Break-even analysis: The break-even point on a cost–volume–profit (CVP) chart is the intersection of which two lines?

Introduction / Context:Break-even analysis studies how costs and revenues change with volume to determine the output level at which a business neither makes a profit nor a loss. The break-even point (BEP) is a cornerstone of managerial decision-making.

Given Data / Assumptions:

• Total cost = Fixed cost + Variable cost.
• Sales revenue = Selling price per unit * Quantity.
• Linear relationships are assumed over the relevant range.

Concept / Approach:On a CVP graph, the total cost line starts at the fixed cost on the Y-axis and rises with slope equal to unit variable cost. The sales revenue line passes through the origin with slope equal to selling price per unit. The BEP occurs where total cost equals total revenue, i.e., profit = 0.

Step-by-Step Solution:

Verification / Alternative check:Algebraically, BEP quantity Q = Fixed cost / (Price per unit - Variable cost per unit). At this Q, total cost equals total revenue, matching the graph intersection.

Why Other Options Are Wrong:

• Fixed vs variable cost lines: their intersection is not BEP.
• Fixed vs total cost lines: they intersect at the fixed-cost intercept only.
• Variable vs total cost lines: always parallel difference by fixed cost; no BEP meaning.

Common Pitfalls:Using average cost instead of marginal; forgetting the relevant range where linearity holds.

Final Answer:Sales revenue and total cost lines