5.5 Break-even analysis Topic Practice

IB Business Management syllabusBusiness Management SL/HLFirst assessment 2025

Students practise calculating and interpreting break-even metrics—including contribution, BEQ, margin of safety, and profit—using fully labelled charts and case-specific…

Exam points

calculate break-even quantity or profit/loss using fixed costs, selling price, and variable costs drawn
explain how changes in pricing or costs affect unit contribution or the total cost line on a break-even chart

[Maximum number: 6]

1. AXL
A X L has two factories, in which it manufactures aluminium cans for the soft drinks industry. A X L has a maximum production capacity of 80 million cans per year.

Table 1: AXL's forecasted sales revenue and costs for 2023

AXL plans to close its two factories and move production to a new, larger factory to obtain economies of scale.

In the first six months of 2022, increased competition led to a fall in AXL's sales. For the final two months of 2022, AXL plans to increase the trade credit period it offers to customers from 30 to 60 days.

(a)

Using Table 1, calculate:

[ 3 ]

(i)

the contribution per unit (show all your working);

[ 2 ]

(ii)

the break-even level of output (no working required).

[ 1 ]

(b)

If AXL produces 75 million cans in 2023, using Table 1, calculate:

[ 3 ]

(i)

the margin of safety (no working required);

[ 1 ]

(ii)

the profit (show all your working).

[ 2 ]

[Maximum number: 4]

1. Roscas
Roscas produces and sells sugar donuts. Monthly fixed costs are $15000, monthly sales revenue is $ 70000, and total variable costs per month are $ 25000. To increase its productivity rate, Roscas wants to buy a new high-efficiency machine that produces chocolate-filled donuts. The finance manager has forecasted the following information.

Table 1: Forecasted information for the production of chocolate-filled donuts

Table 2: Forecasted cash flow for the new machine

(a)

Using the information provided above and in Table 1, calculate:

[ 4 ]

(i)

the total contribution per month for the production of 20000 chocolate-filled donuts (show all your working);

[ 2 ]

(ii)

the monthly profit if Roscas sells sugar donuts and chocolate-filled donuts (show all your working).

[ 2 ]

[Maximum number: 8]

2. Alfombras Horizonte (AH)
Alfombras Horizonte (AH) produces natural henequen* rugs in Yucatán, Mexico, and sells them online. AH rugs are very popular among young people because of their eco-friendly materials and AH's mission statement: "We are responsible with Mother Earth for our environment and ourselves."
In 2022, A H 's costs increased, but it kept prices unchanged. For 2023, A H decided to change its pricing

strategy and pass on all cost increases to customers.

$Table 2: Selected financial information for \(\boldsymbol{A$

Table 2: Selected financial information for \(\boldsymbol{A

* henequen: a fibre plant from Mexico and Guatemala. Fabrics made from henequen fibre are used to make a wide variety of products, including bags, rugs and hammocks.

(a)

Using relevant information from Table 2, calculate:

[ 6 ]

(i)

the break-even quantity of rugs in 2022 (show all your working);

[ 2 ]

(ii)

the profit or loss for A H if 500 rugs were sold in 2022 (show all your working);

[ 2 ]

(iii)

the margin of safety in 2023 if AH sells 750 rugs (show all your working).

[ 2 ]

(b)

Explain whether A H's change in pricing strategy for 2023 will have an impact on its unit contribution.

Answer one question from this section.

[ 2 ]

[Maximum number: 8]

2. Florian Stones (FS)
Florian Stones (FS) sells handmade bracelets made from natural stones. FS enjoys strong brand awareness.

Table 2: Forecasted figures for FS for the year ending 31 December 2022

(a)

Using Table 2, draw a fully labelled break-even chart, to scale, for FS for 2022.

[ 4 ]

(b)

Using Table 2, calculate:

[ 4 ]

(i)

the profit or loss in 2022 for FS if production and sales increase to 1200 bracelets (show all your working);

[ 2 ]

(ii)

the price FS would need to charge per bracelet if it sells 800 bracelets and wants to make a profit of $ 10000. Assume that the costs remain the same (show all your working).

Answer one question from this section.

[ 2 ]

[Maximum number: 8]

2. Florian Stones (FS)
Florian Stones (FS) sells handmade bracelets made from natural stones. FS enjoys strong brand awareness.

Table 3: Forecasted figures for FS for the year ending 31 December 2022

(a)

Using Table 3, draw a fully labelled break-even chart, to scale, for FS for 2022.

