BUSS1030 · Accounting For Decision Making
Cost Behaviour and CVP
Before you can ask “how many must we sell?” you have to know how each cost behaves as volume changes. This chapter is the numeric heart of the In-Semester Test. It splits costs into fixed, variable and mixed (plus the direct/indirect and product/period classifications and the relevant-range caveat), then builds the full Cost-Volume-Profit toolkit on that split: the contribution margin per unit and the CM ratio, break-even in units (FC ÷ CM per unit) and dollars (FC ÷ CM ratio), target-profit volume, the margin of safety, the break-even chart, sensitivity (which way break-even and profit move when an input changes), and the contribution-margin income-statement format. Both exams are closed-book, so the formulas have to live in your head — and the single most-tested cost idea is the reversal that “constant” means different things for fixed and variable costs.
What this chapter covers
- 013.1 The behaviour split: fixed, variable, mixed (semi-variable)
- 023.2 Direct vs indirect; product vs period
- 033.3 The relevant range
- 043.4 Contribution margin — CM per unit and CM ratio
- 05Break-even in units and in dollars
- 06Target-profit volume; profit at a given volume
- 073.5 Margin of safety (units, $, %)
- 083.6 The contribution-margin income statement
- 093.7 The break-even chart and sensitivity direction rules
Worked example: CVP end-to-end
- +1Contribution margin first. CM = $24 − $9 = $15 per unit.
- +1(a) Break-even units. = Fixed costs ÷ CM per unit = $90,000 ÷ $15 = 6,000 units.
- +2(b) Profit at 10,000 units. = (CM × units) − FC = ($15 × 10,000) − $90,000 = $150,000 − $90,000 = $60,000.
- +2(c) Units for a $30,000 target. = (FC + target) ÷ CM = ($90,000 + $30,000) ÷ $15 = $120,000 ÷ $15 = 8,000 units.
Key terms
- Variable cost
- A cost that is constant per unit but rises proportionally in total as volume rises (materials, packaging). The “constant” describes the per-unit figure — the opposite of a fixed cost.
- Fixed cost
- A cost that is constant in total within the relevant range but falls per unit as volume rises (rent, salaried staff, insurance). Spread over more units, the per-unit fixed cost shrinks.
- Contribution margin
- Selling price minus variable cost per unit — what each unit contributes first to covering fixed costs, then to profit. The CM ratio is CM per unit ÷ selling price (or total CM ÷ total sales).
- Break-even point
- The volume at which total contribution margin exactly equals total fixed costs, so profit is zero. In units = FC ÷ CM per unit; in dollars = FC ÷ CM ratio.
- Margin of safety
- How far sales can fall from the actual or budgeted level before hitting break-even — a direct read on risk. MoS (units or $) = actual sales − break-even sales; MoS % = MoS ÷ actual sales.
Cost Behaviour and CVP FAQ
What is the difference between break-even in units and in dollars?
Both start from fixed costs but use a different denominator. Break-even in units = fixed costs ÷ contribution margin per unit; break-even in dollars = fixed costs ÷ the contribution-margin ratio. Mixing the two denominators is the #1 CVP error. They reconcile: break-even units × selling price = break-even dollars (e.g. 6,000 units × $24 = $144,000).
Where does target profit go in the formula?
In the numerator, added to fixed costs: target units = (fixed costs + target profit) ÷ CM per unit. Putting target profit in the denominator is the second-most common CVP mistake. The logic: you need enough contribution to cover fixed costs and the desired profit, so both sit on top.
What is the margin of safety telling me?
How much sales can drop before the business stops making a profit. If budgeted sales are 10,000 units and break-even is 6,000, the margin of safety is 4,000 units, or 40% of sales — sales could fall 40% before a loss. A larger margin of safety means lower risk. If break-even comes out above budgeted volume, the plan loses money — that is a finding, not a mistake.
Which way does break-even move when an input changes?
Break-even moves opposite to the contribution margin. Anything that thins the CM — a higher variable cost or a lower price — makes break-even rise (you need more units to cover the same fixed costs). A change in fixed cost moves break-even the same direction as the change (FC up → break-even up) but leaves CM untouched. Examiners often ask only the direction, not a recomputation.
Exam move
Lock the fixed/variable split first — everything downstream depends on it, and the per-unit-vs-total reversal is the single most-tested cost MCQ. Drill the four CVP formulas as a reflex (CM, break-even units, break-even dollars, target volume) and always show formula → substitution → answer with units, because closed-book markers award method marks for the stated formula. Pick the denominator on purpose (CM per unit → units; CM ratio → dollars) and keep target profit in the numerator. For “what happens if…?” questions, answer the direction via the chain change → effect on CM → effect on profit and break-even, and remember break-even moves opposite to CM. State the “within the relevant range” caveat in short answers — it is a full-mark detail.
