Business calculations and data interpretation

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Core calculations

Revenue = selling price per item × quantity sold for a single constant price. Add separate revenues for multiple products. Total cost = total fixed costs + total variable costs; variable cost per item must first be multiplied by output. Profit = revenue − the relevant total costs for the same period.
Average cost = total costs ÷ output, in pounds per item. £600 ÷ 200 = £3 per item. Output and quantity sold may differ; state any assumption that all output is sold.

Check totals and unit costs

Percentages and change

Percentage change = (new − original) ÷ original × 100, provided the original value is nonzero. £400 to £500 is +25%; £800 to £600 is −25%, a 25% fall. A margin rise from 20% to 25% is 5 percentage points or 25% relative growth.
Market share = firm sales ÷ total market sales × 100, on the same value or volume basis and period. Gross margin = gross profit ÷ revenue × 100; net margin = net profit ÷ revenue × 100. Lower margin means less profit per pound of revenue, not necessarily lower absolute profit.

Percentages use different bases

Break-even

Contribution per item = selling price − variable cost per item. Break-even sales = total fixed costs ÷ contribution per item when contribution is positive. £1,200 ÷ (£8 − £2) = 200 items. At 200 sales, revenue and total cost both equal £1,600.
Margin of safety = actual or budgeted sales − break-even sales, using the same units and period. 260 − 200 = 60 items. Assume constant price and variable unit cost, unchanged fixed costs within the relevant range and sales matching the calculation. Round up a fractional break-even threshold for indivisible items. Required formula work varies by board; AQA GCSE specifies interpreting break-even charts rather than using the formula.

Break-even and safety margin

Averages and rates

Mean = total ÷ number of observations; median is the middle ordered value, or the mean of the two middle values in an even list; mode is the most frequent value. For 2, 4, 4, 6, 9, they are 5, 4 and 4 respectively. Range describes spread, not an average.
ARR = average annual profit ÷ initial investment × 100. Average annual profit may be total profit ÷ project years if total profit is supplied. Use the stated profit convention and avoid treating cash inflow as profit. £3,000 ÷ £20,000 × 100 = 15%.
Extension, subject to board requirements: ROCE = operating profit ÷ capital employed × 100; current ratio = current assets ÷ current liabilities. £9,000 ÷ £6,000 = 1.5:1; timing and asset quality still matter. A zero denominator makes division undefined.

Average rate of return

Cash flow

Net cash flow = cash inflows − cash outflows. Closing balance = opening balance + net cash flow. With £1,500 opening, £4,000 in and £5,200 out, net flow is −£1,200 and closing cash is £300.
A negative flow can reduce a positive balance without creating a negative closing balance. Profit differs from cash because of timing and transactions such as credit sales or loan receipts. Forecast cash flows depend on assumptions.

Flow and balance are different

Interpreting data

Check the title, axes, units, scales, period and data source. Compare like with like and identify the size and direction of change. Distinguish sales revenue in pounds from sales volume in items.
Fictional shop annual revenue is £80,000, £100,000 and £120,000 in Years 1–3: a £40,000 or 50% overall increase. The graph joins recorded observations for readability; it does not measure intervening values or forecast Year 4. Revenue alone does not establish profit or expansion capacity.

Recorded annual revenue

Using data in answers

Show the method, substituted values and working; retain precision until the requested final rounding, and label pounds, items, percentages or ratios. Use relevant figures to explain an effect for this business rather than only repeating numbers.
A growing shop might investigate extra capacity, but should compare additional costs, cash needs, customer demand and relevant non-financial factors. Check comparability and forecast uncertainty before making a justified judgement. All worked datasets in this lesson are fictional.

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Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 38 câu hỏi. Đăng ký để xem tất cả.

1.What is revenue?
Easy
- Aprice multiplied by quantity sold
- Bprice plus quantity
- Ccosts minus profit
- Dtax
2.What is profit?
Easy
- Arevenue plus costs
- Bcosts minus revenue
- Ctax minus revenue
- Drevenue minus total costs
3.Revenue £90,000 and costs £75,000. Profit?
Easy
- A£75,000
- B£90,000
- C£15,000
- D£165,000
4.A product sells for £5 per item and 300 items are sold. What is revenue?
Easy
- A£295
- B£1,500
- C£305
- D£60
5.Total fixed costs are £500 and total variable costs are £700 for the period. What is total cost?
Easy
- A£1,200
- B£200
- C£500
- D£700
6.Costs rose from £400 to £500. Percentage change?
Easy
- A20%
- B100%
- C10%
- D25%
7.Sales fell from £800 to £600. Percentage change?
Easy
- A-20%
- B-75%
- C-25%
- D-33%
8.Gross profit £12,000 on sales £48,000. Gross margin?
Easy
- A75%
- B25%
- C4%
- D40%

