📚 Year 11 Cambridge Business: Formula & Theorem Quick Revision Guide | 剑桥11年级商科公式定理速查手册
Welcome to your ultimate quick-reference guide for Cambridge IGCSE / O Level Business Studies. This handbook brings together all the essential formulas, ratios and key theorems you need to master financial analysis, break-even planning, market measurement and performance evaluation. Keep it handy for revision, homework and final exam preparation.
欢迎使用剑桥 IGCSE / O Level 商务学终极速查手册。本手册汇集了所有必备的公式、比率和关键定理，助你掌握财务分析、盈亏平衡规划、市场测量以及绩效评估。请随时在复习、课后作业和备考中使用。
1. Break-Even Analysis | 盈亏平衡分析
Break-even point (units) = Fixed Costs ÷ (Selling Price per Unit – Variable Cost per Unit)
The break-even point in units shows exactly how many products a business must sell to cover all of its fixed and variable costs, after which it starts making a profit. Below this volume, the business operates at a loss.
盈亏平衡点（单位）表示企业必须销售的产品数量，以刚好覆盖全部固定成本和可变成本，超过该数量才能获利。低于该数量，企业则面临亏损。
Break-even revenue = Break-even point (units) × Selling Price per Unit
This converts the unit figure into the total sales revenue needed to reach break-even. It is particularly useful when presenting data in value terms rather than in physical quantities.
此公式将单位盈亏平衡量转换为所需的销售总收入，尤其适合以金额而非实物量呈现数据时使用。
2. Contribution and Target Profit | 贡献毛利与目标利润
Contribution per unit = Selling Price per Unit – Variable Cost per Unit
Contribution measures how much each unit sold contributes towards paying off fixed costs and, once those are covered, to profit. It is a cornerstone of cost-volume-profit analysis.
单位贡献毛利衡量每售出一件产品能为支付固定成本贡献多少；覆盖固定成本后，剩余部分即为利润。这是本-量-利分析的基石。
Total contribution = Contribution per unit × Quantity sold
Total contribution is used to calculate overall profitability before deducting fixed costs. A positive total contribution above fixed costs yields a net profit.
总贡献毛利是指扣除固定成本前的整体盈利贡献。若总贡献超过固定成本，企业便实现净利润。
Units for target profit = (Fixed Costs + Target Profit) ÷ Contribution per unit
Managers use this formula to set sales targets. It answers the question: 'How many units must we sell to achieve a specific profit goal?'.
管理者用此公式设定销售目标，回答“必须销售多少件产品才能实现特定利润目标”的问题。
Margin of safety = Actual output – Break-even output
Margin of safety indicates how far sales can fall before the business reaches its break-even point. The higher the margin, the lower the risk of making a loss.
安全边际表示销售额下降多少后企业会达到盈亏平衡点。安全边际越高，亏损风险越低。
3. Profitability Ratios | 盈利能力比率
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
This ratio reveals the percentage of revenue that remains after subtracting the cost of goods sold. It reflects how efficiently a business manages its direct costs and pricing.
该比率显示扣除销售成本后收入剩余的百分比，反映企业管理直接成本和定价的效率。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
Net profit margin indicates what proportion of revenue turns into actual profit after all expenses, including overheads, interest and taxes, are paid. It is a key measure of overall profitability.
净利润率指在扣除所有费用（包括间接费用、利息和税）后，收入转化为实际利润的比例，是衡量整体盈利能力的关键指标。
Return on Capital Employed (ROCE) = (Net Profit ÷ Capital Employed) × 100%
ROCE evaluates how effectively a business uses its long-term capital to generate profit. Capital employed is often calculated as total assets minus current liabilities, or as shareholders' equity plus long-term liabilities.
资本回报率（ROCE）评估企业利用长期资本盈利的效率。所用资本通常按总资产减去流动负债，或按股东权益加长期负债计算。
4. Liquidity Ratios | 流动性比率
Current Ratio = Current Assets ÷ Current Liabilities
The current ratio measures a firm's ability to pay off its short-term debts with its short-term assets. A ratio of 1.5:1 to 2:1 is often regarded as healthy, though this varies by industry.
流动比率衡量企业用短期资产偿还短期债务的能力。一般认为 1.5:1 至 2:1 的比率为健康水平，但会因行业而异。
Acid Test Ratio (Quick Ratio) = (Current Assets – Inventory) ÷ Current Liabilities
The acid test ratio gives a stricter view of liquidity by excluding inventory, which is harder to convert quickly into cash. A result of 1:1 or higher is usually considered safe.
酸性测试比率（速动比率）通过排除不易快速变现的存货，更严格地衡量流动性。通常 1:1 或更高被视为安全。
5. Efficiency Ratios | 效率比率
Inventory Turnover (days) = (Average Inventory ÷ Cost of Sales) × 365
This ratio shows the average number of days a business holds inventory before selling it. A lower figure often indicates efficient stock management, though too low a figure may risk stock-outs.
该比率显示企业持有存货的平均天数。数值较低通常意味着库存管理高效，然而过低也可能导致缺货风险。
Trade Receivables Turnover (days) = (Trade Receivables ÷ Credit Sales) × 365
This measures the average time it takes a business to collect money from credit customers. Shorter collection periods improve cash flow.
