📚 Year 12 CIE Business Formula & Theorem Quick Reference Handbook | Year 12 CIE 商务公式定理速查手册
Mastering the key formulas and quantitative concepts is essential for success in CIE AS Level Business. This quick reference handbook compiles the most important calculations, from break‑even analysis and profitability ratios to liquidity, efficiency, and operational measures. Use it to revise, practise, and build confidence for your examinations.
掌握关键公式和量化概念是 CIE AS 商务考试成功的基础。这本速查手册汇集了从盈亏平衡分析、盈利比率到流动性、效率及运营指标等最重要的计算。用它来复习、练习并增强考试信心。
1. Revenue, Costs and Profit Formulas | 收入、成本与利润公式
A firm’s financial performance starts with understanding its revenue, costs, and the resulting profit or loss. These are the foundational equations for any business calculation.
企业的财务表现始于理解其收入、成本以及由此产生的利润或亏损。这些是任何商业计算的基础方程式。
Total revenue (also called sales turnover) equals the selling price per unit multiplied by the quantity of units sold.
Total Revenue = Selling Price per Unit × Quantity Sold
总收入（也称销售额）等于单位售价乘以销售数量。
总收入 = 单位售价 × 销售数量
Total costs are the sum of all fixed costs and total variable costs. Variable costs change directly with output, while fixed costs remain constant in the short run.
Total Costs = Fixed Costs + Total Variable Costs
总成本是所有固定成本与总变动成本之和。变动成本随产量直接变化，固定成本在短期内保持不变。
总成本 = 固定成本 + 总变动成本
Profit (or loss) is the difference between total revenue and total costs. It can also be expressed as total contribution minus fixed costs.
Profit = Total Revenue − Total Costs
利润（或亏损）是总收入与总成本之间的差额。它也可以表示为总贡献减去固定成本。
利润 = 总收入 − 总成本
2. Contribution and Break‑even Analysis | 贡献与盈亏平衡分析
Contribution is central to short‑term decision‑making. It shows how much each unit sold contributes towards covering fixed costs and generating profit. Break‑even analysis identifies the output level where total revenue equals total costs.
贡献是短期决策的核心。它显示每售出一单位产品能为覆盖固定成本和产生利润做出多少贡献。盈亏平衡分析确定了总收入等于总成本的产量水平。
Contribution per unit is the selling price minus the variable cost per unit.
Contribution per Unit = Selling Price − Variable Cost per Unit
单位贡献等于售价减去单位变动成本。
单位贡献 = 售价 − 单位变动成本
Total contribution is the unit contribution multiplied by the number of units sold, or total revenue minus total variable costs.
ontribution = Contribution per Unit × Quantity Sold = Total Revenue − Total Variable Costs
总贡献是单位贡献乘以销售数量，或总收入减去总变动成本。
总贡献 = 单位贡献 × 销售数量 = 总收入 − 总变动成本
The break‑even point in units is found by dividing fixed costs by the contribution per unit.
Break‑even Output (units) = Fixed Costs ÷ Contribution per Unit
以数量表示的盈亏平衡点，由固定成本除以单位贡献得出。
盈亏平衡产量（单位） = 固定成本 ÷ 单位贡献
Break‑ on to sales (C/S) ratio, where C/S ratio = Contribution per Unit ÷ Selling Price per Unit.
Break‑even Revenue = Fixed Costs ÷ (Contribution per Unit ÷ Selling Price per Unit)
盈亏平衡收入由固定成本除以贡献销售比（C/S 比）计算得出，其中 C/S 比 = 单位贡献 ÷ 单位售价。
盈亏平衡收入 = 固定成本 ÷ (单位贡献 ÷ 单位售价)
The margin of safety shows how far output or sales can fall before a loss is made. It can be expressed in units, revenue, or as a percentage.
