📚 Year 10 Cambridge IGCSE Business: Formula & Theorem Quick Reference Handbook | 剑桥IGCSE商务公式定理速查手册
This quick reference handbook pulls together the essential formulas, ratios and decision rules you will meet in Year 10 Cambridge IGCSE Business Studies. Mastering these relationships not only helps you solve numerical problems but also gives you the language to analyse financial performance, assess risk and justify business decisions. Use it as a memory aid and a checklist when working through past paper questions.
本速查手册汇集了Year 10剑桥IGCSE商务课程中的核心公式、比率与决策定理。掌握这些数量关系不仅能帮你解答计算题，还能让你用专业语言分析财务表现、评估风险并论证商业决策。请将它作为记忆工具和答题清单，配合真题练习使用。
1. Revenue, Cost and Profit | 收入、成本与利润
Revenue is the total income a business receives from selling its products. It is calculated by multiplying the selling price per unit by the quantity sold. If a firm sells multiple products, total revenue is the sum of revenue from each product line.
收入是企业销售产品获得的总收入。它等于单位售价乘以销售数量。如果企业销售多种产品，总收入是各产品收入之和。
Revenue (TR) = Selling Price per unit × Quantity sold
Total costs are split into fixed costs, which do not change with the level of output (e.g. rent, salaries), and variable costs, which vary directly with production (e.g. raw materials, packaging). Total cost is the sum of the two.
总成本分为固定成本和可变成本。固定成本不随产量变化（如租金、管理人员工资）；可变成本随产量成比例变动（如原材料、包装）。总成本是两者之和。
Total Costs (TC) = Fixed Costs (FC) + Variable Costs (VC)
costs. A negative profit is a loss. Profit can be expressed as a total amount or on a per‑unit basis (profit per unit = selling price − average total cost).
利润是企业承担风险的回报，等于总收入减去总成本。利润为负即为亏损。利润可以表示为总额，也可以按单位计算（单位利润 = 售价 − 平均总成本）。
Profit = TR − TC
A fundamental theorem is that profit is maximised at the output level where the gap between total revenue and total cost is greatest. In simple terms, a business should aim to produce and sell where additional revenue from one more unit equals the additional cost.
一条基本定理是，利润最大化发生在总收入与总成本之差最大的产量水平上。简单地说，企业应追求在额外一单位带来的收入等于额外成本的产量上进行生产和销售。
2. Break‑even Point | 盈亏平衡点
The break‑even point is the level of output at which total revenue exactly equals total costs, so the business makes neither a profit nor a loss. It is a critical planning tool for new ventures and for launching new products.
盈亏平衡点是总收入恰好等于总成本时的产出水平，此时企业既不盈利也不亏损。它是新创企业和推出新产品时的重要规划工具。
Break‑even output (units) = Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)
The denominator (selling price − variable cost per unit) is known as contribution per unit. Contribution is the amount each unit sold contributes towards covering fixed costs and then generating profit.
分母（售价 − 单位可变成本）称为单位贡献。贡献是指每销售一单位产品可用于补偿固定成本并产生利润的金额。
Contribution per unit = Selling Price − Variable Cost per unit
Break‑even revenue can be found by multiplying break‑even units by the selling price, or by using the formula: Break‑even revenue = (Fixed Costs ÷ Contribution per unit) × Selling Price.
盈亏平衡收入可以通过盈亏平衡单位数乘以售价得到，或使用公式：盈亏平衡收入 = (固定成本 ÷ 单位贡献) × 售价。
A key theorem: at break‑even, total contribution exactly equals fixed costs. Understanding this relationship allows managers to assess the impact of changes in costs or price on the minimum sales needed.
关键定理：在盈亏平衡点，总贡献恰好等于固定成本。理解这一关系有助于管理者评估成本或价格变动对最低销售量的影响。
3. Margin of Safety and Target Profit | 安全边际与目标利润
Margin of safety is the difference between actual (or budgeted) sales and break‑even sales. It shows how far output or revenue can fall before the business makes a loss. A larger margin of safety means lower risk.
安全边际是实际（或预算）销售额与盈亏平衡销售额之间的差额。它表明在出现亏损之前，产量或收入可以下降多少。安全边际越大，风险越低。
Margin of Safety = Actual Sales (units) − Break‑even Sales (units)
s) × 100. This percentage helps compare risk levels between different periods or products.
