2. Planning and Control

Cost–Volume–Profit Analysis

Turn price, cost and capacity assumptions into a transparent profit model

Cost–Volume–Profit Analysis

For one product within a relevant range:

Profit=(pricevariable cost)Qfixed cost\text{Profit} = (\text{price} - \text{variable cost})Q - \text{fixed cost}

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.
MeasureCalculationResult
Unit contribution£600 − £360£240
Break-even units£480,000 / £2402,000
Units for £120,000 target profit(£480,000 + £120,000) / £2402,500
Forecast profit2,800 × £240 − £480,000£192,000
Margin of safety2,800 − 2,000800 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

Py

Northstar CVP scenario

Idle

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?

Answer
Unit contribution is £210. Break-even is £480,000 / £210 = 2,285.7, so at least 2,286 whole bikes under the model.

Next: Budgeting and Variances

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