📚 Year 10 CIE Business: Formula & Theorem Quick Reference Handbook | Year 10 CIE 商务：公式定理速查手册
This quick reference handbook compiles all the essential formulas and accounting theorems you will encounter in Year 10 CIE Business (0450). Each concept is presented with a clear definition in English, followed by its Chinese equivalent, so you can master the terminology and calculations from both linguistic perspectives. Mastering these equations will not only help you solve quantitative problems but also deepen your understanding of business performance, decision-making, and financial health.
本速查手册汇编了 Year 10 CIE 商务（0450）课程中所有必背公式与会计定理。每个概念先用英文清晰地给出定义，再用中文配对解释，帮助你从双语角度掌握术语和计算方法。熟练掌握这些公式，不仅能解决计算题，更能让你深刻理解企业绩效、决策和财务健康状况。
1. Revenue, Cost and Profit | 收入、成本与利润
Revenue is the total income a business receives from selling goods or services in a given period. It is calculated by multiplying the selling price per unit by the quantity of units sold. Cost refers to the expenses incurred in producing or buying the goods. Total costs are split into fixed costs (which do not change with output, e.g. rent) and variable costs (which vary directly with output, e.g. raw materials). Profit is what remains after total costs are deducted from total revenue. These are the foundation of any business calculation.
收入是企业在特定时期内通过销售商品或服务获得的总所得，由单位售价乘以销售数量计算得出。成本指生产或采购商品所发生的开支。总成本分为固定成本（不随产量变化，如租金）和可变成本（随产量直接变化，如原材料）。利润则是总收入扣除总成本后的剩余。这些是所有商业计算的基石。
Total Revenue = Selling Price per unit × Quantity sold
Total Revenue = Selling Price per unit × Quantity sold
总收入的公式为：单价 × 销售数量。
总收入 = 单价 × 销售数量
Total Cost = Fixed Cost + Total Variable Cost
Total Cost = Fixed Cost + (Variable Cost per unit × Quantity)
总成本等于固定成本加上总可变成本（单位可变成本 × 产量）。
总成本 = 固定成本 + （单位可变成本 × 产量）
Profit = Total Revenue − Total Cost
Profit = Total Revenue − Total Cost
利润等于总收入减去总成本。
利润 = 总收入 − 总成本
2. Break‑even Analysis | 盈亏平衡分析
Break‑even is the level of output at which total revenue equals total cost — the business makes neither a profit nor a loss. The break‑even point can be expressed in units or in sales revenue. Contribution per unit is the amount each unit sold contributes towards covering fixed costs after variable costs have been paid.
盈亏平衡是指总收入等于总成本的产出水平——企业既不盈利也不亏损。盈亏平衡点可用数量或销售收入来表示。单位贡献毛益是每售出一件产品在扣除可变成本后，用于弥补固定成本的金额。
Break‑even point (units) = Fixed Cost ÷ (Selling Price per unit − Variable Cost per unit)
Break‑even point (units) = Fixed Cost ÷ (Selling Price per unit − Variable Cost per unit)
盈亏平衡数量 = 固定成本 ÷ （单价 − 单位可变成本），也就是固定成本除以单位贡献毛益。
盈亏平衡点（数量） = 固定成本 ÷ 单位贡献毛益
Break‑even point in revenue = Break‑even units × Selling Price per unit
Break‑even revenue = Break‑even units × Selling Price per unit
盈亏平衡收入 = 盈亏平衡数量 × 单价。
盈亏平衡收入 = 盈亏平衡数量 × 单价
Margin of safety = Actual sales − Break‑even sales
Margin of safety (units) = Current output − Break‑even output
安全边际 = 实际销售量 − 盈亏平衡销售量，衡量企业销售下降多少才会开始亏损。
安全边际（数量） = 当前产量 − 盈亏平衡产量
3. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm's ability to generate profit relative to sales, assets or equity. They help assess how efficiently a business is turning its resources into earnings. The three key ratios for Year 10 are gross profit margin, net profit margin and return on capital employed (ROCE).
