📚 IGCSE Business: Calculation Questions Drill | IGCSE 商务：计算题专项训练
Calculation questions are a staple of the IGCSE Business examination, appearing mainly in Paper 2 short‑answer and data‑response sections. Students must not only memorise formulas but also understand how to apply them in realistic business contexts. This drill covers all the essential quantitative topics, from break‑even analysis to profitability and liquidity ratios, investment appraisal and working capital management. Work through each section carefully, practise the examples, and you will build both speed and accuracy for the exam.
计算题是IGCSE商务考试的常规组成部分，主要出现在Paper 2的简答题和数据分析题中。学生不仅需要记住公式，还必须理解如何在真实的商业情境中应用这些公式。本次专项训练涵盖了所有核心的定量主题，包括盈亏平衡分析、盈利能力与流动性比率、投资评估以及营运资金管理。仔细学习每一节，练习例题，你就能在考试中提高速度与准确性。
1. Revenue, Cost and Profit | 收入、成本与利润
Revenue is the income a business receives from selling its goods or services. It is calculated as selling price per unit multiplied by the quantity sold. Total costs are split into fixed costs (which do not vary with output) and variable costs (which vary directly with output). Profit is the difference between total revenue and total costs, and it can be calculated as: Total Profit = Total Revenue − Total Costs.
收入是企业通过销售产品或服务所获得的款项。计算公式为：每单位售价乘以销售数量。总成本分为固定成本（不随产量变化）和变动成本（直接随产量变化）。利润是总收入与总成本之间的差额，计算公式为：总利润 = 总收入 − 总成本。
Example: A café sells 200 cups of coffee per day at £3.50 each. The variable cost per cup is £1.20, and daily fixed costs are £180. Revenue = 200 × £3.50 = £700; Total variable cost = 200 × £1.20 = £240; Total cost = £240 + £180 = £420; Profit = £700 − £420 = £280.
例题：一家咖啡馆每天卖出200杯咖啡，每杯售价3.50英镑。每杯变动成本为1.20英镑，每日固定成本为180英镑。收入 = 200 × 3.50 = 700英镑；总变动成本 = 200 × 1.20 = 240英镑；总成本 = 240 + 180 = 420英镑；利润 = 700 − 420 = 280英镑。
2. Break-even Analysis | 盈亏平衡分析
Break-even is the level of output where total revenue equals total costs, so the business makes neither profit nor loss. The break-even point in units is found by: Break‑even output = Fixed costs ÷ (Selling price per unit − Variable cost per unit). The contribution per unit is the denominator of this formula. Break-even can also be drawn on a chart, but calculation questions often require using the formula directly.
盈亏平衡点是指总收入等于总成本的产出水平，此时企业既不盈利也不亏损。盈亏平衡产量（单位）的计算公式为：固定成本 ÷ (每单位售价 − 每单位变动成本)。分母就是每单位的贡献毛利。盈亏平衡也可以用图表展示，但计算题通常要求直接使用公式。
Example: Fixed costs = £12,000, Selling price = £25, Variable cost per unit = £15. Contribution per unit = £10. Break‑even output = £12,000 ÷ £10 = 1,200 units. To find break‑even revenue: 1,200 × £25 = £30,000.
例题：固定成本 = 12,000英镑，销售单价 = 25英镑，每单位变动成本 = 15英镑。每单位贡献毛利 = 10英镑。盈亏平衡产量 = 12,000 ÷ 10 = 1,200件。盈亏平衡收入 = 1,200 × 25 = 30,000英镑。
3. Contribution and Margin of Safety | 贡献毛利与安全边际
Contribution per unit is the amount each unit sold contributes towards fixed costs and profit: Contribution per unit = Selling price per unit − Variable cost per unit. Total contribution = Contribution per unit × Quantity sold. Margin of safety measures the amount by which actual sales exceed the break-even level. It can be expressed in units: Margin of safety = Actual output − Break‑even output, or as a percentage of actual output.
每单位贡献毛利是指每售出一单位产品对固定成本和利润的贡献：每单位贡献毛利 = 每单位售价 − 每单位变动成本。总贡献毛利 = 每单位贡献毛利 × 销售数量。安全边际衡量实际销售额超出盈亏平衡水平的程度。可以用单位数表示：安全边际 = 实际产量 − 盈亏平衡产量，或者以实际产量的百分比表示。
Example: A firm sells 2,000 units. Break-even output is 1,200 units. Margin of safety = 2,000 − 1,200 = 800 units. In percentage: (800 ÷ 2,000) × 100 = 40%. This means sales can fall by 40% before the firm starts making a loss.
