📚 IB CIE Business: Formula Summary Handbook | IB CIE 商务：公式汇总手册
Mastering key business formulas is essential for success in IB and CIE Business examinations. This handbook brings together the most important formulas from the financial, marketing, operational and human resource topics of both syllabuses, with clear definitions, worked logic and the application points examiners reward. Whether you are calculating break-even output, analysing profitability ratios, appraising an investment project or interpreting a cash flow forecast, a firm grasp of these formulas will sharpen your analysis, improve the accuracy of your calculations and lift your final grade.
掌握关键商务公式对 IB 和 CIE 商务考试至关重要。本手册汇集了 IB 与 CIE 两个考纲中财务、市场营销、运营与人力资源等主题最重要的公式，并配有清晰定义、推导逻辑与考官认可的作答要点。无论您是在计算盈亏平衡产量、分析盈利能力比率、评估投资项目，还是解读现金流量预测，扎实掌握这些公式都能提升分析深度、提高计算准确度，并最终提升考试成绩。
1. Cost Behaviour, Contribution and Profit | 成本性态、边际贡献与利润
Almost every calculation in IB and CIE Business starts from one classification: costs are either fixed or variable. Fixed costs do not change with the level of output in the short run, for example rent, insurance and salaried managers. Variable costs change in direct proportion to output, for example raw materials, packaging and piece-rate wages. Separating the two lets you calculate contribution - the amount each unit sold leaves behind to cover fixed costs and then generate profit.
IB 与 CIE 商务中几乎所有计算都始于一个分类：成本要么是固定成本，要么是可变成本。固定成本在短期内不随产量变化，例如租金、保险费和领取固定薪金的管理人员；可变成本则与产量成正比变化，例如原材料、包装和计件工资。把两者区分开，才能计算边际贡献——即每售出一单位产品所留下的、用于覆盖固定成本并进而创造利润的金额。
Contribution per unit = Selling price per unit − Variable cost per unit
Total contribution = Contribution per unit × Quantity sold
Profit = Total contribution − Total fixed costs
Contribution is not the same as profit. Contribution becomes profit only after total fixed costs have been covered. Total revenue equals selling price multiplied by quantity sold, and total cost equals fixed costs plus total variable costs, so profit can equally be written as total revenue minus total cost. Examiners frequently test the distinction in a short 'explain' question worth two or three marks, so learn the definition as well as the arithmetic.
边际贡献并不等于利润。只有当总固定成本被完全覆盖之后，边际贡献才转化为利润。总营业收入等于单位售价乘以销售量，总成本等于固定成本加总可变成本，因此利润也可以写成总营业收入减总成本。考官常在 2 至 3 分的简答题中考查这一区别，因此既要记公式，也要记定义。
- Fixed cost / 固定成本: unchanged by output in the short run.
- Variable cost / 可变成本: rises and falls with output.
- Semi-variable cost / 半可变成本: contains both elements, for example a utility bill.
- Contribution / 边际贡献: sales revenue minus variable costs.
半可变成本同时包含固定和可变成分，例如水电费中既有基本月租又有按用量计费部分。在绘制盈亏平衡图时，边际贡献决定了营业收入线与总成本线之间的夹角，因此单位边际贡献越大，达到平衡所需的产量就越低。
2. Break-even Analysis | 盈亏平衡分析
Break-even analysis is a vital tool for determining the volume of sales needed to avoid losses. Break-even output is the quantity at which total revenue equals total cost, so profit is exactly zero. Using contribution, break-even output is found by dividing total fixed costs by the contribution per unit.
盈亏平衡分析是确定避免亏损所需销售量的重要工具。盈亏平衡产量是总营业收入等于总成本、利润恰好为零的产量。借助边际贡献，盈亏平衡产量等于总固定成本除以单位边际贡献。
Break-even output (units) = Total fixed costs ÷ Contribution per unit
Break-even revenue is the sales value required to break even. It can be calculated either from the break-even output or from the contribution to sales ratio, which measures the proportion of each pound or dollar of revenue that contributes towards fixed costs and profit.
盈亏平衡收入是达到盈亏平衡所需的销售额。它既可以通过盈亏平衡产量推算，也可以通过边际贡献销售比率推算。该比率衡量每一元营业收入中用于覆盖固定成本并创造利润的比重。
Break-even revenue = Break-even output × Selling price per unit
Contribution to sales ratio = Contribution per unit ÷ Selling price per unit
Break-even revenue = Total fixed costs ÷ Contribution to sales ratio
For example, if fixed costs are $60,000, the selling price is $20 and the variable cost per unit is $8, contribution per unit is $12 and break-even output is 5,000 units. Break-even revenue is 5,000 × $20 = $100,000, which is also $ ent - units, dollars or pounds - because examiners deduct marks for answers without units.
