📚 Year 12 CAIE Business: Formula & Theorem Quick Reference Handbook | CAIE 商务AS阶段公式定理速查手册
This quick reference handbook compiles essential formulas and theorems for Year 12 CAIE Business students. Mastering these calculations is vital for financial analysis, decision‑making and exam success. Each entry provides a clear formula, followed by paired explanations in English and Chinese so you can learn and revise effectively.
本速查手册汇集了Year 12 CAIE商务课程的核心公式与定理。掌握这些计算对财务分析、决策制定和考试成功至关重要。每个条目都给出清晰公式，并配以英文和中文解释，帮助你高效学习与复习。
1. Market Metrics | 市场指标公式
Market Share = (Firm’s Sales ÷ Total Market Sales) × 100%
Market share shows the portion of total market sales a company captures. A higher market share often indicates stronger competitive position and pricing power.
市场份额反映企业销售额在市场总销售中所占的百分比。较高的市场份额通常意味着更强的竞争力和定价权。
Market Growth = (Change in Market Size ÷ Original Market Size) × 100%
Market growth measures how much the total market has expanded or contracted over a period. Positive growth offers opportunities for all firms; negative growth signals a shrinking market.
市场增长率衡量整个市场规模的增减幅度。正增长为所有企业带来机遇，负增长则预示市场萎缩。
Price Elasticity of Demand (PED) = % Change in Quantity Demanded ÷ % Change in Price
PED indicates how sensitive demand is to price changes. If the absolute value is greater than 1, demand is elastic; if less than 1, inelastic. Businesses use PED to set revenue‑maximising prices.
需求价格弹性反映需求量对价格变化的敏感程度。绝对值大于1为富有弹性，小于1为缺乏弹性。企业据此制定收益最大化的价格策略。
2. Operations Ratios | 运营效率公式
Productivity = Total Output ÷ Number of Workers (or Hours Worked)
Productivity measures output per worker or per hour. Improving productivity reduces unit costs and boosts competitiveness.
生产率衡量每名员工或每工时的产出。提高生产率可降低单位成本，增强竞争力。
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100%
This ratio shows how much of a firm’s productive potential is being used. Very high capacity utilisation may strain resources; very low indicates wasted fixed costs.
产能利用率显示企业实际产出占最大产能的百分比。利用率过高可能透支资源，过低则浪费固定成本。
Average Cost per Unit = Total Costs ÷ Quantity Produced
Also called unit cost, this figure helps businesses set prices and analyse profitability. As output rises, average fixed costs spread over more units, often reducing average total cost.
平均单位成本又称单位成本，帮助企业定价和盈利分析。随着产量增加，平均固定成本被摊薄，平均总成本通常下降。
3. Human Resource Ratios | 人力资源比率
Labour Turnover = (Number of Staff Leaving ÷ Average Number of Staff) × 100%
Labour turnover tracks the rate at which employees leave an organisation. High turnover raises recruitment and training costs and may indicate low morale.
员工流失率反映员工离职的比率。高流失率增加招聘与培训成本，并可能暗示士气低落。
Absenteeism Rate = (Number of Days Absent ÷ Total Possible Working Days) × 100%
Absenteeism measures the proportion of working days lost to unscheduled absence. It impacts productivity and operational continuity.
缺勤率衡量因非计划缺勤损失的工作日比例，直接影响生产率和运营连续性。
Labour Retention Rate = (Number of Employees Staying ÷ Average Staff) × 100%
Retention rate is the inverse of turnover, showing the percentage of staff retained over a period. High retention supports a skilled, stable workforce.
员工留任率是流失率的反向指标，显示期内留任员工的比例。高留任率有利于维持熟练稳定的员工队伍。
4. Cost, Revenue and Profit Fundamentals | 成本、收入与利润基础公式
Total Revenue = Selling Price per Unit × Quantity Sold
Total revenue is the income a business generates from sales before deducting costs. Managers monitor this to gauge sales performance.
总收入是企业在扣除成本之前的销售收入总额，管理者借此评估销售业绩。
Total Costs = Fixed Costs + Total Variable Costs
Total cost is the sum of all expenses incurred. Fixed costs remain constant regardless of output, while variable costs change with production volume.
总成本是全部支出的总和。固定成本不随产量变动，而变动成本随产量变化。
Profit = Total Revenue − Total Costs
Profit is the positive difference between revenue and costs. A negative result indicates a loss. All businesses aim to maximise profit in the long term.
