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First, we need to find the breakeven point in units, and then compare that with the actual units sold to determine how many additional units should have been sold in order to break even. The formula for the breakeven point in units is: FC ÷ Unit Contribution Margin = BEP in units So we need to find fixed costs and the unit contribution margin. Given a loss of $40,000, then fixed costs must be $160,000. The formula is: $300,000 sales ? $180,000 variable costs ? X = ($40,000) $120,000 ? X = ($40,000) X = $160,000 Next, find the unit contribution margin. The total contribution margin is $300,000 ? $180,000, or $120,000. The sales price (given in the problem) was $12.50 per unit. With sales of $300,000 at $12.50 per unit, a total of 24,000 units was sold ($300,000 ÷ $12.50). Therefore, the Unit Contribution Margin is $120,000 ÷ 24,000, or $5. Now, we can calculate the BEP in units. BEP in units = $160,000 ÷ $5 = 32,000 units The final step is to determine the additional number of units that would have been required, over and above what was actually sold, in order to break even. We have already calculated that 24,000 units were actually sold and that 32,000 units would have been needed to break even. Thus, 8,000 additional units should have been sold in order for the company to break even (32,000 ? 24,000).
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32,000 is the total units needed in order for the company to break even. However, the question asks for the additional units needed in order for the company to break even. So the correct answer is the difference between the number of units that actually were sold and the breakeven volume.
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