📚 Year 11 AQA Business: Formula & Theorem Quick Reference Handbook | Year 11 AQA 商务：公式定理速查手册
This handbook compiles all the essential formulas and key theorems required for the Year 11 AQA Business course. The quick reference format helps students memorise and apply financial and operational calculations with confidence. Each formula is accompanied by clear explanations and practical examples in both English and Chinese to support bilingual learning. Whether you are revising for mocks or the final exam, keep this guide handy for rapid revision.
本手册汇总了Year 11 AQA商务课程所需的全部核心公式和关键定理。速查格式帮助学生自信地记忆并应用财务与运营计算。每条公式均配有清晰的中英文解释和实用示例，以支持双语学习。无论你是在准备模拟考试还是最终大考，都可以随时参考本手册进行快速复习。
1. Revenue, Costs and Profit | 收入、成本与利润
Revenue is the total amount of money a business earns from selling its goods or services before any costs are deducted. It is also called sales revenue or turnover and forms the top line of the income statement.
收入是企业在扣除任何成本之前，通过销售商品或服务所获得的总金额。它也被称作销售收入或营业额，是利润表的第一行。
Total Revenue = Selling Price per Unit × Quantity Sold
For instance, if a street food stall sells 120 wraps at £5 each, total revenue for that day is £5 × 120 = £600.
例如，一个街头小吃摊以每份5英镑的价格卖出120份卷饼，当天的总收入就是 5 × 120 = 600 英镑。
Total costs are the sum of all fixed costs and variable costs a business incurs. Fixed costs do not change with output in the short run (e.g., rent, salaries), while variable costs change directly with the quantity produced (e.g., raw materials).
总成本是企业发生的全部固定成本和变动成本之和。固定成本短期内不随产量变化（如租金、工资），而变动成本则随产量直接变化（如原材料）。
Total Costs = Fixed Costs + (Variable Cost per Unit × Quantity)
If a bakery pays £800 in rent and each cake costs £3 in ingredients, producing 200 cakes gives total costs of £800 + (3 × 200) = £1,400.
如果一家面包店支付800英镑租金，每个蛋糕的原料成本为3英镑，生产200个蛋糕的总成本为 800 + (3 × 200) = 1,400 英镑。
Profit is the financial reward for a business after all costs have been subtracted from revenue. It is a key measure of success and can be reinvested or distributed to owners.
利润是收入扣除所有成本后的财务回报，是衡量企业成功的关键指标，可以用于再投资或分配给所有者。
Profit = Total Revenue – Total Costs
Using the bakery example, if the 200 cakes are sold at £10 each, revenue is £2,000 and profit equals £2,000 – £1,400 = £600.
以面包店为例，如果200个蛋糕都以10英镑售出，收入为2,000英镑，利润为 2,000 – 1,400 = 600 英镑。
2. Break-even Analysis | 盈亏平衡分析
The break-even point is the level of output at which total revenue equals total costs, meaning the business makes neither a profit nor a loss. It is a vital planning tool for new and existing businesses.
盈亏平衡点是指总收入等于总成本时的产量水平，此时企业既不盈利也不亏损。它是新创和现有企业的重要规划工具。
Break-even Output = Fixed Costs ÷ (Selling Price per Unit – Variable Cost per Unit)
The term in brackets is called contribution per unit. Contribution represents the amount each unit sold contributes towards covering fixed costs, after variable costs are paid.
括号中的部分称为单位贡献。单位贡献是指每售出一单位产品，在支付变动成本后，能贡献多少用于覆盖固定成本。
If a toy maker has fixed costs of £5,000, sells each toy for £15 and each toy costs £7 in variable expenses, the break-even output is £5,000 ÷ (15 – 7) = 625 units.
如果一个玩具制造商固定成本为5,000英镑，每个玩具售价15英镑，每个玩具变动成本7英镑，那么盈亏平衡产量为 5,000 ÷ (15 – 7) = 625 件。
Margin of safety shows how much sales can fall before the business reaches its break-even point. A larger margin of safety implies lower risk.
安全边际表示在达到盈亏平衡点之前，销售额可以下降多少。安全边际越大，风险越低。
Margin of Safety = Actual Sales (units) – Break-even Sales (units)
If the toy maker actually sells 800 units, the margin of safety is 800 – 625 = 175 units, indicating that sales could drop by 175 units before a loss occurs.
如果该制造商实际售出800件，安全边际为 800 – 625 = 175 件，表明销量在下降175件之前仍不会亏损。
3. Cash Flow | 现金流
Cash flow is the movement of money into and out of a business over a period. Positive cash flow is crucial for survival, even if a business is profitable on paper.
