Which of the following statements is true of the profit-volume chart?

Question

BlackTom AI · Accepted Answer

Profit on a profit–volume (P/V) chart is expressed by π(Q) = (p − v)Q − F, where p = selling price per unit, v = variable cost per unit, c = contribution per unit = (p − v), F = total fixed costs, and Q = quantity sold. 1. Relevant concepts - Profit-volume chart: plots profit (vertical axis) against volume/units sold (horizontal axis). - Contribution per unit (c) determines the slope of the profit line. - Break-even point: volume where profit = 0. - At Q = 0 profit = −F (fixed cost outflow), so the profit line intercepts the vertical axis at −F. 2. Step-by-step reasoning - Start from π(Q) = cQ − F. - The profit line on the chart is a straight line with slope c and vertical intercept −F. - Set π(Q) = 0 to find break-even: 0 = cQ − F. 3. Intermediate calculations - Solve for break-even quantity Q*: Q* = F / c. - At Q = 0: π(0) = −F (maximum operating loss at zero sales equals fixed costs). - For Q > Q*, π(Q) > 0 (operating profit); for Q < Q*, π(Q) < 0 (operating loss). 4. Why the correct answer is correct - The profit line intersects the horizontal zero-profit line exactly where π(Q) = 0, i.e., at Q = F/c. That intersection point is the break-even point by definition. Therefore the statement “The profit line intersects the horizontal zero operating profit line at the break-even point” is true. 5. Why the other options are incorrect - Option 1: “It plots both costs and revenues…” describes a cost–volume–profit or break-even chart that shows costs and revenues; a P/V chart specifically shows profit versus volume, not both costs and revenues. - Option 2: “Maximum operating loss equals total fixed and variable costs” is wrong: at zero sales variable costs are zero, so maximum loss equals fixed costs (−F), not fixed plus variable. - Option 4: “Maximum operating profit equals 200% of fixed costs” is arbitrary and false; profit beyond break-even can grow without such a fixed relationship. 6. Conclusion All reasoning confirms the correct choice: The profit line intersects the horizontal zero operating profit line at the break-even point. This matches the provided answer.

Which of the following statements is true of the profit-volume chart?单项选择题

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