📚 AS CIE Business: Quick Reference Handbook of Formulas and Principles | AS CIE 商务：公式定理速查手册
This quick reference handbook brings together the essential formulas, key ratios, and guiding principles required for the AS CIE Business syllabus. It covers quantitative techniques for finance, operations, and human resources, as well as strategic frameworks that frequently appear in examination questions. Use it for rapid revision before your exam to reinforce calculation methods and conceptual understanding.
本速查手册汇总了 AS CIE 商务课程中必须掌握的公式、关键比率和核心原理。手册涵盖财务、运营和人力资源方面的定量方法，以及考试中常出现的战略分析框架。你可以在考前使用它来快速回顾计算方法和加深概念理解。
1. Revenue, Costs and Profit | 收入、成本与利润
Revenue is the total income generated from selling goods or services. It is calculated as selling price per unit multiplied by the quantity sold.
收入是指销售商品或服务产生的总收入，计算公式为销售单价乘以销售数量。
Revenue = Price × Quantity
Total costs are divided into fixed costs, which do not change with output (e.g. rent), and variable costs, which vary directly with output (e.g. raw materials). Total cost is the sum of both.
总成本分为固定成本（不随产量变化，如租金）和变动成本（随产量直接变化，如原材料）。总成本是两者之和。
Total Costs (TC) = Fixed Costs (FC) + Variable Costs (VC)
Profit is the surplus remaining after all costs have been deducted from revenue. It is a fundamental measure of business success and can be expressed as total profit or profit per unit.
利润是收入扣除所有成本后的结余，是衡量商业成功的基本指标，可用总利润或单位利润表示。
Profit = Revenue − Total Costs
Managers often calculate average cost (unit cost) to set prices or control expenses. It is obtained by dividing total cost by the number of units produced.
管理者常计算平均成本（单位成本）以制定价格或控制支出，方法是用总成本除以产量。
Average Cost (AC) = Total Cost ÷ Quantity
Contribution is the amount each unit sale contributes towards covering fixed costs and then generating profit. It is central to decision-making, especially when scarce resources must be allocated.
贡献是指每单位销售收入在弥补固定成本后对利润的贡献，是决策的核心，尤其在资源稀缺时。
Contribution per unit = Selling Price − Variable Cost per unit
2. Break-even Analysis and Margin of Safety | 盈亏平衡分析与安全边际
The break-even point (BEP) is the level of output where total revenue equals total costs, so the business makes neither profit nor loss. It can be expressed in units or in sales value.
盈亏平衡点是指总收入等于总成本的产量水平，此时企业不盈不亏，可用销售量或销售额表示。
Break-even Point (units) = Fixed Costs ÷ Contribution per unit
Break-even Point (value) = Break-even units × Selling Price
Margin of safety indicates how much sales can fall before the business starts making a loss. A higher margin of safety represents lower risk.
安全边际表明销售额可下降多少企业才会开始亏损，较高的安全边际代表较低的风险。
Margin of Safety (units) = Actual Sales (units) − Break-even Sales (units)
Margin of Safety (%) = (Margin of Safety ÷ Actual Sales) × 100
Target profit output can be determined by adding the desired profit to fixed costs and dividing by contribution per unit. This helps set production targets.
目标利润产量可通过将目标利润与固定成本相加后除以单位贡献来计算，有助于设定生产目标。
Output for Target Profit = (Fixed Costs + Target Profit) ÷ Contribution per unit
Break-even charts visually present the relationships between costs, revenue, and output. The point where the total revenue line crosses the total cost line is the break-even point.
盈亏平衡图直观地展示成本、收入和产量之间的关系，总收入线与总成本线的交点即为盈亏平衡点。
3. Budgeting and Variance Analysis | 预算与差异分析
A budget is a financial plan for a future period. Variance analysis compares actual results with budgeted figures to identify areas where performance differed from expectations.
预算是针对未来期间的财务计划。差异分析将实际结果与预算数据进行比较，找出表现与预期不符之处。
Variance = Actual Figure − Budgeted Figure
A favourable variance occurs when actual revenue is higher than budgeted, or actual costs are lower than budgeted. Adverse variance means the opposite, potentially signalling a need for corrective action.
有利差异指实际收入高于预算或实际成本低于预算；不利差异则相反，可能意味着需要采取纠正措施。
A sales revenue variance can be broken down into price variance and volume variance to understand whether the difference came from charging different prices or selling more/less units.
销售收入差异可拆分为价格差异和销量差异，以判断差异是来自价格变化还是销量变化。
Variance analysis is not just about numbers; it prompts investigation into causes, such as market shifts or internal inefficiencies, and helps managers take informed decisions.
差异分析并非仅看数字，它还促使对原因进行调查，如市场变化或内部低效，并帮助管理者做出明智决策。
4. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm’s ability to generate earnings relative to sales, assets, or equity. They are vital for comparing performance over time or against competitors.
