📚 Year 9 CIE Business: Formulas & Theorems Quick Reference | Year 9 CIE 商务：公式定理速查手册
This quick reference handbook compiles the essential formulas, key theorems and economic laws required for the Year 9 CIE Business syllabus. Whether you are calculating profit, analysing break-even, interpreting ratios or applying the laws of demand and supply, mastering these tools is critical for solving numerical problems and explaining business behaviour.
本速查手册汇编了 Year 9 CIE 商务课程所需的核心公式、关键定理和经济定律。无论你是在计算利润、分析盈亏平衡、解读比率，还是在运用需求与供给定律，掌握这些工具对于解决计算问题和解释企业行为都至关重要。
1. Profit, Revenue and Cost Foundations | 利润、收入与成本基础
Profit is the reward for taking business risks. It is the surplus remaining after all costs have been subtracted from total revenue.
利润是对承担商业风险的回报，它是从总收入中扣除所有成本后的剩余金额。
Profit = Total Revenue (TR) – Total Cost (TC)
If total costs are greater than total revenue, the business makes a loss.
如果总成本大于总收入，企业就会发生亏损。
Total revenue is the income generated from selling goods or services. It is calculated by multiplying the selling price per unit by the quantity sold.
总收入是销售产品或服务所产生的收入，由单位售价乘以销售数量计算得出。
Total Revenue (TR) = Selling Price per Unit × Quantity Sold
Total cost is the sum of all fixed costs and variable costs a business incurs during production.
总成本是企业在生产过程中发生的全部固定成本和变动成本之和。
Total Cost (TC) = Fixed Costs (FC) + Variable Costs (VC)
Average cost (also called unit cost) shows the cost of producing one unit of output. It falls as output spreads fixed costs over more units.
平均成本（也称单位成本）表示生产一单位产品所需的成本。随着产量增加，固定成本被更多单位分摊，平均成本会下降。
Average Cost = Total Cost ÷ Output
Gross profit focuses on the direct costs of buying or making goods, while net profit accounts for all other expenses.
毛利润关注的是购买或制造商品的直接成本，而净利润则涵盖了所有其他费用。
Gross Profit = Revenue – Cost of Sales
Net Profit = Gross Profit – Expenses
2. Break-Even Analysis and Contribution | 盈亏平衡分析与贡献毛益
Break-even analysis determines the point at which a business covers all its costs—neither making a profit nor a loss.
盈亏平衡分析用于确定企业刚覆盖全部成本、既不盈利也不亏损的临界点。
The break-even point in units is found by dividing total fixed costs by the contribution per unit. Contribution measures how much each unit sold contributes towards paying fixed costs and then generating profit.
盈亏平衡产量由总固定成本除以单位贡献毛益得出。贡献毛益衡量的是每售出一单位产品能为支付固定成本和创造利润所做的贡献。
Contribution per Unit = Selling Price per Unit – Variable Cost per Unit
Break-Even Point (units) = Fixed Costs ÷ Contribution per Unit
Businesses often calculate the break-even point in revenue terms as well.
企业通常也会计算以收入表示的盈亏平衡点。
Break-Even Revenue = Break-Even Units × Selling Price per Unit
The margin of safety shows how much sales can fall before a business reaches break-even. It provides a cushion against uncertainty.
安全边际显示销售在达到盈亏平衡点之前可以下跌多少，它为企业提供了抵御不确定性的缓冲。
Margin of Safety (units) = Actual Sales Units – Break-Even Units
Target profit can be incorporated into break-even formulas: the required output level to achieve a specific profit is (Fixed Costs + Target Profit) ÷ Contribution per Unit.
目标利润可以纳入盈亏平衡公式：为达到特定利润所需的产量水平 = (固定成本 + 目标利润) ÷ 单位贡献毛益。
3. Profitability Ratios | 盈利能力比率
Profitability ratios measure a business's ability to generate earnings relative to its sales, costs or capital. They are essential for comparing performance over time or against competitors.
盈利能力比率衡量企业相对于其销售、成本或资本创造盈利的能力。它们对于比较不同时期的业绩或与竞争对手进行对比至关重要。
Gross profit margin indicates the percentage of revenue left after covering the cost of sales. A higher margin suggests efficient control of production or purchasing costs.
毛利率表示在覆盖销售成本后剩余的收入百分比。更高的毛利率表明对生产或采购成本的有效控制。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
Net profit margin reveals the percentage of revenue that remains as net profit after all expenses. It is a key indicator of overall cost management.
