Business Studies

1. 1.

   A fictional maker sells each item for $10. Variable cost is $6 per item and fixed cost is $1200 per month. Assume constant prices and unit costs, capacity of 600 items per month and that every item produced is sold. On your own axes, construct a monthly break-even chart for output 0 to 600 and money $0 to $6000. Plot total revenue, total cost and fixed cost using output values 0, 300 and 600. Label the break-even point and identify the loss-making and profit-making output regions. Coordinates must use (items per month, dollars per month).

   [6 marks]

   Syllabus placement evidence: Cambridge IGCSE Business Studies 0450, 2026 syllabus version 2, 4.2.3 Break-even analysis, printed p.20.. Directly practises prescribed chart construction and interpretation using original coordinates and the existing operations area. Core means the single 2026 syllabus, not an examination tier.

   Worked explanation

   1. Use TR=10Q and TC=1200+6Q to calculate each plotted money value. Fixed cost is not zero at zero output and is not added to revenue.
   2. Draw straight lines through the plotted coordinates. Their intersection satisfies 10Q=1200+6Q, so Q=300. To its left total cost lies above revenue; to its right revenue lies above total cost, within the modelled range.

   Common mistake: Starting total cost at the origin omits fixed cost and destroys the intended break-even intersection.

   Marking points

   • Labels output horizontally and monthly dollars vertically, using linear scales that include 0-600 items and $0-$6000.
   • Plots and labels total revenue through (0,0), (300,3000) and (600,6000).
   • Plots and labels total cost through (0,1200), (300,3000) and (600,4800).
   • Plots fixed cost as a horizontal line at $1200.
   • Labels break-even at 300 items per month and $3000 per month, where total revenue equals total cost.
   • Identifies losses below 300 and profits above 300 within the stated capacity; exactly 300 gives zero profit.

   Examiner tip: Starting total cost at the origin omits fixed cost and destroys the intended break-even intersection.

2. 2.

   An original fictional chart is supplied by coordinates: total revenue is the straight line from (0,0) to (800,9600), and total cost is the straight line from (0,1600) to (800,8000). Coordinates are (monthly units sold, monthly dollars); all output is sold and the lines apply throughout 0-800 units. Reconstruct both lines on labelled axes. Identify fixed cost and the break-even output. At actual sales of 600 units, mark and calculate both the profit and the margin of safety in units. Explain why these last two quantities are shown by different directions of distance on the chart.

   [6 marks]

   Syllabus placement evidence: Cambridge IGCSE Business Studies 0450, 2026 syllabus version 2, 4.2.3, printed p.20: chart interpretation and margin of safety.. Uses a self-contained coordinate stimulus to test prescribed interpretation, profit and safety-margin meanings without requiring an external graph image.

   Worked explanation

   1. The revenue slope is 9600/800=$12 per unit; the total-cost slope is (8000-1600)/800=$8 per unit. Solve 12Q=1600+8Q to locate the intersection at Q=400.
   2. At Q=600, the vertical distance is 7200-6400=$800. The horizontal distance back to break-even is 600-400=200 units. Do not compare distances measured on different axes as if they shared units.

   Common mistake: A 200-unit margin of safety is not a $200 profit; the chart's axes measure different quantities.

   Marking points

   • Reconstructs both straight lines with labelled units and appropriate scales, including the supplied endpoints.
   • Reads fixed cost as the total-cost intercept, $1600 per month.
   • Finds break-even at 400 units, with revenue and cost both $4800.
   • At 600 units reads revenue $7200 and total cost $6400, so profit is $800, a vertical money gap.
   • Calculates margin of safety as 600-400=200 units, shown horizontally along the output scale.
   • Explains that profit compares money amounts at one output, whereas margin of safety measures how far sales can fall before reaching break-even.

   Examiner tip: A 200-unit margin of safety is not a $200 profit; the chart's axes measure different quantities.

3. 3.

   A fictional shop's original monthly chart has revenue through (0,0) and (400,3200), and total cost through (0,800) and (400,2400). Coordinates are (units sold per month, dollars per month). Rent then raises fixed cost by $400 per month; selling price and variable cost per unit are unchanged. Draw the original chart and add the amended total-cost line. Identify its new intercept, explain whether its slope changes, and calculate old and new break-even outputs. At 350 units sold, calculate old and new margins of safety. Assume all output is sold and both cost models apply up to 400 units.

   [6 marks]

   Syllabus placement evidence: Cambridge IGCSE Business Studies 0450, 2026 syllabus version 2, 4.2.3, printed p.20: amend a chart and use break-even analysis in decisions.. Tests a genuine chart amendment, not a duplicate arithmetic-only break-even item, and holds other model inputs explicitly constant.

   Worked explanation

   1. Read price as 3200/400=$8 and variable unit cost as (2400-800)/400=$4. Adding rent moves TC from 800+4Q to 1200+4Q, so the two cost lines are parallel.
   2. The fixed-cost rise requires 100 more units of $4 contribution to break even. The revenue line still crosses the original cost line at 200 and the new line at 300; the same 350 sales therefore has less protection against a sales fall.

