Business · 4 Operations management

4.4.3 Break-even analysis

Before you start

Fixed costs, variable costs and total cost, with their formulas (4.4.1).
Revenue = Selling price per unit × number of units sold, and Profit = Total revenue – total costs.
Plotting points on a graph with labelled axes and joining them with a ruled straight line.

Syllabus objectives covered (7)

concept of break-even
complete or amend a simple break-even chart
interpret a break-even chart
calculate break-even output
define, calculate and interpret the margin of safety
use break-even analysis to help make decisions: effect of changes in price, changes in fixed costs, changes in variable cost per unit
limitations of break-even analysis

Part 1 of 7

The break-even idea

A business makes a loss when its total costs are greater than its total revenue, and a profit when its total revenue is greater than its total costs. Between the two there is a level of output where they are exactly equal.
That level is break-even: the level of output at which total revenue equals total costs, so the business makes neither a profit nor a loss.
Why is there a loss at low output? Because fixed costs must be paid even if nothing is sold. Each unit sold pays off a little more of them, and break-even is the output at which they have been fully covered.
Break-even analysis answers practical questions. How many must we sell before we make any profit? Is that number realistic? What happens if we change our price, or our costs rise? A new business can use it in a business plan to show a lender that the idea can work.

Part 2 of 7

Contribution, and calculating break-even output

The key idea is contribution. When a business sells one unit it receives the selling price, but it also has to pay that unit's variable cost. What is left over contributes towards paying the fixed costs.
$Contribution per unit = selling price per unit - variable cost per unit$
Lumo Lamps sells desk lamps for $$ 25$ each. Each lamp costs $$ 10$ in parts and packaging. So each sale contributes $$ 25$ − $$ 10$ = $$ 15$ towards Lumo's fixed costs of $$ 6,000$ a month.
To break even, Lumo needs enough $$ 15$ contributions to add up to $$ 6,000$ . Finding how many is a division.
$Break-even output = \frac{Fixed costs}{Contribution per unit}$
For Lumo:
$\frac{$ 6,000}{$ 15} = 400 lamps$
The answer is a number of units — lamps — not dollars. Writing $$ 400$ is a common slip: dividing dollars by dollars per lamp leaves lamps.
Check any break-even answer by working out total revenue and total costs at that output. At 400 lamps, revenue = $$ 25$ × 400 = $$ 10,000$ , and total costs = $$ 6,000$ + ( $$ 10$ × 400) = $$ 10,000$ . They are equal, so 400 is right.
The rounding trap. When the division does not give a whole number, always round up. Break-even is the output at which the business stops making a loss, and a business cannot sell part of a unit.
Suppose fixed costs were $$ 5,000$ , the price $$ 12$ and the variable cost $$ 5$ . Contribution is $$ 7$ , and $$ 5,000$ ÷ $$ 7$ = 714.28… At 714 units the contributions come to 714 × $$ 7$ = $$ 4,998$ — still $$ 2$ short, so still a loss. At 715 units they come to $$ 5,005$ . Break-even output is 715 units, even though ordinary rounding would give 714.

Part 3 of 7

Drawing a break-even chart

A break-even chart shows the same idea as a picture. Output goes on the horizontal axis; costs and revenue, in dollars, go on the vertical axis. The chart has three straight lines.
Fixed costs: a horizontal line at the level of fixed costs, because they do not change with output. For Lumo, a flat line at $$ 6,000$ .
Total costs: this line starts at the fixed-costs level on the vertical axis — not at zero — because at zero output the business still pays its fixed costs. It then rises by the variable cost for every unit. For Lumo it runs from $$ 6,000$ at 0 lamps to $$ 6,000$ + ( $$ 10$ × 800) = $$ 14,000$ at 800 lamps.
Total revenue: this line starts at zero, because selling nothing earns nothing. For Lumo it runs from $$ 0$ at 0 lamps to $$ 25$ × 800 = $$ 20,000$ at 800 lamps.
Because every line is straight, you need only two points for each: its value at zero output and its value at the highest output on the chart. Calculate them, plot them, join them with a ruler, and label every line so it is clear which is which.
The break-even point is where the total revenue line crosses the total costs line. For Lumo they cross at 400 lamps and $$ 10,000$ — the same break-even output the formula gave.
Total costs start at $$ 6,000$ , not at zero. The lines cross at 400 lamps; to the right of that point every lamp adds profit, and 600 − 400 = 200 lamps is the margin of safety.
To complete a chart, you add whatever is missing — a line, a label or the break-even point — from the figures you are given. To amend a chart, you draw a new line after something changes; the section on decisions below shows exactly how each change moves the lines.

