📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook compiles the essential formulas and analytical ratios required for the Cambridge International AS & A Level Business (Year 12) syllabus. Designed for revision, each formula is explained with its components and application to help you confidently tackle examination calculations and case studies.
本速查手册汇编了剑桥国际AS与A Level商务（12年级）课程所需的核心公式与分析比率。专为复习设计，每个公式都附有组成部分与应用说明，帮助你自信应对考试计算和案例分析。
1. Revenue, Costs and Profit | 收入、成本与利润
Total Revenue (TR) is the income a business receives from selling its products. It is calculated as the selling price per unit multiplied by the quantity sold.
总收入（TR）是企业销售产品所获得的收入，计算公式为单位售价乘以销售数量。
Total Revenue = Selling Price per unit × Quantity sold
总收入 = 单位售价 × 销售数量
Total Costs (TC) are split into fixed costs and variable costs. Fixed costs remain constant regardless of output, while variable costs change directly with the level of production.
总成本（TC）分为固定成本和可变成本。固定成本不随产量变动，而可变成本直接随生产水平变化。
Total Costs = Fixed Costs + Variable Costs
总成本 = 固定成本 + 可变成本
Profit (or loss) measures the financial performance by subtracting total costs from total revenue.
利润（或亏损）通过从总收入中减去总成本来衡量财务表现。
Profit = Total Revenue − Total Costs
利润 = 总收入 − 总成本
2. Contribution and Break-Even Analysis | 贡献与盈亏平衡分析
Contribution per unit is the amount each unit sold contributes towards covering fixed costs and then generating profit. It is found by deducting the variable cost per unit from the selling price.
单位贡献是每售出一件产品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
单位贡献 = 售价 − 单位可变成本
Total contribution can be calculated either as contribution per unit multiplied by quantity, or total revenue minus total variable costs.
总贡献可以用单位贡献乘以数量计算，也可用总收入减去总可变成本。
Total Contribution = Contribution per unit × Quantity = TR − TVC
总贡献 = 单位贡献 × 数量 = 总收入 − 总可变成本
The break-even point is the level of output where total revenue equals total costs. It can be expressed in units or in value.
盈亏平衡点是总收入等于总成本的产出水平，可用数量或金额表示。
Break-Even Output = Fixed Costs ÷ Contribution per unit
盈亏平衡产量 = 固定成本 ÷ 单位贡献
Break-Even Revenue = Break-Even Output × Selling Price
盈亏平衡收入 = 盈亏平衡产量 × 售价
Margin of safety indicates how much sales can fall before the business reaches its break-even point. It can be shown in units or as a percentage of budgeted sales.
安全边际表示销售额可以下降多少才会达到盈亏平衡点，可用数量或预算销售额的百分比表示。
Margin of Safety (units) = Budgeted Output − Break-Even Output
安全边际（数量）= 预算产量 − 盈亏平衡产量
Margin of Safety (%) = (Margin of Safety ÷ Budgeted Sales) × 100
安全边际（%）= （安全边际 ÷ 预算销售额）× 100
3. Profit Margins | 利润率
Gross profit margin shows the percentage of revenue left after deducting the cost of goods sold. It measures how efficiently a business manages its direct costs.
毛利率显示扣除销售成本后剩余收入的百分比，衡量企业管理直接成本的效率。
Gross Profit = Revenue − Cost of Sales
毛利润 = 收入 − 销售成本
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
毛利率（%）= （毛利润 ÷ 收入）× 100
Operating profit margin takes into account all operating expenses, offering a view of profitability from core operations.
营运利润率考虑了所有营运支出，反映核心业务的盈利能力。
Operating Profit = Gross Profit − Operating Expenses
营运利润 = 毛利润 − 营运费用
Operating Profit Margin (%) = (Operating Profit ÷ Revenue) × 100
营运利润率（%）= （营运利润 ÷ 收入）× 100
Net profit margin is the final percentage of revenue remaining after all expenses, interest and tax have been deducted.
净利润率是扣除所有费用、利息和税费后最终剩余的收入的百分比。
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
净利润率（%）= （净利润 ÷ 收入）× 100
Mark-up is the percentage added to the cost price to determine the selling price. It is often confused with margin but is based on cost, not revenue.
加成率是加在成本价上确定售价的百分比，常与毛利率混淆，但基于成本而非收入。
Mark-up (%) = (Gross Profit ÷ Cost of Sales) × 100
加成率（%）= （毛利润 ÷ 销售成本）× 100
4. Return on Capital Employed (ROCE) | 资本回报率
ROCE measures how efficiently a business generates profit from the capital invested. It is a key profitability ratio used by investors and analysts.
资本回报率衡量企业利用投入资本创造利润的效率，是投资者和分析师使用的关键盈利比率。
ROCE (%) = (Operating Profit ÷ Capital Employed) × 100
资本回报率（%）= （营运利润 ÷ 已用资本）× 100
Capital employed is usually calculated as total assets minus current liabilities, or as equity plus non-current liabilities.
已用资本通常按总资产减流动负债，或权益加非流动负债计算。
Capital Employed = Total Assets − Current Liabilities
已用资本 = 总资产 − 流动负债
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm’s ability to meet its short-term obligations. 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
流动比率 = 流动资产 ÷ 流动负债
The acid test (quick) ratio provides a stricter measure by excluding inventory, which may not be quickly convertible to cash.
