IB Business Management SL 5.5 Break Even Analysis Questions

Calculate and interpret break-even output, contribution and margin of safety to support decisions in IB Business Management SL.

Exam points

Define and identify the key concepts and tools in 5.5 Break-even analysis.
Apply 5.5 Break-even analysis to business calculations, case evidence or management decisions where relevant.
Analyse and evaluate 5.5 Break-even analysis using case context, stakeholder impacts and business trade-offs.

Covered syllabus points

5.5.1—Contribution 5.5.2—Break-even chart and analysis 5.5.3—Effects of price and cost changes 5.5.4—Limitations of break-even

[Maximum number: 8]

In 2022, AH’s costs increased, but it kept prices unchanged. For 2023, AH decided to change its pricing strategy and pass on all cost increases to customers.

Table 2: Selected financial information for AH for 2022 and forecasted financial information for 2023

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, AH's costs increased, but it kept prices unchanged. For 2023, AH decided to change its pricing

Figure for Question 1 — IB Business Management SL

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 ]

Break-even = fixed cost / contribution.
Break-even = $\$2000$ / ( $\$105$ - $\$65$ ) = $\$2000$ / $\$40$ = 50 rugs.

Alternative answer:
Break-even point ( $\$$ ):
Price per unit x units = fixed cost + (variable cost per unit x units).
Q = quantity/units/rugs.
$\$105$ Q = $\$2000$ + $\$65$ Q.
$\$105$ Q - $\$65$ Q = $\$2000$ .
$\$40$ Q = $\$2000$ .
Q = $\$2000$ / $\$40$ = 50 rugs.

\frac{2000}{105-65}=\frac{2000}{40}=50

Accept if the candidate does not say rugs or units.
Award [1] for the correct working and [1] for the correct answer.
Award [2] for a correct answer with working.
Award [1] for correct answer without working.
Award [1] for correct method with an error in the calculation.

(ii)

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

[ 2 ]

Profit = total revenue - total cost.
Profit = ( $\$105$ x 500) - ( $\$2000$ + ( $\$65$ x 500)).
Profit = $\$52500$ - ( $\$2000$ + $\$32500$ ) = $\$52500$ - $\$34500$ = $\$18000$ .

Alternative method:
450 x $\$40$ = $\$18000$ .

\begin{aligned}\text{Profit}&=105\times500-(2000+65\times500)\\&=52500-34500=18000\end{aligned}

Award the marks if the unit sign is shown somewhere in the working and omitted in the final answer.
Award [2] for a correct answer with working.
Award [1] for correct answer without working.
Award [1] for correct method with an error in the calculation.

(iii)

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

[ 2 ]

Margin of safety = current output (units) - break-even output.
MoS = 750 - ( $\$2000$ / ( $\$120$ - $\$70$ )).
MoS = 750 - 40 = 710 rugs.

\begin{aligned}\mathrm{MoS}&=750-\frac{2000}{120-70}=710\\\mathrm{MoS}_{\$}&=90000-4800=85200\\\mathrm{MoS}_{\%}&=\frac{90000-4800}{90000}\times100=94.67\%\end{aligned}

Apply Own Figure Rule.
Provided that the candidate uses a mathematically correct method, they may express the margin of safety in dollars or as a percentage.

MoS in dollars:
(750 x $\$120$ ) - (40 x $\$120$ ) = $\$90000$ - $\$4800$ = $\$85200$ .
MoS = $\$85200$ .

MoS as a percentage:
(Total revenue - break-even revenue) / total revenue x 100
= ( $\$90000$ - $\$4800$ ) / $\$90000$ x 100 = 94.66666667%.

Allow rounding, provided they have rounded correctly. Accept 94.67%, 94.7%, or 95%.
Award [2] for a correct answer with working.
Award [1] for correct answer without working.
Award [1] for correct method with an error in the calculation.

(b)

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

[ 2 ]

A H decided to pass on all cost increases to its customers, therefore, the $\$5$ increase in variable cost means that the new selling price of $\$120$ will represent a $\$10$ unit contribution increase.
Or,
Since unit contribution is the difference between the selling price and its variable cost, according to the figures from the table in 2023, $\$120$ - $\$70$ = $\$50$ , which is a $\$10$ increase in contribution from 2022.

Candidates do not have to word their responses in exactly the same way.

Award [1] for some understanding.
Award [2] for a clear explanation such as those mentioned above.
N.B. If a candidate says only "it will increase" (or something to that effect, without further explanation), award [1].

[Maximum number: 2]

The sportswear manufacturing industry is becoming more competitive. Some foreign manufacturers have begun using penetration pricing to gain market share. For three years, none of HA’s revenue streams have increased, despite increasing unit sales. HA’s gross and net profit margins have declined. However, its sales have increased for the last three years. HA has had to raise additional external finance to increase production.

Hums Athletics (HA) manufactures running shorts, sweat shirts, and sports bras. Operating only in the secondary sector, HA has a head office and three manufacturing facilities, one for each product. These are located in its home country in Europe. Labour costs are high. The quality of labour is excellent. HA produces goods under its own HA brand, which it sells to wholesalers. HA also manufactures for other sportswear companies. HA puts the other sportswear companies’ logos on the running shorts, sweat shirts, and sports bras. Sales to other sportswear companies are an important revenue stream for HA. HA has many levels of hierarchy. Managers at each level have a narrow span of control, and the company is organized by product. HA’s management believe that these features of organizational structure ensure product quality, which they view as essential for brand loyalty.

Hums Athletics (HA)

Hums Athletics (HA) manufactures running shorts, sweat shirts, and sports bras. Operating only in the secondary sector, HA has a head office and three manufacturing facilities, one for each product. These are located in its home country in Europe. Labour costs are high. The quality of labour is excellent.
HA produces goods under its own HA brand, which it sells to wholesalers. HA also manufactures for other sportswear companies. HA puts the other sportswear companies' logos on the running shorts, sweat shirts, and sports bras. Sales to other sportswear companies are an important revenue stream for HA.
HA has many levels of hierarchy. Managers at each level have a narrow span of control, and the company is organized by product. HA's management believe that these features of organizational structure ensure product quality, which they view as essential for brand loyalty.
The sportswear manufacturing industry is becoming more competitive. Some foreign manufacturers have begun using penetration pricing to gain market share. For three years, none of HA's revenue streams have increased, despite increasing unit sales. HA's gross and net profit margins have declined. However, its sales have increased for the last three years. HA has had to raise additional external finance to increase production.
In response to the increasing competition, HA is considering two options:
- Option 1: Outsourcing some of its manufacturing overseas.
- Option 2: Entering the rapidly growing online business-to-consumer (B2C) retail market.
Market research has shown that consumers increasingly expect to buy online.

Explain:

the impact of price changes by foreign competition on H A 's break-even point;

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)

Question 2