ACF5955 Chap.5 Cost-Volume-Profit Analysis
Cost-Volume-Profit Analysis
Cost-volume-profit analysis links selling price, variable cost, fixed cost and activity through contribution margin. This chapter derives break-even in units and sales dollars, extends the model to target profit and after-tax targets, measures margin of safety and operating leverage, and handles sales mix through weighted contribution.
It also identifies capacity steps, price changes and other assumptions that require a new relevant-range model. Worked checks substitute the result back into the contribution equation and keep units separate from sales dollars. Scenario analysis shows why a discount, cost-rate change or expansion cannot always be handled by adjusting an old break-even figure.
The chapter therefore treats CVP as a conditional planning model, with explicit limits for demand, capacity and product mix.
What this chapter covers
- 01
Contribution margin
- 02
Break-even units and revenue
- 03
Target profit
- 04
After-tax targets
- 05
Margin of safety
- 06
Sales mix and CVP assumptions
Worked example · free
Plan break-even and target profit
- +2Unit contribution is $9 minus $3.60, which equals $5.40.
- +2Break-even is $32,400 divided by $5.40, which equals 6,000 drinks.
- +2Target volume is $43,200 divided by $5.40, which equals 8,000 drinks.
- +2Check: 8,000 times $5.40 less $32,400 equals the $10,800 target.
Key terms
- Contribution margin
- Contribution margin is revenue less variable cost and covers fixed cost before creating profit.
- Break-even point
- The break-even point is the activity where total contribution exactly equals fixed cost.
- Margin of safety
- Margin of safety is budgeted sales above break-even sales and measures how far sales can fall before profit reaches zero.
- Sales mix
- Sales mix is the relative proportion of products sold and determines weighted contribution in a multi-product model.
Cost-Volume-Profit Analysis FAQ
Why does break-even use contribution margin?
Each unit's contribution first covers fixed cost. Dividing fixed cost by contribution per unit therefore finds the number of units needed before any profit remains. The same logic supports target-profit calculations.
What invalidates a single CVP line?
A capacity step, volume discount, variable-rate change or changing product mix alters the model parameters. Separate relevant ranges should be calculated rather than extending one linear relationship across every activity level.
What does margin of safety tell management?
It measures the distance between planned sales and break-even. A narrow margin signals immediate demand risk, but the measure remains conditional on the current price, variable rate, fixed cost and sales mix.
Exam move
Rebuild every formula from Profit = total contribution minus fixed cost. Show units beside each denominator and verify target profit by substitution. For multiple products, calculate a composite contribution using the stated mix and unpack the bundle. Finish with sensitivity: identify which assumption is most likely to move and how that change shifts the break-even boundary.
Begin each problem with a compact contribution statement: selling price, variable cost, contribution per unit, contribution ratio and fixed cost. Label every value as dollars per unit, total dollars or a percentage. This dimensional habit reveals whether dividing fixed cost will produce units or sales revenue. Derive break-even by setting profit to zero rather than recalling an isolated formula.
For target profit, add the target to fixed cost and substitute the resulting volume back into revenue less variable and fixed cost. If the target is after tax, convert it to a pretax amount first and label the tax basis. Draw the sales and total-cost lines with their intercepts and slopes.
Use the graph to explain why contribution covers capacity before generating profit and why the same straight lines cannot survive a price discount or capacity step. At the calculated intersection, verify that revenue equals total cost and contribution equals fixed cost. Build a safety-margin table in units, dollars and percentage, always dividing the margin by budgeted or actual sales rather than break-even sales.
Link a narrow margin to demand exposure. For operating leverage, explain why a fixed-cost structure produces greater percentage movement in profit without claiming that high leverage is automatically good or bad. In multi-product cases, define one composite bundle from the stated sales mix, calculate its weighted contribution and translate bundle break-even back into product quantities.
Then change the mix toward the lower-contribution item and predict the direction of the new boundary. Create segmented models when assumptions change across ranges: one set of parameters before a capacity addition, another after it, and separate price tiers where discounts apply. Compare alternatives at realistic volumes and identify their crossover.
Finish with a sensitivity paragraph naming the parameter nearest to a decision threshold and the qualitative constraint that the equation omits, such as capacity, demand, quality or flexibility. Timed drills should end with an answer unit, an arithmetic check and one assumption whose failure would require rebuilding rather than merely adjusting the model.
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