📚 Year 12 CAIE Business: Formulas & Theories Quick Reference Handbook | 12年级CAIE商务：公式定理速查手册
This quick reference handbook covers the essential formulas and key theories required for the CAIE AS Level Business syllabus (9609). It is designed to help Year 12 students quickly revise calculations for break-even analysis, ratios, elasticities, employee performance, investment appraisal, decision trees, and more, alongside concise summaries of major motivational and strategic models.
本速查手册涵盖了CAIE AS商务课程（9609）所需的核心公式与关键理论。旨在帮助12年级学生快速回顾盈亏平衡分析、各类比率、弹性、员工绩效、投资评估、决策树等计算内容，以及主要激励与战略模型的简明总结。
1. Cost and Revenue Basics | 成本与收入基础
Total Costs (TC) = Total Fixed Costs (TFC) + Total Variable Costs (TVC). Fixed costs remain unchanged when output varies, while variable costs change directly with production volume.
总成本 (TC) = 总固定成本 (TFC) + 总可变成本 (TVC)。固定成本在产出变动时保持不变，可变成本随产量直接变化。
Total Variable Cost (TVC) = Variable Cost per unit × Quantity produced (Q). It represents the costs that rise as more units are made.
总可变成本 (TVC) = 单位可变成本 × 产量 (Q)。它代表随着产量增加而上升的成本。
Total Revenue (TR) = Selling Price per unit (P) × Quantity sold (Q). This is the income a business receives from selling goods or services.
总收入 (TR) = 单位售价 (P) × 销售数量 (Q)。这是企业出售商品或服务所获得的收入。
Profit = Total Revenue – Total Costs, or Profit = Total Contribution – Total Fixed Costs. A positive result indicates a surplus; a negative result is a loss.
利润 = 总收入 – 总成本，或 利润 = 总贡献 – 总固定成本。正值表示盈余，负值表示亏损。
Contribution per unit = Selling Price per unit – Variable Cost per unit. It shows how much each unit sold contributes towards covering fixed costs and generating profit.
单位贡献 = 单位售价 – 单位可变成本。它表明每售出一个单位可为覆盖固定成本和创造利润做出多大贡献。
Total Contribution = (Selling Price – Variable Cost) × Quantity sold. This is the total amount available to cover fixed costs before profit is earned.
总贡献 = (售价 – 可变成本) × 销售数量。指在获得利润前可用于覆盖固定成本的总金额。
2. Break-even Analysis | 盈亏平衡分析
Break-even Point (BEP) in units = Total Fixed Costs ÷ (Selling Price per unit – Variable Cost per unit). This is the number of units that must be sold to reach a position where total revenue equals total costs.
盈亏平衡点产量 = 总固定成本 ÷ (单位售价 – 单位可变成本)。这是必须出售的单位数量，使得总收入等于总成本。
Break-even Revenue = BEP units × Selling Price per unit, or using the contribution ratio: Total Fixed Costs ÷ (Contribution per unit ÷ Selling Price).
盈亏平衡收入 = 盈亏平衡产量 × 单位售价，或使用贡献率：总固定成本 ÷ (单位贡献 ÷ 售价)。
Margin of Safety = Actual Sales units – Break-even Sales units. It measures the amount by which demand can fall before a loss is made. A higher safety margin means lower risk.
安全边际 = 实际销量 – 盈亏平衡销量。它衡量在业务出现亏损前销量可以下降的幅度。安全边际越大，风险越低。
Output needed for Target Profit = (Total Fixed Costs + Target Profit) ÷ Contribution per unit. This formula helps managers plan the production volume required to achieve a specific profit goal.
实现目标利润所需产量 = (总固定成本 + 目标利润) ÷ 单位贡献。此公式帮助管理者规划实现特定利润目标所需的产量。
Break-even Chart: A graphical representation showing total revenue and total cost lines. The point where the two lines intersect is the break-even point. The area between the lines after this point shows profit, and before shows loss.
盈亏平衡图：用图形展示总收入线和总成本线。两条线的交点为盈亏平衡点。交点之后两线之间的区域代表利润，交点之前代表损失。
3. Profitability Ratios | 盈利能力比率
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100. It shows the percentage of revenue left after paying for direct costs of production. A high percentage indicates efficient production or strong pricing.
毛利率 = (毛利 ÷ 收入) × 100。它展示支付直接生产成本后剩余收入的百分比。高毛利率表明生产效率高或定价能力强。
Net Profit Margin = (Net Profit ÷ Revenue) × 100. This ratio reveals how much of each pound/dollar of revenue remains as profit after all expenses are deducted. It is a key measure of overall profitability.
净利率 = (净利润 ÷ 收入) × 100。该比率显示扣除所有费用后每一英镑/美元收入中保留的利润。它是衡量整体盈利能力的关键指标。
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100. It evaluates the return generated from the long-term capital invested in the business. A high ROCE shows efficient use of resources.
已动用资本回报率 (ROCE) = (营业利润 ÷ 已动用资本) × 100。它评估企业投入的长期资本所产生的回报。高ROCE表明资源利用效率高。
Mark-up = (Gross Profit ÷ Cost of Sales) × 100. It expresses the gross profit as a percentage of the cost of goods sold, helping businesses set selling prices.
