5.5.2—Break-even chart and analysis

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.