📚 IGCSE OCR Business: Formula Summary Handbook | IGCSE OCR 商务：公式汇总手册
This comprehensive guide brings together every essential formula you need for IGCSE OCR Business Studies. Each formula is explained with clear definitions, worked examples and paired English–Chinese explanations to support bilingual learners. Use it as a quick reference, a revision checklist or a daily drill resource to build confidence for the examination.
本手册汇集了 IGCSE OCR 商务课程所有核心公式。每个公式均配有清晰定义、计算示例和中英双语解释，方便双语学习者掌握。你可以把它当作速查手册、复习清单或每日练习工具，帮助你在考试中建立扎实的信心。
1. Revenue, Cost and Profit Fundamentals | 收入、成本与利润基础公式
Revenue is the income earned from selling goods or services. It is calculated by multiplying the selling price per unit by the quantity sold.
收入是企业通过销售商品或服务获得的款项，由单位售价乘以销量得出。
Revenue = Price × Quantity
Total costs are the sum of all fixed costs and variable costs. Fixed costs do not change with output in the short run, while variable costs vary directly with output.
总成本是所有固定成本与可变成本之和。固定成本在短期内不随产量变化，可变成本则直接随产量变化。
Total Costs = Fixed Costs + Variable Costs
Total Variable Costs = Variable Cost per Unit × Quantity
Profit measures the financial gain after all costs have been deducted from revenue. It is the fundamental measure of business success.
利润衡量从收入中扣除所有成本后的财务收益，是评估企业成功的基本指标。
Profit = Total Revenue − Total Costs
Gross profit focuses on the direct trading activities: it is revenue less cost of sales (the direct cost of making the product or buying stock).
毛利关注直接经营活动，即收入减去销售成本（生产产品或购买库存的直接成本）。
Gross Profit = Revenue − Cost of Sales
Net profit takes account of all overheads, interest and tax. It is what remains for reinvestment or distribution to owners.
净利润考虑了所有间接费用、利息和税费，是企业可用于再投资或分配给所有者的最终剩余。
Net Profit = Gross Profit − Expenses
2. Gross and Net Profit Margins | 毛利率与净利润率
The gross profit margin expresses gross profit as a percentage of revenue. It shows how efficiently a business turns sales into direct profit before overheads.
毛利率将毛利表示为收入的百分比，反映企业在扣除间接费用前将销售转化为直接利润的效率。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
A higher gross margin is usually better, but businesses must compare against industry norms. For a cafe, 65% might be typical; for a supermarket, 15% could be excellent.
毛利率通常越高越好，但必须与行业标准比较。咖啡馆 65% 可能属于常态，而超市 15% 可能已十分出色。
The net profit margin reveals what percentage of every pound of sales becomes net profit. It is a key indicator of overall cost control.
净利润率显示每一英镑销售收入最终转化为净利润的比例，是衡量整体成本控制的关键指标。
Net Profit Margin = (Net Profit ÷ Revenue) × 100
If net profit margin is falling despite steady gross margin, it signals rising overheads. Businesses must then investigate administration, distribution or finance costs.
如果毛利率稳定而净利润率下降，就表明间接费用在上升，企业需核查行政、分销或财务支出。
3. Break-Even Analysis | 盈亏平衡分析
The break-even point is the level of output at which total revenue exactly equals total costs, resulting in neither profit nor loss. It helps managers make decisions about pricing, cost control and production volume.
盈亏平衡点是指总收入恰好等于总成本的产量水平，此时既无利润也无亏损。它帮助管理者就定价、成本控制和产量做出决策。
Break-Even Point (units) = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
The denominator (selling price minus variable cost per unit) is known as the contribution per unit. Only when total contribution covers fixed costs does profit begin.
分母（售价减去单位可变成本）即单位贡献。只有当总贡献覆盖固定成本后，企业才开始盈利。
You can also express break-even in sales revenue terms by multiplying the break-even units by the selling price.
也可以用销售额表示盈亏平衡点，将保本销量乘以售价即可。
Break-Even Revenue = Break-Even Units × Selling Price
Drawing a break-even chart with total revenue and total cost lines gives a visual picture. The intersection is the break-even point; the area to the right represents profit, to the left represents loss.
绘制总收入线和总成本线的盈亏平衡图表可以直观呈现。两条线的交点为盈亏平衡点；交点右侧区域为盈利区，左侧为亏损区。
4. Contribution and Margin of Safety | 贡献与安全边际
Contribution per unit is the amount each unit sold contributes towards covering fixed costs and then generating profit. It is calculated by subtracting variable cost per unit from selling price.