利润是收入减去成本后的正值，负值则为亏损。所有企业的长期目标都是利润最大化。
Contribution per Unit = Selling Price per Unit − Variable Cost per Unit
Contribution represents the amount each unit sold contributes towards covering fixed costs before generating profit. It is a key concept for break‑even and decision‑making.
单位贡献额是每件产品销售收入扣除变动成本后用于覆盖固定成本的金额，是盈亏平衡和决策的关键概念。
Total Contribution = Total Revenue − Total Variable Costs
Alternatively, Total Contribution = Contribution per Unit × Quantity Sold. Total contribution is used to evaluate overall coverage of fixed costs and profitability.
也可表示为总贡献额 = 单位贡献额 × 销售数量。总贡献额用于评估整体固定成本覆盖能力和盈利水平。
5. Break‑even Analysis | 盈亏平衡分析
Break‑even Point (Units) = Total Fixed Costs ÷ Contribution per Unit
Break‑even output is the number of units a business must sell to cover all costs exactly, making zero profit or loss. Below this level, the firm makes a loss; above, a profit.
盈亏平衡产量是企业需售出的产品数量，以获得刚好覆盖全部成本的零利润状态。低于此量则亏损，高于则盈利。
Break‑even Revenue = Break‑even Units × Selling Price per Unit
This calculates the sales revenue required to reach break‑even. It is useful when a firm sells multiple products and wishes to assess safety in revenue terms.
盈亏平衡收入即达到盈亏平衡所需的销售收入。当企业销售多种产品时，用收入衡量更便于评估安全程度。
Margin of Safety (Units) = Actual or Budgeted Sales Units − Break‑even Units
The margin of safety shows how far sales can fall before the business incurs a loss. A higher margin provides a cushion against demand fluctuations.
安全边际表示销售可下滑多少而不至于亏损。安全边际越大，抵御需求波动的缓冲越强。
Target Profit Units = (Fixed Costs + Target Profit) ÷ Contribution per Unit
This formula calculates the sales volume needed to achieve a desired profit level. It combines fixed costs and the target profit, divided by the unit contribution.
目标利润销量公式用于计算达到特定利润所需的销售数量，将固定成本与目标利润之和除以单位贡献额。
6. Profitability Ratios | 盈利能力比率
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
Where Gross Profit = Revenue − Cost of Sales. This margin reveals how efficiently a business controls its direct production or purchasing costs. A declining margin may signal rising material costs or discounting pressure.
毛利 = 收入 − 销售成本。毛利率揭示企业控制直接生产成本或采购成本的效率。毛利率下滑可能暗示原材料涨价或折价压力。
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100%
Operating profit is gross profit less operating expenses. This ratio reflects operational efficiency before interest and tax. A higher margin indicates strong cost control in core activities.
营业利润是毛利扣除营业费用后的利润。营业利润率反映剔除利息和税费前的经营效率，比率越高说明核心业务的成本控制越强。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
Net profit considers all expenses, including interest and tax. This metric shows the overall bottom‑line profitability after every obligation.
净利润考虑了利息和税费等全部支出。净利润率展示最终底线盈利水平，是整体获利能力的体现。
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%
Capital Employed is often calculated as Total Equity + Non‑current Liabilities, or Total Assets − Current Liabilities. ROCE measures how effectively a business generates profit from its long‑term funding. It is a key ratio for investors and management.
已动用资本通常为总权益 + 非流动负债，或总资产 − 流动负债。ROCE衡量企业利用长期资本创造利润的效率，是投资者和管理层的关键指标。
7. Liquidity Ratios | 流动性比率
Current Ratio = Current Assets ÷ Current Liabilities
The current ratio assesses a firm’s ability to meet short‑term obligations with short‑term assets. A healthy ratio is usually between 1.5 and 2.0, though it varies by industry.
流动比率衡量企业用短期资产偿还短期负债的能力。健康值通常在1.5至2.0之间，因行业而异。
Acid Test Ratio (Quick Ratio) = (Current Assets − Inventories) ÷ Current Liabilities
This stricter liquidity test excludes inventories, as they may not be quickly convertible to cash. A ratio of 1.0 or above is generally considered safe.
