CVP analysis, one business, three real decisions
Most CVP examples are a single isolated calculation on a single imaginary product. This one follows one small coffee roaster through three connected decisions in sequence: a price increase, an equipment purchase, and a product mix shift, the way CVP actually gets used in practice.
Riverside Roasters' starting position: a thin $2,320 operating income on $67,200 in sales, with a margin of safety of just 5.75%.
The business: Riverside Roasters
Riverside Roasters sells bags of coffee at $16 each. Beans, roasting labor, packaging, and the card processing fee together cost $6.40 per bag, a $9.60 contribution margin, a 60% ratio. Monthly fixed costs (rent, a salaried roaster, insurance, admin) total $38,000. Current volume is 4,200 bags a month.
The starting CVP income statement
A 5.75% margin of safety is thin. A slow month, one lost wholesale account, or a small cost increase could push the business back to a loss. This is the actual starting condition that makes the three decisions below worth working through carefully rather than guessing.
Decision 1: a price increase
The owner considers raising price from $16.00 to $17.50, a 9.4% increase. New contribution margin: $17.50 − $6.40 = $11.10, a 63.4% ratio. New break-even: $38,000 ÷ $11.10 = 3,423 bags, 535 fewer bags needed than before, purely from the wider margin per bag.
Even in the pessimistic case, a 10% volume drop, which would be a meaningfully strong customer reaction to a 9.4% price increase, operating income still climbs from $2,320 to $3,958, and margin of safety widens considerably since break-even itself dropped by 535 bags. The price increase is a clear improvement across a realistic range of volume responses, not just in the best case.
Decision 2: automating the roaster
Separately, a supplier offers financing on an automated roasting line: $1,400 a month in loan payments and maintenance, added to fixed costs, in exchange for cutting $2.10 of roasting labor out of every bag's variable cost. New variable cost: $6.40 − $2.10 = $4.30. New fixed costs: $38,000 + $1,400 = $39,400. This is the classic higher-fixed/lower-variable tradeoff, and it has a specific crossover volume where it stops being a clear answer.
Below 667 bags a month, staying labor-based (lower fixed cost) produces more profit. Above 667 bags, automation wins, and the gap widens the further above that line volume actually sits. Riverside Roasters sells 4,200 bags a month, more than six times the crossover point, so this isn't a close call: at current volume, status quo profit is $2,320 while automated profit is 4,200 × $11.70 − $39,400 = $9,740, more than four times higher. The higher fixed cost is easily absorbed at this volume, and every bag above the crossover point captures $2.10 more in margin than it did before.
The same equipment purchase that would sink a business selling 400 bags a month is the single best decision available to one selling 4,200. Operating leverage cuts both ways, and the crossover volume is the only number that tells you which side you're on.
Decision 3: shifting the product mix
A third, independent option: introduce a premium single-origin bag at $24.00, with a higher $8.40 variable cost (better beans, more careful roasting time), still a $15.60 contribution margin, a 65% ratio, five points richer than the standard bag's 60%. Rather than adding volume, the owner considers shifting the existing customer base's mix: the same 4,200 total bags a month, but 3,600 standard and 600 premium instead of 4,200 standard.
Operating income at this mix, same total volume: (3,600 × $9.60) + (600 × $15.60) − $38,000 = $5,920, up from the original $2,320, without selling a single additional bag. Break-even at the new blended margin drops to $38,000 ÷ $10.457 ≈ 3,634 bags, a meaningfully wider cushion than the original 3,958. The lever here isn't volume at all. It's which products that same volume is actually made of.
The CVP chart across all three decisions
Plotting operating income against the same 4,200-bag volume for the starting position and all three decisions makes the comparison immediate:
All four bars use the identical 4,200-bag volume. Every dollar of difference comes purely from price, cost structure, or product mix, not from selling more.
Combining decisions
These three decisions aren't mutually exclusive. Riverside Roasters could raise price, automate, and shift its product mix all at once. Combining the price increase and automation alone: contribution margin becomes $17.50 − $4.30 = $13.20 per standard bag, fixed costs $39,400. At the same 4,200 bags: 4,200 × $13.20 − $39,400 = $16,040, nearly seven times the original $2,320, and each individual lever's effect stacks cleanly on top of the others because contribution margin and fixed costs combine additively. Layering a product mix shift on top would push the number higher still.
What this case study actually shows
None of the three levers above required more customers. Price, cost structure, and product mix all moved profit independently, and combine additively when stacked.
The same automation decision would have been wrong at 400 bags a month and was clearly right at 4,200. The crossover point, not intuition, is what separates the two cases.
Riverside Roasters started at 5.75% margin of safety, thin enough that running the actual numbers on each option, rather than picking one on instinct, was the difference between a risky guess and a confident decision.
Run your own numbers through the same framework on the CVP analysis calculator, which covers break-even, target profit, and margin of safety together, or see break-even point on its own for the core formula this entire case study builds from.
Frequently asked questions
A worked calculation applying cost-volume-profit math (contribution margin, break-even, margin of safety) to a specific business decision. The case study above follows one company through three connected decisions: a price increase, an equipment purchase, and a product mix change.
Sales, minus total variable costs, equals contribution margin; contribution margin minus fixed costs equals operating income. Unlike a standard income statement, costs are grouped by behavior (variable vs. fixed) rather than by function (COGS vs. operating expenses).
Find the crossover volume where both options produce identical profit, then compare it to your actual or expected volume. Above the crossover, the higher-fixed-cost option wins; below it, the higher-variable-cost option wins. See the automation decision in the case study above for a full worked example.
A higher price raises the contribution margin per unit, which lowers the break-even volume. Even a price increase that costs some sales volume can leave a business with a wider margin of safety than before, as shown in the price-increase decision above.
Multiply each product's contribution margin by its unit volume, sum those figures, then divide by total units across all products. See the product mix decision above for a full worked example with two products.
Run your own CVP scenarios on the CVP analysis calculator, or see five more industry examples in break-even analysis examples.