📚 Year 10 CIE Business: Formula & Theorem Quick Reference Handbook | Year 10 CIE 商务：公式定理速查手册
This handbook compiles essential formulas and theorems required for the Year 10 CIE Business syllabus. Mastering these quantitative tools is crucial for analysing business performance, making decisions, and excelling in exams. Keep this guide handy for quick revision.
本手册汇编了 Year 10 CIE 商务课程所必需的核心公式与定理。掌握这些量化工具对于分析企业绩效、做出决策以及在考试中取得优异成绩至关重要。请随身携带本指南以便快速复习。
1. Revenue, Costs, and Profit | 收入、成本与利润
Understanding how revenue, costs, and profit are calculated forms the foundation of business finance. These basic equations are used to construct profit and loss statements and to evaluate a firm's financial health.
理解收入、成本和利润的计算方式构成了企业财务的基础。这些基本方程式用于编制损益表及评估企业的财务状况。
Total Revenue = Selling Price per Unit × Quantity Sold
Total Revenue (TR) represents the income generated from sales before any costs are deducted.
总收入 (TR) 代表扣除任何成本之前从销售中产生的收入。
Total Variable Costs = Variable Cost per Unit × Quantity
Variable costs change in direct proportion to the level of output or sales.
变动成本与产出或销售水平成正比变化。
Total Costs = Fixed Costs + Total Variable Costs
Fixed costs remain constant regardless of output, such as rent and salaries.
固定成本如租金和薪水，无论产出多少都保持不变。
Profit = Total Revenue − Total Costs
Profit is the surplus after all costs have been subtracted from revenue. A positive profit indicates the business is generating more income than it spends.
利润是收入减去所有成本后的盈余。正利润表明企业产生的收入大于支出。
2. Break-even Analysis | 盈亏平衡分析
Break-even analysis identifies the level of sales at which total revenue equals total costs, resulting in zero profit or loss. It helps businesses plan production and set sales targets.
盈亏平衡分析确定了总收入等于总成本、利润或亏损为零的销售水平。它帮助企业规划生产并设定销售目标。
Break-even Point (units) = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
The denominator (Selling Price per Unit − Variable Cost per Unit) is the contribution per unit.
分母（单位售价 − 单位变动成本）是单位贡献毛利。
Break-even Point (in revenue) = Break-even Units × Selling Price per Unit
Alternatively, break-even revenue can be found using the contribution margin ratio.
或者，盈亏平衡收入也可以使用贡献毛利率来计算。
Margin Ratio = (Selling Price per Unit − Variable Cost per Unit) ÷ Selling Price per Unit
Then Break-even Revenue = Fixed Costs ÷ Contribution Margin Ratio.
那么盈亏平衡收入 = 固定成本 ÷ 贡献毛利率。
3. Contribution and Margin of Safety | 贡献毛利与安全边际
Contribution is a vital concept for covering fixed costs and generating profit. Margin of safety shows how far sales can fall before the business reaches break-even.
贡献毛利是弥补固定成本并产生利润的重要概念。安全边际表明在达到盈亏平衡点之前，销售可以下降多少。
Contribution per Unit = Selling Price per Unit − Variable Cost per Unit
n = Contribution per Unit × Number of Units Sold, or Total Revenue − Total Variable Costs.
总贡献 = 单位贡献 × 销售数量，或总收入 − 总变动成本。
Profit = Total Contribution − Fixed Costs
This formula highlights why increasing contribution improves profitability.
该公式突显了为什么提高贡献毛利能提升盈利能力。
Margin of Safety (units) = Actual or Budgeted Sales Units − Break-even Units
of Margin of Safety can also be expressed as a percentage: (Margin of Safety ÷ Actual Sales) × 100.
安全边际也可以用百分比表示：（安全边际 ÷ 实际销售）× 100。
4. Profitability Ratios | 盈利能力比率
Profitability ratios measure a company's ability to generate earnings relative to sales, assets, and equity. These are crucial for assessing business success.
盈利能力比率衡量公司相对于销售额、资产和权益创造盈利的能力。这些对于评估企业成功至关重要。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100%
Gross Profit = Sales Revenue − Cost of Goods Sold.
毛利 = 销售收入 − 销售成本。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100%
Net Profit = Gross Profit − Expenses (overheads).
净利润 = 毛利 − 费用（间接费用）。
Return on Capital Employed (ROCE) = (Net Profit ÷ Capital Employed) × 100%
Capital Employed is often calculated as total assets − current liabilities, or equity + non-current liabilities. ROCE indicates how efficiently a firm uses its long-term capital.