Margin of Safety (units) = Current Output − Break‑even Output
安全边际表明在发生亏损之前产出或销售可以下降多少。它可以用数量、收入或百分比表示。
安全边际（单位） = 当前产量 − 盈亏平衡产量
3. Profitability Ratios | 盈利比率
Profitability ratios measure a business’s ability to generate earnings relative to its sales, assets, or equity. They are crucial for assessing financial health.
盈利比率衡量企业相对于其销售额、资产或权益创造收益的能力。它们对评估财务健康状况至关重要。
Gross profit margin indicates the percentage of revenue remaining after deducting the cost of goods sold.
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
毛利率显示扣除销售成本后剩余收入的百分比。
毛利率 = (毛利 ÷ 收入) × 100%
Net profit margin reflects the percentage of revenue left after all operating expenses, interest, and tax are deducted.
Net Profit Margin = (Net Profit before Tax ÷ Revenue) × 100%
净利率反映扣除所有营业费用、利息和税费后剩余收入的百分比。
净利率 = (税前净利润 ÷ 收入) × 100%
Return on capital employed (ROCE) assesses how efficiently a company uses its long‑term capital. It is one of the most important profitability indicators.
ROCE = (Net Profit before Interest and Tax ÷ Capital Employed) × 100%
已动用资本回报率 (ROCE) 评估公司使用其长期资本的效率。这是最重要的盈利指标之一。
ROCE = (息税前净利润 ÷ 已动用资本) × 100%
Capital employed is commonly defined as total equity plus non‑current liabilities, or total assets minus current liabilities.
已动用资本通常定义为总权益加非流动负债，或总资产减去流动负债。
4. Liquidity Ratios | 流动比率
Liquidity ratios measure a firm’s ability to meet its short‑term obligations as they fall due. A business must hold sufficient liquid assets to avoid cash‑flow crises.
流动比率衡量企业偿还到期短期债务的能力。企业必须持有足够的速动资产以避免现金流危机。
The current ratio compares all current assets to all current liabilities. A ratio of around 1.5:1 to 2:1 is often considered healthy, but this varies by industry.
Current Ratio = Current Assets ÷ Current Liabilities
流动比率将所有流动资产与所有流动负债进行比较。通常 1.5:1 至 2:1 的比率被认为是健康的，但会因行业而异。
流动比率 = 流动资产 ÷ 流动负债
The acid test (quick) ratio removes inventories from current assets, as stock may not be quickly convertible into cash. A ratio of 1:1 or higher is often seen as safe.
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
酸性测试（速动）比率从流动资产中剔除了存货，因为库存可能无法迅速变现。通常 1:1 或高于 1:1 的比率被视为安全。
速动比率 = (流动资产 − 存货) ÷ 流动负债
5. Activity (Efficiency) Ratios | 活动（效率）比率
Efficiency ratios show how well a company uses its assets and manages its trade payables and receivables. They are sometimes called activity or turnover ratios.
效率比率显示公司使用其资产以及管理应付账款和应收账款的状况。它们有时被称为活动比率或周转率。
Inventory turnover measures how many times a company sells and replaces its stock over a period. It can be expressed in times or in days.
Inventory Turnover (times) = Cost of Goods Sold ÷ Average Inventory
Inventory Turnover (days) = (Average Inventory ÷ Cost of Goods Sold) × 365
存货周转率衡量公司在一定时期内销售和补充库存的次数。它可以用次数或天数表示。
存货周转率（次） = 销售成本 ÷ 平均存货
存货周转天数 = (平均存货 ÷ 销售成本) × 365
Trade receivables days (debtor days) show the average time it takes for a business to collect money from credit customers. A shorter period normally improves cash flow.
Trade Receivables Days = (Trade Receivables ÷ Credit Sales Revenue) × 365
应收账款周转天数显示企业从赊销客户收回款项的平均时间。较短的期限通常改善现金流。
应收账款周转天数 = (应收账款 ÷ 赊销收入) × 365
Trade payables days (creditor days) reflect how long a business takes to pay its suppliers. Delaying payment can help cash flow but may damage supplier relationships.
