📚 Year 10 Edexcel Business: Quick Formula & Theorem Reference Guide | 爱德思 Year 10 商务公式定理速查手册
Welcome to your essential quick reference for all key formulae and theorems in the Year 10 Edexcel GCSE Business course. This guide is designed to help you memorise, understand and apply the quantitative tools needed for success in Theme 1 and early Theme 2 topics. Each formula is presented clearly, followed by a concise explanation in both English and Chinese, making it suitable for revision, homework support or last-minute checking before assessments.
欢迎阅读爱德思 GCSE 商务 Year 10 关键公式定理速查手册。本指南旨在帮助你记忆、理解和应用 Theme 1 及 Theme 2 前期主题中所需的定量工具。每个公式都以清晰的方式呈现，并附有中英文简明解释，非常适合复习、作业辅助或评估前的快速查阅。
1. Total Revenue | 总收入
Total Revenue = Selling Price per Unit × Quantity Sold
Total revenue is the income a business receives from selling its goods or services during a specific period. It is calculated by multiplying the price charged for one unit by the number of units sold. Revenue does not account for any costs and forms the 'top line' of a profit and loss statement.
总收入是企业在特定时期内通过销售商品或服务所获得的收入。它的计算方式为：单位售价乘以销售数量。总收入尚未扣除任何成本，是损益表中的“首行”。
A business selling 200 units at £15 each will generate total revenue of £15 × 200 = £3,000.
一家企业以每件 15 英镑的价格售出 200 件商品，其总收入为 15 × 200 = 3000 英镑。
2. Total Costs | 总成本
Total Costs = Fixed Costs + Total Variable Costs
Total Variable Costs = Variable Cost per Unit × Quantity Produced
Total costs represent all the expenses a business incurs to produce and sell its output. Fixed costs, such as rent and salaries, remain constant regardless of production volume. Variable costs, like raw materials, change directly with the level of output. To find total variable costs, simply multiply the variable cost per unit by the number of units made.
总成本代表企业为生产和销售产出而发生的所有支出。固定成本（例如租金和工资）无论产量多少都保持不变。变动成本（例如原材料）则直接随产量水平而变化。要计算总变动成本，只需将单位变动成本乘以生产数量即可。
If a factory has fixed costs of £5,000 per month and variable costs of £3 per unit, producing 1,000 units results in total costs of £5,000 + (£3 × 1,000) = £8,000.
如果一家工厂每月固定成本为 5000 英镑，单位变动成本为 3 英镑，那么生产 1000 件产品的总成本为 5000 + (3 × 1000) = 8000 英镑。
3. Profit | 利润
Profit = Total Revenue − Total Costs
Gross Profit = Revenue − Cost of Sales
Net Profit = Gross Profit − Other Operating Expenses
Profit measures the financial gain made by a business when its revenue exceeds all costs. The simplest form is overall profit. Gross profit focuses on the difference between sales income and the direct costs of making the products (cost of sales). Net profit is what remains after deducting all other expenses, such as marketing and administration. A business can have high revenue but still make a loss if costs are higher than income.
利润衡量的是当收入超过所有成本时企业所获得的财务收益。最简单的形式是总体利润。毛利润侧重于销售收入与产品直接生产成本（销售成本）之间的差额。净利润是扣除所有其他费用（如营销和管理）后剩余的金额。企业可能收入很高，但如果成本高于收入，仍会出现亏损。
Using the previous example: revenue of £3,000 with total costs of £8,000 would mean a loss of £5,000, showing the importance of controlling costs.
如上例：收入 3000 英镑，总成本 8000 英镑，则意味着亏损 5000 英镑，这说明了控制成本的重要性。
4. Average Unit Cost | 平均单位成本
Average Unit Cost = Total Production Cost ÷ Number of Units Produced
Average unit cost tells a business how much, on average, it costs to make one item in a batch. As output increases, total production costs are spread over more units, so the average cost per unit typically falls, leading to economies of scale.