Part 4 of 7

Reading a break-even chart

Break-even output: from the point where total revenue crosses total costs, read straight down to the output axis. For Lumo: 400 lamps.
Break-even revenue: from the same point, read straight across to the vertical axis. For Lumo: $$ 10,000$ . Check which one the question wants — output is in units, revenue in dollars.
Loss: to the left of the break-even point, the total costs line is above the total revenue line. The vertical gap between them is the loss at that output. At 200 lamps, revenue is $$ 5,000$ and total costs are $$ 8,000$ : a loss of $$ 3,000$ .
Profit: to the right of the break-even point, total revenue is above total costs, and the vertical gap is the profit. At 600 lamps, revenue is $$ 15,000$ and total costs are $$ 12,000$ : a profit of $$ 3,000$ .
Profit and loss are vertical gaps, measured straight up from one output. A horizontal distance on this chart is a number of units, not an amount of money.

Part 5 of 7

The margin of safety

The margin of safety is the amount by which actual sales are above break-even sales. It tells you how far sales could fall before the business starts to make a loss.
$Margin of safety = Actual number of sales - break-even number of sales$
Lumo actually sells 600 lamps a month. Its margin of safety is 600 − 400 = 200 lamps: sales could drop by 200 lamps a month before Lumo stops making a profit.
On a break-even chart, the margin of safety is the horizontal distance along the output axis between break-even output and actual sales — for Lumo, from 400 to 600.
Like break-even output, the margin of safety is measured in units.
Interpreting it: a larger margin of safety means the business is safer, because a fall in sales is less likely to push it into a loss. A small one means a slight fall in sales could wipe out its profit.
A negative margin of safety means actual sales are below break-even, so the business is already making a loss. If Lumo sold only 350 lamps, its margin of safety would be 350 − 400 = −50 lamps: it would need 50 more sales a month just to break even.

Part 6 of 7

Using break-even analysis to make decisions

Break-even analysis lets a business test a decision before making it. The syllabus names three changes. For each, be ready to say what happens to contribution, to break-even output and to the chart.
The price rises. Contribution per unit rises, so fewer units are needed to cover fixed costs, and break-even output falls. On the chart the total revenue line still starts at zero but is steeper, so it crosses total costs further to the left.
If Lumo raised its price from $$ 25$ to $$ 30$ , contribution would be $$ 30$ − $$ 10$ = $$ 20$ and break-even output $$ 6,000$ ÷ $$ 20$ = 300 lamps. The amended total revenue line runs from $$ 0$ at 0 lamps to $$ 30$ × 800 = $$ 24,000$ at 800 lamps.
A price cut does the opposite. At $$ 20$ , contribution is $$ 10$ and break-even output rises to 600 lamps; the total revenue line becomes flatter.
The catch: a higher price usually means fewer sales. A lower break-even output is only good news if actual sales do not fall by more. The last worked example tests exactly this.
Fixed costs rise — say Lumo moves to a workshop with higher rent, and fixed costs become $$ 7,500$ . Contribution is still $$ 15$ , but more contributions are needed: break-even output rises to $$ 7,500$ ÷ $$ 15$ = 500 lamps.
On the chart, the fixed costs line moves up to $$ 7,500$ , and the total costs line moves up by the same $$ 1,500$ but keeps its slope: it now runs from $$ 7,500$ at 0 lamps to $$ 15,500$ at 800 lamps. The total revenue line does not move.
Variable cost per unit rises — say the supplier of lamp parts raises its prices and variable cost goes from $$ 10$ to $$ 13$ . Contribution falls to $$ 25$ − $$ 13$ = $$ 12$ , so break-even output rises to $$ 6,000$ ÷ $$ 12$ = 500 lamps.
On the chart, the fixed costs line does not move. The total costs line starts at the same point, $$ 6,000$ , but is steeper: it now reaches $$ 6,000$ + ( $$ 13$ × 800) = $$ 16,400$ at 800 lamps.
The trap is mixing up the last two. A change in fixed costs moves the cost lines up or down without changing their slope. A change in variable cost per unit changes the slope of the total costs line, which still starts from the fixed-costs level.
One rule covers every case: anything that shrinks contribution per unit (a lower price, a higher variable cost) or raises fixed costs pushes break-even output up and, if sales stay the same, the margin of safety down.

