📚 Year 10 Eduqas Business: Formula & Theorem Quick Reference | Eduqas Year 10 商务：公式定理速查手册
This guide consolidates every essential formula, calculation technique and key theoretical concept you are expected to master for the Year 10 Eduqas Business course. Whether you are revising for an end-of-topic test or preparing for your mocks, having these definitions and equations at your fingertips will boost your confidence in multiple-choice questions, data-response tasks and case-study analysis.
本手册汇总了 Year 10 Eduqas 商务课程中你必须掌握的所有核心公式、计算方法和关键理论概念。无论你是在为单元测验复习，还是在为模拟考试做准备，随时查阅这些定义和公式都能增强你应对选择题、数据分析题和案例研究题的信心。
1. Revenue, Total Costs and Profit | 收入、总成本与利润
Revenue is the total income generated by a business from selling its goods or services before any costs are deducted. It is calculated by multiplying the selling price per unit by the quantity sold. The formula is simply:
Revenue = Selling Price per Unit × Quantity Sold
收入是企业在扣除任何成本之前通过销售商品或服务获得的总收入。它是用单位售价乘以销售数量计算出来的。公式非常简单：
收入 = 每件售价 × 销售数量
For example, if a smoothie shop sells 300 cups at £3 each, revenue = £3 × 300 = £900. Revenue does not tell the whole story; we must also understand costs.
例如，如果一家冰沙店以 3 英镑的单价卖出 300 杯，收入 = 3 × 300 = 900 英镑。收入并不能说明全部问题，我们还需要了解成本。
Total costs are the sum of all expenditure incurred by a business. They are split into fixed costs (which do not vary with output, e.g. rent) and variable costs (which change directly with output, e.g. raw materials). The equation is:
Total Costs = Fixed Costs + Variable Costs
总成本是企业发生的所有支出的总和。它们分为固定成本（不随产量变化，例如租金）和变动成本（直接随产量变化，例如原材料）。公式为：
总成本 = 固定成本 + 变动成本
If fixed costs are £2,000 per month and variable costs are £1.50 per item, total costs for 1,000 items = £2,000 + (£1.50 × 1,000) = £3,500.
如果固定成本为每月 2,000 英镑，变动成本为每件 1.50 英镑，那么生产 1,000 件产品的总成本 = 2,000 + (1.50 × 1,000) = 3,500 英镑。
Profit is the difference between revenue and total costs. It is the main financial objective of most businesses and is calculated as:
Profit = Revenue − Total Costs
利润是收入与总成本之间的差额。它是大多数企业的主要财务目标，计算公式为：
利润 = 收入 − 总成本
If revenue is £900 and total costs are £700, profit is £200. A business making a loss occurs when total costs exceed revenue.
如果收入为 900 英镑，总成本为 700 英镑，利润就是 200 英镑。当总成本超过收入时，企业就会出现亏损。
2. Break-Even Analysis | 盈亏平衡分析
Break-even analysis identifies the level of output where a business covers all of its costs, with neither profit nor loss. The break-even point is calculated using the contribution method, where contribution per unit = selling price per unit − variable cost per unit:
Break-Even Output (units) = Fixed Costs / (Selling Price per Unit − Variable Cost per Unit)
盈亏平衡分析用于确定企业刚好覆盖所有成本、利润为零的产量水平。盈亏平衡点可用边际贡献法计算，其中单位边际贡献 = 单位售价 − 单位变动成本：
盈亏平衡产量（件） = 固定成本 / (单位售价 − 单位变动成本)
For instance, a café has fixed costs of £4,000 per month, sells sandwiches at £5 each and incurs variable costs of £2 per sandwich. Break-even output = 4,000 / (5 − 2) = 4,000 / 3 = 1,333.33, therefore 1,334 sandwiches must be sold to break even.
例如，一家咖啡馆每月的固定成本为 4,000 英镑，三明治售价为 5 英镑，每份变动成本为 2 英镑。盈亏平衡产量 = 4,000 / (5 − 2) = 4,000 / 3 = 1,333.33，因此必须卖出 1,334 个三明治才能实现盈亏平衡。
Break-even revenue can be found by multiplying the break-even output by the selling price:
Break-Even Revenue = Break-Even Output × Selling Price per Unit
盈亏平衡收入可通过将盈亏平衡产量乘以售价得出：
盈亏平衡收入 = 盈亏平衡产量 × 单位售价
For the café, break-even revenue = 1,333.33 × £5 = £6,666.67. This means the café needs to earn at least £6,667 in sales to avoid a loss.
对这家咖啡馆而言，盈亏平衡收入 = 1,333.33 × 5 = 6,666.67 英镑。这意味着咖啡馆至少需要赚取 6,667 英镑的销售收入才能避免亏损。
3. Margin of Safety | 安全边际
The margin of safety measures how much actual sales can fall before the business reaches its break-even point. A higher margin of safety indicates lower risk. It is expressed in units or as a percentage.
