Cost–Volume–Profit Analysis
Cost–Volume–Profit Analysis
For one product within a relevant range:
Unit contribution margin is price less unit variable cost. It is the amount available to cover fixed cost and then profit.
Northstar base case
- price: £600 per City bike;
- variable cost: £360 per bike;
- annual fixed cost: £480,000;
- forecast sales: 2,800 bikes.
| Measure | Calculation | Result |
|---|---|---|
| Unit contribution | £600 − £360 | £240 |
| Break-even units | £480,000 / £240 | 2,000 |
| Units for £120,000 target profit | (£480,000 + £120,000) / £240 | 2,500 |
| Forecast profit | 2,800 × £240 − £480,000 | £192,000 |
| Margin of safety | 2,800 − 2,000 | 800 units, 28.6% of forecast |
Break-even is not a goal. It is the point at which the modelled profit is zero.
The 5% discount is not a 5% volume problem
If price falls 5% to £570 and variable cost remains £360:
- contribution falls from £240 to £210, a 12.5% decline;
- break-even rises to 2,286 units;
- target-profit volume rises from 2,500 to 2,857 units, a 14.3% increase.
Small price changes can have large profit effects because contribution, not revenue, absorbs the change.
Explore the model
Northstar CVP scenario
Change price, variable cost or fixed cost one at a time, then together. The purpose is to see which assumption drives the decision.
Assumptions to expose
Basic CVP assumes:
- constant unit price and variable cost within the range;
- fixed total cost within the range;
- units produced equal units sold, or inventory effects are handled separately;
- a stable sales mix for multiple products;
- volume is the main activity driver.
At 3,000 bikes Northstar may need a second shift, making fixed cost step upward. A model beyond its relevant range is mathematically correct and economically wrong.
Multiple products
Use a weighted-average contribution only if the sales mix is explicit and reasonably stable. If demand shifts toward lower-contribution Cargo contracts, a single break-even total can conceal the mix effect.
Quick check
Variable cost rises to £390 with price and fixed cost unchanged. What is break-even?