Rollag Corp.has a selling price of $30 and variable costs of $20 per unit.When 14,000 units are sold,profits equaled $45,000.What is the margin of safety?
A)$420,000
B)$135,000
C)$142,500
D)$75,000

Question

Quizplus · Accepted Answer

The margin of safety is calculated as (Actual Sales - Break-Even Sales). First, find the break-even point in units by dividing the fixed costs by the contribution margin per unit. The contribution margin per unit is the selling price minus variable costs ($30 - $20 = $10). Given profits of $45,000, we can find the fixed costs by adding the profit to the total variable costs at the break-even point. Since profit = total contribution margin - fixed costs, rearranging gives fixed costs = total contribution margin - profit. With 14,000 units sold, the total contribution margin is 14,000 units * $10 = $140,000. Thus, fixed costs = $140,000 - $45,000 = $95,000. The break-even point in units is $95,000 / $10 = 9,500 units. To find the break-even sales in dollars, multiply the break-even units by the selling price: 9,500 units * $30 = $285,000. Actual sales are 14,000 units * $30 = $420,000. Therefore, the margin of safety in dollars is $420,000 - $285,000 = $135,000.