The correct answer is B. 11,600 units.
The break-even point is the point at which a company’s revenue equals its costs. In other words, it is the point at which the company neither makes nor loses money.
To calculate the break-even point, we can use the following formula:
Break-even point = Fixed costs / Contribution margin per unit
The contribution margin per unit is the amount of revenue that each unit sold contributes to covering the company’s fixed costs. It is calculated by subtracting the variable costs per unit from the selling price per unit.
In this case, the contribution margin per unit is $4.80, which is calculated as follows:
$6.00 selling price per unit – $1.20 variable production cost per unit – $0.40 variable selling cost per unit = $4.80 contribution margin per unit
The fixed costs are $40,000, which is calculated as follows:
$4.00 fixed production cost per unit x 10,000 units = $40,000 fixed costs
Therefore, the break-even point is 8,333 units, which is calculated as follows:
$40,000 fixed costs / $4.80 contribution margin per unit = 8,333 units break-even point
However, the question states that the variable production cost per unit and the selling price per unit will each increase by 10%, and fixed production cost will rise by 25%. This means that the new variable production cost per unit will be $1.32, the new selling price per unit will be $6.60, and the new fixed production cost will be $50,000.
The new contribution margin per unit will be $5.28, which is calculated as follows:
$6.60 selling price per unit – $1.32 variable production cost per unit – $0.40 variable selling cost per unit = $5.28 contribution margin per unit
Therefore, the new break-even point is 11,600 units, which is calculated as follows:
$50,000 fixed costs / $5.28 contribution margin per unit = 11,600 units break-even point
In conclusion, the new break-even point is 11,600 units.