Part 7 of 7

Limitations of break-even analysis

Break-even analysis is only as good as the assumptions behind it. When you judge it, look for where those assumptions fail for the business in the question.
It assumes all output is sold. The chart treats every unit made as a unit sold. In reality a business may be left with unsold inventory, so its revenue is lower than the chart shows.
It assumes the selling price is the same at every level of output. A business may give discounts to customers who buy in large quantities, so the total revenue line would not really be straight.
It assumes fixed costs stay fixed. Beyond a certain output, a business may need a bigger building, more machinery or more managers, and fixed costs jump up.
It assumes variable cost per unit stays the same. A business producing more may get bulk-buying discounts — the purchasing economies of scale from 4.4.2 — so variable cost per unit falls, and the total costs line would not really be straight either.
It is only as accurate as its data. Break-even charts are often drawn from forecasts. If costs rise or sales are lower than forecast, the break-even output and margin of safety will be wrong.
To explain a limitation fully, take three steps: state the assumption [k], show why it may not hold for this business [app], and say what that does to the result [an] — for example, "if the business gives bulk discounts, its real break-even output is higher than the chart shows, so it could make a loss while believing it has broken even".

Worked examples

Example 1. Lumo Lamps has fixed costs of $$ 6,000$ a month. It sells each lamp for $$ 25$ , and the variable cost of each lamp is $$ 10$ . Calculate Lumo's break-even output, and check your answer.

Show the working

Break-even needs contribution per unit first. Write the formula, then substitute.
$Contribution per unit = $ 25 - $ 10 = $ 15$
Divide fixed costs by contribution per unit.
$Break-even output = \frac{$ 6,000}{$ 15} = 400$
The answer is in units: 400 lamps, not $$ 400$ .
Check with total revenue at 400 lamps:
$$ 25 \times 400 = $ 10,000$
and total costs at 400 lamps:
$$ 6,000 + ($ 10 \times 400) = $ 6,000 + $ 4,000 = $ 10,000$
Total revenue equals total costs, so there is no profit and no loss. 400 lamps is correct.

Answer: 400 lamps a month.

Example 2. A bakery has fixed costs of $$ 2,000$ a month. It sells birthday cakes for $$ 30$ each, and each cake has a variable cost of $$ 13$ . Calculate the break-even output.

Show the working

Contribution per unit:
$$ 30 - $ 13 = $ 17$
Break-even output:
$\frac{$ 2,000}{$ 17} = 117.647 \dots$
This is not a whole number, and the bakery cannot sell part of a cake. Test the whole numbers either side.
At 117 cakes the contributions total 117 × $$ 17$ = $$ 1,989$ — $$ 11$ short of the fixed costs, so the bakery still makes a loss.
At 118 cakes they total 118 × $$ 17$ = $$ 2,006$ , which covers the fixed costs.
So break-even output is 118 cakes. For break-even, round up whatever the decimal: rounding down gives an output that still makes a loss.

Answer: 118 cakes a month.

Example 3. Lumo Lamps (fixed costs $$ 6,000$ a month, price $$ 25$ , variable cost $$ 10$ per lamp) can make up to 800 lamps a month and actually sells 600. Calculate the points needed to draw its break-even chart. Then use the chart to identify the break-even revenue, the profit at 600 lamps and the margin of safety.