例题：一家企业销售2,000件产品。盈亏平衡产量为1,200件。安全边际 = 2,000 − 1,200 = 800件。按百分比计算：(800 ÷ 2,000) × 100 = 40%。这意味着销售额可以下降40%后企业才开始亏损。
4. Cash Flow Forecasting | 现金流预测
A cash flow forecast predicts the inflows and outflows of cash over a future period. The net cash flow for each month is: Net cash flow = Total cash inflows − Total cash outflows. The closing balance is the amount of cash at the end of a period, which becomes the opening balance for the next period: Closing balance = Opening balance + Net cash flow. Questions may ask you to complete a table, identify months with negative cash flow, or suggest how to improve the position.
现金流预测是对未来一段时间内现金流入和流出的预估。每个月的净现金流 = 总现金流入 − 总现金流出。期末余额是期末的现金数额，并成为下一期的期初余额：期末余额 = 期初余额 + 净现金流。考题可能会让你完成表格、找出净现金流为负数的月份，或者建议如何改善现金状况。
Example: Opening balance for January is £800. Inflows: sales £2,000; Outflows: wages £1,200, materials £600, rent £300. Net cash flow = £2,000 − (£1,200 + £600 + £300) = −£100. Closing balance = £800 + (−£100) = £700.
例题：1月份期初余额为800英镑。流入：销售收入2,000英镑；流出：工资1,200英镑、原材料600英镑、租金300英镑。净现金流 = 2,000 − (1,200 + 600 + 300) = −100英镑。期末余额 = 800 + (−100) = 700英镑。
5. Profitability Ratios (Gross & Net Profit Margin) | 盈利能力比率（毛利率与净利率）
The gross profit margin shows the percentage of sales revenue remaining after subtracting the cost of goods sold. Formula: Gross profit margin = (Gross profit ÷ Sales revenue) × 100. A higher percentage means the business is retaining more from each sale to cover other expenses. The net profit margin takes all expenses into account: Net profit margin = (Net profit ÷ Sales revenue) × 100. These ratios allow comparison of performance across time or with competitors.
毛利率显示在扣除销售成本后，销售收入中留存下来的百分比。公式：毛利率 = (毛利润 ÷ 销售收入) × 100。百分比越高，意味着企业从每笔销售中保留的资金越多，用于覆盖其他费用。净利率将所有费用都考虑在内：净利率 = (净利润 ÷ 销售收入) × 100。这些比率可用于比较不同时间段或与竞争对手的业绩表现。
Example: A retailer has sales revenue of £500,000 and cost of sales £300,000. Gross profit = £200,000. Gross profit margin = (£200,000 ÷ £500,000) × 100 = 40%. If operating expenses are £120,000, net profit = £200,000 − £120,000 = £80,000. Net profit margin = (£80,000 ÷ £500,000) × 100 = 16%.
例题：一家零售商销售收入为500,000英镑，销售成本为300,000英镑。毛利润 = 200,000英镑。毛利率 = (200,000 ÷ 500,000) × 100 = 40%。如果运营费用为120,000英镑，净利润 = 200,000 − 120,000 = 80,000英镑。净利率 = (80,000 ÷ 500,000) × 100 = 16%。
6. Return on Capital Employed (ROCE) | 资本回报率
ROCE measures the return a business makes on the money invested in it. It is often used to judge the profitability of an investment or the whole business: ROCE = (Operating profit ÷ Capital employed) × 100. Capital employed is usually total equity plus non‑current liabilities, or total assets minus current liabilities. Exam questions may give you these figures directly or ask you to extract them from a balance sheet.
资本回报率衡量企业从投入的资本中赚取的回报，通常用于判断一项投资或整个企业的盈利能力：资本回报率 = (营业利润 ÷ 已动用资本) × 100。已动用资本通常等于总权益加上非流动负债，或者总资产减去流动负债。考题可能会直接给出这些数字，或者要求你从资产负债表中提取。
Example: Operating profit is £64,000. Capital employed is £400,000. ROCE = (£64,000 ÷ £400,000) × 100 = 16%. A higher ROCE indicates more efficient use of the money invested in the business.
