IB DP Business Management: Break-even analysis

This guide teaches section 5.5 (Break-even analysis) of the IB Business management guide, first assessment 2024. The section sits in Unit 5 (Operations management) and applies to both SL and HL, because the guide does not mark any of it as HL only. The guide asks for total contribution versus contribution per unit, a break-even chart with six aspects of break-even analysis, the effects of changes in price or cost using graphical and quantitative methods, and the limitations of break-even as a decision-making tool. The depth-of-teaching labels are AO2 and AO4 for the calculations and chart, and AO3 for the limitations.

Related pages: the 5.5 revision notes for quick recall and the 5.5 practice questions for original questions. Costs are taught in the 3.3 costs and revenues guide. See the IB Business Management hub, the printable checklist and the free diagnostics to find weak spots.

What the guide lists for 5.5

Guide point	What you must be able to do	Depth
Total contribution versus contribution per unit	Calculate both and say how they differ	AO2
A break-even chart	Read, draw and interpret the chart	AO2, AO4
Break-even quantity/point	Find the output where revenue equals total cost	AO2, AO4
Profit or loss	Find it at any output, by chart or formula	AO2, AO4
Margin of safety	Find the gap between actual and break-even output	AO2, AO4
Target profit output	Find the output needed for a chosen profit	AO2, AO4
Target profit	Find the profit made at a chosen output	AO2, AO4
Target price	Find the price needed to reach a chosen profit	AO2, AO4
Effects of changes in price or cost	Show the change on the chart and by calculation	AO2, AO4
Limitations of break-even	Explain why the tool can mislead	AO3

The guide gives no formulas for this section. Every formula below is a usual textbook form, not a quotation from the guide.

Contribution: per unit and total

Break-even analysis separates costs into fixed costs (they do not change with output, such as rent) and variable costs (they change with output, such as materials). If those terms feel shaky, read the 3.3 guide first.

Contribution per unit is the selling price per unit minus the variable cost per unit. It is the amount each unit sold adds towards covering fixed costs, and then towards profit.

Total contribution is contribution per unit multiplied by the number of units sold. It is also total revenue minus total variable costs.

The difference matters because each answers a different question. Contribution per unit tells you how strong one sale is. Total contribution tells you how much money the whole sales volume has available to pay fixed costs. Profit is total contribution minus fixed costs.

Running example

Kilbrook Pottery is an invented studio that makes ceramic mugs. All figures below are invented and all money amounts are in dollars.

• Selling price: 40 per mug
• Variable cost: 16 per mug
• Fixed costs: 12,000 per month
• Capacity: 800 mugs per month
• Current output and sales: 650 mugs per month

Contribution per unit = 40 − 16 = 24.

Total contribution at 650 mugs = 650 × 24 = 15,600.

Profit = 15,600 − 12,000 = 3,600.

The studio sells more than it needs to pay its bills, so it makes a profit. How much more? The margin of safety answers that, below.

Break-even quantity (point)

The break-even quantity is the output at which total revenue equals total costs, so profit is zero. At lower output the business makes a loss. At higher output it makes a profit.

Standard form:

Break-even quantity = fixed costs / contribution per unit

For Kilbrook Pottery: 12,000 / 24 = 500 mugs.

The break-even point is often given in revenue terms too: 500 × 40 = 20,000. If the sum is not a whole number, round up, because you cannot sell part of a unit and still break even.

Profit or loss at any output

Use the contribution route:

Profit (or loss) = (output × contribution per unit) − fixed costs

At 200 mugs: 200 × 24 = 4,800, then 4,800 − 12,000 = −7,200, a loss of 7,200.

At 800 mugs: 800 × 24 = 19,200, then 19,200 − 12,000 = 7,200 profit.

Check this against the long way. At 650 mugs, total revenue is 650 × 40 = 26,000. Total cost is 12,000 + (650 × 16) = 22,400. Profit is 26,000 − 22,400 = 3,600, the same answer.

The break-even chart

A break-even chart is a graph. Output in units goes along the bottom, and money (cost and revenue) goes up the side. Draw four things.

1. Fixed cost line. A horizontal line at 12,000.
2. Total cost line. It starts at 12,000 on the vertical axis (output zero) and rises by 16 for every extra mug.
3. Total revenue line. It starts at the origin and rises by 40 per mug.
4. Break-even point. The point where the total revenue and total cost lines cross.

Values to plot for Kilbrook Pottery:

Output (mugs)	Fixed costs	Total costs	Total revenue
0	12,000	12,000	0
200	12,000	15,200	8,000
500	12,000	20,000	20,000
800	12,000	24,800	32,000

A rough sketch in words:

32,000 |                         / TR
24,800 |                    ___/_ TC
20,000 |              ____X/        X = break-even, 500 mugs
12,000 |-------------/- - - - - - FC
       |
       +------------------------- output

On the chart you can read each aspect:

• Break-even quantity: drop a vertical line from the crossing point to the output axis.
• Loss: the gap between the lines, where total cost is above total revenue, to the left of the crossing point.
• Profit: the gap to the right of the crossing point, where revenue is above cost.
• Margin of safety: the horizontal distance from the break-even output to the actual output.

Label both axes and every line, and mark the break-even point.

Margin of safety

Margin of safety is the amount by which actual (or planned) output is above the break-even output. It tells you the fall in sales the business can absorb and still avoid a loss.

Margin of safety (units) = actual output − break-even quantity

For Kilbrook Pottery: 650 − 500 = 150 mugs.