盈利能力比率衡量企业相对于销售额、资产或权益创造利润的能力，对于纵向比较或与竞争对手比较至关重要。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
This ratio shows the percentage of revenue left after covering direct costs (cost of sales). A high gross margin indicates effective control over production or purchasing costs.
该比率显示扣除直接成本（销售成本）后剩余收入的百分比，高毛利率表明对生产或采购成本的有效控制。
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100
Operating profit margin reveals how much profit a company makes on each dollar of sales after paying for variable and fixed operating expenses, but before interest and tax.
营业利润率揭示扣除变动和固定营业费用后每元销售额带来的利润，尚未扣除利息和税费。
Net Profit Margin = (Net Profit ÷ Revenue) × 100
Net margin represents the ultimate profitability after all expenses, including interest and tax. It is the bottom-line measure for shareholders.
净利润率表示扣除所有费用（包括利息和税费）后的最终盈利能力，是股东的底线指标。
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100
ROCE is a key efficiency indicator showing how well the business uses its long-term funds. Investors often compare ROCE with the cost of borrowing to assess viability.
资本回报率是关键效率指标，显示企业利用长期资金的效果。投资者常将 ROCE 与借贷成本比较以评估可行性。
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess a business’s ability to meet its short-term obligations as they fall due. Insufficient liquidity can lead to insolvency even if the firm is profitable.
流动性比率评估企业偿还到期短期债务的能力。流动性不足可致破产，即使企业盈利。
Current Ratio = Current Assets ÷ Current Liabilities
A ratio between 1.5 and 2 is often considered safe, but the ideal level depends on the industry. Too high a ratio may indicate poor asset utilization.
通常 1.5 至 2 倍的比率被视为安全，但理想水平因行业而异，过高的比率可能表明资产利用不佳。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
Also known as the quick ratio, this strips out inventories because they may not be quickly convertible to cash. A ratio of 1:1 is generally regarded as adequate.
又称速动比率，它剔除存货，因为存货未必能快速变现。一般认为 1:1 的比率较为充足。
When interpreting these ratios, it is important to consider the type of business, seasonal factors, and the composition of current assets and liabilities. A supermarket might have a low acid test ratio yet remain healthy due to fast inventory turnover.
解释这些比率时，须考虑业务类型、季节性因素以及流动资产和负债的构成。一家超市可能速动比率较低，但由于存货周转快仍保持健康。
6. Efficiency and Gearing Ratios | 效率与杠杆比率
Efficiency ratios measure how effectively a business uses its resources, while gearing ratios examine the financial structure, particularly the proportion of borrowed funds.
效率比率衡量企业利用资源的效能，而杠杆比率审视财务结构，尤其是借入资金的比例。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
High inventory turnover suggests strong sales or effective inventory management, although too high a turnover might indicate stock shortages.
存货周转率高表明销售强劲或存货管理有效，但过高可能意味着缺货。
Trade Receivable Days = (Trade Receivables ÷ Revenue) × 365
This shows the average number of days it takes to collect money from credit customers. A shorter period improves cash flow.
它显示从赊销客户收款的平均天数。天数越短，现金流越佳。
Trade Payable Days = (Trade Payables ÷ Cost of Sales) × 365
This indicates how long a business takes to pay its suppliers. Extending payment days conserves cash but may strain supplier relationships.
这表明企业向供应商付款的时长。延长付款天数可保留现金，但可能损害供应商关系。
Gearing Ratio = (Long-term Liabilities ÷ Capital Employed) × 100
A highly geared firm relies more on debt, which magnifies risk but can also boost returns to shareholders when profits are high. A ratio over 50% is often viewed as high gearing.
高杠杆企业更依赖债务，放大了风险，但在利润高时也能提高股东回报。超过 50% 常被视为高杠杆。
7. Investment Appraisal Methods | 投资评估方法
Investment appraisal helps businesses evaluate the desirability and financial return of large projects. Three core methods are payback period, average rate of return (ARR), and net present value (NPV).
投资评估帮助企业评价大型项目的可取性和财务回报，三种核心方法是回收期、平均回报率 (ARR) 和净现值 (NPV)。
Payback Period = Number of years to recover initial investment
Payback period is the simplest method, focusing on how quickly the initial outlay is recovered from net cash flows. Managers often set a maximum acceptable payback.
回收期是最简单的方法，关注从净现金流收回初始投资的速度。管理者常设定最高可接受的回收期限。
Average Rate of Return (ARR) = (Average Annual Profit ÷ Initial Investment) × 100
ARR expresses the average yearly profit as a percentage of the amount invested. It allows easy comparison with bank interest rates or other projects.
ARR 将平均年度利润表示为投资额的百分比，便于与银行利率或其他项目比较。
Net Present Value (NPV) = Σ [Net Cash Flow in year t ÷ (1 + r)t] − Initial Investment
NPV accounts for the time value of money by discounting future cash flows at a chosen discount rate (r). A positive NPV suggests the project is financially acceptable.
