📚 IB & Edexcel Business: Formula Handbook | IB 与爱德思商务公式手册
This handbook brings together the essential quantitative formulas required for both IB Business Management and Edexcel A Level Business. Mastering these formulas is vital for analysing financial performance, making investment decisions and evaluating business efficiency. Each formula is presented with its purpose, precise calculation and immediate bilingual explanation, helping you build confidence for internal assessments and final examinations.
本手册汇集了 IB 商务管理与爱德思 A Level 商务所需的全部核心定量公式。掌握这些公式对于分析财务表现、制定投资决策和评价企业效率至关重要。每个公式都配有用途说明、精确计算和中英双语即时解读，帮助你为内部评估和最终考试建立信心。
1. Profitability Ratios | 盈利能力比率
The gross profit margin reveals how efficiently a business converts sales into gross profit, which covers operating expenses and generates net profit. It is a direct measure of pricing strategy and control over direct costs.
毛利润率揭示了企业将销售转化为毛利（用于覆盖营业费用并形成净利润）的效率。它是定价策略和控制直接成本的直接量度。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100
毛利率 = (毛利 ÷ 销售收入) × 100
The net profit margin shows the proportion of revenue that remains as profit after all business expenses have been deducted. It reflects overall cost management and profitability.
净利润率显示扣除所有业务支出后净利润占收入的比例，反映整体成本管理和盈利能力。
Net Profit Margin = (Net Profit Before Interest and Tax ÷ Sales Revenue) × 100
净利润率 = (息税前净利润 ÷ 销售收入) × 100
Return on capital employed (ROCE) evaluates the return generated from the funds invested by shareholders and lenders. It is a key indicator of the effectiveness with which a business uses its long-term capital.
资本运用回报率（ROCE）衡量股东和贷款人投入资金所创造的回报。它是企业运用长期资本有效性的关键指标。
ROCE = (Net Profit Before Interest and Tax ÷ Capital Employed) × 100
资本运用回报率 = (息税前净利润 ÷ 资本占用) × 100
Capital employed is usually defined as total equity plus non‑current liabilities, or as total assets minus current liabilities. For IB examinations, clearly state your definition when using the ratio.
资本占用通常定义为权益总额加非流动负债，或总资产减流动负债。在 IB 考试中运用该比率时，请明确说明所用定义。
2. Liquidity Ratios | 流动性比率
The current ratio indicates a firm’s ability to meet its short‑term obligations using its current assets. A ratio above 1.5 is generally considered safe, although benchmarks vary by industry.
流动比率显示企业用流动资产偿还短期债务的能力。虽然基准因行业而异，但比率高于 1.5 通常被视为安全。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
The acid‑test ratio (quick ratio) offers a stricter view by excluding inventory, which may be harder to convert into cash quickly. It focuses on cash, receivables and marketable securities.
速动比率（酸性测试比率）剔除了较难快速变现的存货，提供了更严格的视角，重点考察现金、应收账款和有价证券。
Acid‑Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
速动比率 = (流动资产 − 存货) ÷ 流动负债
A low acid‑test ratio may signal potential cash‑flow difficulties, while an excessively high ratio could imply inefficient use of resources. Both ratios must be interpreted alongside industry norms.
速动比率过低可能预示现金流困难，过高则可能意味着资源利用效率低下。两个比率都需要结合行业标准解读。
3. Efficiency Ratios | 效率比率
Inventory turnover (stock turnover) measures how many days, on average, inventory is held before being sold. A lower number of days suggests efficient stock management and strong demand.
存货周转天数衡量存货在被售出前的平均持有天数。天数越少，表明库存管理越高效且需求旺盛。
Inventory Turnover (days) = (Average Inventory ÷ Cost of Goods Sold) × 365
存货周转天数 = (平均存货 ÷ 销货成本) × 365
Debtor days (trade receivables collection period) shows how long customers take to pay on average. Reducing this period improves cash flow.
应收账款周转天数显示客户平均付款所需时间。缩短这一期限可以改善现金流。
Debtor Days = (Trade Receivables ÷ Credit Sales Revenue) × 365
应收账款周转天数 = (应收账款 ÷ 赊销收入) × 365
Creditor days (trade payables payment period) indicates the average time taken to pay suppliers. A longer period helps retain cash but may risk damaging supplier relationships.
应付账款周转天数显示支付供应商货款的平均时长。较长的期限有助于保留现金，但可能损害与供应商的关系。
Creditor Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 = (应付账款 ÷ 赊购金额) × 365
Asset turnover evaluates how effectively a business uses its assets to generate sales. A higher ratio implies greater efficiency.