盈利能力比率衡量企业相对于销售额、资产或权益产生利润的能力。它们帮助评估企业将资源转化为收益的效率。Year 10 需要掌握三个关键比率：毛利率、净利润率和已用资本回报率。
Gross Profit = Sales Revenue − Cost of Sales
Gross Profit = Sales Revenue − Cost of Sales
毛利等于销售收入减去销售成本（即直接成本）。
毛利 = 销售收入 − 销售成本
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
毛利率 = （毛利 ÷ 销售收入）× 100%，反映企业产品基本盈利能力和定价策略。
毛利率 (%) = （毛利 ÷ 收入）× 100
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
净利润率 = （净利润 ÷ 销售收入）× 100%，净利润为毛利扣除所有费用后的利润。
净利润率 (%) = （净利润 ÷ 收入）× 100
ROCE = (Net Profit ÷ Capital Employed) × 100
ROCE (%) = (Net Profit ÷ Capital Employed) × 100
已用资本回报率 = （净利润 ÷ 已用资本）× 100%，其中已用资本通常为股东出资加上长期贷款。
ROCE (%) = （净利润 ÷ 已用资本）× 100
4. Liquidity Ratios | 流动性比率
Liquidity ratios assess a business’s ability to meet its short‑term debts as they fall due. They focus on the current assets and current liabilities shown on the statement of financial position. The two main ratios are the current ratio and the acid test (quick) ratio.
流动性比率评估企业偿还到期短期债务的能力，关注财务状况表中列示的流动资产和流动负债。两个主要比率是流动比率和酸性测试（速动）比率。
Current Ratio = Current Assets ÷ Current Liabilities
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债。通常认为 1.5:1 至 2:1 较为健康。
流动比率 = 流动资产 ÷ 流动负债
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
酸性测试比率 = （流动资产 − 存货）÷ 流动负债。存货被认为变现速度最慢，因此排除。
酸性测试比率 = （流动资产 − 存货）÷ 流动负债
5. Efficiency Ratios | 效率比率
Efficiency ratios indicate how well a business uses its assets and manages its trade payables and receivables. The most common efficiency ratio at Year 10 is the inventory turnover (or stock turnover) ratio, which measures how quickly inventory is sold. A faster turnover often means better liquidity and less risk of obsolete stock.
效率比率表明企业利用资产和管理应付账款及应收账款的效率。Year 10 最常见的效率比率是存货周转率，它衡量存货销售的速度。周转越快通常意味着流动性越强，存货过时风险越小。
Inventory (Stock) Turnover = Cost of Sales ÷ Average Inventory
Inventory Turnover = Cost of Sales ÷ Average Inventory
存货周转率 = 销售成本 ÷ 平均存货（若题中未给平均数，有时直接用期末存货）。
存货周转率 = 销售成本 ÷ 平均存货
The result shows how many times inventory is sold and replaced in a year. A high figure suggests efficient stock management, but could also indicate a risk of stock‑outs.
该结果表示一年内存货售出并补进的次数。高数值意味着存货管理效率高，但可能也表明有缺货风险。
6. Accounting Equation | 会计等式
The accounting equation is the fundamental theorem of the statement of financial position (balance sheet). It states that everything the business owns (assets) is financed either by what it owes (liabilities) or by the owners’ investment (equity). This equation must always balance.
会计等式是财务状况表（资产负债表）的基本定理。它表明企业拥有的一切（资产）要么来源于债务（负债），要么来源于所有者的投入（权益）。该等式必须始终保持平衡。
Assets = Liabilities + Equity
Assets = Liabilities + Equity
资产等于负债加所有者权益。这是复式记账的核心。
资产 = 负债 + 所有者权益
nged, Equity = Assets − Liabilities, which is also known as the net worth of the business.
