📚 IGCSE CIE Business: Calculation Questions Intensive Practice | IGCSE CIE 商务：计算题专项训练
The IGCSE Cambridge Business Studies (0450) examination includes a range of calculation-based questions that test your ability to apply numerical skills in business contexts. Mastering these calculations is essential for achieving high marks in both Paper 1 and Paper 2. This article provides focused practice on the most common calculation topics, with step-by-step examples and bilingual explanations.
IGCSE 剑桥商务（0450）考试包含一系列计算题，考查你在实际商务情境中应用数字技能的能力。掌握这些计算对于在卷一和卷二取得高分至关重要。本文针对最常见的计算题型进行专项训练，配有分步示例和双语解释。
1. Contribution and Break-even Output | 贡献与盈亏平衡产量
Contribution is the amount of money left after deducting variable costs from sales revenue. It is used to cover fixed costs and, once fixed costs are covered, to generate profit.
贡献是指销售收入扣除变动成本后剩余的金额。它用于弥补固定成本，并在弥补完固定成本后产生利润。
The formula for contribution per unit is:
单位贡献的公式为：
Contribution per unit = Selling price − Variable cost per unit
Total contribution can be found by multiplying contribution per unit by the number of units sold.
总贡献可以通过单位贡献乘以销售数量求得。
Total contribution = Contribution per unit × Quantity sold
Break-even output is the number of units a business must sell so that total revenue equals total costs (profit is zero).
盈亏平衡产量是指企业必须售出的产品数量，使得总收入等于总成本（利润为零）。
The break-even formula is:
盈亏平衡公式为：
Break-even output (units) = Total fixed costs ÷ Contribution per unit
Example: A business sells a gadget for £40. The variable cost to make one gadget is £25. Monthly fixed costs are £9,000.
示例：某企业以40英镑的单价出售一件小装置，生产一件的变动成本为25英镑，每月的固定成本为9,000英镑。
Contribution per unit = £40 − £25 = £15.
单位贡献 = 40 − 25 = 15英镑。
Break-even output = £9,000 ÷ £15 = 600 units per month.
盈亏平衡产量 = 9,000 ÷ 15 = 600 件/月。
Break-even revenue = Break-even output × Selling price = 600 × £40 = £24,000.
盈亏平衡收入 = 盈亏平衡产量 × 单价 = 600 × 40 = 24,000英镑。
2. Margin of Safety, Profit and Target Output | 安全边际、利润与目标产量
Margin of safety shows how far sales can fall before the business reaches the break-even point. It can be expressed in units or as a percentage.
安全边际表明在达到盈亏平衡点之前销售额可以下降多少。可以用数量或百分比表示。
Margin of safety (units) = Current output − Break-even output
Margin of safety (%) = [(Current output − Break-even output) ÷ Current output] × 100
Using the previous example, if the business currently sells 800 units per month, margin of safety in units = 800 − 600 = 200 units.
沿用前例，如果企业目前每月销售800件，安全边际（件数）= 800 − 600 = 200件。
Margin of safety percentage = (200 ÷ 800) × 100 = 25%.
安全边际百分比 = (200 ÷ 800) × 100 = 25%。
Profit can be calculated once break-even output is exceeded. Every unit sold above break-even generates profit equal to the contribution per unit.
当超过盈亏平衡产量时，就可以计算利润。每多销售一单位的产品，其利润就等于单位贡献。
Profit = (Output − Break-even output) × Contribution per unit
At 800 units, profit = (800 − 600) × £15 = 200 × £15 = £3,000.
在800件时，利润 = (800 − 600) × 15 = 200 × 15 = 3,000英镑。
To achieve a target profit, you can rearrange the formula:
要实现目标利润，可以重新整理公式：
Required output = (Total fixed costs + Target profit) ÷ Contribution per unit
If the business wants a profit of £4,500, required output = (£9,000 + £4,500) ÷ £15 = 900 units.
如果企业希望获得4,500英镑的利润，所需产量 = (9,000 + 4,500) ÷ 15 = 900件。
3. Average Rate of Return (ARR) | 平均报酬率
ARR measures the average annual profit of an investment as a percentage of the initial investment cost. It helps compare different projects.
平均报酬率衡量一项投资的平均年度利润占初始投资成本的百分比，用于比较不同项目。
ARR = (Average annual profit ÷ Initial investment) × 100
Average annual profit is the total profit over the project’s life divided by the number of years.
平均年度利润是项目寿命期内的总利润除以年数。
Example: A company invests £50,000 in new machinery. The machinery is expected to generate total profit of £80,000 over 5 years and has no residual value.
示例：公司投资50,000英镑购买新机器，预计5年内产生总利润80,000英镑，无残值。
Average annual profit = £80,000 ÷ 5 = £16,000.
平均年度利润 = 80,000 ÷ 5 = 16,000英镑。
ARR = (£16,000 ÷ £50,000) × 100 = 32%.
ARR = (16,000 ÷ 50,000) × 100 = 32%。
If another project offers an ARR of 20%, this project is more attractive based on ARR alone.
如果另一个项目的ARR为20%，仅从ARR来看此项目更具吸引力。
4. Payback Period | 投资回收期
The payback period is the time it takes for an investment to recover its initial cost from the net cash flows it generates.
投资回收期是指投资从产生的净现金流中收回初始成本所需的时间。
When annual net cash flows are constant, use:
当年净现金流恒定时，使用：
Payback period = Initial investment ÷ Annual net cash flow
Example: A project costs £30,000 and is expected to generate a net cash flow of £10,000 each year.
