What is Cost-Volume-Profit (CVP) Analysis?
A technique that examines the relationship between costs, volume (activity level), and profit. It helps managers understand how changes in costs and volume affect profit and make informed decisions.
What is the Break-Even Point (BEP)?
The level of activity (sales volume) at which total revenue equals total costs. At this point, the business makes neither a profit nor a loss. Below BEP = loss, Above BEP = profit.
Break-Even Point in Units Formula
BEP (units) = Total Fixed Costs / Contribution per unit
Where:
- Total Fixed Costs = all fixed costs for the period
- Contribution per unit = Selling Price per unit - Variable Cost per unit
This tells you how many units must be sold to break even.
Break-Even Point Example 1 (Units)
Selling price per unit = £50
Variable cost per unit = £30
Fixed costs = £40,000
Contribution per unit = £50 - £30 = £20
BEP (units) = £40,000 / £20 = 2,000 units
Must sell 2,000 units to break even.
Break-Even Point Example 2 (Units)
Selling price per unit = £100
Variable cost per unit = £60
Fixed costs = £80,000
Contribution per unit = £100 - £60 = £40
BEP (units) = £80,000 / £40 = 2,000 units
Must sell 2,000 units to break even.
Break-Even Point in Revenue Formula
BEP (revenue) = Total Fixed Costs / Contribution to Sales (C/S) Ratio
Where:
- C/S Ratio = (Contribution per unit / Selling Price per unit) × 100
OR
- C/S Ratio = (Total Contribution / Total Sales Revenue) × 100
This tells you the sales revenue needed to break even.
Contribution to Sales (C/S) Ratio Formula
C/S Ratio = (Contribution / Sales Revenue) × 100
OR
C/S Ratio = (Contribution per unit / Selling Price per unit) × 100
This shows what percentage of each sales pound is contribution. Also called Profit-Volume (P/V) Ratio.
C/S Ratio Example
Selling price per unit = £50
Variable cost per unit = £30
Contribution per unit = £20
C/S Ratio = (£20 / £50) × 100 = 40%
This means 40% of each £1 of sales contributes to covering fixed costs and profit.
Break-Even Point Example (Revenue)
Fixed costs = £40,000
Selling price per unit = £50
Variable cost per unit = £30
C/S Ratio = 40% (from previous example)
BEP (revenue) = £40,000 / 0.40 = £100,000
Must achieve £100,000 in sales revenue to break even.
Check: 2,000 units × £50 = £100,000 ✓
What is the Margin of Safety?
The amount by which actual or budgeted sales EXCEED the break-even sales level. It measures how much sales can fall before a loss is made. A larger margin = less risk.
Margin of Safety in Units Formula
Margin of Safety (units) = Budgeted/Actual Sales Units - Break-Even Sales Units
This shows how many units of buffer exist above break-even.
Margin of Safety as Percentage Formula
Margin of Safety (%) = (Margin of Safety in Units / Budgeted/Actual Sales Units) × 100
This expresses the safety margin as a percentage of budgeted/actual sales.
Margin of Safety Example
Break-even sales = 2,000 units
Budgeted sales = 2,500 units
Margin of Safety (units) = 2,500 - 2,000 = 500 units
Margin of Safety (%) = (500 / 2,500) × 100 = 20%
Sales can fall by 500 units or 20% before making a loss.
Interpreting Margin of Safety
High Margin of Safety (e.g., >30%): Lower risk, substantial buffer before losses
Medium Margin (15-30%): Moderate risk, reasonable buffer
Low Margin (<15%): High risk, vulnerable to demand fluctuations
Negative Margin: Currently making a loss, below break-even
What is Target Profit?
The desired level of profit a business wants to achieve. CVP analysis can calculate the sales volume needed to achieve this target.
Target Profit Formula (Units)
Units to achieve Target Profit = (Fixed Costs + Target Profit) / Contribution per unit
This shows how many units must be sold to achieve the desired profit.
Target Profit Example 1
Fixed costs = £40,000
Contribution per unit = £20
Target profit = £30,000
Units required = (£40,000 + £30,000) / £20 = £70,000 / £20 = 3,500 units
Must sell 3,500 units to make £30,000 profit.
Target Profit Example 2
Fixed costs = £100,000
Selling price = £80 per unit
Variable cost = £50 per unit
Target profit = £50,000
Contribution per unit = £80 - £50 = £30
Units required = (£100,000 + £50,000) / £30 = £150,000 / £30 = 5,000 units
Target Profit Formula (Revenue)
Sales Revenue to achieve Target Profit = (Fixed Costs + Target Profit) / C/S Ratio
This shows the sales revenue needed to achieve the desired profit.
Target Profit Example (Revenue)
Fixed costs = £40,000
Target profit = £30,000
C/S Ratio = 40%
Sales Revenue required = (£40,000 + £30,000) / 0.40 = £70,000 / 0.40 = £175,000
Must achieve £175,000 in sales to make £30,000 profit.
What are the assumptions of CVP Analysis?
- Selling price per unit is constant (no volume discounts)
- Variable cost per unit is constant (no economies of scale)
- Fixed costs remain constant over the relevant range
- All units produced are sold (no inventory changes)
- Sales mix remains constant (for multi-product analysis)
- Technology and efficiency remain constant
What is a Limiting Factor?
A scarce resource that restricts an organization’s ability to meet demand or achieve objectives. Also called a key factor or bottleneck. Examples: limited machine hours, labour hours, materials, or floor space.
When does Limiting Factor Analysis apply?
When demand exceeds the organization’s capacity due to a scarce resource. The business must decide which products to produce/sell to maximize profit given the constraint.
Limiting Factor Analysis - Decision Rule
Prioritize production of products that generate the HIGHEST contribution per unit of the limiting factor. Produce/sell these products first until demand is met or the limiting factor is exhausted.