安全边际常用百分比表示：(安全边际 ÷ 实际销售量) × 100。利用该百分比可以比较不同时期或不同产品的风险水平。
Businesses often set a target profit figure. To find the output required to hit that target, simply add the target profit to fixed costs in the break‑even formula.
企业常设定目标利润。计算实现该目标所需的产量，只需在盈亏平衡公式的分子中加入目标利润即可。
Required units = (Fixed Costs + Target Profit) ÷ Contribution per unit
The theorem embedded here is that every unit sold beyond break‑even generates profit equal to its contribution. This simple linear relationship is the backbone of many short‑term decisions.
此处的定理是，超过盈亏平衡点后，每多销售一单位产品所产生的利润等于该单位的贡献。这一简单线性关系是许多短期决策的基础。
4. Gross and Net Profit Margins | 毛利率与净利率
Profitability ratios measure a firm’s ability to generate earnings compared with its revenue. The gross profit margin focuses on the direct relationship between sales and the cost of making those sales.
盈利能力比率衡量企业相对于其收入创造利润的能力。毛利率关注销售收入与生产成本之间的直接关系。
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
. A high gross margin suggests the business adds significant value through its production process, while a falling margin may signal rising material costs or heavy discounting.
毛利润 = 收入 − 销售成本。高毛利率表明企业通过生产过程创造了较高的附加价值，而毛利率下降可能预示材料成本上升或大规模打折。
The net profit margin takes all expenses into account, including operating expenses, interest and tax. It indicates overall profitability after all costs.
净利率则考虑了所有费用，包括运营费用、利息和税收，反映扣除全部成本后的综合盈利能力。
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
As a decision theorem, a business should compare its margins with those of competitors and with its own historical trend. Improvements in margins often result from cost control and adding value, not merely from raising prices.
作为决策定理，企业应将自身利润率与竞争对手及历史趋势进行比较。利润率的改善通常源于成本控制和附加价值的提升，而非单纯提价。
5. Current and Acid Test Ratios | 流动比率与速动比率
Liquidity ratios assess whether a business has enough short‑term assets to meet its short‑term liabilities. The current ratio uses all current assets.
流动性比率评估企业是否有足够的短期资产来偿还短期负债。流动比率使用全部流动资产。
Current Ratio = Current Assets ÷ Current Liabilities
An often‑cited benchmark is 2:1, meaning for every $1 of current liabilities the business should hold $2 of current assets. However, the ideal ratio varies by industry.
常见的参考基准是2:1，即每1美元的流动负债应有2美元的流动资产作为保障，但理想比率因行业而异。
The acid test (quick) ratio removes inventories, which are the least liquid current asset. It gives a stricter test of immediate liquidity.
速动比率（酸性测试比率）剔除了流动性最差的流动资产——存货，能更严格地衡量即时偿债能力。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
An acid test ratio around 1:1 is generally considered safe. If the ratio falls significantly below 1, the business might struggle to pay debts as they fall due. A ratio that is too high, however, may indicate idle resources that could be invested more productively.
速动比率约1:1通常被视为安全线。若比率显著低于1，企业可能在债务到期时面临支付困难；但比率过高也可能意味着资金闲置，未能更高效地运用。
Theorem: liquidity ratios must be interpreted alongside cash flow forecasts and the nature of the firm’s receivables. A high ratio driven by slow‑paying customers can still hide a cash crisis.
定理：流动性比率必须结合现金流预测和应收账款的性质进行解读。由回款缓慢的客户撑起来的高比率仍可能掩盖现金危机。
6. Inventory Turnover and Trade Receivables/Payables Days | 存货周转率与应收/应付账款天数
Efficiency ratios measure how well a business manages its resources. Inventory turnover calculates how many times the average inventory is sold and replaced during a period.
效率比率衡量企业管理资源的水平。存货周转率计算在一定时期内平均存货被售出并重新进货的次数。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
A higher turnover generally indicates efficient stock management and strong sales, but an excessively high figure may mean the business risks running out of stock and losing sales.
周转率较高通常表明库存管理高效且销售强劲，但过高也可能意味着企业面临缺货和错失销售的风险。
Trade receivables days (debtor days) show the average time it takes for credit customers to pay. A rising figure can signal poor credit control or worsening customer liquidity.