平均单位成本告诉企业，一批产品中平均每件要花费多少成本。随着产量的增加，总生产成本被分摊到更多单位上，因此单位平均成本通常会下降，从而产生规模经济效应。
If total production cost is £12,000 and 3,000 units are produced, the average unit cost is £12,000 ÷ 3,000 = £4 per unit.
如果总生产成本为 12000 英镑，生产了 3000 件产品，则平均单位成本为 12000 ÷ 3000 = 每件 4 英镑。
5. Break-even Point | 盈亏平衡点
Contribution per Unit = Selling Price per Unit − Variable Cost per Unit
Break-even Point (units) = Fixed Costs ÷ Contribution per Unit
Break-even Point (£) = Break-even Units × Selling Price per Unit
The break-even point is the level of output at which total revenue equals total costs, so the business makes neither a profit nor a loss. Contribution per unit shows how much each sold unit contributes towards covering fixed costs and then generating profit. The formula divides total fixed costs by this contribution to find exactly how many units must be sold to cover all costs. The monetary break-even point can also be expressed in pounds.
盈亏平衡点是指总收入等于总成本的产出水平，此时企业既不盈利也不亏损。单位贡献额表示每售出一件产品，能够为弥补固定成本和创造利润贡献多少金额。该公式用总固定成本除以此贡献额，即可求出必须销售多少件产品才能覆盖所有成本。盈亏平衡点也可以用货币金额来表示。
If fixed costs are £10,000, the selling price is £25 and the variable cost per unit is £10, then contribution per unit = £25 − £10 = £15. Break-even units = £10,000 ÷ £15 = 667 units (rounded up). Break-even sales = 667 × £25 = £16,675.
如果固定成本为 10000 英镑，售价为 25 英镑，单位变动成本为 10 英镑，则单位贡献额 = 25 − 10 = 15 英镑。盈亏平衡销售量 = 10000 ÷ 15 = 667 件（向上取整）。盈亏平衡销售额 = 667 × 25 = 16675 英镑。
6. Margin of Safety | 安全边际
Margin of Safety (units) = Actual (or Forecast) Sales − Break-even Sales (units)
Margin of Safety (%) = (Margin of Safety (units) ÷ Actual Sales (units)) × 100
Margin of safety measures how far sales can fall before the business reaches its break-even point and starts making a loss. A higher margin of safety indicates lower risk. It can be expressed in units or as a percentage of current sales.
安全边际衡量的是销售额可以下降多少，才会触及盈亏平衡点并开始亏损。安全边际越高，表明风险越低。它可以用销售数量或当前销售的百分比来表示。
e margin of safety is 1,000 − 667 = 333 units. As a percentage: (333 ÷ 1,000) × 100 = 33.3%.
如果实际销售为 1000 件，盈亏平衡销售为 667 件，则安全边际为 1000 − 667 = 333 件。以百分比表示为：(333 ÷ 1000) × 100 = 33.3%。
7. Net Cash Flow | 净现金流
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
Net cash flow represents the difference between all cash received by the business (inflows) and all cash paid out (outflows) over a period. It is important to remember that cash flow is not the same as profit, because some inflows and outflows are not related to trading, and profit includes non-cash items such as depreciation.
净现金流表示一段时间内企业收到的所有现金（流入）与支付的所有现金（流出）之间的差额。必须牢记，现金流与利润不同，因为某些流入和流出与贸易无关，而利润包含折旧等非现金项目。
A business with cash inflows of £20,000 and outflows of £15,000 has a positive net cash flow of £5,000, which helps it meet short-term obligations.
一家企业现金流入为 20000 英镑，流出为 15000 英镑，其净现金流为正的 5000 英镑，这有助于其履行短期偿债义务。
8. Opening & Closing Balances | 期初与期末余额
Closing Balance = Opening Balance + Net Cash Flow
In a cash flow forecast, the opening balance is the amount of cash available at the start of a month. After adding the net cash flow for that month, you obtain the closing balance, which then becomes the next month's opening balance. This formula helps businesses plan for periods of negative cash flow and avoid insolvency.
在现金流量预测中，期初余额是月初可用的现金金额。加上当月的净现金流后，便可得到期末余额，该期末余额进而成为下个月的期初余额。这一公式有助于企业为负现金流期间进行规划，避免破产。
If a business starts the month with £2,000 and has a net cash flow of −£300, the closing balance will be £2,000 + (−£300) = £1,700.