Show the working

Each line is straight, so calculate two points for each: at 0 lamps and at 800 lamps, the maximum output, which sets the end of the horizontal axis.
Fixed costs: $$ 6,000$ at 0 lamps and $$ 6,000$ at 800 lamps — a horizontal line.
Total costs: at 0 lamps only the fixed costs, $$ 6,000$ . At 800 lamps:
$$ 6,000 + ($ 10 \times 800) = $ 14,000$
Total revenue: $$ 0$ at 0 lamps. At 800 lamps:
$$ 25 \times 800 = $ 20,000$
Choose scales that fit the largest value, $$ 20,000$ : output from 0 to 800 in steps of 100 lamps, and costs and revenue from 0 to $$ 20,000$ in steps of $$ 2,000$ . Plot the points, rule the three lines and label each one.
The total revenue and total costs lines cross at 400 lamps. Reading across from that point to the vertical axis gives the break-even revenue: $$ 10,000$ .
At 600 lamps, read up to each line: total revenue $$ 15,000$ , total costs $$ 12,000$ . The vertical gap is the profit.
$$ 15,000 - $ 12,000 = $ 3,000$
Margin of safety, in units:
$600 - 400 = 200 lamps$
Check the profit another way. Each of the 200 lamps sold beyond break-even contributes $$ 15$ , and 200 × $$ 15$ = $$ 3,000$ . The two methods agree.

Answer: Points: fixed costs from (0, $$ 6,000$ ) to (800, $$ 6,000$ ); total costs from (0, $$ 6,000$ ) to (800, $$ 14,000$ ); total revenue from (0, $$ 0$ ) to (800, $$ 20,000$ ). Break-even revenue $$ 10,000$ ; profit at 600 lamps $$ 3,000$ ; margin of safety 200 lamps.

Example 4. Lumo is thinking of raising its price from $$ 25$ to $$ 30$ , and expects sales to fall from 600 to 450 lamps a month. Fixed costs ( $$ 6,000$ ) and variable cost ( $$ 10$ per lamp) stay the same. Calculate the new break-even output, margin of safety and profit, and consider whether Lumo should raise its price.

Show the working

New contribution per unit:
$$ 30 - $ 10 = $ 20$
New break-even output:
$\frac{$ 6,000}{$ 20} = 300 lamps$
New margin of safety, using the expected sales of 450:
$450 - 300 = 150 lamps$
New profit = total revenue − total costs:
$($ 30 \times 450) - ($ 6,000 + $ 10 \times 450) = $ 13,500 - $ 10,500 = $ 3,000$
Now compare with the current position: break-even output 400 lamps, margin of safety 200 lamps, profit $$ 3,000$ .
Break-even output falls by 100 lamps, which looks like good news. But profit stays at $$ 3,000$ , and the margin of safety shrinks from 200 to 150 lamps, so a smaller fall in sales would now push Lumo into a loss.
On these figures the price rise adds risk and no profit. It would only be worth it if sales stayed above 450 lamps — and 450 is a forecast, which is one of the limitations of break-even analysis.

Answer: New break-even output 300 lamps; margin of safety 150 lamps; profit $$ 3,000$ , the same as now. On these forecasts Lumo should not raise its price: profit does not rise and the margin of safety falls, unless Lumo is confident sales will stay above 450 lamps.

Where people go wrong

Mistake: Rounding a break-even output such as 714.28 down to 714.

Instead: Always round break-even output up: 715.

At 714 units the contributions still fall short of the fixed costs, so the business is still making a loss.

Mistake: Giving break-even output or the margin of safety in dollars.

Instead: Both are numbers of units: 400 lamps, not $$ 400$ .

Fixed costs in dollars divided by contribution in dollars per unit leaves units.

Mistake: Dividing fixed costs by the selling price.

Instead: Divide by contribution per unit: selling price per unit – variable cost per unit.

Each sale must pay its own variable cost first. Only the contribution left over pays the fixed costs.

Mistake: Starting the total costs line at zero.

Instead: Start it at the level of fixed costs on the vertical axis.

At zero output the business still pays its fixed costs, so total costs cannot be zero.

Mistake: Moving the total costs line up in parallel when variable cost per unit rises.

Instead: A variable cost change makes the total costs line steeper or flatter from the same start. A fixed cost change is the parallel move.

Variable cost is added for every unit, so it sets the slope. Fixed cost sets where the line starts.

Mistake: Deciding a price rise is good simply because break-even output falls.

