A product manager sees variable cost climb $2 per unit and asks how many extra units must ship to hold operating income. CVP turns that question into a single calculation by linking price, cost behavior, and volume.
CVP isolates one input at a time. Hold price, variable cost per unit, and fixed cost constant; vary volume. Or hold volume and vary price. The model assumes a relevant range where unit price stays constant, variable cost per unit stays constant, fixed cost stays fixed, and sales mix stays put. Step outside that range and the line bends.
Inside that range, operating income is linear in volume:
Plug Q = 0 and OI = −F (a loss equal to fixed cost). Plug Q = breakeven and OI = 0. Every unit beyond breakeven adds exactly CM per unit to operating income because fixed cost is already covered.
KEY: Past breakeven, each additional unit lifts operating income by CM per unit, not by price. Beginners credit the full sales dollar; the exam credits only CM.
Common mistakes
- Forgetting the tax gross-up for after-tax targets. Plugging $90,000 directly into the numerator instead of grossing up to $120,000 (at 25%) understates required units. The gross-up converts after-tax to pretax before CVP runs.
- Treating taxes as if they shift breakeven. Breakeven has zero pretax income, so tax is zero. The breakeven point itself is unaffected by the tax rate; only target-net-income problems need the gross-up.
- Crediting full sales price per incremental unit. Each unit past breakeven adds CM per unit (price minus variable cost), not the full price. The exam plants the full-price distractor.
Bottom line
- CVP examines how total revenue, total cost, and operating income shift when selling price, variable cost per unit, fixed cost, or volume changes (one variable at a time).
- Contribution margin (CM) = Price − Variable cost per unit. CM ratio = CM / Price. Operating income = (CM per unit × Q) − Fixed cost.
- Breakeven units = Fixed cost / CM per unit. Breakeven dollars = Fixed cost / CM ratio. Add Target OI to the numerator for a target income.
- For target net income after tax, gross up: Target OI = Target NI / (1 − tax rate). Taxes never touch the breakeven point itself (BE has zero pretax income).
Exam shortcut
When the question gives a target after-tax net income, immediately gross up to pretax (NI / (1 − t)) before touching the CVP formula. Skip the gross-up only when the target is stated as operating income. When a multi-product firm changes its sales mix, recompute weighted CM and breakeven from scratch.
The full lesson (about 2,521 words, 17 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- 2C1
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