📚 Pre-U OCR Business: Formula & Theorem Quick Reference Handbook | Pre-U OCR 商务：公式定理速查手册
This quick-reference handbook collates the essential formulae, ratios and decision-making tools required for the OCR Pre-U Business specification. Each entry is presented as a clear statement followed by its Chinese equivalent, enabling bilingual learners to revise efficiently and apply concepts confidently in calculation-based questions.
本速查手册汇集了 OCR Pre-U 商务课程要求掌握的核心公式、比率和决策工具。每个条目均以清晰的英文陈述及对应的中文呈现，帮助双语学习者高效备考，在计算类题目中自信运用相关概念。
1. Break-even Analysis | 盈亏平衡分析
Break-even point (units) = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
盈亏平衡点（单位） = 固定成本 ÷ （每单位售价 − 每单位变动成本）
Contribution per Unit = Selling Price per Unit − Variable Cost per Unit
单位贡献 = 每单位售价 – 每单位变动成本
Contribution Margin Ratio = Contribution per Unit ÷ Selling Price per Unit
贡献毛利率 = 单位贡献 ÷ 每单位售价
Break-even Revenue = Fixed Costs ÷ Contribution Margin Ratio
盈亏平衡收入 = 固定成本 ÷ 贡献毛利率
s volume for target profit (units) = (Fixed Costs + Target Profit) ÷ Contribution per Unit
实现目标利润的销售量（单位） = （固定成本 + 目标利润） ÷ 单位贡献
Margin of Safety (units) = Actual Sales Volume − Break-even Sales Volume
安全边际（单位） = 实际销售量 − 盈亏平衡销售量
2. Contribution and Profit | 贡献与利润
Total Contribution = Total Sales Revenue − Total Variable Costs
总贡献 = 总销售收入 − 总变动成本
Total Contribution = Contribution per Unit × Quantity Sold
总贡献 = 单位贡献 × 销售数量
Profit = Total Contribution − Fixed Costs
利润 = 总贡献 − 固定成本
Profit = (Contribution per Unit × Quantity Sold) − Fixed Costs
利润 = （单位贡献 × 销售数量） − 固定成本
3. Profitability Ratios | 盈利能力比率
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
毛利率 = （毛利 ÷ 收入） × 100%
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
净利率 = （净利润 ÷ 收入） × 100%
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100%
营业利润率 = （营业利润 ÷ 收入） × 100%
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%
资本回报率（ROCE） = （营业利润 ÷ 已用资本） × 100%
Capital Employed = Total Assets − Current Liabilities
已用资本 = 总资产 − 流动负债
4. Liquidity Ratios | 流动性比率
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
速动比率 = （流动资产 − 存货） ÷ 流动负债
Working Capital = Current Assets − Current Liabilities
营运资金 = 流动资产 − 流动负债
5. Efficiency Ratios | 营运效率比率
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
存货周转率（次数） = 销售成本 ÷ 平均存货
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 = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 = （应付账款 ÷ 赊购金额） × 365
Asset Turnover = Revenue ÷ Net Assets
资产周转率 = 收入 ÷ 净资产
6. Gearing and Investor Ratios | 杠杆与投资比率
Gearing Ratio = (Non-current Liabilities ÷ Capital Employed) × 100%
杠杆比率 = （非流动负债 ÷ 已用资本） × 100%
Interest Cover = Operating Profit ÷ Interest Payable
利息保障倍数 = 营业利润 ÷ 应付利息
Earnings per Share (EPS) = (Net Profit − Preference Dividends) ÷ Number of Ordinary Shares
每股收益 = （净利润 − 优先股股息） ÷ 普通股股数
Dividend per Share = Total Ordinary Dividends ÷ Number of Ordinary Shares
