Final answer:
To calculate the sales needed for Crowne Company to reach its target operating profit, we add the target profit divided by the contribution margin ratio to the break-even sales. The correct calculation leads to a required sales amount of $650,000 to meet the $70,000 target profit.
Step-by-step explanation:
To determine how much sales Crowne Company would need to meet its target operating profit, we first understand the contribution margin ratio and its relation to the break-even point and target profits. The contribution margin ratio indicates what portion of the sales contribute to covering fixed costs and profit.
The company's break-even point in sales is $300,000, which means at this sales level, the company covers all its costs with no profit. Given that their contribution margin ratio is 20%, we can calculate the required sales for any profit target with this formula: Required Sales = (Fixed Costs + Target Profit) / Contribution Margin Ratio. To calculate the target profit sales, we take the break-even sales and add the additional sales needed to achieve the target profit, which is calculated as:
Required Sales = ($300,000 + $70,000) / 0.20
Required Sales = $370,000 / 0.20
Required Sales = $1,850,000
However, this calculated figure seems far too large based on the provided options. There may have been an error in the calculation. The correct approach is to divide the sum of the break-even sales and target profit by the contribution margin ratio, not to multiply:
Correct Required Sales = ($300,000 + $70,000) / 0.20 = $1,850,000 / 0.20
This submitted calculation too is incorrect because the division operation is wrong. The right calculation should not divide the sum by the contribution margin ratio again as it's already factored in the break-even point calculation. Instead, simply add the target profit divided by the contribution margin ratio to the break-even sales:
Correct Required Sales = $300,000 + ($70,000 / 0.20)
Correct Required Sales = $300,000 + $350,000
Correct Required Sales = $650,000 (Option B)