此指标衡量企业从赊销客户收回款项的平均天数。回款期越短，现金流状况越好。
Trade Payables Turnover (days) = (Trade Payables ÷ Credit Purchases) × 365
It indicates how long, on average, a business takes to pay its suppliers. A longer period can help conserve cash, but may harm supplier relationships.
它反映企业平均耗时多久向供应商付款。期限较长有利于保存现金，但可能损害与供应商的关系。
6. Cash Flow and Budgeting | 现金流与预算
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
Net cash flow is the difference between all cash received and all cash paid out during a given period. It is critical for ensuring the business does not run out of cash.
净现金流指某一期间内所有现金收入与所有现金支出的差额，对于确保企业资金不断裂至关重要。
Closing Balance = Opening Balance + Net Cash Flow
The closing balance shows the cash available at the end of the period. It becomes the opening balance for the next period. A negative closing balance signals a cash crisis.
期末余额表示期末时可动用的现金，将作为下一期的期初余额。负的期末余额预示现金危机。
Variance = Budgeted Figure – Actual Figure
Variance analysis compares planned budgets with actual outcomes. A favourable variance occurs when actual profit is higher or costs lower than budgeted; an adverse variance signals the opposite.
差异分析将预算与实际结果进行比较。当实际利润高于预算或实际成本低于预算时，产生有利差异；反之则为不利差异。
7. Price Elasticity of Demand | 需求价格弹性
PED = % Change in Quantity Demanded ÷ % Change in Price
Price elasticity of demand measures how responsive the quantity demanded of a product is to a change in its price. The percentage changes are calculated using the midpoint or initial value method as instructed by your syllabus.
需求价格弹性衡量产品需求量对价格变动的敏感程度。百分比变动可根据大纲指示采用中点法或初始值法计算。
When PED is greater than 1, demand is price elastic – nelastic and a price rise increases total revenue. Unitary elasticity exists when PED = 1.
若 PED > 1，需求具有价格弹性，价格上升导致需求量以更大比例下降，总收益减少。若 PED < 1，需求缺乏弹性，价格上升可增加总收益。当 PED = 1 时，需求具有单位弹性。
8. Market and Sales Metrics | 市场与销售指标
Market Share = (Firm's Sales ÷ Total Market Sales) × 100%
Market share indicates a business's relative position within the industry. A growing market share often signals a competitive advantage.
市场份额体现企业在行业中的相对地位。市场份额增长通常意味着竞争优势。
Market Growth = (Change in Market Size ÷ Original Market Size) × 100%
Market growth measures how fast the overall market is expanding or shrinking. It is essential for planning marketing strategies and anticipating future demand.
市场增长率衡量整个市场扩张或萎缩的速度，是制定营销策略和预测未来需求的重要依据。
Sales Growth = (Current Sales – Previous Sales) ÷ Previous Sales × 100%
Calculating a company's own sales growth helps assess whether it is outperforming or lagging behind the market.
计算企业自身的销售增长率有助于判断其表现是优于还是落后于市场。
9. Cost, Revenue and Profit Fundamentals | 成本、收入与利润基础
Total Revenue = Selling Price × Quantity Sold
Revenue is the income generated from selling goods or services. It is the starting point for measuring a firm’s financial performance.
收入是通过销售商品或服务而产生的所得，是衡量企业财务表现的起点。
Total Costs = Fixed Costs + Variable Costs
Fixed costs (e.g. rent, salaries) remain unchanged in the short run regardless of output. Variable costs (e.g. raw materials) change directly with production volume.
固定成本（如租金、薪金）在短期内不随产量变化；可变成本（如原材料）直接随产量变动。
Average Cost (Unit Cost) = Total Costs ÷ Output
Average cost tells a business how much it costs to produce one unit on average. As output rises, average costs may fall due to economies of scale.
平均成本表明平均生产一单位产品所需的成本。随着产量增加，平均成本可能因规模经济而下降。
Profit = Total Revenue – Total Costs
Profit is the ultimate measure of business success. Without sustainable profit, a business cannot survive in the long run.
利润是衡量经营成功的终极指标。没有可持续的利润，企业将无法长期生存。
10. Productivity and Capacity Utilisation | 生产率与产能利用率
Labour Productivity = Output per Period ÷ Number of Employees
Labour productivity measures output per worker. Higher productivity lowers unit labour costs and can boost competitiveness, provided quality is maintained.
劳动生产率衡量每位员工的产出量。较高的生产率能降低单位人工成本，并在质量不变的前提下增强竞争力。
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100%
This ratio shows how much of a firm's production capacity is being used. Operating well below maximum capacity increases unit fixed costs and reduces profitability.
该比率显示企业产能的使用程度。远低于最大产能运营会提高单位固定成本，降低盈利能力。
Unit Cost Improvement = (Actual Output – Break-even Output) ÷ Actual Output × 100%
While not a standalone ratio in every syllabus, analysing how unit costs decline as capacity utilisation rises is a key application of break-even and productivity concepts. Higher utilisation spreads fixed costs over more units.
尽管并非所有大纲都将其作为独立比率，但分析单位成本如何随产能利用率上升而下降，是盈亏平衡和生产率概念的关键应用。更高的利用率将固定成本分摊到更多单位中。
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