酸性测试（速动）比率排除可能无法快速变现的存货，提供更严格的度量。
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
酸性测试比率 = （流动资产 − 存货）÷ 流动负债
6. Efficiency Ratios | 效率比率
Inventory turnover measures how many times a business sells and replaces its inventory over a period. A higher ratio suggests efficient stock management.
存货周转率衡量企业在一定时期内销售和补充存货的次数，比率较高表明库存管理效率高。
Inventory Turnover = Cost of Sales ÷ Average Inventory
存货周转率 = 销售成本 ÷ 平均存货
Average inventory is typically found by taking an average of opening and closing inventory for the period.
平均存货通常取期初存货与期末存货的平均值。
Average Inventory = (Opening Inventory + Closing Inventory) ÷ 2
平均存货 = （期初存货 + 期末存货）÷ 2
Trade receivable days show the average number of days a business takes to collect payment from credit customers.
应收账款周转天数反映企业平均收取赊销客户款项所需的天数。
Trade Receivable Days = (Trade Receivables ÷ Credit Sales) × 365
应收账款周转天数 = （应收账款 ÷ 赊销收入）× 365
Trade payable days measure how long a business takes to pay its suppliers.
应付账款周转天数衡量企业向供应商付款的平均时间。
Trade Payable Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 = （应付账款 ÷ 赊购额）× 365
7. Investment Appraisal | 投资评估
Investment appraisal helps businesses decide whether to proceed with capital projects. Payback period calculates the time needed to recover the initial investment from net cash inflows.
投资评估帮助企业决定是否进行资本项目。回收期法计算从净现金流入中收回初始投资所需的时间。
Payback Period = Point in time when cumulative net cash inflow equals initial investment
回收期 = 累计净现金流入等于初始投资的时间点
For uneven cash flows, add full years until the remaining amount is less than the next year’s inflow, then calculate the fraction of that year.
对于不平稳现金流，累加整年直到剩余额小于下一年流入，再计算该年的分数部分。
The Accounting Rate of Return (ARR) assesses profitability by comparing average annual profit to the initial investment.
会计收益率（ARR）通过比较年平均利润与初始投资来评估盈利能力。
Average Annual Profit = (Total Net Profit from project) ÷ Number of Years
年平均利润 = （项目总净利润）÷ 年数
ARR (%) = (Average Annual Profit ÷ Initial Investment) × 100
ARR（%）= （年平均利润 ÷ 初始投资）× 100
8. Capacity Utilisation and Labour Productivity | 产能利用率与劳动生产率
Capacity utilisation shows the extent to which a firm uses its productive capacity. It is expressed as a percentage of the maximum possible output.
产能利用率显示企业使用其生产能力的程度，以最大可能产出的百分比表示。
Capacity Utilisation (%) = (Actual Output ÷ Maximum Possible Output) × 100
产能利用率（%）= （实际产出 ÷ 最大可能产出）× 100
Labour productivity measures output generated per worker, often linked to efficiency and profit potential.
劳动生产率衡量每位员工创造的产出，通常与效率和利润潜力相关。
Labour Productivity = Total Output ÷ Number of Employees
劳动生产率 = 总产出 ÷ 员工人数
9. Workforce Performance Metrics | 员工绩效指标
Labour turnover measures the rate at which employees leave a business and need to be replaced. High turnover may indicate dissatisfaction.
劳动力流失率衡量员工离职并需要被替换的速度，高流失率可能反映满意度低。
Labour Turnover (%) = (Number of Staff Leaving during Period ÷ Average Number of Staff) × 100
劳动力流失率（%）= （期间离职人数 ÷ 平均员工人数）× 100
Absenteeism shows the proportion of working days lost due to employee absence, impacting productivity and costs.
缺勤率反映因员工缺勤损失的工作日比例，影响生产效率与成本。
Absenteeism (%) = (Total Days Lost due to Absence ÷ Total Possible Working Days) × 100
缺勤率（%）= （缺勤损失总天数 ÷ 总应出勤工作日）× 100
Labour cost per unit helps price-setting and cost control by linking total labour expenditure to output.
单位劳动成本将总劳动支出与产出挂钩，有助于定价和成本控制。
Labour Cost per Unit = Total Labour Costs ÷ Total Output
单位劳动成本 = 总劳动成本 ÷ 总产出
10. Market Share, Market Growth and Budget Variances | 市场份额、市场增长和预算差异
Market share indicates the percentage of total industry sales captured by a business. It is a measure of competitive strength.
市场份额表示企业占行业总销售额的百分比，是衡量竞争力的指标。
Market Share (%) = (Company Sales Revenue ÷ Total Market Sales Revenue) × 100
市场份额（%）= （企业销售收入 ÷ 市场总销售收入）× 100
Market growth rate shows how the size of a market is changing over time.
市场增长率反映市场规模随时间的变化程度。
Market Growth (%) = [(Market Size this Year − Market Size last Year) ÷ Market Size last Year] × 100
市场增长率（%）= [（今年市场规模 − 去年市场规模）÷ 去年市场规模] × 100
Budget variances help managers control finances by comparing actual figures to the budget. A variance can be favourable or adverse.
预算差异通过将实际数字与预算比较，帮助管理者控制财务，差异可以是顺差或逆差。
Variance = Actual Figure − Budgeted Figure
差异 = 实际数字 − 预算数字
A positive variance for revenue is favourable; for costs, a positive variance is adverse unless it represents a deliberate saving.
收入的顺差为正数；成本的正差则为逆差，除非是刻意节省。
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