📚 Year 9 CIE Business: Formulas & Theorems Quick-Reference Handbook | Year 9 CIE 商务：公式定理速查手册
The following is a carefully compiled quick-reference guide to the essential formulas and key concepts required for Year 9 CIE Business Studies. Mastering these calculations and fundamental principles will help you analyse business performance, make informed decisions and excel in your assessments. Each section pairs an English explanation with a Chinese translation to support bilingual learning.
以下是为 Year 9 CIE 商务课程精心整理的核心公式与关键概念速查手册。掌握这些计算方法和基本原理，将帮助你分析企业业绩、做出明智决策并在学业评估中脱颖而出。每个部分都配有中英双语解释，助力双语学习。
1. Revenue, Costs and Profit | 收入、成本与利润
Total revenue is the income a business receives from selling goods or services. It is calculated by multiplying the selling price per unit by the number of units sold. Costs are divided into fixed costs, which do not change with output, and variable costs, which vary directly with the level of production. Profit is the positive difference between total revenue and total costs; it is the reward for taking business risks.
总收入是企业销售商品或服务所获得的收入，由单位售价乘以销售数量计算得出。成本分为不随产量变化的固定成本和与产量直接相关的变动成本。利润是总收入与总成本之间的正差额，是对承担商业风险的回报。
Total revenue equals price multiplied by quantity sold.
总收入等于价格乘以销售数量。
Total Revenue = Price × Quantity
Total costs are the sum of all fixed costs and variable costs.
总成本是所有固定成本与变动成本之和。
Total Costs = Total Fixed Costs + Total Variable Costs
Profit is the amount remaining after subtracting total costs from total revenue.
利润是从总收入中减去总成本后的剩余金额。
Profit = Total Revenue – Total Costs
2. Break-even Analysis | 盈亏平衡分析
Break-even analysis determines the level of sales at which a business covers all its costs, earning neither a profit nor a loss. The break-even point in units is found by dividing total fixed costs by the contribution per unit (selling price minus variable cost per unit). The margin of safety shows how much sales can fall before the business reaches break-even.
盈亏平衡分析用于确定企业刚好覆盖全部成本、不盈不亏的销售水平。用总固定成本除以单位贡献毛利（售价减单位变动成本）可得到实物量的盈亏平衡点。安全边际则表明在达到盈亏平衡之前销售额可以下降的幅度。
Contribution per unit is the difference between the selling price per unit and the variable cost per unit.
单位贡献毛利是单位售价与单位变动成本之差。
Contribution per Unit = Selling Price per Unit – Variable Cost per Unit
Break‑even point in units equals fixed costs divided by contribution per unit.
以数量表示的盈亏平衡点等于固定成本除以单位贡献毛利。
Break‑even Point (units) = Fixed Costs ÷ Contribution per Unit
Break‑even point in sales revenue is found by multiplying break‑even units by the selling price.
盈亏平衡销售额等于盈亏平衡数量乘以售价。
Break‑even Revenue = Break‑even Units × Selling Price
Margin of safety equals actual sales minus break‑even sales.
安全边际等于实际销售额减去盈亏平衡销售额。
Margin of Safety = Actual Sales – Break‑even Sales
3. Profit Margin and Markup | 利润率与加成
Profit margins measure how much profit a business makes for every pound or dollar of sales revenue. Gross profit margin considers only direct costs of production, while net profit margin takes all expenses into account. Markup is a different concept that expresses gross profit as a percentage of the cost of sales, often used when setting selling prices.
利润率衡量企业每获得一英镑或一美元销售收入能创造多少利润。毛利率只考虑直接生产成本，而净利率则涵盖所有费用。加成是另一个概念，它将毛利表示为销售成本的百分比，通常用于制定售价。
Gross profit is revenue minus cost of sales. Gross profit margin expresses this as a percentage of revenue.
毛利为收入减去销售成本。毛利率将其表示为收入的百分比。
Gross Profit = Revenue – Cost of Sales
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
Net profit is gross profit minus all other expenses. Net profit margin shows the final percentage of profit from revenue.