例题：营业利润为64,000英镑，已动用资本为400,000英镑。资本回报率 = (64,000 ÷ 400,000) × 100 = 16%。资本回报率越高，说明企业投入资金的利用效率越高。
7. Liquidity Ratios (Current & Acid Test) | 流动性比率（流动比率与速动比率）
Liquidity ratios assess a business’s ability to pay its short‑term debts. The current ratio is: Current ratio = Current assets ÷ Current liabilities. A result between 1.5 and 2 is often regarded as healthy, though it depends on the industry. The acid test ratio (quick ratio) excludes inventories from current assets because they may be harder to convert quickly into cash: Acid test = (Current assets − Inventories) ÷ Current liabilities. A ratio of around 1 is generally acceptable.
流动性比率用于评估企业偿还短期债务的能力。流动比率的公式为：流动比率 = 流动资产 ÷ 流动负债。结果在1.5到2之间通常被认为是健康的，但也要视行业而定。速动比率（酸性测试比率）在分子中剔除存货，因为存货变现可能较慢：速动比率 = (流动资产 − 存货) ÷ 流动负债。速动比率约为1一般可以接受。
Example: Current assets = £85,000, Inventories = £25,000, Current liabilities = £50,000. Current ratio = £85,000 ÷ £50,000 = 1.7. Acid test = (£85,000 − £25,000) ÷ £50,000 = 1.2. Both ratios suggest the business has a reasonable liquidity position.
例题：流动资产 = 85,000英镑，存货 = 25,000英镑，流动负债 = 50,000英镑。流动比率 = 85,000 ÷ 50,000 = 1.7。速动比率 = (85,000 − 25,000) ÷ 50,000 = 1.2。这两个比率表明企业的流动性状况不错。
8. Investment Appraisal: Payback Period | 投资评估：回收期法
The payback period is the length of time it takes for an investment to recover its initial cost from the net cash inflows it generates. It is calculated by accumulating annual net cash flows until the initial outlay is covered. For uneven cash flows, you may need to calculate the exact point within a year. The method is simple and focuses on risk, but it ignores the time value of money and cash flows after payback.
回收期是指通过项目产生的净现金流入收回初始投资成本所需的时间长度。计算方法是累积每年的净现金流，直到覆盖初始投资为止。对于不均匀的现金流，可能需要计算年内精确的回收点。这种方法简单且注重风险，但忽略了货币的时间价值和回收期之后的现金流。
Example: Machine costs £60,000. Net cash inflows: Year 1 £15,000, Year 2 £25,000, Year 3 £30,000. After Year 2, total inflow = £40,000. Remaining £20,000 is recovered in Year 3. The fraction of Year 3 = £20,000 ÷ £30,000 = 2/3. Payback period = 2 years + 2/3 year = 2 years 8 months.
例题：一台机器成本为60,000英镑。净现金流入：第1年15,000英镑，第2年25,000英镑，第3年30,000英镑。第2年底累计流入40,000英镑。剩余的20,000英镑在第3年收回。第3年所需的比例 = 20,000 ÷ 30,000 = 2/3。因此回收期 = 2年 + 2/3年 = 2年8个月。
9. Investment Appraisal: Average Rate of Return (ARR) | 平均回报率
ARR measures the average annual profit of an investment as a percentage of the initial cost. The steps are: first, calculate the total net cash inflow over the project’s life, subtract the initial investment to get total profit; next, divide by the number of years to find the average annual profit; finally, ARR = (Average annual profit ÷ Initial investment) × 100. The higher the ARR, the more attractive the investment appears, but ARR does not consider the timing of cash flows.
平均回报率衡量投资的平均年利润占初始投资成本的百分比。计算步骤：首先，计算项目寿命期内的总净现金流入，减去初始投资得到总利润；然后除以年数，得出平均年利润；最后，ARR = (平均年利润 ÷ 初始投资) × 100。ARR越高，投资越有吸引力，但ARR没有考虑现金流发生的时间点。
Example: A project costs £80,000 and has a lifespan of 4 years. Total net cash inflows are £120,000. Total profit = £120,000 − £80,000 = £40,000. Average annual profit = £40,000 ÷ 4 = £10,000. ARR = (£10,000 ÷ £80,000) × 100 = 12.5%.
