📚 Year 10 AQA Business: Quick-Reference Formula Handbook | Year 10 AQA 商务：公式定理速查手册
This handbook brings together all the essential quantitative formulas and key business concepts you will meet in Year 10 AQA Business. Use it as a quick reference to reinforce your understanding of revenue, costs, profit, break-even, cash flow, financial ratios and market calculations. Every formula is presented in a clean, easy-to-read layout with paired English and Chinese explanations, so you can revise wherever you are and build the numerical confidence needed for your exams.
本手册汇集了 Year 10 AQA 商务课程中所有重要的定量公式和关键商业概念。你可以把它当作快速参考工具，来巩固对收入、成本、利润、盈亏平衡、现金流量、财务比率和市场计算的理解。每个公式都配有清晰易读的排版和中英双语解释，让你可以随时复习，建立起考试所需的数字分析信心。
1. Revenue, Total Costs and Profit | 收入、总成本与利润
Revenue is the income earned by a business from selling its goods or services. It is calculated by multiplying the selling price per unit by the quantity sold in a given period. Understanding revenue is the first step in measuring business performance.
Total Revenue = Selling Price per Unit × Quantity Sold
收入是企业通过销售商品或服务获得的资金流入，等于单位售价乘以某个时期内的销售数量。理解收入是衡量企业绩效的第一步。
Total costs represent all the expenses a business incurs in producing and delivering its products. They can be split into fixed costs (which do not change with output, such as rent) and variable costs (which rise and fall with production, such as raw materials).
Total Costs = Fixed Costs + Variable Costs
总成本代表企业在生产和交付产品过程中发生的全部支出，可以分为固定成本（不随产量变化，如租金）和可变成本（随生产量变化，如原材料）。
Profit is the surplus left after total costs have been deducted from total revenue. It is the fundamental reward for taking business risks.
Profit = Total Revenue − Total Costs
利润是从总收入中扣除总成本后的剩余部分，是承担商业风险的根本回报。
2. Average Unit Cost | 平均单位成本
Average unit cost tells a business how much it costs to produce one unit of output on average. It is vital for pricing decisions and efficiency analysis.
Average Unit Cost = Total Costs ÷ Number of Units Produced
平均单位成本反映了企业平均生产一件产品需要花费多少成本，对于定价决策和效率分析至关重要。
As a business grows, it may experience economies of scale, which lower the average unit cost. In the short run, however, the average unit cost can be used to calculate the profit per unit when compared with the selling price.
随着企业成长，可能会产生规模经济，从而降低平均单位成本。但在短期内，平均单位成本可以与售价比较，用来计算单件产品的利润。
3. Break-even Analysis | 盈亏平衡分析
Break-even analysis helps a business determine the level of sales needed to cover all its costs exactly. At the break-even point, total revenue equals total costs and the profit is zero.
盈亏平衡分析帮助企业确定恰好覆盖所有成本所需的销售水平。在盈亏平衡点，总收入等于总成本，利润为零。
The break-even output is calculated by dividing the total fixed costs by the contribution per unit. Contribution per unit is the difference between the selling price and the variable cost per unit.
Break-even Output (units) = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
Contribution per Unit = Selling Price per Unit − Variable Cost per Unit
盈亏平衡产量等于总固定成本除以单位贡献。单位贡献是单位售价与单位可变成本之间的差额。
Margin of safety shows how far sales can fall before the business reaches the break-even point. It is a key measure of risk.
Margin of Safety (units) = Actual or Budgeted Sales Units − Break-even Sales Units
安全边际显示销售可以下降多少而不至于亏损，是衡量风险的关键指标。安全边际（单位）= 实际或预算销售量 − 盈亏平衡销售量。
4. Cash Flow | 现金流量
Cash flow is the movement of money into and out of a business. It is not the same as profit, because it considers the timing of receipts and payments. Positive net cash flow is essential for survival.
现金流量是资金进出企业的流动过程，与利润不同，因为它关注收支的时间点。正向净现金流对生存至关重要。
The net cash flow for a period is found by subtracting total cash outflows from total cash inflows. The closing cash balance is then carried forward to the next period.