净利润率揭示扣除所有费用后剩余为净利润的收入百分比，它是衡量整体成本管理的关键指标。
Net Profit Margin = (Net Profit ÷ Revenue) × 100
Return on Capital Employed (ROCE) evaluates how effectively a business uses its long-term funds to generate profit. It is one of the most watched profitability ratios.
已动用资本回报率 (ROCE) 评估企业利用其长期资金创造利润的效率，是最受关注的盈利能力比率之一。
ROCE = (Net Profit ÷ Capital Employed) × 100
Capital employed is usually defined as total equity plus non-current liabilities, or total assets minus current liabilities.
已动用资本通常定义为总股本加非流动负债，或者总资产减去流动负债。
4. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet its short-term obligations as they fall due. A business that lacks liquidity may face insolvency even if it is profitable.
流动性比率评估企业偿还到期短期债务的能力。缺乏流动性的企业即使盈利也可能面临资不抵债的风险。
The current ratio compares all current assets to all current liabilities. A result around 1.5 to 2 is often considered healthy, though benchmarks vary by industry.
流动比率将所有流动资产与所有流动负债进行比较。结果在1.5至2之间通常被认为是健康的，尽管基准因行业而异。
Current Ratio = Current Assets ÷ Current Liabilities
The quick ratio (acid test) is a stricter measure that excludes inventory from current assets, because inventory may not be easily converted into cash.
速动比率（酸性测试比率）是一项更严格的衡量指标，它将存货从流动资产中剔除，因为存货可能不易迅速转换为现金。
Quick Ratio = (Current Assets – Inventory) ÷ Current Liabilities
If the quick ratio is significantly lower than the current ratio, the business may be holding too much inventory.
如果速动比率明显低于流动比率，表明企业可能持有过多的存货。
5. Efficiency and Productivity Measures | 效率与生产率计量
Efficiency ratios show how well a business uses its resources. Productivity measures the output obtained from a given input, such as labour.
效率比率展示企业利用资源的程度。生产率衡量从给定投入（如劳动力）中所获得的产出。
Labour productivity is a fundamental indicator of workforce efficiency. Increasing productivity can reduce unit costs and raise competitiveness.
劳动生产率是衡量劳动力效率的基本指标。提高生产率可以降低单位成本并增强竞争力。
Labour Productivity = Total Output ÷ Number of Employees
Inventory turnover measures how many times a business sells and replaces its inventory over a period. A higher turnover suggests efficient stock management and strong sales.
存货周转率衡量企业在一定时期内销售并重置其存货的次数。更高的周转率表明高效的库存管理和强劲的销售。
Inventory Turnover = Cost of Goods Sold ÷ Average Inventory
Where average inventory is often approximated as (Opening Inventory + Closing Inventory) ÷ 2.
其中平均存货通常近似计算为（期初存货 + 期末存货）÷ 2。
eful measure: (Actual Output ÷ Maximum Possible Output) × 100. It shows how much of a firm's productive capacity is being used.
产能利用率是另一个有用的指标：(实际产量 ÷ 最大可能产量) × 100。它显示企业的生产性产能有多少被实际利用。
6. Core Economic Theorems: Demand, Supply and Equilibrium | 核心经济定理：需求、供给与均衡
The Law of Demand states that, ceteris paribus (all other things being equal), as the price of a good falls, the quantity demanded rises, and as the price rises, the quantity demanded falls.
需求定律指出，在其他条件不变的前提下，当商品价格下降时，需求量会上升；当价格上升时，需求量会下降。
The demand curve therefore slopes downward from left to right, reflecting the inverse relationship between price and quantity demanded.
因此，需求曲线从左向右下倾斜，反映了价格与需求量之间的反向关系。
The Law of Supply states that, ceteris paribus, as the price of a good rises, the quantity supplied increases, and as the price falls, the quantity supplied decreases.
供给定律指出，在其他条件不变的前提下，当商品价格上升时，供给量会增加；当价格下降时，供给量会减少。
The supply curve slopes upward, showing a direct relationship between price and quantity supplied. Producers are motivated by higher profits at higher prices.
供给曲线向上倾斜，显示价格与供给量之间的直接关系。更高的价格激励生产者追求更高的利润。
Market equilibrium occurs where the demand curve and supply curve intersect. At the equilibrium price, quantity demanded equals quantity supplied, so there is no shortage or surplus.
市场均衡发生在需求曲线与供给曲线相交之处。在均衡价格下，需求量等于供给量，因而没有短缺也没有盈余。
When the market price is above equilibrium, a surplus exists; when it is below equilibrium, a shortage emerges. Market forces tend to push the price back towards equilibrium.
