Question 1 · Short Answer and Calculation
10 marksA student-run enterprise produces custom printed t-shirts. They have the following financial information:
- Fixed costs: $120
- Selling price per t-shirt: $15
- Variable cost per t-shirt: $7
(a) Define the term 'variable cost'. [2]
(b) Calculate the number of t-shirts the enterprise needs to sell to break even. Show your working. [4]
(c) Explain two limitations of using break-even analysis for an enterprise. [4]
- Fixed costs: $120
- Selling price per t-shirt: $15
- Variable cost per t-shirt: $7
(a) Define the term 'variable cost'. [2]
(b) Calculate the number of t-shirts the enterprise needs to sell to break even. Show your working. [4]
(c) Explain two limitations of using break-even analysis for an enterprise. [4]
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Worked solution
(a) A variable cost is a cost that changes directly in proportion to the level of output or sales (such as raw materials or components). [2]
(b) Break-even calculation:
\(\text{Break-even units} = \frac{\text{Fixed Costs}}{\text{Selling Price} - \text{Variable Cost per Unit}}\)
\(\text{Break-even units} = \frac{120}{15 - 7} = \frac{120}{8} = 15\) t-shirts. [4]
(c) Two limitations are:
1. It assumes all produced items are sold, which may not happen (leading to unsold stock).
2. It assumes that costs and prices remain constant, which ignores potential volume discounts or price reductions. [4]
(b) Break-even calculation:
\(\text{Break-even units} = \frac{\text{Fixed Costs}}{\text{Selling Price} - \text{Variable Cost per Unit}}\)
\(\text{Break-even units} = \frac{120}{15 - 7} = \frac{120}{8} = 15\) t-shirts. [4]
(c) Two limitations are:
1. It assumes all produced items are sold, which may not happen (leading to unsold stock).
2. It assumes that costs and prices remain constant, which ignores potential volume discounts or price reductions. [4]
Marking scheme
Part (a): 2 marks for a complete definition (costs that vary/change directly with the level of output/sales). 1 mark for a partial definition or example with no definition.
Part (b): 1 mark for correct formula or correct substitution of figures; 1 mark for calculating contribution ($8); 1 mark for division step ($120 / $8); 1 mark for the correct final answer of 15 (allow 15 t-shirts).
Part (c): 2 marks for each well-explained limitation (1 mark for identifying a valid limitation, 1 mark for explanation), up to a maximum of 4 marks.
Part (b): 1 mark for correct formula or correct substitution of figures; 1 mark for calculating contribution ($8); 1 mark for division step ($120 / $8); 1 mark for the correct final answer of 15 (allow 15 t-shirts).
Part (c): 2 marks for each well-explained limitation (1 mark for identifying a valid limitation, 1 mark for explanation), up to a maximum of 4 marks.