示例：一个项目成本为30,000英镑，预计每年产生10,000英镑的净现金流。
Payback period = £30,000 ÷ £10,000 = 3 years.
回收期 = 30,000 ÷ 10,000 = 3年。
If net cash flows are uneven, you must calculate cumulative cash flows. For example:
如果净现金流不均衡，则必须计算累计现金流。例如：
| Year | Net cash flow | Cumulative cash flow |
|---|---|---|
| 0 | (£40,000) | (£40,000) |
| 1 | £12,000 | (£28,000) |
| 2 | £18,000 | (£10,000) |
| 3 | £15,000 | £5,000 |
The initial investment is recovered during Year 3. The exact payback period = 2 years + (£10,000 ÷ £15,000) = 2.67 years.
初始投资在第3年内收回。精确回收期 = 2年 + (10,000 ÷ 15,000) = 2.67年。
5. Liquidity Ratios: Current Ratio and Acid Test Ratio | 流动比率与速动比率
Liquidity ratios assess a firm’s ability to meet its short-term debts. The current ratio compares all current assets to current liabilities.
流动性比率评估企业偿还短期债务的能力。流动比率将所有流动资产与流动负债进行比较。
Current ratio = Current assets ÷ Current liabilities
The acid test ratio (quick ratio) excludes inventory because it may not be easily converted into cash.
速动比率（酸性测试比率）剔除了存货，因为存货可能不容易变现。
Acid test ratio = (Current assets − Inventory) ÷ Current liabilities
Example: A firm has current assets of £80,000, inventory of £30,000 and current liabilities of £40,000.
示例：某企业拥有流动资产80,000英镑，存货30,000英镑，流动负债40,000英镑。
Current ratio = £80,000 ÷ £40,000 = 2 : 1. This suggests good short-term solvency.
流动比率 = 80,000 ÷ 40,000 = 2:1，表明短期偿债能力良好。
Acid test ratio = (£80,000 − £30,000) ÷ £40,000 = £50,000 ÷ £40,000 = 1.25 : 1. A ratio above 1 is generally considered safe.
速动比率 = (80,000 − 30,000) ÷ 40,000 = 50,000 ÷ 40,000 = 1.25:1。通常认为高于1是比较安全的。
6. Profitability Ratios: Gross and Net Profit Margins | 盈利能力比率：毛利率与净利率
Gross profit margin shows the proportion of revenue left after paying for the cost of goods sold. It indicates how efficiently a business manages its production or purchasing costs.
毛利率显示收入中扣除销售成本后剩余的比例，表明企业管理生产或采购成本的效率。
Gross profit margin = (Gross profit ÷ Revenue) × 100
Net profit margin takes all expenses into account, including overheads. It reveals overall profitability.
净利率将所有费用（包括间接费用）考虑在内，揭示了企业的整体盈利能力。
Net profit margin = (Net profit ÷ Revenue) × 100
Example: A retailer has revenue of £200,000, cost of sales of £120,000 and total expenses of £50,000.
示例：一家零售商的收入为200,000英镑，销售成本为120,000英镑，总费用为50,000英镑。
Gross profit = £200,000 − £120,000 = £80,000. Gross profit margin = (£80,000 ÷ £200,000) × 100 = 40%.
毛利润 = 200,000 − 120,000 = 80,000英镑。毛利率 = (80,000 ÷ 200,000) × 100 = 40%。
Net profit = £80,000 − £50,000 = £30,000. Net profit margin = (£30,000 ÷ £200,000) × 100 = 15%.
净利润 = 80,000 − 50,000 = 30,000英镑。净利率 = (30,000 ÷ 200,000) × 100 = 15%。
7. Labour Productivity | 劳动生产率
Labour productivity measures output per worker over a given period. Higher productivity can reduce costs and improve competitiveness.
劳动生产率衡量每名工人在一定时期内的产出。提高生产率可以降低成本并增强竞争力。
Labour productivity = Total output ÷ Number of workers
Example: A factory produces 24,000 units in a month with 80 workers.
示例：一家工厂在30天内用80名工人生产了24,000件产品。
Labour productivity = 24,000 ÷ 80 = 300 units per worker per month.
劳动生产率 = 24,000 ÷ 80 = 300件/工人/月。
If after training the same 80 workers produce 28,000 units, productivity becomes 350 units per worker. The increase can reduce labour cost per unit.
如果培训后同样80名工人生产28,000件，劳动生产率变为350件/工人，单位产品的劳动成本就可能降低。
8. Inventory Turnover | 存货周转率
Inventory turnover (or stock turnover) measures how many times a business sells and replaces its inventory in a period. A higher figure often suggests efficient inventory management.
存货周转率衡量企业在一定时期内销售并重置存货的次数。数值较高通常表明存货管理效率良好。
Inventory turnover = Cost of goods sold ÷ Average inventory
Average inventory is typically calculated as (Opening inventory + Closing inventory) ÷ 2.
平均存货通常按（期初存货 + 期末存货）÷ 2 计算。
Example: A shop has opening inventory of £15,000, closing inventory of £25,000 and cost of goods sold for the year is £120,000.
示例：某商店期初存货为15,000英镑，期末存货为25,000英镑，当年销售成本为120,000英镑。
Average inventory = (£15,000 + £25,000) ÷ 2 = £20,000.
平均存货 = (15,000 + 25,000) ÷ 2 = 20,000英镑。
Inventory turnover = £120,000 ÷ £20,000 = 6 times per year. This means the shop sells and restocks its inventory roughly every two months.
存货周转率 = 120,000 ÷ 20,000 = 6次/年，意味着商店大约每两个月周转一次库存。
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