Trade Payables Days = (Trade Payables ÷ Credit Purchases or Cost of Sales) × 365
应付账款周转天数反映企业支付供应商款项所需的时间。延迟付款有助于现金流，但可能损害供应商关系。
应付账款周转天数 = (应付账款 ÷ 赊购额或销售成本) × 365
6. Gearing and Capital Structure Ratios | 杠杆与资本结构比率
Gearing examines the proportion of a firm’s capital that comes from long‑term debt. High gearing implies greater financial risk, as interest must be paid regardless of profit levels.
杠杆比率考察企业资本中来源于长期债务的比例。高杠杆意味着更大的财务风险，因为无论利润水平如何都必须支付利息。
The gearing ratio is commonly calculated as the percentage of non‑current liabilities in the total long‑term capital base.
Gearing Ratio = (Non‑current Liabilities ÷ (Total Equity + Non‑current Liabilities)) × 100%
杠杆比率通常以非流动负债在长期资本总额中所占百分比计算。
杠杆比率 = (非流动负债 ÷ (总权益 + 非流动负债)) × 100%
An alternative is the debt‑to‑equity ratio, which directly compares long‑term debt to shareholders’ equity.
Debt‑to‑Equity Ratio = Non‑current Liabilities ÷ Total Equity
另一种选择是债务权益比，它直接将长期债务与股东权益进行比较。
债务权益比 = 非流动负债 ÷ 总权益
7. Market Share and Growth | 市场份额与市场增长
Marketing objectives are often set in terms of market share and market growth. These simple calculations help a business evaluate its competitive position and the attractiveness of a market.
营销目标通常以市场份额和市场增长来设定。这些简单的计算帮助企业评估其竞争地位和市场的吸引力。
Market share expresses a company’s sales as a percentage of total sales in the entire market.
arket Share = (Company’s Sales Value or Volume ÷ Total Market Sales Value or Volume) × 100%
市场份额将企业的销售额表示为整个市场销售总额的百分比。
市场份额 = (公司销售额或销量 ÷ 市场总销售额或总销量) × 100%
Market growth measures the percentage change in the overall market size from one period to the next.
Market Growth = ((New Market Size − Old Market Size) ÷ Old Market Size) × 100%
市场增长率衡量整体市场规模从一个时期到下一个时期的变化百分比。
市场增长率 = ((新市场规模 − 旧市场规模) ÷ 旧市场规模) × 100%
8. Operational Performance Measures | 运营绩效指标
Operations managers use quantitative measures to track productivity, capacity, and unit costs. These indicators support efficiency improvements and cost control.
运营管理者使用量化指标来追踪生产率、产能和单位成本。这些指标有助于提高效率和控制成本。
Labour productivity can be measured as output per employee or output per hour worked. Higher productivity often lowers unit costs.
Labour Productivity = Total Output ÷ Number of Employees
or Labour Productivity = Total Output ÷ Total Hours Worked
劳动生产率可以按每个员工的产出或每个工作小时的产出来衡量。较高的生产率通常能降低单位成本。
劳动生产率 = 总产出 ÷ 员工人数
或劳动生产率 = 总产出 ÷ 总工作小时数
Unit cost (average cost) is the total cost of production divided by the number of units produced. Reducing unit cost is a common business objective.
Unit Cost = Total Costs ÷ Output (units)
单位成本（平均成本）是总生产成本除以生产的数量。降低单位成本是常见的商业目标。
单位成本 = 总成本 ÷ 产出（单位）
Capacity utilisation shows the extent to which a company uses its productive capacity. Low utilisation suggests wasted resources; very high utilisation may strain facilities.
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100%
产能利用率显示公司利用其生产能力的程度。利用率低表明资源浪费；利用率过高则可能使设施紧张。
产能利用率 = (实际产出 ÷ 最大可能产出) × 100%
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