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Business calculations and data interpretation

边玩边学

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课程笔记

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

Check totals and unit costsCalculationWorkingResultRevenue£5 × 300 sold£1,500Total cost£500 + £700£1,200Profit£1,500 − £1,200£300Average cost£600 ÷ 200 output£3 per item

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

Percentages use different basesMeasureWorkingResultGross margin£12,000 ÷ £48,000 × 10025%Net margin£6,000 ÷ £120,000 × 1005%Market share by value£60m ÷ £400m × 10015%Cost change(£500 − £400) ÷ £400 × 100+25%

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

Break-even and safety marginStepWorkingResultUnit contribution£8 − £2£6 peritemBreak-even sales£1,200 ÷ £6200 itemsRevenue at break-even200 × £8£1,600Total cost atbreak-even£1,200 + (200 ×£2)£1,600Margin of safety260 sold − 20060 items

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

Average rate of returnInput or stepValueInitial investment£20,000Average annual profit£3,000ARR calculation£3,000 ÷ £20,000 × 100ARR result15%

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

Flow and balance are differentItemAmountOpening cash balance£1,500Cash inflows£4,000Cash outflows£5,200Net cash flow−£1,200Closing cash balance£300

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

Recorded annual revenueO20406080100120140123YearRevenue (£000)

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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练习题

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  1. 1.What is revenue?

    Easy
    • Aprice multiplied by quantity sold
    • Bprice plus quantity
    • Ccosts minus profit
    • Dtax

  2. 2.What is profit?

    Easy
    • Arevenue plus costs
    • Bcosts minus revenue
    • Ctax minus revenue
    • Drevenue minus total costs

  3. 3.Revenue £90,000 and costs £75,000. Profit?

    Easy
    • A£75,000
    • B£90,000
    • C£15,000
    • D£165,000

  4. 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. 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. 6.Costs rose from £400 to £500. Percentage change?

    Easy
    • A20%
    • B100%
    • C10%
    • D25%

  7. 7.Sales fell from £800 to £600. Percentage change?

    Easy
    • A-20%
    • B-75%
    • C-25%
    • D-33%

  8. 8.Gross profit £12,000 on sales £48,000. Gross margin?

    Easy
    • A75%
    • B25%
    • C4%
    • D40%

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