单位贡献是指每销售一件产品可用于弥补固定成本并创造利润的金额。由售价减去单位可变成本得出。
Contribution per Unit = Selling Price − Variable Cost per Unit
sold. This is used to quickly calculate profit: profit = total contribution − fixed costs.
总贡献等于单位贡献乘以销量。可快速计算利润：利润 = 总贡献 − 固定成本。
Profit = (Contribution per Unit × Quantity) − Fixed Costs
The margin of safety measures how far actual output exceeds the break-even output. It indicates the amount sales can fall before the business starts making a loss.
安全边际衡量实际产出超出盈亏平衡产出的幅度，反映企业在开始亏损前销售额可以下降的空间。
Margin of Safety (units) = Actual Output − Break-Even Output
e cushion: (Margin of Safety ÷ Actual Output) × 100. A high margin of safety reduces risk.
也可用百分比表示安全边际：(安全边际 ÷ 实际产出) × 100。高安全边际可降低经营风险。
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet short-term debts as they fall due. The two main ratios are the current ratio and the acid test ratio.
流动性比率评估企业偿还到期短期债务的能力，主要有流动比率和酸性测试比率两种。
Current Ratio = Current Assets ÷ Current Liabilities
A healthy current ratio is often quoted as between 1.5:1 and 2:1. Too low suggests possible cash flow problems; too high might indicate inefficient use of resources.
健康的流动比率通常介于 1.5:1 至 2:1 之间。过低预示可能出现现金流问题，过高则可能表示资源利用效率低下。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
The acid test ratio excludes inventories because they may not be quickly convertible into cash. A ratio of 1:1 is generally considered safe.
酸性测试比率剔除存货，因为存货可能无法迅速变现。该比率达到 1:1 通常被认为是安全的。
An alternative quick ratio formula removes only the slowest-moving stock. Examinations often expect the standard version with inventories subtracted fully.
另一种速动比率公式只扣除周转最慢的存货，但考试通常要求使用减去全部存货的标准公式。
6. Profitability Ratios | 盈利率比率
Return on Capital Employed (ROCE) measures how efficiently a business generates profit from its capital employed. It is one of the most important profitability ratios.
已用资本回报率 (ROCE) 衡量企业利用其已用资本创造利润的效率，是最重要的盈利率比率之一。
ROCE = (Net Profit ÷ Capital Employed) × 100
Capital employed is often calculated as total assets minus current liabilities, or as shareholders’ funds plus long-term liabilities. The higher the ROCE, the better the return on investment.
已用资本通常计算为总资产减去流动负债，或股东资金加长期负债。ROCE 越高，投资回报越好。
Another useful measure is Return on Net Assets (RONA), which uses net assets instead of capital employed. It is similar in interpretation.
另一个有用指标是净资产回报率 (RONA)，使用净资产替代已用资本，解释方式相似。
RONA = (Net Profit ÷ Net Assets) × 100
For a sole trader or partnership, net profit margin and gross profit margin often give sufficient insight. ROCE becomes especially relevant when comparing firms with different capital structures.
对独资企业或合伙企业而言，净利润率和毛利率已能提供充分信息。ROCE 在比较不同资本结构的企业时尤为重要。
7. Efficiency Ratios: Inventory and Receivables | 效率比率：存货与应收账款
Inventory turnover ratio measures how many times a firm sells and replaces its inventory over a period. It helps assess stock management efficiency.
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，有助于评估存货管理效率。
Inventory Turnover = Cost of Sales ÷ Average Inventory
If stock turnover is too low, it may indicate obsolete stock or overstocking. If too high, stockouts might occur, leading to lost sales.
存货周转率过低可能表示存货陈旧或积压；过高则可能导致缺货，造成销售损失。
Trade receivables days (debtor days) show the average time taken by credit customers to pay. It is a vital liquidity indicator.
应收账款周转天数显示赊销客户付款的平均时间，是关键的流动性指标。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales Revenue) × 365
A high figure suggests poor credit control and can strain cash flow. Businesses often aim for a figure close to their credit terms.
该数值过高表明信用控制不力，可能造成现金流紧张。企业通常希望该数字接近其授予的信用期限。
8. Labour Productivity and Turnover | 劳动生产率与员工流动
Labour productivity measures output per employee or per hour worked. Improving productivity can lower unit costs and increase competitiveness.
劳动生产率衡量每位员工或每工作小时的产出。提高生产率可降低单位成本并增强竞争力。
Labour Productivity = Total Output ÷ Number of Employees
Revenue per employee is another common workforce metric, linking sales directly to the workforce size.