Margin of Safety (units) = Actual Output (or Sales) − Break-Even Output
安全边际衡量的是在企业达到盈亏平衡点之前，实际销售量可以下降多少。安全边际越高，风险越低。它可以表示为件数，也可以表示为百分比。
安全边际（件） = 实际产量（或销量） − 盈亏平衡产量
If the café sells 2,000 sandwiches and its break-even output is 1,334, the margin of safety is 2,000 − 1,334 = 666 sandwiches. In percentage terms: (Margin of safety / Actual sales) × 100 = (666 / 2,000) × 100 = 33.3%. Sales could drop by 33.3% before the café incurs a loss.
如果咖啡馆售出 2,000 个三明治，盈亏平衡产量为 1,334，则安全边际为 2,000 − 1,334 = 666 个。若按百分比计算：（安全边际 / 实际销量）× 100 = (666 / 2,000) × 100 = 33.3%。在咖啡馆出现亏损之前，销售额可以下降 33.3%。
4. Gross and Net Profit Margins | 毛利率与净利率
Profit margins express profitability as a percentage of revenue, allowing comparisons between businesses of different sizes. Gross profit margin focuses on direct trading profitability and is calculated as:
Gross Profit Margin (%) = (Gross Profit / Revenue) × 100
利润率将盈利能力表示为收入的百分比，便于在不同规模的企业之间进行比较。毛利率侧重于直接交易的盈利能力，计算公式为：
毛利率 (%) = (毛利润 / 收入) × 100
Gross profit = Revenue − Cost of sales (direct costs such as materials). If a clothing retailer has revenue of £50,000 and cost of sales of £30,000, gross profit is £20,000. Gross profit margin = (20,000 / 50,000) × 100 = 40%. This means for every £100 of sales, £40 is gross profit.
毛利润 = 收入 − 销售成本（如材料等直接成本）。如果一家服装零售商的收入为 50,000 英镑，销售成本为 30,000 英镑，则毛利润为 20,000 英镑。毛利率 = (20,000 / 50,000) × 100 = 40%。这意味着每 100 英镑的销售额中，有 40 英镑是毛利润。
Net profit margin takes account of all expenses, including overheads like rent and salaries. It shows the overall profitability of a business:
Net Profit Margin (%) = (Net Profit / Revenue) × 100
净利率考虑了所有费用，包括租金和工资等间接费用。它反映了企业的总体盈利能力：
净利率 (%) = (净利润 / 收入) × 100
If the same retailer has total expenses (including cost of sales and overheads) of £45,000, net profit = £50,000 − £45,000 = £5,000. Net profit margin = (5,000 / 50,000) × 100 = 10%. A higher margin suggests a business is controlling its costs effectively.
如果同一家零售商的总费用（包括销售成本和间接费用）为 45,000 英镑，则净利润 = 50,000 − 45,000 = 5,000 英镑。净利率 = (5,000 / 50,000) × 100 = 10%。更高的利润率表明企业有效地控制了成本。
5. Average Rate of Return (ARR) | 平均回报率
The average rate of return (ARR) method is used to evaluate the profitability of an investment project by comparing the average annual profit to the initial investment cost. It is expressed as a percentage.
ARR (%) = (Average Annual Profit / Initial Investment Cost) × 100
平均回报率 (ARR) 法通过将平均年利润与初始投资成本进行比较来评估投资项目的盈利能力。它以百分比表示。
ARR (%) = (平均年利润 / 初始投资成本) × 100
Average annual profit is calculated by summing the total net profit over the life of the project and dividing by the number of years. Suppose a company invests £100,000 in new machinery, expecting total net profit of £40,000 over 4 years. The average annual profit = £40,000 / 4 = £10,000. ARR = (10,000 / 100,000) × 100 = 10%. The business would compare this with its target rate to decide whether to proceed.
平均年利润的计算方法是：将项目生命周期内的总净利润相加，再除以年数。假设一家公司投资 10 万英镑购买新机器，预计 4 年内总净利润为 4 万英镑。平均年利润 = 4 万 / 4 = 1 万英镑。ARR = (1 万 / 10 万) × 100 = 10%。企业会将这个比率与目标回报率进行比较，以决定是否投资。
6. Cash Flow Forecast Components | 现金流量预测的构成
A cash flow forecast predicts the cash inflows and outflows over a period, helping businesses manage liquidity. The key equations are:
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
现金流量预测用于预测一段时期内的现金流入和流出，帮助企业进行流动性管理。其关键公式如下：
净现金流量 = 现金流入总额 − 现金流出总额
For example, if a company receives £12,000 from sales and has £9,500 in total outflows (rent, wages, materials), the net cash flow for the month is £12,000 − £9,500 = £2,500.