如果一家企业月初有 2000 英镑，净现金流为 −300 英镑，则期末余额为 2000 + (−300) = 1700 英镑。
9. Percentage Change | 百分比变化
Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
Percentage change is used to compare the difference between two values over time or between plans and actual outcomes. A positive result indicates growth, while a negative result signals a decline. This tool is essential for analysing everything from revenue growth to cost changes.
百分比变化用于比较两个数值之间随时间或计划与实际结果之间的差异。正数结果表示增长，负数结果表示下降。该工具对于分析从收入增长到成本变化的各种情况都至关重要。
If last year's profit was £12,000 and this year's profit is £15,000, the percentage change is ((£15,000 − £12,000) ÷ £12,000) × 100 = 25% increase.
如果去年利润为 12000 英镑，今年利润为 15000 英镑，则百分比变化为 ((15000 − 12000) ÷ 12000) × 100 = 增长 25%。
10. Market Share | 市场份额
Market Share (%) = (Company's Sales ÷ Total Market Sales) × 100
Market share indicates the proportion of a total market that a single business controls, measured by sales volume or value. It is a key indicator of competitive strength. A firm can grow its market share by increasing sales or by acquiring competitors, but total market size may also change over time.
市场份额是指一家企业通过销售量或销售额所控制的整个市场的比例，是衡量竞争实力的关键指标。企业可以通过增加销售或收购竞争对手来提升市场份额，但整体市场规模也可能随时间而变化。
A company with sales of £2 million in an industry where total sales are £20 million holds a market share of (2,000,000 ÷ 20,000,000) × 100 = 10%.
一家企业在总销售额为 2000 万英镑的行业中实现了 200 万英镑的销售，其市场份额为 (2000000 ÷ 20000000) × 100 = 10%。
11. Gross Profit Margin & Net Profit Margin | 毛利率与净利率
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
Profit margins express profitability as a percentage of revenue, making it easier to compare performance across different periods or against competitors. The gross profit margin reveals how efficiently a business turns sales into gross profit, while the net profit margin shows the percentage of revenue remaining after all expenses are paid. A declining margin may signal rising costs or pricing pressure.
利润率将盈利能力表示为收入的百分比，便于比较不同时期或与竞争对手的表现。毛利率揭示了企业将销售转化为毛利润的效率，而净利率则显示了支付所有费用后剩余收入的百分比。利润率下降可能预示着成本上升或定价压力。
If a business has revenue of £100,000 and gross profit of £40,000, the gross profit margin is 40%. If net profit is £15,000, the net profit margin is (15,000 ÷ 100,000) × 100 = 15%.
如果一家企业的收入为 100000 英镑，毛利润为 40000 英镑，则毛利率为 40%。如果净利润为 15000 英镑，则净利率为 (15000 ÷ 100000) × 100 = 15%。
12. Average Rate of Return (ARR) | 平均回报率
Average Annual Profit = Total Profit from Investment ÷ Number of Years
ARR (%) = (Average Annual Profit ÷ Initial Investment) × 100
The average rate of return is a financial tool used to evaluate the profitability of an investment project. It calculates the average yearly return as a percentage of the sum initially invested. ARR allows a business to compare different investment options and choose the one with the highest expected return, though it ignores the timing of cash flows.
平均回报率是用于评估投资项目盈利能力的财务工具。它计算的是平均年回报占初始投资总额的百分比。ARR 使企业能够比较不同的投资方案，并选择预期回报率最高的一个，但它忽略了现金流发生的时间。
A project requires an initial investment of £50,000 and is expected to generate total profits of £30,000 over 4 years. Average annual profit = £30,000 ÷ 4 = £7,500. ARR = (£7,500 ÷ £50,000) × 100 = 15%.
一个项目需要初始投资 50000 英镑，预计在 4 年内产生总利润 30000 英镑。平均年利润 = 30000 ÷ 4 = 7500 英镑。ARR = (7500 ÷ 50000) × 100 = 15%。
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