例如，若固定成本为 60,000 元，单位售价 20 元，单位可变成本 8 元，则单位边际贡献为 12 元，盈亏平衡产量为 5,000 件。盈亏平衡收入为 5,000 × 20 = 100,000 元，也等于 60,000 ÷ 0.6。作答时务必写明计量单位（件、元或英镑），因为缺少单位会被扣分。
3. Target Profit and Margin of Safety | 目标利润与安全边际
Break-even is only the starting point. Businesses usually want to know the output required to earn a specific target profit rather than simply to avoid a loss. The formula adds the target profit to fixed costs before dividing by contribution per unit.
盈亏平衡只是起点。企业通常想知道要赚取特定目标利润需要达到多少产量，而不仅仅是不亏损。此时应在分子中把目标利润加到固定成本上，再除以单位边际贡献。
Target output = (Total fixed costs + Target profit) ÷ Contribution per unit
The margin of safety indicates how much sales can fall before a loss occurs. It can be expressed in units or as a percentage. A high margin of safety signals that demand could fall sharply without pushing the business into loss, which is a useful point of evaluation in longer answers.
安全边际表示销售量还能下降多少而不至于出现亏损，可以用产量单位或百分比表示。安全边际高，说明即使需求大幅下滑企业也不会陷入亏损，这在长答题中是很有用的评价点。
Margin of safety (units) = Actual output − Break-even output
Margin of safety (%) = (Actual output − Break-even output) ÷ Actual output × 100
Use 'actual' or 'budgeted' output in the denominator, never the break-even figure. If actual output is 8,000 units and break-even is 5,000 units, the margin of safety is 3,000 units or 37.5 per cent. Evaluation points worth making include the fact that break-even assumes constant selling prices, that variable costs per unit stay the same at all volumes, and that stock is sold as soon as it is produced.
分母应使用实际产量或预算产量，绝不能用盈亏平衡产量。若实际产量为 8,000 件，盈亏平衡为 5,000 件，则安全边际为 3,000 件，即 37.5%。可用于评价的要点包括：盈亏平衡分析假设售价不变、单位可变成本在各产量水平下保持恒定，以及产量一完成即可售出（不存在存货积压）。
4. Profitability Ratios | 盈利能力比率
Profitability ratios compare profit with the revenue or capital that produced it, which makes businesses of different sizes comparable. Gross profit is revenue minus cost of sales, while net profit is the profit after all expenses, interest and taxation have been deducted.
盈利能力比率把利润与其创造的营业收入或资本进行比较，从而使不同规模的企业可以相互对比。毛利等于营业收入减去销售成本；净利润则是扣除全部费用、利息与税项之后的利润。
Gross profit = Revenue − Cost of sales
Gross profit margin = Gross profit ÷ Revenue × 100
Net profit margin = Net profit ÷ Revenue × 100
Return on capital employed = Operating profit ÷ Capital employed × 100
Return on capital employed, usually shortened to ROCE, shows how efficiently long-term funds have been used. Capital employed is normally shareholders' equity plus non-current liabilities, which is equivalent to total assets minus current liabilities. A falling net profit margin while the gross profit margin is stable usually points to rising overheads or higher interest charges, a strong analytical comment.
资本回报率（通常简称 ROCE）反映长期资金的使用效率。所用资本通常等于股东权益加非流动负债，也等于总资产减流动负债。若毛利率保持稳定而净利润率下降，通常说明间接费用上升或利息负担加重，这是很有力的分析性评论。
- Compare ratios over time and against competitors / 应做纵向比较与同业比较。
- A ratio is meaningless alone / 单一比率本身没有意义。
- State the percentage sign / 结果以百分比表示时不要漏写 %。
5. Liquidity Ratios | 流动性比率
Liquidity measures a firm's ability to meet short-term debts as they fall due. Profitability does not guarantee liquidity, and a profitable business can still fail if it runs out of cash. The current ratio compares all current assets with current liabilities.
流动性衡量企业偿付到期短期债务的能力。盈利并不保证流动性，一家盈利的企业仍可能因现金枯竭而倒闭。流动比率把全部流动资产与流动负债进行比较。
Current ratio = Current assets ÷ Current liabilities
Acid test ratio = (Current assets − Inventory) ÷ Current liabilities
Working capital = Current assets − Current liabilities
The acid test, or quick ratio, removes inventory because stock may be difficult to convert into cash quickly. A result below 1 does not automatically mean failure, but it does signal risk, especially for firms with slow-moving inventory. When analysing, mention the nature of the industry: supermarkets and restaurants can operate safely with lower liquidity ratios because their inventory turns over very fast.
酸性测试比率（速动比率）剔除存货，因为存货可能难以迅速变现。低于 1 并不必然意味着失败，但确实提示风险，尤其是存货周转缓慢的企业。分析时应结合行业特性：超市和餐饮企业的存货周转极快，因此以较低的流动性比率经营也是安全的。
6. Efficiency and Working Capital Ratios | 效率与营运资本比率
Efficiency ratios examine how well a business manages its inventory, receivables and payables, which together determine the length of the working capital cycle. Stock turnover can be expressed in times per year or in days.