Net Cash Flow = Total Inflows − Total Outflows
Closing Balance = Opening Balance + Net Cash Flow
某一时期的净现金流量等于总流入减去总流出。期末余额等于期初余额加上净现金流量，并结转至下一期。
Cash flow forecasts help managers plan for shortages and arrange overdrafts or loans in advance. A healthy cash flow position allows a business to pay suppliers, staff and other expenses on time.
现金流量预测帮助管理者提前规划资金短缺问题，并安排透支或贷款。健康的现金流状况使企业能够按时支付供应商、员工和其他费用。
5. Gross and Net Profit Margins | 毛利率与净利率
Profit margins measure how much profit is generated from sales revenue. Gross profit focuses on trading efficiency, while net profit accounts for all expenses.
利润率衡量销售收入产生多少利润。毛利率关注交易效率，而净利率则把全部费用都考虑在内。
Gross profit is the difference between sales revenue and the direct cost of producing or buying the goods sold (cost of sales). The gross profit margin expresses this as a percentage.
Gross Profit = Sales Revenue − Cost of Sales
Gross Profit Margin (%) = (Gross Profit ÷ Sales Revenue) × 100
毛利是销售收入减去已售商品的直接成本（营业成本）后的余额。毛利率是以百分比形式表示的毛利占销售收入的比例。
Net profit is the ultimate profit after all other expenses, such as rent, salaries and interest, have been deducted. The net profit margin shows the overall profitability of the business.
Net Profit = Gross Profit − Other Expenses
Net Profit Margin (%) = (Net Profit ÷ Sales Revenue) × 100
净利润是扣除所有其他费用（如房租、工资和利息）后的最终利润。净利率反映了企业的整体盈利能力。
6. Average Rate of Return (ARR) | 平均回报率
The average rate of return helps a business compare the profitability of different investment projects. It expresses the average annual profit as a percentage of the initial amount invested.
平均回报率帮助企业在不同投资项目之间比较盈利水平，它将平均年利润表示为初始投资额的百分比。
Average Rate of Return (%) = (Average Annual Profit ÷ Initial Investment) × 100
平均年利润通常通过将项目总利润除以项目年限得出。ARR 百分比越高，项目通常越有吸引力，但还应考虑风险和时间尺度。
Average annual profit is usually found by dividing the total project profit by the number of years. The higher the ARR percentage, the more attractive a project tends to be, though risk and timescale must also be considered.
ARR 的计算第一步是确定项目的总预期利润，减去初始投资成本后得到净总收益，再除以年数即可得到平均年利润。ARR 是商业决策中常用的投资评估工具。
7. Interest on Loans | 贷款利息
Many businesses borrow money to start up or expand. The cost of borrowing is interest. It is useful to express the total interest paid as a percentage of the original loan amount to understand the true cost.
许多企业通过借款来创业或扩张，借款的成本就是利息。将支付的总利息表示为原贷款金额的百分比，有助于理解真实的借款成本。
Interest Rate (%) = (Total Interest Paid ÷ Original Loan Amount) × 100
当比较不同贷款方案时，不仅要看名义利率，还要考虑总还款额。总还款额等于贷款本金加上全部利息。低息贷款可以大幅度降低企业财务压力。
When comparing loan options, focus on the total repayment (principal plus all interest) rather than just the advertised rate. Low-interest borrowing can significantly reduce a firm’s financial pressure.
在比较贷款方案时，关注总还款额（本金加全部利息）而非只是广告利率更为重要。低息借贷可以显著降低企业的财务压力。
8. Percentage Changes | 百分比变化
Businesses frequently need to measure changes in revenue, costs, market size or profits over time. The percentage change formula provides a standard way to express growth or decline.
企业经常需要衡量收入、成本、市场规模或利润随时间发生的变化。百分比变化公式提供了一种表达增长或下降的标准方法。
Percentage Change (%) = ((New Value − Original Value) ÷ Original Value) × 100
如果结果是正数，表示增长；如果是负数，表示下降。这个公式在编制趋势分析、设定目标和评估营销活动效果时被广泛使用。
A positive result indicates growth, while a negative result indicates a decline. This formula is used widely in trend analysis, setting objectives and evaluating the impact of marketing campaigns.
