IB BM SL 5.5.2 Break-even Analysis

[Maximum number: 6]

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 IB Business Management SL 5.5.2 Break Even Chart and Analysis Questions 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.

IB Business Management SL 5.5.2 Break Even Chart and Analysis Questions question 1

Question (a)

Question (i)

Question (ii)

Question (iii)