效率比率考察企业如何管理存货、应收账款与应付账款，三者共同决定营运资本周期的长度。存货周转率既可用一年周转几次表示，也可用周转天数表示。
Stock turnover (times) = Cost of sales ÷ Average inventory
Stock turnover (days) = Average inventory ÷ Cost of sales × 365
Debtor days = Trade receivables ÷ Revenue × 365
Creditor days = Trade payables ÷ Cost of sales × 365
Cash conversion cycle (days) = Stock days + Debtor days − Creditor days
Average inventory is normally opening inventory plus closing inventory divided by two. A rising debtor days figure means the business is collecting cash more slowly, which increases the risk of bad debts and forces it to borrow more. Extending creditor days improves cash flow in the short term but can damage supplier relationships and may lose early-settlement discounts.
平均存货通常等于期初存货加期末存货除以 2。应收账款周转天数上升，说明现金回收变慢，会增加坏账风险并迫使企业增加借款。延长应付账款周转天数短期内改善现金流，但可能损害与供应商的关系，并可能失去提前付款折扣。
7. Gearing, Shareholder and Capital Structure Ratios | 杠杆、股东回报与资本结构比率
Gearing measures the proportion of capital employed financed by long-term debt. A highly geared business must service interest payments regardless of profit levels, so it carries greater financial risk during a downturn.
杠杆比率衡量所用资本中由长期债务融资的比重。高杠杆企业无论盈利水平如何都必须支付利息，因此在经济下行时承担更大的财务风险。
Gearing ratio = Non-current liabilities ÷ Capital employed × 100
Interest cover = Operating profit ÷ Interest expense
Earnings per share = Profit after tax ÷ Number of ordinary shares issued
Dividend per share = Total dividends paid ÷ Number of ordinary shares issued
Dividend yield = Dividend per share ÷ Market price per share × 100
Interest cover shows how many times operating profit could pay the interest bill; a figure below about three is often treated as a warning sign. Check your syllabus carefully, because some specifications include short-term loans and overdrafts in gearing while others use only non-current liabilities. Always use the definition given in the case or the formula sheet.
利息保障倍数表示营业利润能够支付利息费用的倍数；一般低于约 3 倍常被视为警示信号。请仔细核对考纲，因为有些考纲把短期借款和透支计入杠杆，有些则只用非流动负债。作答时应采用案例材料或公式表给出的定义。
8. Investment Appraisal | 投资评估
Investment appraisal compares the cost of a project with the future cash flows it is expected to generate. Payback measures how quickly the initial outlay is recovered and is popular because it is simple and focuses on liquidity.
投资评估把项目成本与其预期产生的未来现金流进行比较。回收期衡量初始投资收回的速度，因其简单且关注流动性而被广泛使用。
eriod = Years before full recovery + (Unrecovered amount ÷ Cash flow in the recovery year)
Average rate of return expresses the average annual profit as a percentage of the investment. Remember that profit is net cash flow minus depreciation, so convert cash flows into profits before calculating.
平均报酬率把年均利润表示为投资的百分比。请注意：利润等于净现金流量减去折旧，因此计算前需先把现金流转换为利润。
Average annual profit = Total profit over the project ÷ Number of years
Average rate of return = Average annual profit ÷ Initial investment × 100
Net present value recognises that money received in the future is worth less than money today. Each year's net cash flow is multiplied by a discount factor taken from the table provided in the examination.
净现值承认未来收到的钱比今天的钱价值更低。每年的净现金流量应乘以考试中提供的折现系数表中的对应系数。
Discount factor = 1 ÷ (1 + r)ⁿ
Net present value = Σ (Net cash flow ÷ (1 + r)ⁿ) − Initial investment
In this formula r is the discount rate expressed as a decimal and n is the number of years into the future. A positive net present value means the project should add value, while a negative figure suggests it should be rejected. Payback ignores cash flows after the payback date, ARR ignores the timing of returns and NPV depends heavily on the accuracy of the discount rate chosen, so use these limitations as evaluation points.
公式中 r 为以小数表示的折现率，n 为距现在的年数。净现值为正说明项目能够增加价值，为负则建议拒绝。回收期忽略回收之后的现金流，平均报酬率忽略收益的时间分布，而净现值高度依赖折现率的准确性，这些局限都可以用作评价点。
9. Cash Flow Forecasting | 现金流预测
A cash flow forecast records expected inflows and outflows month by month and shows the closing balance that is carried forward. It is a planning document, not a statement of profit, and the two concepts must be kept apart in examination answers.
现金流量预测逐月记录预期现金流入与流出，并显示结转的期末余额。它是计划文件而非利润表，考试作答时必须把两个概念严格区分。
Net cash flow = Total cash inflows − Total cash outflows
Closing balance = Opening balance + Net cash flow
Opening balance of next period = Closing balance of the previous period
Positive net cash
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