例题：一个项目成本为80,000英镑，使用寿命4年。总净现金流入为120,000英镑。总利润 = 120,000 − 80,000 = 40,000英镑。平均年利润 = 40,000 ÷ 4 = 10,000英镑。ARR = (10,000 ÷ 80,000) × 100 = 12.5%。
10. Working Capital and Trade Payables/Receivables Days | 营运资金与应付/应收周转天数
Working capital (net current assets) is the capital available for the day‑to‑day running of the business: Working capital = Current assets − Current liabilities. A positive figure means the business should be able to pay its short‑term debts. Two efficiency ratios often examined are trade receivables days and trade payables days. Trade receivables days = (Trade receivables ÷ Credit sales) × 365. It shows the average time taken to collect money from customers. Trade payables days = (Trade payables ÷ Credit purchases) × 365, showing the average time taken to pay suppliers.
营运资金（净流动资产）是可供企业日常运营使用的资金：营运资金 = 流动资产 − 流动负债。正数意味着企业应当能够偿还短期债务。经常考查的两个效率比率是应收账款周转天数和应付账款周转天数。应收账款周转天数 = (应收账款总额 ÷ 赊销收入) × 365，显示企业向客户收款的平均时长。应付账款周转天数 = (应付账款总额 ÷ 赊购金额) × 365，显示企业支付供应商的平均时长。
Example: Trade receivables = £30,000, credit sales = £180,000. Trade receivables days = (£30,000 ÷ £180,000) × 365 = 60.8 days. If the industry average is 45 days, this business might need to improve its credit control. Trade payables = £24,000, credit purchases = £120,000. Trade payables days = (£24,000 ÷ £120,000) × 365 = 73 days.
例题：应收账款 = 30,000英镑，赊销收入 = 180,000英镑。应收账款周转天数 = (30,000 ÷ 180,000) × 365 = 60.8天。如果行业平均为45天，这家企业可能需要改善信贷控制。应付账款 = 24,000英镑，赊购金额 = 120,000英镑。应付账款周转天数 = (24,000 ÷ 120,000) × 365 = 73天。
11. Earnings per Share and Dividend Cover | 每股收益与股息保障倍数
Earnings per share (EPS) shows the amount of profit attributable to each ordinary share. Formula: EPS = (Net profit after tax − Preference dividends) ÷ Number of ordinary shares issued. It gives shareholders an idea of the company’s profitability on a per‑share basis. Dividend cover measures how many times the profit available for dividends covers the actual dividend paid. Dividend cover = Net profit after tax (or profit for the year) ÷ Total dividends paid. A higher cover ratio indicates the company is retaining more profit for reinvestment.
每股收益（EPS）显示归属于每一普通股的利润金额。公式：EPS = (税后净利润 − 优先股股息) ÷ 已发行普通股股数。它让股东了解公司按每股计算的盈利能力。股息保障倍数衡量可用于分红的利润是实际支付股息的多少倍。股息保障倍数 = 税后净利润（或年度利润）÷ 支付的总股息。保障倍数越高，表明企业留存了更多利润用于再投资。
Example: Net profit after tax is £200,000, preference dividends are £20,000, and there are 300,000 ordinary shares. EPS = (£200,000 − £20,000) ÷ 300,000 = £0.60 per share. If total dividends paid to ordinary shareholders are £75,000, dividend cover = £180,000 ÷ £75,000 = 2.4 times.
例题：税后净利润为200,000英镑，优先股股息为20,000英镑，普通股股数为300,000股。EPS = (200,000 − 20,000) ÷ 300,000 = 0.60英镑每股。如果支付给普通股股东的总股息为75,000英镑，股息保障倍数 = 180,000 ÷ 75,000 = 2.4倍。
12. Summary and Exam Tips | 总结与答题技巧
To perform well in calculation questions, always show your working clearly. Write down the formula, substitute the numbers, and state the final answer with the correct unit (%, days, units, £, etc.). In data‑response questions, you will often be asked to interpret the result: for example, ‘The gross profit margin has fallen from 42% to 36%, which suggests the business is facing higher cost of sales or pricing pressure.’ Practise reading balance sheets and income statements to locate the figures you need. Managing time in the exam is crucial, so drill these formulas until they become second nature.
要想在计算题中表现出色，一定要清晰地展示解题步骤。写下公式，代入数字，并注明最终答案的单位（%、天、件、英镑等）。在数据分析题中，你经常需要解读计算结果，例如：“毛利率从42%下降到36%，这表明企业正面临销售成本上升或定价压力。” 练习阅读资产负债表和利润表，以快速定位所需数据。考试中时间管理至关重要，因此要反复训练这些公式，直到你能够熟练运用。
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