  Block, S., Hirt, G., & Danielsen, B. (2017). Foundations of Financial Management. New York, NY: McGraw-Hill Education. 16th edition.Question #8:  Air Purifier Inc. computes its break-even point strictly on the basis of cash expenditures related to fixed costs.  Its total fixed costs are \$2,450,000, but 15% of this value is represented by depreciation.  Its contribution margin (price minus variable costs) for each unit is \$40.  How many units does the firm need to sell to reach the cash break-even point?

Question

Block, S., Hirt, G., & Danielsen, B. (2017). Foundations of Financial Management. New York, NY: McGraw-Hill Education. 16th edition.

Question #8:  Air Purifier Inc. computes its break-even point strictly on the basis of cash expenditures related to fixed costs.  Its total fixed costs are \$2,450,000, but 15% of this value is represented by depreciation.  Its contribution margin (price minus variable costs) for each unit is \$40.  How many units does the firm need to sell to reach the cash break-even point?

Step 1

Break-even point

It is the number of sales units at which a company can cover its costs (fixed and variable). It can be calculated as either sales units or revenue amounts. The break-even units are calculated as:

Break-even units = Fixe cost/Contribution margin per unit

Where, contribution margin per unit = Price per unit – Variable cost per unit

Step 2

As per the question, the firm calculates its break-even point by taking only cash based fixed costs.

Given,

Total Fixed cost = \$2,450,000

Depreciation amount = 15% of \$2,450,000

= 15%*2,450,000

= \$367,500

Thus, cash based fixed cost = \$2,450,000 - \$367,500 = \$2,082,500

Step 3

Contribution margin per unit = \$40

Cash based Fixed cost = \$2,082,500

Thus, cash break-even units = Cash based Fixed cost/Contribution margin per unit

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