净利润是毛利减去所有其他费用。净利率显示最终利润占收入的百分比。
Net Profit = Gross Profit – Expenses
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
Markup shows the gross profit earned for every unit of cost of sales.
加成表示每单位销售成本所赚取的毛利。
Markup = (Gross Profit ÷ Cost of Sales) × 100%
4. Average Rate of Return (ARR) | 平均回报率
ARR is used to assess the profitability of an investment. It calculates the average annual profit as a percentage of the initial investment cost. This allows a business to compare different investment projects and decide whether a project meets its target return.
平均回报率用于评估投资的盈利能力。它将平均年度利润计算为初始投资成本的百分比，使企业能够比较不同的投资项目，并判断项目是否达到目标回报。
Average annual profit is the total profit over the project's life divided by the number of years.
平均年度利润是项目寿命期内的总利润除以年数。
Average Annual Profit = Total Profit from Investment ÷ Number of Years
ARR is the average annual profit shown as a percentage of the initial investment.
平均回报率是将平均年度利润表示为初始投资的百分比。
ARR = (Average Annual Profit ÷ Initial Investment) × 100%
5. Working Capital | 营运资金
Working capital measures the short‑term financial health of a business. It is the money available for day‑to‑day operations after covering immediate debts. A positive working capital indicates that current assets exceed current liabilities, which is generally considered a safe financial position.
营运资金衡量企业的短期财务健康状况。它是在偿还即期债务后可用于日常运营的资金。营运资金为正表明流动资产超过流动负债，通常被视为稳健的财务状况。
Working capital is calculated by subtracting current liabilities from current assets.
营运资金通过流动资产减去流动负债计算得出。
Working Capital = Current Assets – Current Liabilities
6. Liquidity Ratios | 流动比率
Liquidity ratios assess a business’s ability to pay its short‑term debts. The current ratio compares all current assets to current liabilities, while the acid test ratio (or quick ratio) excludes inventory because it may not be quickly converted into cash. A healthy current ratio is usually between 1.5 and 2, but this varies by industry.
流动比率用于评估企业偿还短期债务的能力。流动比率将所有流动资产与流动负债进行比较，而酸性测试比率（速动比率）则剔除存货，因为存货可能无法迅速变现。通常认为健康的流动比率介于1.5至2之间，但会因行业不同而有所差异。
The current ratio shows whether current assets are sufficient to cover current liabilities.
流动比率显示流动资产是否足以覆盖流动负债。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test ratio provides a stricter measure by removing inventories from current assets.
酸性测试比率通过将存货从流动资产中剔除，提供更严格的衡量标准。
Acid Test Ratio = (Current Assets – Inventories) ÷ Current Liabilities
7. Productivity | 生产率
Productivity measures how efficiently a business uses its resources, typically labour. Higher productivity means more output is produced per worker or per hour worked, which can reduce unit costs and increase competitiveness. It is a vital indicator for operations management.
生产率衡量企业利用资源（通常是劳动力）的效率。生产率越高，意味着每位员工或每小时能产出更多产品，从而降低单位成本并提高竞争力。这是运营管理的重要指标。
Labour productivity is the output produced per employee over a given time period.
劳动生产率是指在特定时期内每位员工生产的产出。
Labour Productivity = Total Output ÷ Number of Employees
If labour hours are given, productivity can also be calculated as output per hour.
若已知工时，也可按每小时的产出计算生产率。
Productivity = Total Output ÷ Number of Hours Worked
8. Market Share and Sales Growth | 市场份额与销售增长
Market share indicates the percentage of total industry sales accounted for by one business. It is a key measure of competitiveness. Sales growth measures the percentage change in a firm’s own sales over time, revealing whether the business is expanding or contracting.
市场份额表示一家企业在行业总销售额中所占的百分比，是衡量竞争力的关键指标。销售增长衡量企业自身销售额在一段时间内的百分比变化，反映企业是在扩张还是收缩。
Market share is the firm’s sales revenue divided by total market sales revenue, expressed as a percentage.
市场份额等于企业销售收入除以市场总销售收入，以百分比表示。
Market Share = (Firm’s Sales ÷ Total Market Sales) × 100%
Sales growth compares the change in sales to the previous period’s sales.