速动比率（酸性测试比率）排除存货，因存货变现速度较慢。比率达到1.0或以上通常被视为安全。
8. Efficiency and Gearing Ratios | 效率与杠杆比率
Inventory Turnover (Days) = (Average Inventory ÷ Cost of Sales) × 365
Inventory turnover days show how long on average inventory is held before being sold. A low number of days suggests efficient inventory management, while a very high number may indicate obsolescence or poor demand.
存货周转天数反映存货平均持有时间。天数越少，库存管理效率越高；天数过长可能预示过时或需求不振。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
This ratio measures the average time taken by customers to pay. A shorter collection period improves cash flow and reduces the risk of bad debts.
应收账款周转天数衡量客户平均付款时长。收款期越短，现金流越健康，坏账风险越低。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
Payables days show how long a business takes to settle its own debts to suppliers. Lengthening the period can help cash flow but may damage supplier relationships.
应付账款周转天数反映企业偿还供应商货款的时长。延长付款期有助于现金流，但可能损害供应商关系。
Gearing Ratio = (Non‑current Liabilities ÷ Capital Employed) × 100%
Where Capital Employed = Non‑current Liabilities + Total Equity. Gearing measures the proportion of a business’s capital that comes from debt. A gearing ratio over 50% indicates high financial risk, while a low ratio suggests reliance on equity.
杠杆比率中已动用资本 = 非流动负债 + 总权益。该比率衡量债务在资本结构中的比重。超过50%被视为高财务风险，低比率则表明依赖股权。
Earnings per Share (EPS) = Net Profit ÷ Number of Ordinary Shares
EPS calculates the profit attributable to each ordinary share. It is a fundamental measure of a company’s profitability per share and is closely watched by investors.
每股收益计算每只普通股应占利润，是衡量公司每股盈利能力的基础指标，备受投资者关注。
Price/Earnings Ratio (P/E) = Market Price per Share ÷ Earnings per Share
The P/E ratio indicates how much investors are willing to pay for each unit of profit. A high P/E may suggest growth expectations, while a low P/E could signal undervaluation or caution.
市盈率反映投资者为每单位利润愿意支付的价格。高市盈率可能暗含增长预期，低市盈率或暗示低估或市场谨慎。
9. Investment Appraisal | 投资评估方法
Payback Period = Point at Which Cumulative Cash Inflows Equal Initial Investment
Payback measures the time required to recover an initial investment from net cash flows. It is simple but ignores the time value of money and returns beyond the payback point.
回收期衡量从净现金流中收回初始投资所需的时间。方法简单，但忽略货币时间价值及回收期后的回报。
Average Rate of Return (ARR) = (Average Annual Profit ÷ Initial Investment Cost) × 100%
Average Annual Profit is calculated as (Total Net Cash Flows − Initial Investment) ÷ Number of Years. ARR expresses the average yearly return as a percentage of the initial cost, allowing comparison with interest rates or target returns.
平均年利润 = (总净现金流 − 初始投资) ÷ 年数。ARR将年均回报表示为初始投资的百分比，便于与利率或目标回报比较。
Net Present Value (NPV) = Σ (Cash Flow × Discount Factor) − Initial Investment
NPV converts future cash flows to present value using a chosen discount rate. A positive NPV means the project should create shareholder value; a negative NPV suggests rejection. Choosing an appropriate discount rate is crucial.
净现值使用选定的折现率将未来现金流换算为当前价值。NPV为正表明项目能为股东创造价值，为负则不宜投资。选取合适折现率至关重要。
10. Budgeting and Decision Trees | 预算差异与决策树
Variance = Actual Figure − Budgeted Figure
A positive variance for revenue or profit is favourable (F); for costs, favourable means actual is lower than budget. Negative variances are adverse (A). Variances help managers identify areas needing corrective action.
差异额 = 实际数 − 预算数。收入或利润的正差异为有利差异(F)，成本低于预算亦为有利。负差异则为不利差异(A)。差异分析帮助管理者定位需改进的领域。
Expected Monetary Value (EMV) = Σ (Probability × Payoff) for Each Outcome
In a decision tree, each chance node is assigned an EMV by multiplying the financial outcome by its probability and summing. The net gain is then calculated by deducting any initial cost. The option with the highest expected net gain is recommended.
在决策树中，将每个结果的货币值乘以其概率并加总，得到期望货币值。再减去初始成本得到净收益。通常推荐期望净收益最大的方案。
Published by TutorHao | Business Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导