资本运用通常计算为总资产 − 流动负债，或权益 + 非流动负债。ROCE 表明企业使用其长期资本的效率。
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet short-term obligations. They are essential for creditors and managers to monitor cash solvency.
流动性比率评估企业履行短期债务的能力。它们对于债权人和管理者监控现金偿付能力至关重要。
Current Ratio = Current Assets ÷ Current Liabilities
A ratio above 1 indicates the company can cover its short-term debts. A typical safe ratio is between 1.5 and 2.
比率大于 1 表示公司能够偿还短期债务。通常安全比率在 1.5 到 2 之间。
Acid Test Ratio (Quick Ratio) = (Current Assets − Inventory) ÷ Current Liabilities
This stricter test excludes inventory, which may not be easily converted to cash. A ratio of 1:1 is often considered ideal.
这个更严格的测试剔除了存货，因为存货可能不易变现。1:1 的比率通常被认为是理想的。
6. Efficiency Ratios | 效率比率
Efficiency ratios show how well a business uses its assets and manages its liabilities. They reflect operational performance.
效率比率显示企业利用资产和管理负债的程度。它们反映了运营绩效。
Inventory Turnover (times) = Cost of Goods Sold ÷ Average Inventory
Inventory + Closing Inventory) ÷ 2. A higher turnover suggests efficient stock management.
平均存货 = （期初存货 + 期末存货）÷ 2。较高的周转率表明库存管理高效。
Inventory Turnover (days) = (Average Inventory ÷ Cost of Goods Sold) × 365
This expresses how many days it takes to sell the inventory.
这表示销售存货所需的天数。
Trade Receivable Days = (Trade Receivables ÷ Credit Sales) × 365
This measures how quickly customers pay their debts. A lower number is better for cash flow.
这衡量客户还款的速度。数字越低对现金流越有利。
Trade Payable Days = (Trade Payables ÷ Credit Purchases) × 365
This shows how long the business takes to pay its suppliers. Long payable days can preserve cash but may harm relationships.
这表明企业需要多长时间向供应商付款。较长的付款天数可以保留现金，但可能损害关系。
7. Cash Flow Management | 现金流管理
Cash flow is the lifeblood of a business. Managing inflows and outflows ensures the company can pay its bills on time and avoid insolvency.
现金流是企业的生命线。管理流入和流出确保公司能够按时支付账单并避免资不抵债。
Net Cash Flow = Cash Inflows − Cash Outflows
Cash inflows include sales revenue, loans, and asset sales; outflows include purchases, wages, and rent.
现金流入包括销售收入、贷款和资产出售；流出包括采购、工资和租金。
Closing Balance = Opening Balance + Net Cash Flow
This determines the cash position at the end of a period, used in cash flow forecasts.
这决定了期末的现金头寸，用于现金流量预测。
8. Other Key Formulas: Productivity, Capacity & Unit Cost | 其他关键公式：生产率、产能与单位成本
These operational metrics help businesses improve efficiency and control costs.
这些运营指标帮助企业提高效率并控制成本。
Labour Productivity = Total Output (units) ÷ Number of Employees
Higher labour productivity reduces unit costs and can increase wages.
较高的劳动生产率可以降低单位成本，并可能增加工资。
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100%
This shows the percentage of total capacity being used. Low utilisation means under-used resources.
这显示了已使用总产能的百分比。利用率低意味着资源未充分利用。
Unit Cost (Average Cost) = Total Costs ÷ Total Output
Economies of scale reduce unit cost as output rises.
规模经济随着产量上升而降低单位成本。
9. Key Business Theorems & Laws | 关键商务定理与定律
Several economic theorems underpin business decision-making. These principles help explain market behaviour and resource allocation.
一些经济定理支撑着企业决策。这些原理有助于解释市场行为和资源配置。
Law of Demand: As price increases, quantity demanded decreases, ceteris paribus.
Demand slopes downward; businesses use this to set pricing strategies.
需求曲线向下倾斜；企业利用它来制定定价策略。
Law of Supply: As price increases, quantity supplied increases.
Producers are willing to supply more at higher prices, affecting market equilibrium.
生产者愿意在较高价格下供应更多，影响市场均衡。
Law of Diminishing Marginal Returns: Adding one more unit of a variable factor (e.g., labour) to fixed factors will eventually yield lower additional output.
This concept is important for production decisions and cost analysis.
该概念对生产决策和成本分析很重要。
Economies of Scale Theorem: As a business increases its scale of output, average costs fall due to factors such as bulk buying, technical efficiencies, and specialization.
Diseconomies of scale may occur if the firm grows too large, raising average costs.
如果企业规模过大，可能会出现规模不经济，提高平均成本。
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