当市场价格高于均衡点时出现盈余，低于均衡点时出现短缺。市场力量往往会将价格推回均衡水平。
7. Opportunity Cost, Factors of Production and Specialisation | 机会成本、生产要素与专业化
Opportunity cost is the next best alternative given up when making a choice. It represents the true cost of any decision in terms of lost benefits.
机会成本是在做出选择时所放弃的次优选项，它代表了任何决定在丧失利益方面的真正成本。
For a business, opportunity cost might be the profit it could have earned by investing funds in a different project. For individuals, it could be the income forgone by choosing study over work.
对企业而言，机会成本可能是将资金投入另一个项目原本可以赚取的利润；对个人而言，可能是选择学习而放弃的工作收入。
The four factors of production are land (natural resources), labour (human effort), capital (man-made goods used to produce other goods) and enterprise (the willingness to take risks and organise the other three factors).
四种生产要素分别是土地（自然资源）、劳动力（人类努力）、资本（用于生产其他产品的人造物品）以及企业家才能（承担风险并组织其他三种要素的意愿）。
Specialisation occurs when individuals, businesses or countries concentrate on producing a limited range of goods or services. It increases efficiency and output.
专业化是指个人、企业或国家集中生产有限范围的商品或服务。它提高了效率和产出。
The division of labour is a form of specialisation where the production process is broken into small, repetitive tasks. It can raise productivity but may also lead to worker boredom.
劳动分工是专业化的一种形式，将生产过程分解为细小、重复的任务。它可以提高生产率，但也可能导致工人厌倦。
8. The Law of Diminishing Returns and Economies of Scale | 收益递减定律与规模经济
The Law of Diminishing Returns (also called diminishing marginal returns) applies in the short run when at least one factor of production is fixed. As more units of a variable factor (e.g. labour) are added to a fixed factor (e.g. land), the additional output from each extra unit of the variable factor will eventually fall.
收益递减定律（也称边际收益递减）适用于至少有一种生产要素固定的短期。当越来越多的可变要素（如劳动力）被增加到固定要素（如土地）上时，每额外增加一单位可变要素所带来的额外产出最终会下降。
Total product continues to rise for a while, but marginal product (the extra output from one more worker) declines.
总产量会继续上升一段时间，但边际产量（多雇用一个工人带来的额外产出）会下降。
Economies of scale are the cost advantages a business obtains due to expansion in the long run, when all factors of production are variable. Average costs fall as output increases.
规模经济是企业在长期（所有生产要素都可变时）通过扩张所获得的成本优势。随着产出增加，平均成本下降。
Internal economies of scale can arise from technical, purchasing, managerial, financial or marketing efficiencies. External economies of scale result from the growth of the industry as a whole.
内部规模经济可能源于技术、采购、管理、财务或营销方面的效率提升。外部规模经济来自整个行业的增长。
Diseconomies of scale occur when a business becomes too large and average costs start to rise, often due to communication problems, coordination difficulties or low worker morale.
规模不经济发生在企业变得过于庞大、平均成本开始上升时，通常是由于沟通问题、协调困难或员工士气低落所致。
9. Interest, Exchange Rate and Inflation Calculations | 利率、汇率与通胀计算
Simple interest is calculated on the principal amount only. It is relevant for many business borrowing and saving scenarios.
单利仅按本金计算，适用于许多企业借款和储蓄场景。
Simple Interest = Principal × Rate × Time (years)
For example, borrowing $10,000 at 5% per annum for 3 years yields interest of 10,000 × 0.05 × 3 = $1,500.
例如，以年利率5%借款10,000美元，期限3年，利息为10,000 × 0.05 × 3 = 1,500美元。
value of one currency in terms of another. If the exchange rate is 1 GBP = 1.25 USD, then £1,000 converts to 1,000 × 1.25 = $1,250.
汇率换算使企业能够计算一种货币以另一种货币表示的价值。如果汇率为1英镑 = 1.25美元，那么1,000英镑可兑换为1,000 × 1.25 = 1,250美元。
To convert back from USD to GBP, divide the amount by the exchange rate: $1,250 ÷ 1.25 = £1,000.
要将美元换回英镑，将金额除以汇率：1,250美元 ÷ 1.25 = 1,000英镑。
Inflation measures the rate at which the general level of prices for goods and services is rising. It is often calculated using the Consumer Price Index (CPI).
通货膨胀衡量商品和服务总体价格水平上升的比率，通常使用消费者价格指数 (CPI) 计算。
Inflation Rate = ((CPI in Current Year – CPI in Previous Year) ÷ CPI in Previous Year) × 100
Rising inflation erodes purchasing power and can influence interest rates, wages and business costs.
攀升的通货膨胀会侵蚀购买力，并可能影响利率、工资和企业成本。
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