5.5 Break-even analysis

Contribution per unit is selling price minus variable cost per unit; total contribution pays fixed costs before profit.

A higher contribution can come from price or lower variable cost, but demand may change. Contribution is useful for short-run decisions when fixed costs are unchanged.

Calculate price−variable cost, multiply by volume, then check whether the decision changes fixed costs or demand.

A $10 meal with$6 variable cost contributes $4; 2,000 meals contribute$8,000 toward fixed costs.

Contribution is not profit until fixed costs are covered.

Break-even output is fixed costs divided by contribution per unit; at that volume total revenue equals total cost. Margin of safety shows how far expected sales are above break-even.

The chart makes assumptions visible: constant price, unit variable cost, fixed costs and a relevant output range.

Compute the point, label revenue/cost lines, then interpret what happens if volume or assumptions change.

Fixed costs are $20,000 and contribution$5, so break-even is 4,000 units; expected sales of 5,000 give a 1,000-unit margin of safety.

Break-even is a modelled threshold, not a forecast of demand.

Complete the model with these relationships: contribution per unit = selling price − variable cost per unit; break-even output = fixed costs ÷ contribution per unit; margin of safety = actual or forecast sales − break-even output; target profit output = (fixed costs + target profit) ÷ contribution per unit; profit at a stated output = total contribution − fixed costs; and target price = variable cost per unit + (fixed costs + target profit) ÷ target output. On the chart, output is on the horizontal axis and costs/revenue on the vertical axis: fixed cost is horizontal, total cost starts at fixed cost, total revenue starts at zero, and their intersection is break-even. For fixed costs of $20,000, variable cost of$6 and a $10 selling price, a$4 contribution gives break-even of 5,000 units. A $4,000 target profit needs (20,000 + 4,000) ÷ 4 = 6,000 units; at 7,000 units profit is 7,000 ×$4 − $20,000 =$8,000.

Changing price, variable cost or fixed cost changes contribution, break-even and profit; the direction is mechanical but the sales response may not be.

A price cut lowers contribution per unit but may raise volume; a fixed-cost rise shifts break-even without changing unit contribution.

Recalculate contribution and break-even, then test whether the assumed volume response is credible.

Price falls from $10 to$9 while variable cost stays $6: contribution falls from$4 to $3, so break-even rises unless volume grows enough.

Do not infer higher profit from higher sales without recalculating contribution.

Show each change graphically and quantitatively while holding other factors constant. A higher selling price steepens the total-revenue line, raises contribution, lowers break-even output and increases profit and margin of safety at a stated sales volume; a lower price does the reverse unless extra demand compensates. A higher variable cost steepens the total-cost line, lowers contribution and raises break-even; a higher fixed cost shifts the total-cost line upward in parallel and also raises break-even. Example: with fixed costs of $12,000, price$10 and variable cost $6, break-even is$12,000 ÷ $4 = 3,000 units. If variable cost rises to$7, contribution falls to $3 and break-even rises to 4,000 units; forecast sales of 5,000 then have a 1,000-unit rather than 2,000-unit margin of safety.

Break-even analysis simplifies reality by assuming linear revenue/cost relationships, stable prices and costs, one product or a constant mix, and known output.

Demand, capacity, step costs, quality, uncertainty and multiple products can invalidate the chart. It is best used with scenarios and sensitivity analysis.

State the assumption most likely to fail, then explain how it could change the decision.

A factory reaches overtime capacity, so variable cost rises in steps; the straight-line chart understates the true break-even point.

A precise break-even number can create false confidence when the assumptions are weak.