ACCTG 221 Chap.1 Cost-Volume-Profit and Sales Mix
Cost-Volume-Profit and Sales Mix
Cost-volume-profit analysis converts selling price, variable cost and fixed cost into a contribution model for planning. The core relationship is profit equals total contribution minus fixed cost. Break-even sets profit to zero; target-profit analysis adds the desired profit to fixed cost; margin of safety compares expected sales with break-even.
For multiple products, a stable sales mix creates a weighted average contribution per composite bundle, and every later unit answer must be unpacked using that mix.
What this chapter covers
- 01
Contribution margin per unit and contribution margin ratio
- 02
Break-even in units and sales dollars
- 03
Target-profit volume and after-tax target reasoning
- 04
Margin of safety and operating leverage
- 05
Weighted sales mix and composite bundles
- 06
Sensitivity to price, cost and mix changes
Worked example · free
Tāmaki Drink Bottles: composite break-even
- +2Bundle contribution = 3 × $12 + 2 × $22 = $80.
- +2Break-even bundles = $160,000 ÷ $80 = 2,000 bundles.
- +2Units are 6,000 Standard and 4,000 Premium, preserving the stated three-to-two mix.
Key terms
- Contribution ratio
- Contribution margin divided by sales revenue.
- Break-even point
- The sales level at which total contribution equals fixed cost.
- Composite bundle
- A notional package reflecting the expected sales mix.
- Operating leverage
- The sensitivity of profit to a percentage change in sales.
- Safety margin
- Sales above the break-even level.
Cost-Volume-Profit and Sales Mix FAQ
Why does break-even use contribution rather than revenue?
Revenue must first recover the variable cost caused by each sale. Only the remainder, contribution margin, is available for fixed cost. Dividing fixed cost by revenue would ignore that necessary outflow and understate the required volume.
What changes in a multi-product question?
Replace one product's contribution with contribution for a composite bundle built from the stated sales mix. Calculate break-even bundles first, then unpack the bundles into product units. The answer depends on the sales mix remaining stable.
How do I check a target-profit answer?
Multiply the rounded unit volume by unit contribution, then subtract fixed cost. The resulting profit must meet or exceed the target. If the question asks for whole units, a fractional result is normally rounded upward.
Exam move
Begin every problem by writing selling price, variable cost, contribution and fixed cost with units. Build the profit equation before substituting numbers, because that makes an altered price or cost visible. For sales-mix questions, draw one composite bundle and calculate its contribution on a separate line. Prove break-even by showing total contribution equals fixed cost.
Then test sensitivity one assumption at a time: selling price, variable cost, fixed cost, volume or mix. Do not call a large margin of safety automatically desirable without considering capacity and demand quality. Under time pressure, label whether the requested answer is units, sales dollars, bundles or percentage. A correct calculation in the wrong unit is not a complete decision answer.
Build a four-line error log after each attempt: classification, formula, units and interpretation. If variable manufacturing cost is confused with total manufacturing cost, correct the classification before recomputing. If a contribution ratio is used where dollars per unit are needed, write the dimensional cancellation that exposes the mismatch.
Practise reverse questions as well as direct ones: solve for selling price when a target volume is given, solve for allowable variable cost when price is fixed, and infer fixed cost from a known break-even point. For margin of safety, calculate both units and percentage and explain why the percentage is more comparable across businesses of different size.
For operating leverage, connect a high fixed-cost structure with stronger profit sensitivity on either side of the current sales level rather than treating leverage as automatically favourable. In a multi-product exercise, test a changed mix by rebuilding the composite bundle; do not reuse the old weighted contribution.
Before the final, rehearse a compact response order: define contribution, state the equation, substitute labelled values, round only the decision quantity, prove the result and add one sentence about the relevant range. Include a deliberate trap in practice, such as a step-fixed cost activated above current capacity, and state exactly where the original linear model stops.
This sequence makes assumptions visible and preserves method marks when an arithmetic error occurs. Finally, compare two plausible scenarios in a small table and state which variable causes the largest change in required volume. Explain why a percentage price change and an equal percentage cost change need not have equal profit effects when their dollar bases differ.
Record the answer in both numerical and managerial language so the calculation remains tied to the planning question. Recheck that the final sales quantity is operationally attainable; a mathematically sufficient target outside available capacity is not yet a feasible plan.
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