Question

The following is XYZ’s contribution format income statement for last month:

Sales	$600,000
Variable expenses	400,000
Contribution margin	200,000
Fixed expenses	100,000
Net operating income	$100,000

The company has no beginning or ending inventories and produced and sold 10,000 units during the month.

1 What is the company's contribution margin ratio?

2 What is the company's contribution margin?

3 What is the company's break-even in units?

4 If sales increase by 200 units, by how much should net operating income increase?

5 How many units would the company have to sell to attain a target profit of $200,000?

6 What is the company's margin of safety in dollars?

7 What is the company's degree of operating leverage?

Answer 1

The XYZ Company has produced 10,000 units and sold all of them.

Sale Price per unit = Total Sales / Total no. of units sold = $600,000 / 10,000 = $60

Variable Cost per unit = Total Variable cost / Total no. of units produced = $400,000 / 10,000 = $40

1) Calculation of XYZ's Contribution Margin ratio

Contribution Margin ratio = [(Sales - Variable Cost) / Sales] * 100

                                    = [$600,000 - $400,000) / $600,000] * 100

                                    = [$200,000 / $600,000] * 100

                                    = 33.33%

2) Calculation of XYZ's Contribution Margin

Contribution Margin = Sales - Variable Cost

                             = $600,000 - $400,000

                             = $200,000

3) Calculation of XYZ's Break-even in Units

Break-even in Units = [Fixed Costs / Contribution per unit]

Here, Contribution per unit = Sale price per unit - Variable cost per unit = $60 - $40 = $20

Break-even in Units = [Fixed Costs / Contribution per unit]

                             = [$100,000 / $20]

                             = 5,000 units

4) Calculation of net operating income increase if sales increase by 200 units

Present net operating Income = $100,000

        Revised Sales (10,200 * $60)            = $612,000

Less: Revised Variable cost (10,200 * $40) = ($408,000)

                                Contribution Margin = $204,000

Less : Fixed cost                                     = ($100,000)

                      Net Operating Income        = $104,000

         Revised Net operating income = $104,000

Less: Present net operating Income = ($100,000)

     Net Operating income increase = $4,000

5) No. of units to be sold to attain profit $200,000

Required profit = $200,000   

= [(Fixed cost + Required profit) / Contribution per unit]

= [($100,000 + $200,000) / $20]

= [$300,000 / $20]

= 15,000 units

6) Margin of Safety in Dollars

Margin of Safety (Dollars) = Actual Sales - Break-even Sales

Break-even Sales = Fixed Cost / Contribution Margin = $100,000 / 33.33% = $300,000

Margin of Safety (Dollars) = Actual Sales - Break-even Sales

= $600,000 - $300,000

= $300,000

7) Degree of Operating Leverage

   Degree of Operating Leverage = Contribution Margin / Net Operating Income

                                                   = $200,000 / $100,000

                                                   = 2