Virgil Corp.has a selling price of $30 per unit,and variable costs of $20 per unit.When 12,000 units are sold,profits equaled $55,000.How many units must be sold to break-even?
A)4,000
B)12,000
C)6,500
D)5,500

Question

Quizplus · Accepted Answer

The formula for calculating break-even point is:

Break-even point (in units) = Total fixed costs / Contribution margin per unit

Contribution margin per unit = Selling price per unit - Variable cost per unit

Let's first calculate the contribution margin per unit:

Contribution margin per unit = $30 - $20 = $10

Now, let's use the information given in the question to calculate the break-even point:

$55,000 = Total fixed costs + (12,000 units x $10 contribution margin per unit)
Total fixed costs = $55,000 - $120,000 = -$65,000

This doesn't make sense - you can't have negative fixed costs. So, we know something went wrong with our calculation. We need to check our given information - it's possible that the profit figure was actually a loss, which would make more sense in this scenario.

Let's assume that instead of profits of $55,000, there were losses of $55,000. Now, our calculation looks like this:

-$55,000 = Total fixed costs + (12,000 units x $10 contribution margin per unit)
Total fixed costs = -$175,000

Again, this doesn't make sense - you can't have negative fixed costs. This means that our assumption is incorrect - the problem must be unsolvable with the given information.

However, if we ignore the given profit figure and assume that the company wants to break even, we can use the formula above to find the break-even point:

Break-even point (in units) = Total fixed costs / Contribution margin per unit
Break-even point (in units) = Total fixed costs / ($30 - $20) = Total fixed costs / $10

Since we don't have a specific number for the total fixed costs, we can't find the exact break-even point. However, we can determine that the break-even point would be greater than 12,000 units (since profits were earned at this level). Based on that, the best choice is C) 6,500.