The break-even point (損益分岐点) is the level of sales at which sales exactly equal total costs (fixed plus variable costs), so profit is zero.
Units sold (price 800 yen)
Sales
Total costs (fixed 60,000 yen + 500 yen per unit)
Profit
100 units
80,000 yen
110,000 yen
−30,000 yen
200 units
160,000 yen
160,000 yen
0 yen (break-even point)
300 units
240,000 yen
210,000 yen
30,000 yen
Sales above this level produce a profit, and sales below it mean a loss. What is left after subtracting variable costs from sales is the contribution margin, and the break-even point is where the contribution margin just covers fixed costs. Using the share of sales taken by variable costs (the variable cost ratio), break-even sales = fixed costs ÷ (1 − variable cost ratio).
AnalogyPicture a coffee stand that sets aside what is left from each cup after paying for the ingredients. The moment those savings cover the month's rent is the line between losing money and making it.
How to remember"Break even" means coming out with neither a gain nor a loss. Cross this point and you are in profit; fall short and you are in the red.
Exam points
ExamBreak-even sales (損益分岐点売上高) are found by dividing fixed costs (固定費) by (1 − the variable cost ratio (変動費率)).
ExamThe break-even point ratio (損益分岐点比率) is break-even sales (損益分岐点売上高) as a share of actual sales. The lower this ratio, the larger the part of sales that remains as profit.
Fixed costs (固定費) are costs whose amount stays the same whether sales volume and sales go up or down.
Examples include store rent, depreciation on equipment and the base pay of full-time staff. They arise even when nothing is sold, so the business runs at a loss until the contribution margin has covered them in full.
AnalogyIt is like a monthly gym membership: you pay the same amount every month however often you go, even if you never go.
Exam points
ExamCutting fixed costs (固定費) while the variable cost ratio (変動費率) stays the same shrinks the amount the contribution margin (限界利益) has to cover, so sales at the break-even point (損益分岐点) fall.
ExamFixed costs (固定費) can be worked back as sales − variable costs (変動費) − profit. The most fixed costs can be without a loss at a given sales level is that sales figure × (1 − the variable cost ratio (変動費率)).
Variable costs (変動費) are costs that rise and fall in proportion to sales or production volume.
Units sold
Fixed costs
Variable costs (300 yen per unit)
Total costs
0 units
50,000 yen
0 yen
50,000 yen
100 units
50,000 yen
30,000 yen
80,000 yen
200 units
50,000 yen
60,000 yen
110,000 yen
Examples include raw materials, the purchase cost of goods for resale and fees paid per unit sold. If the variable cost per unit is constant, doubling sales volume doubles total variable costs. Plot total costs against sales volume and fixed costs set the height where the line starts, while the variable cost per unit sets its slope.
AnalogyIt is like fuel for a car: the farther you drive, the more you spend, and if you leave the car parked it costs nothing.
Exam points
ExamWhen the variable cost (変動費) per unit rises, the total cost (総費用) line keeps the same starting height but becomes steeper.
ExamIf fixed costs (固定費), the unit price and the variable cost per unit are the same in two cases, dividing the difference in profit by the difference in sales volume (販売量) gives the contribution margin (限界利益) per unit. Subtract that from the unit price and you have the variable cost (変動費) per unit.
Mix-upThe contribution margin (限界利益) is sales minus variable costs (変動費) only. It is not the same as profit, which also takes away fixed costs (固定費).
Sales volume (販売量) is the quantity of products or services sold in a given period, and unit price × sales volume gives sales.
Sales volume is set
Sales and variable costs follow
Contribution margin = sales − variable costs
Profit = contribution margin − fixed costs
The contribution margin minus fixed costs is profit, and the sales volume at which it reaches zero is the break-even quantity.
4 / 4
When the variable cost per unit is constant, total variable costs also move in proportion to sales volume. Each unit sold therefore adds a contribution margin of unit price − variable cost per unit, and these add up to cover fixed costs. Expressed as a quantity, break-even volume = fixed costs ÷ contribution margin per unit.
AnalogyAt a school fair stall, once you know how much each item leaves after ingredients, you can count how many more you need to sell to earn back the stall fee.
Exam points
ExamThe sales volume (販売量) needed for a target profit (目標利益) is (fixed costs (固定費) + target profit) ÷ contribution margin (限界利益) per unit.
ExamLowering the unit price (販売単価) while fixed costs (固定費) and the variable cost (変動費) per unit stay the same shrinks the contribution margin (限界利益) per unit, so the sales volume (販売量) needed to avoid a loss goes up.
Mix-upAs long as fixed costs (固定費), the unit price and the variable cost (変動費) per unit hold steady, raising sales volume (販売量) does not move break-even sales (損益分岐点売上高). What changes is the amount of profit.
The variable cost ratio (変動費率) is the share of sales taken up by variable costs, found as variable costs ÷ sales.
Variable cost ratio
Contribution margin ratio (1 − variable cost ratio)
Break-even sales (fixed costs 990,000 yen)
0.1
0.9
1,100,000 yen
0.55
0.45
2,200,000 yen
0.85
0.15
6,600,000 yen
If the unit price and the variable cost per unit hold steady, the variable cost ratio stays constant as sales volume rises or falls. 1 − variable cost ratio is the contribution margin ratio, the share of sales that goes toward recovering fixed costs and toward profit. For example, with a variable cost ratio of 0.7, 30% of sales is available to cover fixed costs and profit.
Exam points
ExamIf fixed costs (固定費) and the variable cost ratio (変動費率) are constant, dividing the difference in total costs (総費用) between two periods by the difference in sales gives the variable cost ratio. From there, fixed costs can be worked back too.
ExamLowering the unit price (販売単価) while fixed costs (固定費) and the variable cost (変動費) per unit stay the same raises the variable cost ratio (変動費率), and break-even sales (損益分岐点売上高) rise with it.
Unchanged if unit prices and unit costs stay the same
How to find it
Variable cost per unit × sales volume
Variable costs ÷ sales
Key points
Total costs are the sum of fixed costs and variable costs, and profit is sales minus total costs.
Break-even point sales are fixed costs ÷ (1 − variable cost ratio); expressed as a quantity, the break-even volume is fixed costs ÷ contribution margin per unit.
With a target profit, divide fixed costs plus the target profit by the same denominator.
A drop in fixed costs or in the variable cost ratio lowers the break-even point.