   Common mistake: A fixed-cost increase does not steepen the total-cost line when variable cost per unit is unchanged.

   Marking points

   • Draws labelled original revenue and total-cost lines from the supplied coordinates, keeping revenue unchanged after the rent rise.
   • Draws amended total cost through (0,1200) and (400,2800), a vertical increase of $400.
   • Explains that the cost slope stays $4 per unit because variable cost is unchanged; higher fixed cost changes the intercept, not this slope.
   • Finds original break-even 800/(8-4)=200 units.
   • Finds amended break-even 1200/(8-4)=300 units.
   • Calculates margin of safety at 350 sales falling from 150 units to 50 units.

   Examiner tip: A fixed-cost increase does not steepen the total-cost line when variable cost per unit is unchanged.

4. 4.

   A fictional manufacturer sells indivisible items at $15 each. Its chart originally has revenue from (0,0) to (500,7500) and total cost from (0,1000) to (500,6000). Coordinates are (monthly units sold, monthly dollars). Variable cost rises from $10 to $12 per item while fixed cost stays $1000. Construct the old and amended total-cost lines alongside the revenue line. Explain what happens to the intercept and slope. Calculate the old break-even output, the new continuous intersection and the minimum whole-number sales that avoid a loss. Check the profit or loss at 333 and 334 sales. All output is sold and capacity is 500 units.

   [6 marks]

   Syllabus placement evidence: Cambridge IGCSE Business Studies 0450, 2026 syllabus version 2, 4.2.1 and 4.2.3, printed p.20.. Applies prescribed variable-cost classification and amended chart interpretation. Whole-item rounding is a transparent consequence of the supplied data, not an additional advanced technique.

   Worked explanation

   1. A higher variable cost makes TC=1000+12Q steeper than TC=1000+10Q, while both start at $1000. Revenue remains TR=15Q.
   2. The fractional intersection is a useful chart location, but one-third of an indivisible item cannot be sold. At 333 the contribution is only $999; at 334 it is $1002. Distinguish the continuous zero-profit point from the whole-number no-loss threshold.

   Common mistake: Rounding 333 1/3 down to 333 leaves a loss; the minimum whole-number no-loss threshold must be rounded up.

   Marking points

   • Draws unchanged revenue and original cost using the supplied points, plus amended cost from (0,1000) to (500,7000).
   • Explains that the $1000 intercept is unchanged but the total-cost slope increases from $10 to $12 per unit.
   • Calculates old break-even as 1000/(15-10)=200 units.
   • Calculates the new continuous intersection as 1000/(15-12)=333 1/3 units.
   • Identifies 334 whole items as the minimum sales avoiding a loss, rounding up rather than to the nearest whole number.
   • Checks profit at 333 as 15(333)-[1000+12(333)]=-$1, and at 334 as +$2.

   Examiner tip: Rounding 333 1/3 down to 333 leaves a loss; the minimum whole-number no-loss threshold must be rounded up.

5. 5.

   A fictional workshop's planning sheet extends straight revenue and total-cost lines to 400 units: revenue passes through (0,0) and (400,4000), while total cost passes through (0,1500) and (400,3500). Coordinates are (monthly units sold, monthly dollars). Its existing equipment can produce at most 200 units per month. Construct the planning chart and add a vertical capacity line at 200. Find the plotted break-even output and calculate profit or loss at capacity. Calculate the selling price per unit that would just cover costs at 200 sales if costs stay unchanged. Explain why neither the projected intersection nor the revised price proves the business can achieve break-even. Assume production equals sales in the calculations; no demand forecast is supplied.

   [6 marks]

   Syllabus placement evidence: Cambridge IGCSE Business Studies 0450, 2026 syllabus version 2, 4.2.3, printed p.20: interpretation, decisions and limitations of break-even analysis.. Requires chart construction and a concrete model-limitation judgement using stated capacity. It does not require the optional capacity-utilisation formula or claim a real pricing recommendation.

   Worked explanation

   1. The lines represent TR=10Q and TC=1500+5Q. Their intersection is 5Q=1500, so Q=300, but the current equipment can reach only Q=200.
   2. At capacity, cost is 1500+5(200)=$2500 and revenue is $2000. A hypothetical $12.50 price would cover those costs if all 200 items sold. A break-even chart is conditional cost-revenue arithmetic, not proof of demand or affordable expansion.

   Common mistake: An intersection on an extended planning line is not automatically attainable with current capacity or market demand.

   Marking points

   • Draws labelled revenue and total-cost lines using the supplied coordinates.
   • Finds their mathematical intersection at 300 units and $3000.
   • Adds the 200-unit capacity line and identifies the 300-unit intersection as outside the existing feasible output range.
   • Calculates revenue $2000 and cost $2500 at capacity, giving a $500 monthly loss.
   • Calculates the cost-covering price at 200 sales as $2500/200=$12.50 per unit.
   • Explains that existing capacity prevents reaching 300 and that no evidence establishes 200 customers will buy at $12.50; changing capacity could also change costs.

   Examiner tip: An intersection on an extended planning line is not automatically attainable with current capacity or market demand.

Original, unofficial practice questions from SubjectScout — not official past-paper questions or complete syllabus coverage.