EN.662.611 Chap.10 Breakeven and Cost-Volume-Profit Analysis
Breakeven and Cost-Volume-Profit Analysis
Cost behavior sets the stage
Week 10's second lecture builds on cost behavior. Fixed costs are constant within a relevant range, the band of activity over which the cost structure holds; beyond it, fixed costs step up. Variable costs rise in a straight line with volume.
On a cost-volume-profit graph the breakeven point is where total revenue meets total cost: below it the company makes a loss, above it income.
Contribution margin
Contribution margin is sales minus total variable costs. Below breakeven it contributes to fixed costs; above breakeven it contributes to income, so operating income changes by exactly the change in contribution margin.
Expressed per unit it is price minus variable cost per unit; as a ratio it is contribution margin divided by total revenue.
Breakeven and target profit
Setting revenue minus variable costs minus fixed costs to zero and solving gives breakeven units as fixed costs divided by contribution margin per unit, and breakeven dollars as fixed costs divided by the contribution margin ratio.
A company does not aim to break even, so a target profit is treated as an additional fixed cost: required units equal fixed costs plus target profit, divided by contribution margin per unit.
Formats, what-if questions and assumptions
The traditional or absorption format separates product from period costs and serves external reporting; the contribution format separates variable from fixed and serves planning and decisions.
Cost-volume-profit analysis is a set of what-if tests on fixed costs, variable cost per unit, price and volume, with volume linked to price through elasticity of demand. It assumes a constant price, costs that are purely fixed or variable, linear variable cost, a constant product mix and no material change in inventory.
Where breakeven meets pricing
The most common use of this chapter is pricing.
When an input cost rises, a company can absorb it, pass it on in price, or do a little of both. Breakeven analysis shows the tradeoff: a higher price raises contribution per unit and lowers the breakeven point, but if demand is elastic the volume lost can outweigh the margin gained. Computing operating income under each option, rather than arguing from margin alone, settles the question.
What this chapter covers
- 01
Fixed and variable cost behavior
- 02
The relevant range
- 03
Contribution margin per unit and ratio
- 04
Breakeven in units and in dollars
- 05
Target profit
- 06
Traditional versus contribution format
- 07
Price changes and elasticity
- 08
Simplifying assumptions
Worked example · free
Test a price cut
- 1Now: contribution $16 a unit; income 15,000 times $16 less $192,000 is $48,000.
- 1Now: breakeven is $192,000 divided by $16, or 12,000 units.
- 1Proposal: contribution $12; income 20,000 times $12 less $192,000 is $48,000.
- 1Proposal: breakeven rises to $192,000 divided by $12, or 16,000 units.
Key terms
- Breakeven Point
- The volume at which total revenue equals total cost and operating income is zero.
- Contribution Margin Ratio
- Contribution margin divided by total revenue, the share of each sales dollar left after variable cost.
- Relevant Range
- The span of activity within which fixed costs stay constant and variable cost per unit holds.
- Contribution Format
- An income statement that subtracts variable costs from sales, then fixed costs, to reach operating income.
- Price Elasticity
- How strongly the quantity demanded responds to a change in price.
Breakeven and Cost-Volume-Profit Analysis FAQ
Why does operating income change faster than sales?
Fixed costs do not move with volume, so every extra sale adds its whole contribution margin to income. A given percentage rise in sales therefore produces a larger percentage rise in operating income.
How do I find breakeven in dollars without units?
Divide fixed costs by the contribution margin ratio. The ratio says how much of each sales dollar remains after variable costs, so the result is the sales revenue needed to cover fixed costs exactly.
Is breakeven the goal of this analysis?
No. Companies aim for a profit, so the course treats a target profit as one more cost to cover and solves for the volume that delivers it.
Exam move
For one product, write both income statement formats, compute breakeven three ways, then run three what-if cases: a cost increase, a price rise with a volume loss, and a new fixed cost. Check each result by recomputing income directly.
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