15-12A. (Break-even point) You are a hard-working analyst in the office of finan

Question

15-12A. (Break-even point) You are a hard-working analyst in the office of financial operations for a manufacturing firm that produces a single product. You have developed the following cost
structure information for this company. All of it pertains to an output level of 10 million units.
Using this information, find the break-even point in units of output for the firm.

Return on operating assets = 25%
Operating asset turnover = 5 times
Operating assets = $20 million
Degree of operating leverage = 4 times

Explanation / Answer

Return on Operating Assets =   Net Operating Income / Operating Assets

Net Operating Income = $20,000,000 × 25% = $5,000,000

DOL = Contribution Margin / Net operating Income

Contribution Margin = $5,000,000 × 4 = $20,000,000

Since Net Operating Income = Contribution Margin – Fixed Costs

Fixed Costs = $20,000,000 - $5,000,000

= $15,000,000

Unit Contribution Margin = $20,000,000 / 10,000,000

= $2

Breakeven Point in Units = Fixed Costs/Unit Contribution Margin

Breakeven Point in Units = $15,000,000 / $2

= 7,500,000 units

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