Question

Due to erratic sales of its sole product—a high-capacity battery for laptop computers—PEM, Inc., has been experiencing financial difficulty for some time. The company’s contribution format income statement for the most recent month is given below:

Sales (12,800 units × $20 per unit) $ 256,000
Variable expenses 128,000
Contribution margin 128,000
Fixed expenses 143,000
Net operating loss $ (15,000 )

Compute the company's CM ratio and its break-even point in both units and dollars.

Answer 1

PEM, Inc.'s contribution margin ratio (CM ratio) is 50%, the break-even point in units is 14,300, and the break-even point in dollars is $286,000. To calculate these figures, we use the contribution margin and fixed expenses provided in the income statement, applying formulas for the CM ratio and break-even calculations.

Step-by-step explanation:

To compute the contribution margin ratio (CM ratio) and the break-even point in units and dollars for PEM, Inc., we need to use the given data. The CM ratio is calculated by dividing the contribution margin by the sales. The formula is as follows:

CM ratio = Contribution Margin / Sales

For PEM, Inc., the contribution margin is $128,000, and the sales are $256,000. So, the CM ratio is:

CM ratio = $128,000 / $256,000 = 0.5 or 50%

The break-even point in units is computed by dividing the total fixed expenses by the contribution margin per unit. While the break-even point in dollars is found by multiplying the break-even point in units by the price per unit, or by dividing total fixed expenses by the CM ratio. The contribution margin per unit is:

Contribution Margin per unit = Contribution Margin / Number of units sold

Contribution Margin per unit = $128,000 / 12,800 units = $10 per unit

Therefore, the break-even point in units is:

Break-even point (units) = Fixed Expenses / Contribution Margin per unit

Break-even point (units) = $143,000 / $10 = 14,300 units

And the break-even point in dollars is:

Break-even point (dollars) = Break-even point (units) × Price per unit

or

Break-even point (dollars) = Fixed Expenses / CM ratio

Break-even point (dollars) = $143,000 / 0.5 = $286,000

In conclusion, PEM, Inc.'s CM ratio is 50%, its break-even point is 14,300 units, and the break-even point in dollars is $286,000.

Answer 2

The company's CM ratio: 0.5

Its break-even point in units: 14,300 units and in dollars: $286,000

Step-by-step explanation:

Variable expense per unit = Variable expenses/ number of units = $128,000/12,800 = $10

The contribution margin ratio is calculated by using following formula:

Contribution margin ratio = (Sales - Total Variable cost)/Sales = ($256,000 - $128,000)/$256,000 = 0.5

The break-even point is the level of production at which the costs of production equal the revenues for a product and calculated by using following formula:

Break-even point in units = Fixed expense/(Selling price per unit-Variable expense per unit) = $143,000/($20 - $10) = 14,300 units

Break-even point in dollars = 14,300 units x Selling price per unit = 14,300 x $20 = $286,000