Instead: Also work out the new profit and margin of safety using the sales expected at the new price.

A higher price usually means fewer sales. In the Lumo example break-even fell, but profit did not rise and the margin of safety shrank.

Check yourself

Define break-even.
Answer
The level of output at which total revenue equals total costs, so the business makes neither a profit nor a loss.
Fixed costs are $$ 9,000$ , the selling price is $$ 20$ and variable cost per unit is $$ 8$ . Calculate break-even output.
Answer
Contribution per unit = $$ 20$ − $$ 8$ = $$ 12$ . Break-even output = $$ 9,000$ ÷ $$ 12$ = 750 units.
Fixed costs are $$ 2,000$ , the selling price is $$ 9$ and variable cost per unit is $$ 6$ . Calculate break-even output.
Answer
Contribution = $$ 3$ . $$ 2,000$ ÷ $$ 3$ = 666.67, so break-even output is 667 units — at 666 units the contributions reach only $$ 1,998$ .
Break-even output is 750 units and actual sales are 900 units. Calculate the margin of safety and say what it means.
Answer
900 − 750 = 150 units. Sales could fall by 150 units before the business starts to make a loss.
A business has a margin of safety of −40 units. What does this tell you?
Answer
Actual sales are 40 units below break-even, so the business is making a loss. It needs 40 more sales to break even.
On a break-even chart, what does the vertical distance between the total revenue line and the total costs line show at a particular output?
Answer
The profit at that output if total revenue is above total costs (right of break-even), or the loss if total costs are above total revenue (left of break-even).
A business's fixed costs rise. Describe how you would amend its break-even chart, and state what happens to break-even output.
Answer
Move the fixed costs line up to the new level, and move the total costs line up by the same amount, keeping its slope. The total revenue line stays where it is. Break-even output rises.
State three limitations of break-even analysis.
Answer
Any three of: it assumes all output is sold; it assumes the selling price is the same at every output; it assumes fixed costs stay fixed; it assumes variable cost per unit stays the same; it relies on forecasts that may be wrong.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. Amira owns BrightBrew, which makes reusable coffee cups. It sells cups online and to cafés, which buy them in large quantities. BrightBrew's fixed costs are $$ 8,000$ per month. Each cup sells for $$ 12$ , and the variable cost of each cup is $$ 7$ . Its equipment can make up to 2,500 cups a month. In March, BrightBrew sold 2,000 cups.

(a) Define 'margin of safety'. 2 marks

Mark scheme

pt2 Award 2 marks for clear understanding, 1 mark for some understanding. Clear: the amount by which actual sales exceed break-even sales / how far sales can fall before the business makes a loss (2). Some: sales above break-even / a safe level of sales (1).

(b)(i) Calculate BrightBrew's break-even output. 2 marks

Mark scheme

pt1 Correct method: $$ 8,000$ ÷ ( $$ 12$ − $$ 7$ ) / $$ 8,000$ ÷ $$ 5$ . Do not award $$ 8,000$ ÷ $$ 12$ .
pt1 Correct answer: 1,600 cups. A correct answer with no working earns both marks.

(b)(ii) Calculate BrightBrew's margin of safety in March. 2 marks

Mark scheme

pt1 Correct method: 2,000 − break-even output from (b)(i). Own figure rule applies.
pt1 Correct answer: 400 cups.

(c) Explain two limitations of break-even analysis for BrightBrew. 6 marks

Mark scheme

k1 First limitation identified, e.g. assumes the selling price is the same at every output / assumes all output is sold / assumes fixed costs stay the same / assumes variable cost per unit stays the same / based on forecasts that may be inaccurate.
app1 Applied, e.g. cafés buying in large quantities may be given a discount on the $$ 12$ price / cups made may not all sell / making more than 2,500 cups would need new equipment / reusable coffee cups.
an1 Developed, e.g. discounts lower contribution below $$ 5$ per cup, so real break-even output is above 1,600 and the margin of safety is overstated / unsold cups mean revenue is lower than the chart shows, so BrightBrew could make a loss while appearing to break even.
k1 Second, different limitation identified.
app1 Applied to BrightBrew, e.g. $$ 8,000$ fixed costs / $$ 7$ variable cost / 2,000 cups sold in March.
an1 Developed to an effect on break-even output, margin of safety or profit, e.g. new equipment above 2,500 cups raises fixed costs above $$ 8,000$ , so break-even output rises.

