Cost-volume-profit (CVP): For fixed cost F, variable cost per unit V, and selling price per unit P, the break-even point in units equals…

Introduction / Context:
Break-even analysis is a foundation of operations and manufacturing economics. It determines the output level where total revenue equals total cost, i.e., neither profit nor loss. The relationship among fixed cost, variable cost per unit, and selling price per unit leads directly to a simple formula for break-even units.

Given Data / Assumptions:

• Fixed cost F is independent of volume within the relevant range.
• Variable cost per unit V and selling price per unit P are constant over the range considered.
• No inventory change; units produced = units sold.

Concept / Approach:
Total cost = F + V * Q. Total revenue = P * Q. At break-even, P * Q = F + V * Q. Solve for Q to obtain the units required to cover fixed cost given the contribution margin (P − V) per unit.

Step-by-Step Solution:

Verification / Alternative check:
Check units: numerator is currency, denominator is currency per unit; result is in units. Test a quick example: F = 10,000; P = 100; V = 60 → Q = 10,000 / 40 = 250 units; revenue 25,000, total cost 10,000 + 60250 = 25,000 → balanced.

Why Other Options Are Wrong:
F/(P+V) ignores contribution margin; P/(P−V) lacks fixed cost; (FP)/(P−V) overstates units; F*(P−V) is dimensionally incorrect (currency squared).

Common Pitfalls:
Using total variable cost instead of per-unit variables without consistent units; forgetting price or variable cost changes at different volumes; ignoring capacity constraints.

Final Answer:
F / (P - V)