Final answer:
To find the sales required for Cosgrove Company to achieve an operating income of $100,000, we calculate the contribution margin, break-even point, and the number of units needed for the desired profit, then convert to sales dollars. However, the calculated sales amount doesn't match the provided choices.
Step-by-step explanation:
To calculate the amount of sales required to realize an operating income of $100,000 for Cosgrove Company, we need to use the break-even formula. This includes fixed costs, unit variable cost, and unit selling price. First, we will calculate the contribution margin per unit which is the selling price minus the variable cost per unit. Next, we calculate the break-even point in units by dividing the total fixed costs by the contribution margin per unit. Finally, we need to determine the number of units required to achieve the desired operating income and then convert it into sales dollars.
Here's a step-by-step calculation:
- Contribution margin per unit = Selling price - Variable cost per unit = $50 - $42 = $8 per unit
- Break-even point in units = Fixed costs / Contribution margin per unit = $367,500 / $8 = 45,937.5 units
- Desired profit in units = Desired operating income / Contribution margin per unit = $100,000 / $8 = 12,500 units
- Total units for desired profit = Break-even units + Desired profit units = 45,937.5 + 12,500 = 58,437.5 units
- Amount of sales = Total units for desired profit x Selling price per unit = 58,437.5 units x $50 = $2,921,875
However, this answer does not match with the provided choices, which indicates a possible misunderstanding or typo in the original question. Based on the provided information and necessary calculations, the amount of sales required is not reflected in the multiple-choice options given.