(d) Amira is considering raising the price of a cup to $$ 14$ . She expects monthly sales to fall to 1,500 cups. Do you think Amira should raise the price? Justify your answer. 8 marks

Mark scheme

k2 Identification of relevant points, e.g. contribution per unit rises / break-even output falls / margin of safety changes / profit changes / customers may switch to cheaper competitors / the sales figure is only a forecast.
app2 Relevant application, e.g. contribution rises from $$ 5$ to $$ 7$ / break-even output falls from 1,600 to 1,143 cups / margin of safety falls from 400 to 357 cups / profit $$ 2,500$ against $$ 2,000$ in March / cafés / 1,500 cups.
an2 Relevant development, e.g. fewer cups are needed to cover the $$ 8,000$ of fixed costs, so profit rises by $$ 500$ a month / the smaller margin of safety means a smaller fall in sales would cause a loss / cafés buying in bulk may compare prices and change supplier, so sales could fall below 1,500.
eval2 A justified decision, e.g. "Amira should raise the price, because profit rises by $$ 500$ a month while the margin of safety falls by only 43 cups. But this depends on the 1,500 forecast: if sales fell to 1,428 cups or fewer, profit would be lower than in March." The justification should not repeat earlier points.

Question 2. TrailMix Ltd makes camping stoves. Its break-even chart shows output from 0 to 3,000 stoves. The fixed costs line is horizontal at $$ 30,000$ . The total costs line runs from $$ 30,000$ at 0 stoves to $$ 90,000$ at 3,000 stoves. The total revenue line runs from $$ 0$ at 0 stoves to $$ 120,000$ at 3,000 stoves. TrailMix expects to sell 2,500 stoves this year.

(a) Calculate TrailMix's selling price per stove and variable cost per stove. 2 marks

Mark scheme

pt1 Selling price: $$ 40$ per stove ( $$ 120,000$ ÷ 3,000).
pt1 Variable cost: $$ 20$ per stove (( $$ 90,000$ − $$ 30,000$ ) ÷ 3,000).

(b) Calculate TrailMix's break-even output and its expected margin of safety. 2 marks

Mark scheme

pt1 Break-even output: 1,500 stoves ( $$ 30,000$ ÷ ( $$ 40$ − $$ 20$ )). Own figure rule from (a).
pt1 Margin of safety: 1,000 stoves (2,500 − 1,500). Own figure rule applies.

(c) TrailMix's supplier increases the price of the metal used in each stove. Outline two ways this would change TrailMix's break-even chart. 4 marks

Mark scheme

k1 First change identified, e.g. the total costs line becomes steeper / the break-even point moves to the right / break-even output rises / the margin of safety falls.
app1 Applied, e.g. total costs still start at $$ 30,000$ but end above $$ 90,000$ at 3,000 stoves / break-even output above 1,500 stoves / margin of safety below 1,000 stoves.
k1 Second, different change identified. Do not award "the fixed costs line moves up", as metal is a variable cost.
app1 Applied to TrailMix's figures. The reference must make sense for the change named.

Question 3. InkWell Tees prints designs on T-shirts. It sells them online and to schools and sports clubs, which often order in bulk and ask for a discount. Its blank T-shirts come from one supplier. The owner, Daniel, wants to increase profit and is using break-even analysis to compare three possible changes. Appendix – InkWell Tees monthly figures: fixed costs $$ 12,000$ ; selling price per T-shirt $$ 20$ ; variable cost per T-shirt $$ 12$ ; T-shirts sold 2,000; maximum output 2,600 T-shirts.

