Pre-U CCEA Business: Formula & Theorem Quick Reference Handbook | Pre-U CCEA 商务：公式定理速查手册

📚 Pre-U CCEA Business: Formula & Theorem Quick Reference Handbook | Pre-U CCEA 商务：公式定理速查手册

This quick reference handbook has been compiled for Pre-U CCEA Business students. It pulls together the essential formulas, key theorems, and strategic models that appear most frequently in your examinations. By keeping this guide to hand, you can revise efficiently and learn how to apply these concepts accurately in both data‑response and essay questions. The handbook covers break‑even analysis, investment appraisal, profitability and liquidity ratios, elasticity measures, cost‑revenue‑profit relationships, budget variances, labour productivity and turnover, inventory management, decision trees, and classical strategic models. Each entry presents the core idea in English first, immediately followed by a parallel Chinese explanation, so you can reinforce your understanding in both languages.

这份速查手册是专为 Pre‑U CCEA 商务学科准备的。手册收录了考试中最常见的核心公式、重要定理和战略模型。常备此手册能让你更有效地复习，并帮助你在数据分析题和论文题中准确运用这些概念。手册涵盖了盈亏平衡分析、投资评价、盈利与流动性比率、弹性度量、成本‑收益‑利润关系、预算差异、劳动生产力与员工流失、库存管理、决策树以及经典战略模型。每个知识点都以英文说明在前、中文解读在后，双语对照，强化理解。

1. 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 calculation tells you how many units must be sold before the business starts to make a profit.

单位盈亏平衡点 = 总固定成本 ÷ (单位售价 – 单位可变成本)。该计算告诉你企业需要销售多少件产品才能开始盈利。

Break-even point in sales value can also be found using the contribution margin ratio: BEP (£) = Total Fixed Costs ÷ Contribution Margin Ratio, where Contribution Margin Ratio = (Selling Price – Variable Cost) ÷ Selling Price.

盈亏平衡销售额可通过边际贡献率求得：盈亏平衡销售额 = 总固定成本 ÷ 边际贡献率，其中边际贡献率 = (售价 – 可变成本) ÷ 售价。

Margin of safety = Actual Sales (units or £) – Break-even Sales (units or £). A larger margin of safety indicates lower risk.

安全边际 = 实际销售额（或销售量）− 盈亏平衡销售额（或销售量）。安全边际越大，经营风险越低。

2. Investment Appraisal | 投资评价

Payback Period is the time taken for an investment to recover its initial cost. If annual net cash flows are equal, Payback = Initial Investment ÷ Annual Cash Flow. For uneven cash flows, you cumulate year by year until the total reaches the initial outlay.

回收期是指收回初始投资所需要的时间。若每年净现金流相等，回收期 = 初始投资 ÷ 年现金流。若现金流不相等，则逐年累计直至累计额等于初始投资额。

Average Rate of Return (ARR) = (Average Annual Profit ÷ Initial Investment) × 100%. Some formulas use average investment instead: (Initial Investment + Residual Value) ÷ 2. ARR shows the percentage return expected from a project.

平均收益率 (ARR) = (平均年利润 ÷ 初始投资) × 100%。部分公式用平均投资额计算：平均投资额 = (初始投资 + 残值) ÷ 2。ARR 反映项目的预期百分比回报。

Net Present Value (NPV) = Σ [CFt ÷ (1 + r)ᵗ] – Initial Investment, where CFt is net cash flow in year t and r is the discount rate. NPV recognises the time value of money; a positive NPV suggests the project should be accepted.

净现值 (NPV) = Σ [NCFt ÷ (1 + r)ᵗ] – 初始投资，其中 NCFt 为第 t 年的净现金流，r 为贴现率。净现值考虑了货币的时间价值；NPV 为正时建议接受项目。

3. Profitability & Liquidity Ratios | 盈利与流动性比率

Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%. It measures how efficiently a firm turns raw materials and labour into profit after direct costs.

毛利率 = (毛利 ÷ 营业收入) × 100%。它衡量企业在扣除直接成本后将原材料与人工转化为利润的效率。

Net Profit Margin = (Net Profit ÷ Revenue) × 100%. This ratio reveals the percentage of sales revenue left after all expenses, including overheads and interest, have been paid.

净利率 = (净利润 ÷ 营业收入) × 100%。该比率揭示了支付所有费用（包括间接费用和利息）后剩余的销售收入百分比。

Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%. Capital employed is usually defined as total assets less current liabilities, or as equity plus non‑current liabilities. ROCE is a fundamental measure of how effectively management uses the funds entrusted to it.

运用资本报酬率 (ROCE) = (营业利润 ÷ 运用资本) × 100%。运用资本通常定义为总资产减去流动负债，或

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