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9.Net profit £6,000 on sales £120,000. Net margin?
Easy
- A5%
- B20%
- C50%
- D0.5%
10.In the same market and year, market sales revenue is £400 million and a firm earns £60 million. What is its market share by value?
Easy
- A6.7%
- B60%
- C1.5%
- D15%
11.Fixed costs are £1,200, selling price £8 per item and variable cost £2 per item. Using fixed costs ÷ contribution per item, what are break-even sales?
Easy
- A600 units
- B150 units
- C200 units
- D120 units
12.Break-even sales are 200 items and actual sales are 260 items in the same period. What is the margin of safety?
Easy
- A260 units
- B60 units
- C460 units
- D200 units
13.Opening balance £1,500, inflows £4,000, outflows £5,200. Closing balance?
Easy
- A£300
- B£2,700
- C£10,700
- D-£300
14.Extension: using ROCE = operating profit ÷ capital employed × 100, calculate ROCE for £30,000 operating profit and £300,000 capital employed.
Easy
- A1%
- B30%
- C100%
- D10%
15.Extension: current assets are £9,000 and current liabilities £6,000. What is the current ratio?
Easy
- A3:1
- B15,000:1
- C1.5:1
- D0.67:1
16.Values 2, 4, 4, 6, 9. Mean?
Medium
- A9
- B5
- C4
- D6
17.Values 2, 4, 4, 6, 9. Median?
Medium
- A4
- B5
- C6
- D9
18.Values 2, 4, 4, 6, 9. Mode?
Medium
- A5
- B6
- C9
- D4
19.A fictional shop has annual revenue of £80,000, £100,000 and £120,000 in Years 1–3. Which conclusion follows?
Medium
- ARevenue rose by £20,000 overall
- BYear 4 revenue is guaranteed to be £140,000
- CRevenue rose by 50% from Year 1 to Year 3
- DProfit must have risen by 50%
20.What should you do after calculating a result?
Medium
- Adelete it
- Binterpret what it means for the business
- Cignore it
- Dhide it
21.What should answers include when calculating?
Medium
- Aworking and units
- Bonly the answer
- Cno numbers
- Donly a guess
22.What is a limitation of using past data?
Medium
- Ait is always accurate for the future
- Bit predicts exactly
- Cit has no use
- Dthe future may differ
23.If net profit margin falls, what can be concluded from that ratio alone?
Medium
- AAbsolute total costs must have risen
- BRevenue must have fallen
- CLess of each pound of revenue remains as net profit
- DAbsolute net profit must have fallen
24.Why quote figures in an answer?
Medium
- Ato hide arguments
- Bto support points with evidence
- Cto lengthen it
- Dto avoid analysis
25.Why compare data over time?
Medium
- Ato spot trends
- Bto avoid analysis
- Cto remove costs
- Dto avoid data
26.Why interpret rather than just calculate?
Medium
- Anumbers alone are enough
- Bmeaning is irrelevant
- Cit removes marks
- Ddecisions need meaning, not just numbers
27.Why check units in calculations?
Medium
- Athey remove marks
- Bthey confuse markers
- Cto give a correct, understandable answer
- Dthey never matter
28.Sales volume rose from 40 to 50 items between comparable periods. What is the percentage increase?
Easy
- A50%
- B25%
- C20%
- D10%
29.What is 15% of £2,000?
Easy
- A£300
- B£15
- C£3,000
- D£150
30.Percentage change uses the original value as the base.
Easy
True or false?
31.Revenue equals price divided by quantity.
Easy
True or false?
32.For an odd number of observations, the median is the middle value after ordering the list.
Easy
True or false?
33.You should show working in calculations.
Easy
True or false?
34.Interpreting results is unnecessary.
Medium
True or false?
35.Which are measures of average?
Medium
- Amean
- Bmedian
- Cmode
- Dnone of these
- Erange
36.Which are named financial ratios? Select all that apply.
Medium
- Agross margin
- Bnet margin
- CROCE
- Dcurrent ratio
- Eprice
37.Explain how data can justify a business decision.
Medium
38.An investment costs £20,000 and is forecast to earn an average annual profit of £3,000. Using average annual profit ÷ initial investment × 100, what is its average rate of return?
Easy
- A6.7%
- B£17,000
- C150%
- D15%

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