变形后，权益 = 资产 − 负债，也被称为企业的净资产。
7. Cash Flow Forecasting Formulas | 现金流量预测公式
A cash flow forecast shows the expected inflows and outflows of cash over a future period. It is not a profit statement — it records only actual cash movements. The key formulas used to build a forecast are:
现金流量预测展示未来一段时期内预期的现金流入和流出。它并非利润表，只记录实际的现金流动。构建预测所用的关键公式如下：
Net Cash Flow = Cash Inflows − Cash Outflows for a period
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
净现金流量 = 现金流入总额 − 现金流出总额。正值表示现金增加，负值表示现金减少。
净现金流量 = 现金流入总计 − 现金流出总计
Closing Balance = Opening Balance + Net Cash Flow
Closing Cash Balance = Opening Balance + Net Cash Flow
期末现金余额 = 期初余额 + 净现金流量，一个时期的期末余额成为下一个时期的期初余额。
期末现金余额 = 期初余额 + 净现金流量
8. Productivity and Unit Cost | 生产力与单位成本
Productivity measures how efficiently inputs (like labour) are converted into output. Higher productivity typically lowers unit costs, making the business more competitive. Unit cost is the average cost of producing one item.
生产力衡量投入（如劳动力）转化为产出的效率。较高的生产力通常会降低单位成本，使企业更具竞争力。单位成本是生产一件产品的平均成本。
Labour Productivity = Output per period ÷ Number of workers
Labour Productivity = Total Output ÷ Number of Employees
劳动生产率 = 总产出 ÷ 员工人数。也可按时间计算，如单位/小时。
劳动生产率 = 总产出 ÷ 员工人数
Unit (Average) Cost = Total Cost ÷ Number of units produced
Unit Cost = Total Cost ÷ Quantity Produced
单位成本 = 总成本 ÷ 生产数量。随着产量增加，固定成本分摊到更多单位，单位成本可能下降。
单位成本 = 总成本 ÷ 生产数量
9. Investment Appraisal Methods | 投资评估方法
When a business considers a capital investment, it can use simple quantitative techniques to evaluate returns. For Year 10 CIE, the two main methods are the payback period and the average rate of return (ARR). These help managers decide whether a project is financially worthwhile.
当企业考虑资本投资时，可以使用简单的定量技术来评估回报。Year 10 CIE 主要掌握两种方法：投资回收期和平均回报率（ARR）。这些帮助管理者判断项目在财务上是否可行。
Investment ÷ Annual Net Cash Flow. For uneven flows, cumulative cash flow is tracked until it turns positive.
投资回收期是指收回初始投资成本所需的时间。若现金流量均匀，公式为：回收期 = 初始投资总额 ÷ 年净现金流量。对于不均匀流量，需逐年累计净现金流量，直至累计值变为正数。
ARR = (Average Annual Profit ÷ Initial Investment) × 100
ARR (%) = (Average Annual Profit ÷ Initial Investment) × 100
平均回报率 = （平均年利润 ÷ 初始投资）× 100%。平均年利润通常是总利润除以项目年限。ARR 越高，项目越具吸引力。
ARR (%) = （平均年利润 ÷ 初始投资）× 100
10. Working Capital and the Cash Cycle | 营运资金与现金循环
Working capital measures the short‑term financial health of a business. It is the capital available to meet day‑to‑day expenses. The cash conversion cycle ties together inventory, trade receivables and trade payables to show how long cash is tied up in operations.
营运资金衡量企业短期财务健康状况，它是可用于满足日常开支的资本。现金转换周期将存货、应收账款和应付账款联系起来，显示资金在运营中被占用的时间。
Working Capital = Current Assets − Current Liabilities
Working Capital = Current Assets − Current Liabilities
营运资金 = 流动资产 − 流动负债。正营运资金表示企业有能力偿还短期债务。
营运资金 = 流动资产 − 流动负债
The cash conversion cycle can be estimated as: Inventory turnover period + Trade receivables collection period − Trade payables payment period. A shorter cycle means cash is recovered more quickly.
现金转换周期可估算为：存货周转天数 + 应收账款回收期 − 应付账款付款期。周期越短，现金回收越快。
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