You can also give it as a percentage of actual output: 150 / 650 × 100 = 23.1%. State which base you use, because a percentage of capacity (150 / 800 = 18.75%) would be a different figure. A wide margin means sales can fall without a loss. A narrow margin means a small drop in demand could push the business into loss.

Target profit output and target profit

Target profit output is the output needed to reach a profit the business has chosen.

Target profit output = (fixed costs + target profit) / contribution per unit

If Kilbrook Pottery wants 6,000 profit: (12,000 + 6,000) / 24 = 750 mugs. This is under the 800-mug capacity, so it is possible.

Target profit, in the way the guide lists it, is the profit made at a chosen output. It uses the profit formula above. At 800 mugs the target profit is 7,200, as shown earlier. The two ideas are inverses. One asks “what output gives this profit?” and the other asks “what profit does this output give?”

Target price

Target price is the price that must be charged to reach a target profit at a given output.

Target price = (fixed costs + variable costs at that output + target profit) / output

Suppose Kilbrook Pottery expects to sell 600 mugs and wants a 6,000 profit. Variable costs are 600 × 16 = 9,600. Required revenue is 12,000 + 9,600 + 6,000 = 27,600. Price = 27,600 / 600 = 46.

Check: 600 × (46 − 16) = 18,000, then 18,000 − 12,000 = 6,000. It works. Whether customers will pay 46 is a separate question.

Effects of changes in price or cost

The guide asks for these effects on the break-even quantity, profit and margin of safety, using graphical and quantitative methods. Keep output at 650 mugs and change one thing at a time.

Change	Contribution per unit	Break-even quantity	Profit at 650	Margin of safety
None (base case)	24	500	3,600	150
Price up to 44	28	428.6, so 429	6,200	221
Variable cost up to 20	20	600	1,000	50
Fixed costs up to 15,000	24	625	600	25

Quantitative method: recalculate with the new figure. For the price rise, 12,000 / 28 = 428.6 and profit is 650 × 28 − 12,000 = 6,200. Margin of safety is 650 − 429 = 221.

Graphical method:

• Higher price: the total revenue line becomes steeper, so it crosses the total cost line sooner. The break-even point moves left.
• Higher variable cost: the total cost line becomes steeper, so the crossing moves right.
• Higher fixed costs: the total cost line is lifted by the extra amount and stays parallel to its old position, so the crossing again moves right. The fixed cost line moves up.

Reverse changes move the lines the other way. A price rise may also cut demand, and the table shows only the arithmetic.

Limitations of break-even as a decision-making tool

The guide lists limitations without naming them, so these are the common ones. Pick those that fit the case.

• Straight lines. Revenue and cost lines are drawn straight. Real prices fall with discounts, and bulk buying can cut variable cost per unit.
• Fixed costs may not stay fixed. A business that expands output may need another machine or a larger unit, so fixed costs step up.
• Assumes all output is sold. Stock left on the shelf has been paid for but earns nothing.
• One product. With several products at different prices, splitting fixed costs between them is difficult.
• Forecast data. Costs, price and demand are estimates. An error in any of them shifts the break-even point.
• Static. The chart shows one moment. Costs change, competitors react and demand moves.
• Ignores non-financial factors. Quality, reputation, employee welfare and ethical concerns do not appear on the chart.
• Does not show demand. The tool does not say whether customers will buy the break-even quantity at that price.

For an AO3 answer, do not just list. Take one or two limitations and tie them to the case, then say whether the tool is still useful. For example, it helps a start-up see the sales it needs but cannot show whether those sales are realistic.

Worked example: a short decision

Kilbrook Pottery is thinking about cutting its price to 36 to attract more customers. Fixed and variable costs stay the same.

• Contribution per unit = 36 − 16 = 20.
• Break-even quantity = 12,000 / 20 = 600 mugs, up from 500.
• At 650 mugs, profit = 650 × 20 − 12,000 = 1,000, down from 3,600.
• Margin of safety = 650 − 600 = 50 mugs, down from 150.

The studio would need to sell more than 650 mugs just to equal its present profit. Required output for 3,600 profit = (12,000 + 3,600) / 20 = 780 mugs. That is close to the 800-mug capacity, so the cut looks risky unless demand rises strongly. This is the kind of reasoned use of numbers that the AO4 label points to.

Common errors

• Using total fixed costs as the contribution. Contribution is price minus variable cost per unit.
• Dividing the fixed costs by the selling price, when the divisor must be the contribution on each unit.
• Putting the total cost line through the origin. It starts at the fixed cost level.
• Mixing margin of safety units and percentages without saying which one you give.
• Leaving out units or the currency.

Next steps

Test yourself with the 5.5 practice questions, then revise from the 5.5 revision notes. The IB Business Management hub lists the other units and the checklist tracks your progress. The diagnostics can show you where to start.

Frequently asked questions

What does a break-even chart show? A break-even chart plots output along the horizontal axis and costs and revenue up the side, with fixed cost, total cost and total revenue lines. The break-even point is where total revenue crosses total cost.

How does a price rise affect the break-even point? A higher price makes the total revenue line steeper, so it crosses the total cost line sooner and the break-even point moves left. A price rise may also cut demand, which the chart does not show.

What are the limitations of break-even analysis? It assumes straight-line revenue and costs, fixed costs that stay fixed and that all output is sold. It suits one product, relies on forecasts, is static, ignores non-financial factors and does not show demand.

Where does the total cost line start on a break-even chart? The total cost line starts at the fixed cost level on the vertical axis at zero output, not at the origin.

Official syllabus

International Baccalaureate Organization, Business management guide, first assessment 2024, section 5.5 Break-even analysis.