(a) Explain two advantages and two disadvantages to InkWell Tees of using break-even analysis to decide how to increase its profit. 8 marks

Mark scheme

k1 First advantage identified, e.g. shows the output needed to avoid a loss / shows the margin of safety / shows the profit or loss at different outputs / lets the owner test the effect of a change before making it. Award 1 mark for each advantage (max. 2 advantages).
app1 1 mark for an explanation of the first advantage applied to InkWell Tees, e.g. break-even output is $$ 12,000$ ÷ ( $$ 20$ − $$ 12$ ) = 1,500 T-shirts, so Daniel knows sales can fall by 500 from 2,000 before InkWell makes a loss.
k1 Second, different advantage identified (as above).
app1 1 mark for an explanation of the second advantage applied to InkWell Tees, e.g. Daniel can work out the new break-even output and profit for each of the three changes before choosing one, so he avoids a change that would reduce the current profit of $$ 4,000$ a month.
k1 First disadvantage (limitation) identified, e.g. assumes every T-shirt sells at the same price / assumes all T-shirts made are sold / assumes costs stay the same / relies on sales forecasts that may be wrong. Award 1 mark for each disadvantage (max. 2 disadvantages).
app1 1 mark for an explanation of the first disadvantage applied to InkWell Tees, e.g. schools and sports clubs ordering in bulk may be given a discount below $$ 20$ , so contribution is lower and the real break-even output is higher than 1,500.
k1 Second, different disadvantage identified (as above).
app1 1 mark for an explanation of the second disadvantage applied to InkWell Tees, e.g. the sales Daniel expects after a change are only forecasts, so the calculated profits may not happen / making more than the maximum output of 2,600 T-shirts would need more equipment, raising fixed costs above $$ 12,000$ . Accept all valid responses.

(b) Consider the following three changes Daniel could make to increase InkWell Tees' profit. Which change should InkWell Tees choose? Justify your answer. Raise the price to $$ 23$ per T-shirt; Daniel expects sales to fall to 1,700 T-shirts a month. Use a cheaper supplier of blank T-shirts, cutting the variable cost to $$ 10.50$ per T-shirt; the shirts are thinner, and Daniel expects sales to fall to 1,900 T-shirts a month. Move to a smaller workshop, cutting fixed costs to $$ 10,000$ a month; maximum output would fall to 1,800 T-shirts a month. 12 marks

Mark scheme

Level 3 (9,12 marks): Excellent knowledge and understanding of relevant business concepts using appropriate terminology in context. Detailed discussion of two or more changes. Well-justified recommendation. Candidates discussing all three changes in detail, in context and with a well-justified recommendation including why the alternative changes were rejected should be rewarded with the top marks in the band.
Level 2 (5,8 marks): Good knowledge and understanding of relevant business concepts using appropriate terminology in context. Detailed discussion of at least one change. Judgement with some justification / some evaluation of choice made. Candidates discussing two or more changes in detail and in context should be rewarded with the top marks in the band.
Level 1 (1,4 marks): Limited knowledge and understanding of relevant business concepts in context. Limited ability to discuss the changes with little/no explanation. Simple judgement with limited justification / limited evaluation of choice made. Candidates outlining all three changes in context should be rewarded with the top marks in the band.

Indicative content:

Raise the price, advantage: contribution rises from $$ 8$ to $$ 11$ , so break-even output falls from 1,500 to 1,091 T-shirts ( $$ 12,000$ ÷ $$ 11$ = 1,090.9, rounded up); at 1,700 sales profit is $$ 6,700$ a month, $$ 2,700$ more than now, and the margin of safety rises from 500 to 609 T-shirts.
Raise the price, disadvantage: 1,700 is only a forecast; schools and sports clubs that already ask for discounts may buy elsewhere, and if sales fell below 1,455 T-shirts, profit would be lower than the current $$ 4,000$ .
Cheaper supplier, advantage: contribution rises to $$ 9.50$ , so break-even output falls to 1,264 ( $$ 12,000$ ÷ $$ 9.50$ = 1,263.2, rounded up); at 1,900 sales profit is $$ 6,050$ and the margin of safety is 636 T-shirts, the largest of the three; the price stays at $$ 20$ , so bulk buyers are not put off by a price rise.
Cheaper supplier, disadvantage: thinner shirts may disappoint customers, so sales could fall further than 1,900 — below 1,685 T-shirts, profit would be lower than now; and break-even analysis assumes the $$ 10.50$ cost stays the same, but a new supplier may raise its prices.
Smaller workshop, advantage: fixed costs fall by $$ 2,000$ , so break-even output falls to 1,250 T-shirts ( $$ 10,000$ ÷ $$ 8$ ), while the price and the T-shirts stay the same, so no customers are lost because of a price or quality change.
Smaller workshop, disadvantage: maximum output of 1,800 is 200 below the 2,000 T-shirts InkWell sells now, so those sales are lost; profit is only $$ 4,400$ (1,800 × $$ 8$ − $$ 10,000$ ), just $$ 400$ more than now and the smallest gain of the three; the margin of safety is 550; and InkWell cannot grow above 1,800 without moving again.
A recommendation could be, e.g.: raise the price, because it gives the highest expected profit ( $$ 6,700$ ) and the lowest break-even output (1,091), and sales could fall 245 below Daniel's forecast, to 1,455, with profit still above the current $$ 4,000$ ; the cheaper supplier is rejected because thinner shirts could lose more customers than expected and its profit is lower even if the forecast is right, and the smaller workshop because it adds only $$ 400$ a month and cannot make the 2,000 T-shirts customers already buy. Any change can be recommended if it is well justified with calculations from the appendix.