NPV 通过按选定折现率 (r) 贴现未来现金流来考虑货币时间价值。正的 NPV 表明项目在财务上可接受。
Each method has strengths and limitations; for instance, payback ignores cash flows after the payback point, while NPV requires an estimate of the cost of capital. Therefore, using multiple methods is recommended.
每种方法都有优缺点：例如，回收期忽略回收点之后的现金流，而 NPV 需估计资本成本。因此建议多种方法结合使用。
8. Human Resource Metrics | 人力资源指标
Quantitative HR measures help a business monitor workforce effectiveness and identify issues such as high staff turnover or declining productivity.
量化的人力指标有助于企业监控员工效率，发现人员流失率过高或生产率下降等问题。
Labour Productivity = Total Output in Period ÷ Number of Employees
Productivity can also be measured in value terms: Labour Productivity = Total Revenue ÷ Number of Employees. Growth in productivity often reflects better training or technology.
生产率也可用价值衡量：劳动生产率 = 总收入 / 员工人数。生产率增长通常反映培训改善或技术投入。
Absenteeism Rate = (Number of Staff Days Missed ÷ Total Possible Staff Days) × 100
High absenteeism may indicate low morale, poor working conditions, or health issues. Benchmarking against industry averages helps identify problems.
缺勤率高可能反映士气低落、工作环境差或健康问题。与行业均值比较有助于发现隐患。
Labour Turnover = (Number of Staff Leaving in Period ÷ Average Number of Staff) × 100
Moderate turnover can refresh skills, but excessive turnover raises recruitment and training costs and damages organisational culture.
适度的人员流动能更新技能，但过高的流失率会增加招聘和培训成本，损害组织文化。
These metrics are not just numbers; they should trigger investigation and action, such as improving leadership or offering flexible work arrangements.
这些指标不仅是数字，更应触发调查与行动，如改进领导力或提供弹性工作安排。
9. Demand, Supply and Elasticity | 需求、供给与弹性
The law of demand states that, ceteris paribus, as the price of a good increases, the quantity demanded decreases. The law of supply says that higher prices encourage producers to supply more.
需求定律指出，在其他条件不变时，商品价格上升则需求量下降。供给定律表明，价格上升激励生产者增加供给。
Elasticity measures the responsiveness of one variable to a change in another. Price elasticity of demand (PED) is central to pricing decisions.
弹性衡量一个变量对另一个变量变化的反应程度。需求的价格弹性 (PED) 对定价决策至关重要。
PED = % Change in Quantity Demanded ÷ % Change in Price
If PED > 1, demand is elastic and a price cut can raise total revenue. If PED < 1, demand is inelastic and a price rise may increase total revenue. Unitary elasticity (PED = 1) keeps revenue unchanged.
若 PED 大于 1，需求富有弹性，降价可增加总收入。若 PED 小于 1，需求缺乏弹性，涨价或可增收。单位弹性 (PED = 1) 则收入不变。
Income Elasticity of Demand (YED) = % Change in Demand ÷ % Change in Income
Normal goods have positive YED; luxury goods have YED > 1. Inferior goods have negative YED. This helps firms plan for economic cycles.
正常品 YED 为正，奢侈品的 YED 大于 1。低档品 YED 为负。这有助于企业根据经济周期进行规划。
10. Strategic Analysis Models | 战略分析模型
Businesses use conceptual frameworks to analyse their position and make strategic choices. These models are not mathematical formulas but provide structured thinking.
企业使用概念框架分析自身定位并做出战略选择。这些模型虽非数学公式，但提供结构化思维。
Product Life Cycle: Products pass through introduction, growth, maturity, and decline. Each stage requires different marketing and financial strategies. Sales and profit curves guide investment decisions.
产品生命周期：产品经历导入、成长、成熟和衰退期。各阶段需不同的营销和财务策略，销售额与利润曲线指导投资决策。
Boston Matrix: A portfolio analysis tool that classifies products into Stars (high growth, high market share), Cash Cows (low growth, high share), Question Marks (high growth, low share), and Dogs (low growth, low share). It helps allocate resources.
波士顿矩阵：一种产品组合分析工具，将产品分为明星（高增长、高份额）、金牛（低增长、高份额）、问号（高增长、低份额）和瘦狗（低增长、低份额），有助于资源配置。
Ansoff Matrix: Presents four growth strategies based on markets and products: market penetration, market development, product development, and diversification. Diversification carries the highest risk.
安索夫矩阵：提出基于市场和产品的四种增长战略：市场渗透、市场开发、产品开发和多元化。多元化风险最高。
SWOT Analysis: Summarises internal Strengths and Weaknesses and external Opportunities and Threats. It is a simple but widely used tool for strategic audit.
SWOT 分析：汇总内部优势与劣势、外部机会与威胁，是一种简单而广泛使用的战略审计工具。
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