A division of a corporation manufactures bicycle pumps. Each pump sells for $9, and the variable cost of producing each unit is 40% of the selling price. The monthly fixed costs incurred by the division are $50,000. What is the break-even point for the division?
a) break-even production 1,852 units; break-even revenue $166,662
b) break-even production 1,852 units; break- even revenue $83,331
c) break-even production 9,259 units; break- even revenue $166,662
d) break-even production 9,259 units; break- even revenue $83,331
thank you
when cost = revenue
To find the break-even point for the division, we need to determine the number of units that need to be produced and the corresponding revenue to cover the fixed and variable costs.
Let's start by calculating the variable cost per unit. The variable cost is given as 40% of the selling price, which means it is 0.4 times $9:
Variable cost per unit = 0.4 * $9 = $3.60
Next, we can determine the contribution margin per unit. The contribution margin is calculated as the selling price minus the variable cost per unit:
Contribution margin per unit = $9 - $3.60 = $5.40
The formula to calculate the break-even point in units is:
Break-even point (units) = Fixed costs / Contribution margin per unit
Plugging in the values, we get:
Break-even point (units) = $50,000 / $5.40
Break-even point (units) ≈ 9,259
Therefore, the break-even point for the division is approximately 9,259 units.
To find the break-even revenue, we can multiply the break-even point (9,259) by the selling price per unit:
Break-even revenue = Break-even point (units) * Selling price per unit
Break-even revenue = 9,259 * $9
Break-even revenue ≈ $83,331
So, the correct answer is:
d) break-even production 9,259 units; break-even revenue $83,331