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Break Even Point Calculation

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(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

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We have following information...

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

Operating Profit Margin (OPM)

OPM = Operating Income / Sales

(a) Formula: Return on operating assets = Income/Operating Assets
Then 25% = Income/20
Income = \$5m

(b) Formula: Operating Asset Turnover = Sale/Operating Assets
Then 5 = Sales/20
Sales = \$100m

So, OPM = 5/100 = 5%

(c) Formula: Degree of Operating Leverage (DOL) = Contribution Margin Ratio / Operating Margin

Then 4 = Contribution Margin Ratio/5%
Contribution Margin Ratio = 4*5% = 20%

So, we have Contribution Margin (CM) = Contribution Margin Ratio * Sales
CM = 20%*100 = \$20m

Now we have,

Sales = \$100m, Contribution Margin = \$20m, Operating Income = \$5m

Then Fixed Cost = Contribution Margin - operating income
Fixed Cost = 20 - 5 = \$15m

Sale price per unit = \$100/10 = \$10

Contribution Margin per unit = \$10*20% = \$2

We know,

Breakeven point (BEP) = Fixed Cost/Contribution per unit
BEP = 15/2 = 7.5m or 7,500,000

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