现金流是一定时期内资金流入和流出企业的过程。即使企业账面上盈利，正向现金流对生存仍然至关重要。
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
For a given month, a cafe might have cash inflows of £12,000 from sales and outflows of £10,500 for wages, supplies and rent, giving a net cash flow of £1,500.
在某个月份，一家咖啡馆可能通过销售获得12,000英镑的现金流入，支付工资、原料和租金等流出10,500英镑，净现金流为1,500英镑。
The closing balance is the amount of cash the business has at the end of a period. It becomes the opening balance for the next period.
期末余额是企业在期末持有的现金额，并成为下一期的期初余额。
Closing Balance = Opening Balance + Net Cash Flow
If the cafe started May with £2,000 and had a net cash flow of £1,500, its closing balance would be £3,500. This figure is critical for predicting liquidity problems.
如果咖啡馆5月初余额为2,000英镑，当月净现金流为1,500英镑，期末余额为3,500英镑。该数据对预测流动性问题至关重要。
4. Gross Profit and Net Profit | 毛利与净利润
Gross profit is the profit a business makes after deducting only the direct costs of making or buying the products it sells. These direct costs are called cost of sales.
毛利是企业从销售收入中只扣除生产或购买产品的直接成本后得到的利润。这些直接成本被称为销售成本。
Gross Profit = Sales Revenue – Cost of Sales
A clothing retailer with £80,000 in sales and a cost of sales of £45,000 would have a gross profit of £35,000.
一家服装零售商销售收入为80,000英镑，销售成本为45,000英镑，则毛利为35,000英镑。
Net profit is the final profit after all other operating expenses and interest are deducted from gross profit. It is sometimes called the bottom line.
净利润是从毛利中扣除所有其他营业费用和利息后的最终利润，有时被称为底线利润。
Net Profit = Gross Profit – Other Operating Expenses – Interest
If the clothing retailer pays £18,000 in rent, salaries and marketing, and £1,200 in loan interest, net profit becomes £35,000 – £18,000 – £1,200 = £15,800.
如果该服装零售商支付租金、工资和营销等费用共18,000英镑，贷款利息1,200英镑，净利润为 35,000 – 18,000 – 1,200 = 15,800 英镑。
5. Profitability Ratios | 盈利能力比率
Profit margins express profit as a percentage of sales revenue, allowing comparisons across different periods and with competitors. They measure how effectively a business controls costs.
利润率将利润表现为销售收入的百分比，便于跨时期和与竞争对手进行比较。它们衡量企业控制成本的有效性。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100
earlier clothing retailer figures, gross profit margin is (35,000 ÷ 80,000) × 100 = 43.75%. This means for every £1 of sales, the business keeps nearly 44p after paying direct costs.
使用前述服装零售商数据，毛利率为 (35,000 ÷ 80,000) × 100 = 43.75%。这意味着每1英镑的销售收入中，支付直接成本后企业留存约44便士。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100
Net profit margin for the same retailer is (15,800 ÷ 80,000) × 100 = 19.75%, showing that almost 20p of every sales pound remains as net profit after all expenses.
同一零售商的净利润率为 (15,800 ÷ 80,000) × 100 = 19.75%，表明每1英镑销售收入中，扣除所有费用后约有20便士的净利润。
6. Liquidity Ratios | 流动性比率
Liquidity ratios assess a business's ability to meet its short-term debts as they fall due. Lenders and suppliers use these to judge financial health.
流动性比率评估企业偿还短期到期债务的能力。贷款人和供应商用其判断财务健康状况。
Current Ratio = Current Assets ÷ Current Liabilities
A result between 1.5 and 2.0 is often considered healthy. If a firm has current assets of £50,000 and current liabilities of £30,000, its current ratio is 1.67 : 1, meaning it has £1.67 of current assets for every £1 of short-term debt.
通常认为1.5至2.0之间较为健康。如果一家企业流动资产为50,000英镑，流动负债为30,000英镑，其流动比率为1.67 : 1，即每1英镑短期债务对应1.67英镑流动资产。
Acid Test Ratio = (Current Assets – Inventory) ÷ Current Liabilities
nt Inventory is removed because it is the least liquid current asset. An acid test ratio of 1 : 1 or above is often desirable. If the firm above holds £20,000 of inventory, acid test = (50,000 – ,000) ÷ 30,000 = 1 : 1, indicating it can just pay short-term debts without selling stock.
减去存货是因为其流动性最差。酸性测试比率等于或高于1:1通常较理想。如果上述企业持有20,000英镑存货，酸性测试 = (50,000 – 20,000) ÷ 30,000 = 1 : 1，表明其在不销售存货的情况下刚好能偿还短期债务。
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