百分比变化也适用于计算通货膨胀对成本和价格的影响。掌握这一基础公式将帮助你解释许多商业案例中的数据。
9. Business Operations: Productivity and Efficiency | 运营：生产率与效率
Productivity measures how efficiently a business turns inputs into outputs. Labour productivity, for instance, looks at output per employee and is a key driver of unit costs.
生产率衡量企业将投入转化为产出的效率。例如，劳动生产率考量每个员工的产出，是影响单位成本的关键因素。
Labour Productivity = Total Output ÷ Number of Employees
提高生产率可以在不增加员工数量的情况下提高产出，从而降低平均单位成本。效率也可以通过机器利用率或资本生产率来衡量。
Improving productivity allows higher output with the same number of staff, which reduces average unit cost. Efficiency can also be measured through capacity utilisation or capital productivity.
企业可以通过培训、更好的技术和工作流程重组来提高生产率。生产率提高通常会直接提升竞争力。
10. Market Calculations: Size, Share and Growth | 市场计算：规模、份额与增长
Market size can be measured by value (total revenue generated) or by volume (total units sold). Knowing the size of a market helps a business spot opportunities and assess its own position.
市场规模可以用金额（产生的总收入）或数量（销售的总件数）来衡量。了解市场规模有助于企业发现机会并评估自身地位。
Market Size (by value) = Total Sales Revenue of All Firms in the Market
Market Size (by volume) = Total Units Sold by All Firms in the Market
市场规模（按金额）等于市场中所有企业的销售收入总和；按数量等于所有企业销售的总件数。
Market share indicates the proportion of total market sales held by one business. It is a powerful indicator of competitiveness and brand strength.
Market Share (%) = (Sales of One Business ÷ Total Market Sales) × 100
市场份额指一家企业占总市场销售的比重，是衡量竞争力和品牌实力的有力指标。
Market growth compares the change in market size over time, usually expressed as a percentage. A growing market attracts new entrants, whereas a declining market may lead to intense rivalry.
Market Growth (%) = ((New Market Size − Old Market Size) ÷ Old Market Size) × 100
市场增长率通过比较不同时期的市场规模变化来体现，通常以百分比表示。增长的市场吸引新进入者，而衰退的市场可能导致激烈竞争。
11. Cost and Revenue Classification Tips | 成本与收入分类提示
Having a clear mental map of cost types helps you apply formulas correctly. Fixed costs stay constant regardless of output – rent, insurance and permanent salaries are typical examples.
清晰掌握成本类型有助于正确应用公式。固定成本不随产量变化，例如租金、保险费和固定薪资。
Variable costs move in direct proportion to production, such as raw materials, packaging and piece-rate labour. Some costs, like electricity for lighting and machinery, can be semi-variable and need careful analysis before categorising.
可变成本与生产量成正比变动，如原材料、包装和计件工资。有些成本（如照明和机器的电费）属于半变动成本，分类前需仔细分析。
Revenue is not just about price – it is also influenced by the product mix, seasonal demand and discounts. Always check whether the revenue figure is gross or net of returns.
收入不仅取决于价格，还受产品组合、季节性需求和折扣的影响。务必确认收入数字是毛收入还是扣除退货后的净收入。
12. Quick Check: Putting Formulas to Work | 快速检查：让公式发挥作用
Use this quick checklist when tackling numerical questions: identify which formula is needed, write it out clearly, substitute the correct numbers and always state the units (e.g., pounds, units, percentage). Show your working step by step.
解答计算题时可使用这份快速检查清单：确定需要哪个公式，清晰写出公式，代入正确的数字，并始终注明单位（如英镑、件、百分比）。逐步展示你的计算过程。
Common mistakes include confusing profit with cash flow, forgetting to include all fixed costs in break-even, and calculating percentage change using the new value as the denominator instead of the original. Practice reinforces accuracy.
常见错误包括混淆利润与现金流、在盈亏平衡计算中遗漏部分固定成本，以及用新数值而非原数值作为分母来计算百分比变化。通过练习可以强化准确性。
Keep this handbook handy and test yourself by covering the formula side first. Then challenge yourself with short questions that combine two or more formulas, such as calculating profit margin after a break-even shift.
将本手册放在手边，先遮住公式栏进行自测。然后用结合两个或更多公式的简短题目挑战自己，例如计算盈亏平衡变化后的利润率。
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