加成率 = (毛利 ÷ 销售成本) × 100。它将毛利表示为销售成本的百分比，帮助企业制定售价。
4. Liquidity Ratios | 流动性比率
Current Ratio = Current Assets ÷ Current Liabilities. It measures a firm’s ability to meet short-term obligations as they fall due. A result between 1.5 and 2.0 is often considered healthy, though the ideal level depends on the industry.
流动比率 = 流动资产 ÷ 流动负债。它衡量企业到期偿还短期债务的能力。通常在1.5到2.0之间被认为是健康的，但理想水平取决于行业。
Acid Test (Quick) Ratio = (Current Assets – Inventory) ÷ Current Liabilities. This stricter test excludes inventory, which may take time to convert into cash. It shows whether the business can pay its short-term debts immediately.
酸性测试（速动）比率 = (流动资产 – 存货) ÷ 流动负债。这个更严格的测试剔除了存货，因为存货变现可能需要时间。它显示企业能否立即支付短期债务。
5. Efficiency Ratios | 效率比率
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory. It tells how many times a business sells and replaces its stock over a period. A high turnover suggests efficient stock management.
存货周转率（次数） = 销售成本 ÷ 平均存货。它表明企业在一个时期内出售和补充库存的次数。高周转率表示库存管理效率高。
Inventory Turnover (days) = (Average Inventory ÷ Cost of Sales) × 365. This shows the average number of days goods remain in stock before being sold. Fewer days usually indicate better efficiency.
存货周转天数 = (平均存货 ÷ 销售成本) × 365。它显示商品售出前在库存中停留的平均天数。天数越少通常表示效率越高。
Trade Receivables Days (Debtor Days) = (Trade Receivables ÷ Credit Sales) × 365. It measures the average time taken by customers to pay their invoices. A lower figure means faster cash collection.
应收账款周转天数 = (应收账款 ÷ 赊销收入) × 365。它衡量客户支付发票的平均时长。较低的数字意味着现金回笼速度更快。
Trade Payables Days (Creditor Days) = (Trade Payables ÷ Credit Purchases) × 365. It indicates how long, on average, the business takes to pay its suppliers. Responsible management balances taking credit and settling on time.
应付账款周转天数 = (应付账款 ÷ 赊购额) × 365。它表明企业平均需要多长时间支付供应商。合理的管理应在利用信用与按时结算之间取得平衡。
Asset Turnover = Revenue ÷ Net Assets. It assesses how efficiently a business uses its assets to generate sales. A high ratio means assets are being used productively.
资产周转率 = 收入 ÷ 净资产。它评估企业使用资产创造收入的效率。高比率说明资产得到高效利用。
6. Elasticity of Demand | 需求弹性
Price Elasticity of Demand (PED) = % Change in Quantity Demanded ÷ % Change in Price. PED measures the responsiveness of demand to a change in price. If PED > 1, demand is elastic; if PED < 1, demand is inelastic.
需求价格弹性 (PED) = 需求量变动百分比 ÷ 价格变动百分比。PED衡量需求对价格变动的反应程度。PED > 1 表示富有弹性，PED < 1 表示缺乏弹性。
Income Elasticity of Demand (YED) = % Change in Quantity Demanded ÷ % Change in Income. It shows how demand responds to changes in consumer income. Positive YED indicates a normal good; negative YED indicates an inferior good.
需求收入弹性 (YED) = 需求量变动百分比 ÷ 收入变动百分比。它显示需求如何随消费者收入变化。正的YED表示正常商品；负的YED表示劣质商品。
Elasticity knowledge helps firms predict the impact of pricing and economic conditions on sales revenue and plan marketing strategies accordingly.
弹性知识有助于企业预测定价和经济状况对销售收入的影响，并据此规划营销策略。
7. Labour Performance Metrics | 员工绩效指标
Labour Productivity = Total Output in a Period ÷ Number of Employees. It measures output per worker and is a key indicator of workforce efficiency. Improvements can come from training, technology or better motivation.
劳动生产率 = 某一时期的总产出 ÷ 员工人数。它衡量每个工人的产出，是衡量劳动力效率的关键指标。培训、技术或更好的激励可以促进改进。
Absenteeism Rate = (Total Days Absent ÷ Total Working Days Available) × 100. High absenteeism can signal low morale, poor working conditions or health issues, and it reduces productivity.
缺勤率 = (缺勤总天数 ÷ 可用工作总天数) × 100。高缺勤率可能表明士气低落、工作条件差或健康问题，且会造成生产力下降。
Labour Turnover = (Number of Employees Leaving in a Period ÷ Average Number of Employees) × 100. It shows the rate at which staff leave the business. Excessive turnover increases recruitment costs and disrupts operations.
劳动力流失率 = (某一时期离职员工人数 ÷ 平均员工人数) × 100。它表明员工离职的比率。过高的流失率会增加招聘成本并扰乱运营。
8. Budgetary Variances | 预算差异分析
Sales Volume Variance = (Actual Quantity Sold – Budgeted Quantity) × Standard Selling Price. It isolates the effect of selling a different quantity than planned. A positive variance is favourable.
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