Break-even analysis – definition At the break-even point of an operation or business, which relationship holds true?

Introduction / Context:
Break-even analysis (cost–volume–profit) determines the volume at which a firm neither earns profit nor incurs loss. It is widely used for pricing, budgeting, and feasibility assessments.

Given Data / Assumptions:

• Fixed cost (FC) is constant within the relevant range.
• Variable cost per unit (VC) and price per unit (P) are constant.
• Single-product or fixed sales mix scenario.

Concept / Approach:
Break-even occurs when total revenue (TR) equals total cost (TC). Using contribution margin, the breakeven quantity Q_BE is FC / (P − VC). At Q_BE, profit = 0 because TR − TC = 0.

Step-by-Step Solution:
Write TR = P * Q and TC = FC + VC * Q.Set TR = TC at break-even: P * Q = FC + VC * Q.Rearrange to get Q_BE = FC / (P − VC).At Q_BE, profit = TR − TC = 0 → Total cost equals sales revenue.

Verification / Alternative check:
Graphical break-even chart shows TR and TC lines intersecting at Q_BE, confirming equality.

Why Other Options Are Wrong:
Options (a) and (b) imply loss or profit, not break-even; (d) fixed cost rarely equals variable cost at break-even; (e) contribution per unit equals selling price only if VC = 0, which is not general.

Common Pitfalls:
Applying the formula outside the relevant range, ignoring stepped fixed costs or multi-product complexities.

Final Answer:
Total cost is equal to sales revenue