例如，如果一家公司获得 12,000 英镑的销售收入，而总流出为 9,500 英镑（租金、工资、材料），则该月净现金流量为 12,000 − 9,500 = 2,500 英镑。
The closing balance is the amount of cash held at the end of a period and becomes the opening balance for the next period:
Closing Balance = Opening Balance + Net Cash Flow
期末余额是期末持有的现金金额，并成为下一期的期初余额：
期末余额 = 期初余额 + 净现金流量
If the opening balance in January is £1,000 and net cash flow is £2,500, the closing balance is £3,500. This closing balance then serves as February’s opening balance. A negative closing balance signals a potential cash shortage.
如果 1 月份的期初余额为 1,000 英镑，净现金流量为 2,500 英镑，那么期末余额就是 3,500 英镑。这个期末余额又将成为 2 月份的期初余额。负的期末余额表明可能出现现金短缺。
7. Market Share | 市场份额
Market share indicates the proportion of total industry sales controlled by one company. It is a useful indicator of competitive position.
Market Share (%) = (Company’s Sales / Total Market Sales) × 100
市场份额反映了一家公司控制整个行业销售的比例，是衡量竞争地位的有效指标。
市场份额 (%) = (公司销售额 / 市场总销售额) × 100
If a smartphone manufacturer sells £500 million worth of devices in a market where total sales are £2 billion, its market share = (500m / 2,000m) × 100 = 25%. Businesses strive to increase market share as it can lead to greater pricing power and economies of scale.
如果某智能手机制造商在一个总销售额为 20 亿英镑的市场中售出价值 5 亿英镑的产品，则其市场份额 = (5 亿 / 20 亿) × 100 = 25%。企业努力扩大市场份额，因为这样可以带来更强的定价权和规模经济效应。
8. Interest Calculations | 利息计算
Interest is the cost of borrowing money or the reward for saving. For Year 10, you mainly work with simple interest, although some contexts may require understanding compound growth.
Simple Interest = Principal × Interest Rate × Time
利息是借款的成本或储蓄的回报。Year 10 阶段主要涉及单利，不过在某些情境下也需要理解复利增长。
单利 = 本金 × 利率 × 时间
If a business borrows £10,000 at an annual interest rate of 5% for 3 years, the simple interest = £10,000 × 0.05 × 3 = £1,500. The total repayment (principal plus interest) would be £11,500. Banks often quote an annual percentage rate (APR) to help compare loans.
如果一家公司以 5% 的年利率借款 10,000 英镑，期限为 3 年，单利 = 10,000 × 0.05 × 3 = 1,500 英镑。总还款额（本金加利息）将是 11,500 英镑。银行通常会报出年百分率 (APR) 来帮助比较贷款。
For savings, interest works in the same way: depositing £1,000 at 2% for one year yields £20 in interest. When calculating, remember to express the interest rate as a decimal (e.g. 2% = 0.02).
对于储蓄而言，利息的计算方式相同：以 2% 的利率存入 1,000 英镑一年，可获得 20 英镑的利息。计算时，要记住将利率表示为小数（例如 2% = 0.02）。
9. Exchange Rate Conversions | 汇率换算
Exchange rates allow you to convert one currency into another and are crucial for businesses engaged in international trade. The formula depends on whether you are changing money into a foreign currency or back to the domestic currency.
Foreign Currency Amount = Domestic Amount × Exchange Rate
Domestic Amount = Foreign Currency Amount / Exchange Rate
汇率使你能够将一种货币兑换成另一种货币，对于从事国际贸易的企业至关重要。使用哪个公式取决于你是将本币兑换为外币，还是将外币兑换回本币。
外币金额 = 本币金额 × 汇率
本币金额 = 外币金额 / 汇率
Imagine a UK business buys supplies from the USA and the exchange rate is £1 = $1.25 (USD). To pay a $5,000 invoice, the business needs £5,000 / 1.25 = £4,000. Conversely, if the UK business sells goods worth £2,000 to a US customer, the dollar amount received would be £2,000 × 1.25 = $2,500. A stronger pound makes imports cheaper but exports more expensive.
假设一家英国企业从美国采购，汇率为 1 英镑 = 1.25 美元。要支付一张 5,000 美元的发票，该企业需要 5,000 / 1.25 = 4,000 英镑。相反，如果这家英国企业向美国客户销售价值 2,000 英镑的商品，收到的美元金额便是 2,000 × 1.25 = 2,500 美元。英镑走强会使进口商品更便宜，但出口商品更贵。
10. Key Business Concepts and Theorems | 核心商业概念与定理
Alongside calculations, you are expected to recall and explain several fundamental business concepts. The table below summarises essential definitions that often appear in examinations.
除了计算之外，你还需要记忆并解释若干基本的商业概念。下表总结了考试中经常出现的关键定义。
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