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The breakeven point is 7.5 million units calculated as follows:
It's given that operating assets are 20 million.
The formula for return on operating assets is net income over operating assets. Use some algebra so .25 = x/20. Solve for X and you get net income of 5 million.
The formula for operating asset turnover is sales/operating assets. The algebraic formula would be 5 = x/20. Solve for X and you get sales of 100 million.
The formula for operating leverage is contribution margin/net income. The algebra formula is 4 = x/5. Solve for x and you get a contribution margin of 20 million.
Keep in mind that the formula for breakeven is 0 = Contribution Margin - Fixed Costs.
Contribution margin is sales less variable costs.
We know that the contribution margin is 20 million or $2 per unit from our math above
We can calculate fixed costs as follows. We know that total costs are 95 million (100 million in sales less 5 million net income).
Variable costs are 80 million. 100 million in sales less 20 million contribution margin.
So fixed costs must be 15 million.
Your formula to compute breakeven in units is 0 = 2(x) -15,000,000. X is the number of units. Solve for x and you get 7.5 million units.
Breakeven point = Selling Price(x) - Variable Costs(x) - Fixed Costs
180(x) - 126(x) - 540,000 = 0
54(x) - 540,000=0
54(x) = 540,000
X = 10,000, so the breakeven point is 10,000 units
10,000 units * 180 Selling price = $1,800,000
Since 10,000 is the breakeven point, we know that all sales above this will result in a profit based on the contribution margin (sales price less variable costs). We know this to be $54.
So at 12,000 units, it would be 54 * 2000 or $108,000 profits
At 15,000 units, it would be $54 * 5,000 or 270,000 profits
At 20,000 units, it would be $54 * 10,000 or 540,000 profits
Degree of operating leverage is (Sales - Variable Costs)/(Sales-Variable Costs-Fixed Costs)
At 12,000 units, this would be: 648,000/108,000 = 6
At 15,000, this would be: 810,000/270,000= 3
At 20,000, this would be 1,080,000/540,000 = 2