资产周转率衡量企业利用资产创造销售的效率。比率越高表明效率越高。
Asset Turnover = Sales Revenue ÷ Total Net Assets (or Capital Employed)
资产周转率 = 销售收入 ÷ 净资产总额（或资本占用）
4. Shareholder & Gearing Ratios | 股东与杠杆比率
Gearing assesses the proportion of a firm’s capital that is funded by long‑term debt. High gearing increases financial risk because interest must be paid regardless of profit levels.
杠杆比率评估企业资本中由长期债务提供资金的比例。高杠杆会增加财务风险，因为无论盈利水平如何，利息都必须支付。
Gearing (%) = (Non‑Current Liabilities ÷ Total Capital Employed) × 100
杠杆比率 (%) = (非流动负债 ÷ 资本占用总额) × 100
Where total capital employed = shareholders’ equity + non‑current liabilities. Some specifications also accept the formula (Non‑current liabilities ÷ Shareholders’ equity) × 100. Always check the exact formula required by your syllabus.
其中资本占用总额 = 股东权益 + 非流动负债。某些考试大纲也接受公式 (非流动负债 ÷ 股东权益) × 100。请务必核对你的课程要求的具体公式。
Earnings per share (EPS) distributes the profit attributable to ordinary shareholders across the number of shares in issue. It is widely used by investors to assess profitability per unit of ownership.
每股收益（EPS）将归属于普通股股东的利润分摊到每一发行在外股份，被投资者广泛用来评价单位所有权的盈利能力。
EPS = (Net Profit After Tax − Preference Dividends) ÷ Number of Ordinary Shares Issued
每股收益 = (税后净利润 − 优先股股息) ÷ 已发行普通股股数
Dividend yield expresses the annual dividend per share as a percentage of the current market price. It allows shareholders to compare income returns from different investments.
股息率以每股市价的百分比表示年度每股股息，便于股东比较不同投资的收益回报。
Dividend Yield = (Dividend Per Share ÷ Market Price Per Share) × 100
股息率 = (每股股息 ÷ 每股市价) × 100
5. Break‑Even Analysis | 盈亏平衡分析
The break‑even point is the output level at which total revenue equals total costs, resulting in neither profit nor loss. It is fundamental to pricing and production decisions.
盈亏平衡点是总收入等于总成本的产量水平，此时既不盈利也不亏损，是定价和生产决策的基础。
Break‑Even Output (units) = Fixed Costs ÷ (Selling Price Per Unit − Variable Cost Per Unit)
盈亏平衡产量（单位） = 固定成本 ÷ (单位售价 − 单位变动成本)
Contribution per unit represents the amount each unit sold contributes towards covering fixed costs and generating profit. It is the driving concept behind break‑even and margin of safety calculations.
单位贡献表示每售出一单位用于补偿固定成本并创造利润的金额，是盈亏平衡和安全边际计算的核心概念。
Contribution Per Unit = Selling Price Per Unit − Variable Cost Per Unit
单位贡献 = 单位售价 − 单位变动成本
The margin of safety shows how much output can fall before the business reaches its break‑even point. It provides a cushion against unexpected downturns.
安全边际显示产出下降多少才会达到盈亏平衡点，为意外衰退提供了缓冲。
Margin of Safety = Actual Output (or Forecast Output) − Break‑Even Output
安全边际 = 实际产量（或预测产量） − 盈亏平衡产量
6. Investment Appraisal | 投资评估
The payback period calculates how long it takes for a project to recover its initial investment from net cash inflows. Shorter payback periods are preferred as they reduce risk.
投资回收期计算项目从净现金流入中收回初始投资所需的时间。回收期越短风险越低，因而更受青睐。
Payback Period = Full Years Before Recovery + (Unrecovered Cost at Start of Year ÷ Net Cash Flow During Year)
投资回收期 = 完全回收前的整年数 + (年初未回收成本 ÷ 年内净现金流)
Average rate of return (ARR) compares the average annual profit from an investment to its initial cost. It is expressed as a percentage, allowing straightforward comparison with other projects and with interest rates.
平均会计收益率 (ARR) 将投资的年均利润与初始成本进行比较，以百分比表示，便于与其他项目及利率直接比较。
ARR = (Average Annual Profit from Investment ÷ Initial Investment Cost) × 100
平均会计收益率 = (年均投资利润 ÷ 初始投资成本) × 100
Net present value (NPV) discounts all future net cash flows to their present value and subtracts the initial investment. A positive NPV indicates that the project is expected to increase shareholder wealth.