[ 4 ]

(b)

Using Table 3, calculate:

[ 4 ]

(i)

the profit or loss in 2022 for FS if production and sales increase to 1200 bracelets (show all your working);

[ 2 ]

(ii)

the price FS would need to charge per bracelet if it sells 800 bracelets and wants to make a profit of $ 10000. Assume that the costs remain the same (show all your working).

Answer two questions from this section.

[ 2 ]

[Maximum number: 4]

BRD manufactures Matchfix plastic model kits in its Liverpool factory. The Matchfix product range was profitable until 2020 . The market is competitive, and prices are increasingly important to customers. BRD uses a cost-plus (mark-up) pricing strategy and reviews its kit prices regularly. In 2021, the cost of plastic increased by 20 %, with a further increase in 2022 of 25 %. Matchfix plastic model kit sales fell in 2021 and again in 2022.

By 2022, 50 % of the Liverpool factory space was unused. The marketing director, Simpson Smith, wants to attract a new market segment. He has suggested two options for this unused space: a science and imagination centre and a railway museum.
- Option 1: A science and imagination centre. This would include interactive exhibits, allowing families to experiment with wind, magnets, electricity, and light. Highly trained employees would be needed to assist with experiments.
- Option 2: A railway museum. This would display full-size railway engines and rail cars used in the 20th century. A small number of employees would be needed as guides.

For each option, the entrance fee would be £ 15 per adult, with accompanied children entering for free. BRD would also open a café. Fixed costs for the café are forecasted at £ 25000 per annum and variable costs at £ 10 per customer. Simpson has predicted that 80 % of visitors will visit the café, with an average spend per adult of £ 15. Forecasted costs and visitor numbers for both options are shown in Table 1 and Table 2.

Table 1: Forecasted costs for Option 1 and Option 2

Table 2: Forecasted number of paying visitors for Option 1 and Option 2

(a)

Calculate:

[ 4 ]

(i)

the number of paying café visitors needed for the café to make a profit of £200000 (show all your working);

[ 2 ]

(ii)

the profit that B R D would make in year 3 from operating the café (show all your working).

[ 2 ]

[Maximum number: 4]

Alexa's Apparel Ltd. (AA)

Alexa and Antonio Pérez founded Alexa's Apparel Ltd. (AA) in 2020. AA is located in Arizona, United States (USA). Alexa designs traditional Mexican dresses and offshores the manufacturing to women in indigenous communities in Mexico. The dresses are individually handmade by artisans working at home, who hand-cut, hand-sew, and hand-embroider (decoratively sew) the dresses. Customers order these custom-made dresses at designer markets throughout Arizona. On average, a dress takes 10 days to complete, and artisans typically make two dresses per month.

(a)

Using Table 3:

[ 4 ]

(i)

calculate the break-even quantity for AA in 2024 (show all your working);

[ 2 ]

(ii)

calculate the profit or loss for AA in 2024 if 150 dresses were sold (show all your working).

Alexa has forecasted sales of 600 dresses in 2025. Rogelio would like to grow AA beyond Arizona by selling online. Rogelio believes switching from job production ( A A 's current production method) to batch production is necessary in 2026 to save time and reduce unit costs. Rogelio forecasts that batch production would increase fixed costs by 100 % and decrease variable costs by 50 %. AA would not increase its sales price.

Rogelio noticed that customers preferred five dress styles. Sizes ranged from extra-small to extra-large. Rogelio estimates sales growth, from the forecasted 600 in 2025, of 10 % per year for five years. Rogelio fears that if A A does not change its production method, it will not satisfy demand on time. By changing to batch production, a dress could be finished within two days instead of 10.

Alexa, however, worries about finding storage and workspace. She also fears that A A will lose its unique selling point/proposition (USP). AA's designs cater to a niche market of people willing to pay premium prices for exclusively designed dresses. Another part of A A 's appeal to customers is that it creates jobs in indigenous Mexican communities.

[ 2 ]

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Exam points

Question 1

Question 1(b)

Question 1(b)(i)

Question 1(b)(ii)

Question 1(c)

Question 1(c)(i)

Question 1(c)(ii)

Question 1

Question 1(b)

Question 1(b)(i)

Question 1(b)(ii)

Question 2

Question 2(b)

Question 2(b)(i)

Question 2(b)(ii)

Question 2(b)(iii)

Question 2(c)

Question 2

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Question 2(c)

Question 2(c)(i)

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Question 2

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Question 4

Question 4(c)

Question 4(c)(i)

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Question 3

Question 3(c)

Question 3(c)(i)

Question 3(c)(ii)