人均营收是另一种常用劳动力指标，将销售收入与员工规模直接关联。
Revenue per Employee = Revenue ÷ Number of Employees
Labour turnover reflects the percentage of the workforce that leaves and needs to be replaced over a period. High turnover can be costly.
员工流动率反映在一段时期内离职并需要补聘的员工比例。高流动率可能代价高昂。
Labour Turnover = (Number of Staff Leaving ÷ Average Number of Staff) × 100
A very low turnover may indicate a stable but perhaps under‑motivated workforce. A balanced rate is often seen as healthy.
流动率过低可能表示队伍稳定但缺乏动力。适中的流动率通常被视为健康的信号。
9. Using Formulas: Step‑by‑Step Examples | 公式应用：分步示例
Application is key. Suppose a firm sells 5,000 units at £20 each. Variable cost per unit is £8, and fixed costs are £30,000. Revenue = 5,000 × £20 = £100,000. Total variable costs = 5,000 × £8 = £40,000. Total costs = £30,000 + £40,000 = £70,000. Profit = £100,000 − £70,000 = £30,000.
应用是关键。假设一家企业以单价 £20 销售 5,000 件产品，单位可变成本 £8，固定成本 £30,000。收入 = 5,000 × £20 = £100,000；总可变成本 = 5,000 × £8 = £40,000；总成本 = £30,000 + £40,000 = £70,000；利润 = £100,000 − £70,000 = £30,000。
Break‑even units = £30,000 ÷ (£20 − £8) = £30,000 ÷ £12 = 2,500 units. Margin of safety = 5,000 − 2,500 = 2,500 units or 50%.
盈亏平衡销量 = £30,000 ÷ (£20 − £8) = £30,000 ÷ £12 = 2,500 件。安全边际 = 5,000 − 2,500 = 2,500 件，即 50%。
Now consider a retailer with revenue £200,000, cost of sales £120,000 and expenses £50,000. Gross profit = £200,000 − £120,000 = £80,000. Gross profit margin = (£80,000 ÷ £200,000) × 100 = 40%. Net profit = £80,000 − £50,000 = £30,000. Net profit margin = (£30,000 ÷ £200,000) × 100 = 15%.
再以零售商为例：收入 £200,000，销售成本 £120,000，费用 £50,000。毛利 = £200,000 − £120,000 = £80,000；毛利率 = (80,000 ÷ 200,000) × 100 = 40%；净利润 = £80,000 − £50,000 = £30,000；净利润率 = (30,000 ÷ 200,000) × 100 = 15%。
If year‑end receivables are £15,000 and credit sales were £150,000, trade receivables days = (£15,000 ÷ £150,000) × 365 = 36.5 days. If the firm offers 30‑day terms, collection is slightly late.
若年末应收账款 £15,000，赊销收入 £150,000，应收账款周转天数 = (15,000 ÷ 150,000) × 365 = 36.5 天。若企业提供 30 天信用期，则收款稍有延迟。
10. Quick Reference Formula Table | 公式速查表
The table below gathers all the key formulas in one place. Keep it handy for last‑minute revision.
下表汇总了所有关键公式，方便考前冲刺复习时随手查阅。
| Formula Name | 公式名称 | Formula | 公式 |
|---|---|
| Revenue | 收入 | Price × Quantity |
| Total Costs | 总成本 | Fixed Costs + Variable Costs |
| Profit | 利润 | Total Revenue − Total Costs |
| Gross Profit | 毛利 | Revenue − Cost of Sales |
| Net Profit | 净利润 | Gross Profit − Expenses |
| Gross Profit Margin | 毛利率 | (Gross Profit ÷ Revenue) × 100 |
| Net Profit Margin | 净利润率 | (Net Profit ÷ Revenue) × 100 |
| Contribution per Unit | 单位贡献 | Selling Price − Variable Cost per Unit |
| Break‑Even Point | 盈亏平衡点 | Fixed Costs ÷ Contribution per Unit |
| Margin of Safety | 安全边际 | Actual Output − Break‑Even Output |
| Current Ratio | 流动比率 | Current Assets ÷ Current Liabilities |
| Acid Test Ratio | 酸性测试比率 | (Current Assets − Inventories) ÷ Current Liabilities |
| ROCE | 已用资本回报率 | (Net Profit ÷ Capital Employed) × 100 |
| Inventory Turnover | 存货周转率 | Cost of Sales ÷ Average Inventory |
| Trade Receivables Days | 应收账款周转天数 | (Trade Receivables ÷ Credit Sales) × 365 |
| Labour Productivity | 劳动生产率 | Output ÷ Number of Employees |
| Labour Turnover | 员工流动率 | (Leavers ÷ Average Staff) × 100 |
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