应收账款周转天数（债务人天数）显示赊销客户支付货款的平均时间。该数字上升可能表明信用控制不力或客户资金状况恶化。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
Trade payables days (creditor days) show how long the business takes to pay its suppliers. Extending payables conserves cash but may damage supplier relationships if stretched too far.
应付账款周转天数表示企业支付供应商货款的平均期间。延长付款期可以保留现金，但若推延太久可能损害供应商关系。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
A practical theorem: for healthy cash flow, a business should aim to collect from its customers faster than it pays its suppliers (receivables days < payables days). This reduces the need for external finance.
实用定理：为保持健康的现金流，企业应努力从客户收款速度快于向供应商付款速度（应收账款天数 < 应付账款天数），从而降低对外部融资的需求。
7. Return on Capital Employed (ROCE) | 资本使用回报率
ROCE is a key profitability ratio that measures how efficiently a company uses its long‑term capital to generate operating profit. It is a favourite of investors because it illustrates the return on every pound of capital tied up in the business.
资本使用回报率是衡量企业利用长期资本创造营业利润效率的关键比率。它深受投资者青睐，因为它展示了每一英镑投入资本能产生多少回报。
ROCE (%) = (Operating Profit ÷ Capital Employed) × 100
Capital employed can be calculated as total assets minus current liabilities, or as equity plus non‑current liabilities. Both approaches give the same figure of long‑term funds in the business.
资本使用额可以用总资产减去流动负债，或用股东权益加上非流动负债计算，两者都代表企业使用的长期资金。
A higher ROCE usually indicates better performance. As a decision rule, a project or investment should ideally generate a ROCE greater than the firm’s target return, otherwise the capital might be better used elsewhere.
通常ROCE越高代表绩效越好。作为决策法则，项目或投资所产生的ROCE应高于企业的目标回报率，否则资金或许另有更佳用途。
Capital Employed = Total Assets − Current Liabilities
A useful comparative theorem: ROCE can be split into margin and asset turnover (DuPont analysis), summarising that profitability comes from either high margins or efficient use of assets. Even at IGCSE level, comparing ROCE across firms in the same industry provides powerful insights.
一条有用的比较定理：ROCE可分解为利润率和资产周转率（杜邦分析），说明盈利来源于高利润率或资产的高效使用。即使在IGCSE阶段，比较同行业企业的ROCE也能提供深刻洞见。
8. Working Capital and Liquidity Management Theorems | 营运资金与流动性管理定理
Working capital is defined as current assets minus current liabilities. It represents the funds available for day‑to‑day operations. A positive working capital figure is essential to avoid insolvency in the short term.
营运资金定义为流动资产减去流动负债，表示可用于日常运营的资金。保持正的营运资金对避免短期破产至关重要。
Working Capital = Current Assets − Current Liabilities
Too much working capital, however, can indicate inefficiency, because excess cash could be invested in growth‑generating assets or reducing borrowing. The optimal level balances safety and profitability.
然而，营运资金过多也可能表明效率低下，因为多余现金可以投入能促进增长的资产或用于减少借贷。最优水平需在安全性和盈利性之间取得平衡。
A core liquidity management theorem states that a firm must align the maturity structure of its assets and liabilities: short‑term assets should be financed by short‑term sources, while long‑term investments require long‑term capital. Violating this principle often leads to cash flow crises.
核心流动性管理的定理指出，企业应使资产与负债的期限结构匹配：短期资产应由短期资金来源支持，长期投资则需长期资本支撑。违背这一原则通常会导致现金流危机。
Cash is the lifeblood of any business. Even a profitable firm can fail if it runs out of cash. Thus, cash flow forecasting and liquidity ratios must be monitored together.
现金是企业的生命线。即使一家企业盈利，若现金耗尽也可能倒闭。因此，必须同时监控现金流预测与流动性比率。
9. Market Share, Growth and Price Elasticity | 市场份额、增长与需求价格弹性
Market share measures a firm’s sales as a percentage of total market sales. It is a direct indicator of competitive strength.
市场份额衡量的是企业销售额占市场总销售额的百分比，是反映竞争优势的直接指标。
