Final answer:
To achieve an annual after-tax operating profit of $2,400,000, the company needs to sell 19,000 units, considering a 40% tax rate, fixed costs of $15,000,000, variable costs of $2,000 per unit, and a selling price of $3,000 per unit.
Step-by-step explanation:
The student's question relates to break-even analysis in a business context, specifically calculating the volume of units required to achieve a target after-tax operating profit.
First, let's compute the desired profit before tax, since taxes reduce the operating profit. We need to find the profit before tax that would result in a $2,400,000 profit after a 40% tax:
Operating Profit After Tax = Operating Profit Before Tax * (1 - Tax Rate)
$2,400,000 = Operating Profit Before Tax * (1 - 0.40)
Operating Profit Before Tax = $2,400,000 / (1 - 0.40) = $4,000,000
Now, we determine the number of units needed to achieve this profit, considering the fixed costs and the variable cost per unit. We know the selling price per unit is $3,000, and the variable cost per unit is $2,000.
Therefore, the contribution margin per unit (selling price minus variable cost) is:
Contribution Margin per Unit = Selling Price - Variable Cost
Contribution Margin per Unit = $3,000 - $2,000 = $1,000
Using the contribution margin, we can now calculate the required number of units to cover the fixed costs and yield the desired operating profit before tax:
Required Units = (Fixed Costs + Operating Profit Before Tax) /Contribution Margin per Unit
Required Units = ($15,000,000 + $4,000,000) / $1,000 = 19,000 units
Therefore, the company needs to sell 19,000 units to achieve an annual after-tax operating profit of $2,400,000.