净现值 (NPV) 将未来所有净现金流折现后减去初始投资。正净现值意味着项目有望增加股东财富。
NPV = Σ [Net Cash Flowₜ ÷ (1 + r)ᵗ] − Initial Investment
净现值 = Σ [第t年净现金流 ÷ (1 + r)ᵗ] − 初始投资
In the formula, r is the discount rate (cost of capital) and t is the year number. The sigma (Σ) signifies the sum over all years of the project’s life.
公式中，r 为折现率（资本成本），t 为年份数。求和符号 Σ 表示对项目寿命期内各年求和。
7. Budgeting & Variance Analysis | 预算与差异分析
A variance measures the difference between actual results and budgeted figures. Favourable variances arise when performance is better than budgeted, while adverse variances occur when results are worse.
差异衡量实际结果与预算数据之间的差额。当实际表现优于预算时产生有利差异，反之则为不利差异。
Variance = Actual Figure − Budgeted Figure
差异 = 实际数额 − 预算数额
For revenue, a positive variance is favourable (more revenue than planned). For costs, a positive variance is adverse (higher costs than planned). This sign convention must be applied carefully in examination contexts.
对收入而言，正差异为有利（收入高于计划）；对成本而言，正差异为不利（成本高于计划）。在考试中必须谨慎运用这一符号惯例。
8. Productivity, Capacity & Cost | 生产率、产能与成本
Labour productivity relates output to the number of employees and is a key measure of operational efficiency. Improvements in productivity lower unit costs and enhance competitiveness.
劳动生产率将产出与员工人数联系起来，是衡量运营效率的关键指标。生产率的提高可降低单位成本并增强竞争力。
Labour Productivity = Total Output Per Period ÷ Number of Employees
劳动生产率 = 期间总产量 ÷ 员工人数
Capacity utilisation indicates the extent to which a firm is using its productive potential. Sustained low utilisation may point to over‑investment or weak demand.
产能利用率显示企业利用其生产潜力的程度。持续低利用率可能意味着过度投资或需求疲软。
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100
产能利用率 = (实际产量 ÷ 最大可能产量) × 100
Unit cost (average cost) declines as output rises when fixed costs are spread over more units. This relationship underpins economies of scale.
单位成本（平均成本）随产量上升而下降，因为固定成本被分摊到更多单位上。这种关系是规模经济的基础。
Unit Cost = Total Cost ÷ Number of Units Produced
单位成本 = 总成本 ÷ 生产数量
9. Contribution & Decision‑Making | 贡献与决策
Total contribution is the aggregate amount available to cover fixed costs after deducting total variable costs from sales revenue. It is essential for decisions such as whether to accept special orders or discontinue products.
总贡献是从销售收入中扣除总变动成本后可用于覆盖固定成本的总额，对于是否接受特殊订单或停产产品等决策至关重要。
Total Contribution = Sales Revenue − Total Variable Costs
总贡献 = 销售收入 − 总变动成本
Alternatively, total contribution can be calculated as contribution per unit multiplied by the number of units sold. This is particularly useful when unit data is available and variable cost per unit is constant.
或者总贡献也可按单位贡献乘以销售数量计算。在可获得单位数据且单位变动成本保持不变时，这种方法尤为实用。
Total Contribution = Contribution Per Unit × Quantity Sold
总贡献 = 单位贡献 × 销售数量
10. Financial Statement Terms | 财务报表术语
While not always presented as standalone formulas, several building blocks appear repeatedly in ratio analysis. Familiarity with these terms prevents errors in calculation.
尽管不一定以独立公式呈现，但某些基础构成要素在比率分析中反复出现。熟悉这些术语有助于避免计算错误。
Net book value (NBV) of a non‑current asset reflects its cost less accumulated depreciation to date. It is used in asset turnover and ROCE calculations.
非流动资产的账面净值（NBV）反映其成本减累计折旧，用于资产周转率和资本运用回报率的计算。
Net Book Value = Original Cost − Accumulated Depreciation
账面净值 = 原始成本 − 累计折旧
Revenue is the income generated from ordinary trading activities, while cost of goods sold (cost of sales) includes direct costs of production or purchase. Opening inventory + purchases − closing inventory determines cost of goods sold for a trading business.
收入来自日常经营活动，销货成本（销售成本）包含生产或采购的直接成本。对于贸易类企业，期初存货 + 采购 − 期末存货得出销货成本。
Working capital measures the funds available for day‑to‑day operations. Positive working capital indicates that current assets exceed current liabilities, which supports short‑term stability.
营运资本衡量用于日常运营的资金。正营运资本表明流动资产大于流动负债，有利于短期稳定。
Working Capital = Current Assets − Current Liabilities
营运资本 = 流动资产 − 流动负债
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