销售增长是将销售额的变化与上一期销售额进行比较。
Sales Growth = ((Sales This Year – Sales Last Year) ÷ Sales Last Year) × 100%
9. Added Value | 附加值
Added value is the difference between the selling price of a product and the cost of its raw materials and bought‑in components. It represents the worth a business creates through its production or service process. Higher added value can be achieved by improving product features, branding or customer service without simply raising costs.
附加值是产品售价与其原材料和外购部件成本之间的差额。它代表企业通过生产或服务流程所创造的价值。通过改进产品功能、品牌建设或客户服务，企业可以在不单纯提高成本的情况下增加附加值。
Added value equals selling price minus the cost of raw materials and components.
附加值等于售价减去原材料和部件成本。
Added Value = Selling Price – Cost of Raw Materials and Components
It can also be expressed more generally as sales revenue minus the cost of bought‑in goods and services.
更广义的附加值也可表示为销售收入减去外购商品和服务的成本。
10. Unit Cost and Economies of Scale | 单位成本与规模经济
Unit cost, also called average total cost, is the total cost of production divided by the number of units produced. As a business grows and increases its scale of production, it can experience economies of scale – factors that cause the average cost per unit to fall. These include bulk‑buying discounts, specialisation of labour and more efficient use of machinery.
单位成本，也称平均总成本，是总生产成本除以产出数量。随着企业成长并扩大生产规模，它可以获得规模经济——即导致单位平均成本下降的各类因素，包括批量采购折扣、劳动分工专业化和更高效的机器利用。
Unit cost tells a business how much it costs on average to make one product.
单位成本告知企业平均生产一件产品的成本。
Average Total Cost (Unit Cost) = Total Costs ÷ Output
When economies of scale are achieved, the unit cost decreases as output increases.
当实现规模经济时，单位成本随产量增加而下降。
11. Exchange Rate Calculations | 汇率计算
Businesses that trade internationally need to convert money from one currency to another. The exchange rate shows how much one currency is worth in terms of another. A rise in the exchange rate makes exports more expensive and imports cheaper, while a fall has the opposite effect. Simple multiplication or division is used to perform currency conversions.
从事国际贸易的企业需要将一种货币兑换成另一种货币。汇率表明一种货币以另一种货币表示的价值。汇率上升会使出口更贵、进口更便宜，汇率下跌则产生相反效果。货币兑换采用简单的乘法或除法。
nge rate is given as 1 GBP = 1.30 USD, then to convert pounds to dollars multiply by 1.30.
若汇率为1英镑 = 1.30美元，则将英镑换算为美元需乘以1.30。
Amount in USD = Amount in GBP × 1.30
To convert dollars back to pounds, divide by the exchange rate.
将美元换回英镑则除以汇率。
Amount in GBP = Amount in USD ÷ 1.30
In general, amount in target currency equals amount in home currency multiplied by the exchange rate.
一般来说，目标货币金额等于本币金额乘以汇率。
12. Interest Calculations | 利息计算
Interest is the cost of borrowing money or the reward for saving. Simple interest is calculated only on the original principal amount. Businesses must understand interest calculations when taking out loans or evaluating investment returns. Compound interest, where interest is earned on previous interest, leads to faster growth but may not be tested in detail at this level.
利息是借入资金的成本或储蓄的回报。单利仅按原始本金计算。企业在贷款或评估投资回报时必须理解利息计算。复利是将利息计入本金再计息，会导致更快增长，但在现阶段可能不做详细考查。
Simple interest depends on the principal, the annual interest rate and the time period in years.
单利取决于本金、年利率和年数。
Simple Interest = Principal × Rate × Time (years)
The total amount to repay for a simple interest loan is the principal plus the interest.
单利贷款的总还款额为本金加利息。
Total Repayment = Principal + Simple Interest
While compound interest is not always required, the growth is modelled by multiplying the principal by (1 plus the rate) raised to the power of the number of years.
虽然复利不常考，但其增长可通过本金乘以（1加利 率）的年数次方来建模。
Compound Amount = Principal × (1 + Rate)Time
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