每股股息 = 普通股股息总额 ÷ 普通股股数
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%
股息率 = （每股股息 ÷ 每股市价） × 100%
Price/Earnings Ratio = Market Price per Share ÷ Earnings per Share
市盈率 = 每股市价 ÷ 每股收益
7. Elasticity and Market Metrics | 弹性与市场指标
Price Elasticity of Demand (PED) = % Change in Quantity Demanded ÷ % Change in Price
需求价格弹性（PED） = 需求量变动百分比 ÷ 价格变动百分比
Income Elasticity of Demand (YED) = % Change in Quantity Demanded ÷ % Change in Income
需求收入弹性（YED） = 需求量变动百分比 ÷ 收入变动百分比
Cross Elasticity of Demand (XED) = % Change in Quantity Demanded of Good A ÷ % Change in Price of Good B
需求交叉弹性（XED） = 商品 A 需求量变动百分比 ÷ 商品 B 价格变动百分比
Market Share = (Company Sales ÷ Total Market Sales) × 100%
市场份额 = （企业销售额 ÷ 市场总销售额） × 100%
Market Growth = (Change in Market Size ÷ Original Market Size) × 100%
市场增长率 = （市场规模变化量 ÷ 原有市场规模） × 100%
8. Costs, Revenue and Profit Maximisation | 成本、收入与利润最大化
Total Cost (TC) = Total Fixed Cost + Total Variable Cost
总成本 = 总固定成本 + 总变动成本
Average Cost (AC) = Total Cost ÷ Quantity
平均成本 = 总成本 ÷ 产量
Marginal Cost (MC) = Change in Total Cost ÷ Change in Quantity
边际成本 = 总成本变动量 ÷ 产量变动量
Total Revenue (TR) = Selling Price × Quantity Sold
总收入 = 售价 × 销售数量
Average Revenue (AR) = Total Revenue ÷ Quantity = Price
平均收入 = 总收入 ÷ 数量 = 价格
Marginal Revenue (MR) = Change in Total Revenue ÷ Change in Quantity
边际收入 = 总收入变动量 ÷ 产量变动量
Profit Maximisation condition: Marginal Revenue = Marginal Cost (MR = MC)
利润最大化条件：边际收入 = 边际成本 （MR = MC）
9. Investment Appraisal | 投资评估
ll years before recovery + (Unrecovered cost at start of year ÷ Net cash flow during year)
回收期 = 完全回收前的整年数 + （年初未回收成本 ÷ 该年净现金流量）
Average Rate of Return (ARR) = (Average Annual Profit ÷ Initial Investment) × 100%
平均回报率（ARR） = （平均年利润 ÷ 初始投资额） × 100%
t Present Value (NPV) = Σ (Net Cash Flow in Year t × Discount Factor) − Initial Investment
净现值（NPV） = ∑ （第 t 年净现金流量 × 折现因子） − 初始投资额
10. Decision Trees | 决策树
Expected Value (EV) of an outcome = Probability × Payoff
结果的期望值（EV） = 概率 × 回报
Expected Value of a decision node = Σ (Probability × Payoff) for each branch
决策节点的期望值 = 每个分支的 ∑ （概率 × 回报）
Net Gain = Expected Value − Initial Cost of Decision
净收益 = 期望值 − 决策的初始成本
11. Capacity and Productivity | 产能与生产力
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 = Total Output per Period ÷ Number of Employees
劳动生产率 = 每期总产出 ÷ 员工人数
Unit Cost = Total Cost ÷ Total Output
单位成本 = 总成本 ÷ 总产出
12. Inventory Management | 库存管理
Economic Order Quantity (EOQ) = √( (2 × D × C₀) ÷ Cₕ )
经济订货批量（EOQ） = √ （2 × 年需求量 × 每次订货成本） ÷ 单位年持有成本
Reorder Level = (Lead Time Demand) + Buffer Stock
再订货水平 = （提前期需求量） + 缓冲库存
Average Inventory = Order Quantity ÷ 2 (assuming no buffer stock)
平均库存 = 订货批量 ÷ 2 （假设无缓冲库存）
Buffer Stock = Safety stock held to cover variations in demand or lead time
缓冲库存 = 为应对需求或提前期变动而持有的安全库存
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