How this is examined

Choosing one of three changes to price or costs using break-even figures from an appendix, and saying why the other two lose: a 12-mark Paper 2 case-study part (b), in the specimen's wording: 'Consider the following three changes … Which change should [business] choose? Justify your answer.', marked by levels of response (Level 3 9–12, Level 2 5–8, Level 1 1–4), not by adding up points For each change, the new contribution, break-even output, margin of safety and profit worked out from the appendix, with what they mean for the business, plus a point the numbers cannot show — the sales figure is only a forecast, customers may react to a price or quality change, a cost may not stay the same. Outlining all three changes with a figure but no consequence tops out at Level 1 (4). Detailed discussion of at least one change plus a judgement with some justification is Level 2; two or more changes discussed in detail and in context reach the top of Level 2 (8). Level 3 needs detailed discussion of two or more changes and a well-justified recommendation, and the top of Level 3 goes to an answer that discusses all three in detail and in context, then says why each of the other two was rejected — e.g. "not the cheaper premises, because profit rises least and output can no longer meet current sales".
Using break-even figures to judge a change in price or costs: a final 8-mark part, "Do you think…? Justify your answer.", about a proposed price change or a change in costs Recalculated figures from the case — new contribution, break-even output, margin of safety or profit [app]; what they mean, e.g. "a smaller margin of safety makes a loss more likely if sales fall" [an]; a point beyond the numbers, such as sales being only a forecast [k]; then a decision with a reason that does not repeat earlier points [eval].
Explaining the limitations of break-even analysis for a particular business: an Explain part (6) The assumption [k]; why it fails for this business, e.g. it gives bulk discounts to large customers [app]; the effect, e.g. revenue is lower than the chart shows, so real break-even output is higher [an].
Amending a break-even chart after a change: an Outline part about how the chart changes, or a new line to draw on a chart The right line moving the right way: price change — total revenue line steeper or flatter from zero; fixed costs change — fixed costs and total costs lines move up or down, same slope; variable cost change — total costs line steeper or flatter from the same start. Then the effect on break-even output and margin of safety.
Calculating break-even output and the margin of safety: Calculate parts, often 2 marks each The formula line first; contribution per unit (price − variable cost) worked out before dividing; break-even rounded up; both answers in units.
Reading break-even output, profit or loss off a chart: a short part using a given break-even chart Break-even output read straight down from where total revenue crosses total costs; profit or loss taken as the vertical gap between those two lines at the output named.
Defining the margin of safety: a Define part (2) What it measures, not just the subtraction: "the amount by which actual sales exceed break-even sales — how far sales can fall before the business makes a loss".

Words to know

Break-even: The level of output at which total revenue equals total costs, so there is neither a profit nor a loss.
Contribution per unit: Selling price per unit – variable cost per unit: what each sale adds towards paying fixed costs.
Break-even output: Fixed costs ÷ Contribution per unit, in units, rounded up.
Break-even chart: A graph of fixed costs, total costs and total revenue against output. Break-even is where total revenue crosses total costs.
Margin of safety: Actual number of sales – break-even number of sales, in units: how far sales can fall before the business makes a loss.

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