ACT503 Chap.3 Cost Volume Profit Analysis
Cost Volume Profit Analysis
One rearranged income statement, and everything that falls out of it
Contribution margin is revenue less variable costs, and the course definition says all the variable costs, whatever business function they sit in.
Contribution margin per unit is the selling price less the variable cost per unit, and the contribution margin ratio is total contribution margin divided by total sales, which equals contribution margin per unit divided by selling price.
Once costs are sorted by behaviour rather than by function, profit can be written three ways and the breakeven point, the target income volume, the margin of safety and the operating leverage all follow from three inputs.
Gross margin is a different subtotal: it deducts cost of goods sold, which contains absorbed fixed manufacturing overhead, while contribution margin deducts variable selling and distribution costs that sit far below gross margin in the traditional statement.
Six assumptions, each of which is a question a paper can ask
Volume is the sole cause of changes in revenues and costs.
Total costs divide cleanly into a fixed component and one that varies with output. Both the revenue and the cost functions are linear within the relevant range. Selling price, variable cost per unit and total fixed costs are known and constant. There is a single product, or a sales mix that is known and constant.
And the time value of money is ignored, which is why a capital investment decision is not settled with a breakeven calculation.
A question that changes the sales mix has changed the average contribution margin and every answer that depends on it.
Sensitivity, margin of safety and leverage answer different questions
Sensitivity analysis is the structured what if on price, volume, variable cost per unit or fixed costs, and its discipline is to rebuild the contribution margin from the new inputs rather than nudging the previous answer, because most scenarios change more than one driver at once.
Margin of safety is the distance between budgeted sales and breakeven sales, stated in value, in units or as a ratio, and the ratio form removes the effect of firm size. The degree of operating leverage is contribution margin divided by operating income at a stated volume, and it multiplies a percentage change in sales rather than an amount, which is exactly the distractor a multiple choice item will offer.
What this chapter covers
- 01
Contribution margin, per unit and as a ratio
- 02
Contribution margin against gross margin, and when they diverge
- 03
Three ways of writing profit, and which one gives units
- 04
Six assumptions the model rests on
- 05
Breakeven in units and in sales value
- 06
Target operating income, added into the numerator
- 07
Sensitivity analysis with several drivers moving at once
- 08
Margin of safety in value, units and as a ratio
- 09
Degree of operating leverage and what it multiplies
Run the full chain, then test it with three drivers moving
- 2Contribution margin per unit and as a ratio.
- 3Breakeven in units and in sales value, and confirm they agree.
- 3Volume and sales value for the target operating income.
- 4Rebuild under the proposal and state the verdict with a reason.
Key terms
- Contribution Margin Ratio
- Total contribution margin divided by total sales, which is also contribution margin per unit divided by selling price per unit. It is the form to use whenever a question asks for an answer in sales value rather than in units.
- Breakeven Point
- The sales level that leaves nothing over once every cost has been met. It is found by setting profit to nil and dividing fixed expenses by contribution margin per unit for a unit answer or by the contribution margin ratio for a value answer.
- Margin Of Safety
- The distance between budgeted or actual sales and breakeven sales, showing how far revenue can fall before losses begin. As a ratio it is that distance divided by budgeted sales, which removes the effect of firm size from the comparison.
- Operating Leverage
- A measure of how sensitive operating income is to a percentage change in sales at a given sales level, computed as contribution margin divided by operating income. It cannot be computed at breakeven, where operating income is zero.
- Sensitivity Analysis
- A structured examination of what happens to operating income when selling price, volume, variable cost per unit or fixed costs change. Its discipline is rebuilding the contribution margin from the new inputs rather than adjusting a previous answer.
Cost Volume Profit Analysis FAQ
Why is contribution margin not the same thing as gross margin?
Gross margin deducts cost of goods sold, which contains the fixed manufacturing overhead absorbed into the units, while contribution margin deducts every variable cost including selling and distribution costs that sit well below gross margin in a traditional statement.
A firm with heavy fixed manufacturing overhead reports a lower gross margin than contribution margin, and one paying large sales commissions on a lightly automated product reports the reverse.
Where does the target operating income go in the formula?
Into the numerator, added to fixed costs, with nothing else changing. Dividing by contribution margin per unit gives the required units and dividing by the contribution margin ratio gives the required sales value. The target is an operating income figure rather than an after tax one, so there is no tax gross up unless a question supplies a rate and asks for one explicitly.
If a scenario changes three things at once, can I adjust my earlier answer?
No. Rebuild the contribution margin per unit and the fixed cost total from the new inputs and start again, because an adjustment made from a previous figure assumes only one driver moved. A price cut, a variable cost rise and an advertising increase acting together can raise sales value and lower operating income at the same time, and only a rebuilt calculation shows that.
A ten per cent rise in sales with a leverage of three point four gives what?
A thirty four per cent rise in operating income, because the degree of operating leverage multiplies the percentage change in sales rather than the amount of it. The ten per cent answer exists in a multiple choice option list precisely to catch a candidate who has recalled the measure without recalling what it operates on.
Exam move
Build one contribution statement for a business you know and then attack it four times: cut the price, raise the variable cost, raise the fixed cost and change the volume, rebuilding each time rather than adjusting. Ten minutes of that is worth more than re-reading the formulas, because the formulas are short and the rebuilding habit is what an examination is actually testing.
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