assets and accounts payable:
- Change in Current Assets = New Current Assets - Current Assets
Change in Current Assets = $500 - $400
Change in Current Assets = $100

- Change in Accounts Payable = New Accounts Payable - Accounts Payable
Change in Accounts Payable = $125 - $100
Change in Accounts Payable = $25

4. Determine the total external financing needed:
Total External Financing Needed = Change in Current Assets - Change in Accounts Payable
Total External Financing Needed = $100 - $25
Total External Financing Needed = $75

Therefore, the total external financing needed if sales increase by 25% is $75.

66.25