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
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
To find the break-even point in units of output for the firm, we need to use the formula for break-even point:
Break-even Point (in units) = Fixed Costs / Contribution Margin per Unit
The Fixed Costs can be calculated using the following formula:
Fixed Costs = Operating Assets × (1 - Return on Operating Assets)
Given the information provided:
Return on Operating Assets = 25% = 0.25
Operating Asset Turnover = 5 times
Operating Assets = $20 million
Degree of Operating Leverage = 4 times
First, let's calculate the Fixed Costs:
Fixed Costs = $20 million × (1 - 0.25)
Fixed Costs = $20 million × (0.75)
Fixed Costs = $15 million
Now, to calculate the Contribution Margin per Unit, we need the Operating Assets turnover and the Degree of Operating Leverage:
Contribution Margin per Unit = Operating Asset Turnover × Degree of Operating Leverage
Contribution Margin per Unit = 5 times × 4 times
Contribution Margin per Unit = 20
Finally, we can use the formula for break-even point to find the break-even point in units of output:
Break-even Point (in units) = $15 million / $20
Break-even Point (in units) = 750,000 units
Therefore, the break-even point in units of output for the firm is 750,000 units.