📚 Year 10 WJEC Business: Formulas & Theorems Quick Reference | Year 10 WJEC 商务：公式定理速查手册
This quick-reference handbook consolidates the essential formulas, key ratios and critical concepts that feature in the Year 10 WJEC GCSE Business specification. It is designed as a portable revision companion to strengthen your quantitative skills, support your homework and boost your confidence ahead of tests and exams.
本速查手册整理提炼了 Year 10 WJEC GCSE 商务课程中必考的核心公式、关键比率以及重要概念。你可以把它当作随身复习工具，用来强化计算能力、辅助课后练习，并在单元测验和考试前快速巩固要点。
1. Revenue Formula | 收入公式
Revenue (also called turnover or sales revenue) is the total income a business generates from selling its goods or services before any costs are deducted. The basic revenue equation is:
收入（亦称营业额或销售收入）是企业在扣除任何成本之前，从销售商品或服务中获得的总收入。基本收入公式为：
Revenue = Selling Price × Quantity Sold
- Example: A cinema sells 300 tickets at £8 each. Its revenue is 300 × £8 = £2 400.
示例：一家影院以 8 英镑的单价售出 300 张电影票，收入为 300 × 8 = 2 400 英镑。
2. Total Costs: Fixed and Variable | 总成本：固定成本与变动成本
A business incurs two main types of cost. Fixed costs remain constant regardless of output (e.g. rent, management salaries, insurance). Variable costs change directly with the level of production (e.g. raw materials, packaging, piece-rate labour). Total cost is the sum of the two.
企业会产生两类主要成本。固定成本不随产量变化而改变（如租金、管理人员工资、保险费）。变动成本则直接随产量水平变动（如原材料、包装、计件工资）。总成本为两者之和。
Total Costs = Fixed Costs + Variable Costs
- Example: A factory has fixed costs of £5 000 per month and variable costs of £3 per unit. If it produces 2 000 units, total costs = £5 000 + (£3 × 2 000) = £11 000.
示例：一家工厂每月固定成本为 5 000 英镑，单位变动成本为 3 英镑。若生产 2 000 件产品，总成本 = 5 000 + (3 × 2 000) = 11 000 英镑。
3. Profit Calculation | 利润计算
Profit is the financial reward a business earns when revenue exceeds its costs. Gross profit focuses on trading activity: it is the difference between sales revenue and the cost of sales (direct costs of buying or making goods). Net profit (often called operating profit) subtracts all other expenses from gross profit.
利润是企业在收入超过成本时所获得的经济回报。毛利润关注交易活动本身，即销售收入与销售成本（直接购买或生产商品的支出）之间的差额。净利润（常被称为营业利润）则从毛利润中扣除所有其他费用。
Profit = Revenue – Total Costs
Gross Profit = Revenue – Cost of Sales
Net Profit = Gross Profit – Operating Expenses
- Example: A boutique sells dresses with sales revenue of £40 000. The cost of buying those dresses is £15 000; other expenses (rent, wages, marketing) total £12 000. Gross profit = £40 000 – £15 000 = £25 000. Net profit = £25 000 – £12 000 = £13 000.
示例：一家时装精品店销售收入为 40 000 英镑，采购服装的成本为 15 000 英镑，其他费用（租金、工资、营销）合计 12 000 英镑。毛利润 = 40 000 – 15 000 = 25 000 英镑，净利润 = 25 000 – 12 000 = 13 000 英镑。
4. Gross Profit Margin | 毛利率
Gross profit margin measures the proportion of revenue that remains after paying for the direct costs of sales. It shows how efficiently a business controls its production or purchasing costs. The result is expressed as a percentage.
毛利率衡量在支付直接销售成本之后剩余的销售收入占比，反映企业控制生产或采购成本的效率。计算结果以百分比形式表示。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
- Example: If a business has gross profit of £50 000 and revenue of £120 000, the gross profit margin is (50 000 ÷ 120 000) × 100 ≈ 41.67%.
示例：某企业毛利润为 50 000 英镑，销售收入为 120 000 英镑，则毛利率为 (50 000 ÷ 120 000) × 100 ≈ 41.67%。
5. Net Profit Margin | 净利率
Net profit margin gives a more complete picture of profitability because it accounts for all business expenses, including overheads. It indicates how much of every £1 of revenue translates into final profit after all costs are covered.
净利率提供了一个更全面的盈利图景，因为它考虑了包括间接费用在内的所有业务支出。该指标显示每 1 英镑销售收入中，在覆盖所有成本之后最终能转化为多少利润。
Net Profit Margin = (Net Profit ÷ Revenue) × 100
- Example: With net profit of £8 000 and revenue of £50 000, the net profit margin is (8 000 ÷ 50 000) × 100 = 16%.
示例：净利润为 8 000 英镑，收入为 50 000 英镑，则净利率为 (8 000 ÷ 50 000) × 100 = 16%。
6. Break-even Output | 盈亏平衡产量
The break-even point is where a business sells just enough units to cover its total costs – it makes neither a profit nor a loss. The formula uses the idea of contribution per unit (selling price minus variable cost per unit), which is the amount each sale contributes towards fixed costs.
盈亏平衡点指企业刚好售出足够数量的产品以弥补全部总成本的状态，此时既无利润也无亏损。该公式应用了单位贡献毛利（销售单价减去单位变动成本）的概念，即每件售出产品对固定成本的贡献额。
Break-even output = Fixed Costs ÷ (Selling Price – Variable Cost per Unit)
- Example: Fixed costs are £12 000, selling price is £25 per unit, and variable cost is £15 per unit. Contribution per unit = £25 – £15 = £10. Break-even output = 12 000 ÷ 10 = 1 200 units.
示例：固定成本为 12 000 英镑，销售单价为 25 英镑，单位变动成本为 15 英镑。单位贡献毛利 = 25 – 15 = 10 英镑。盈亏平衡产量 = 12 000 ÷ 10 = 1 200 件。
7. Margin of Safety | 安全边际
Margin of safety shows how much sales can fall before a business reaches its break-even point. It can be expressed in units or as a monetary value, and it helps assess the risk of making a loss.
安全边际表明销售量可以下降多少才会使企业达到盈亏平衡点。它可以按数量或金额表示，有助于评估企业面临亏损的风险。
Margin of Safety = Actual Sales (units) – Break-even Output (units)
- Example: memberships and its break-even output is 1 200 memberships, the margin of safety is 1 800 – 1 200 = 600 memberships.
示例：一家健身房实际售出 1 800 张会员卡，而盈亏平衡点销量为 1 200 张，安全边际 = 1 800 – 1 200 = 600 张。
8. Net Cash Flow and Closing Balance | 净现金流与期末余额
Cash flow is the movement of money into and out of a business over a period. Net cash flow is simply the difference between total cash inflows and total cash outflows. The closing balance becomes the opening balance for the next period.
现金流是一定时期内企业资金的流入与流出。净现金流即现金流入总额与现金流出总额之间的差额。期末余额会成为下一期的期初余额。
Net Cash Flow = Total Inflows – Total Outflows
Closing Balance = Opening Balance + Net Cash Flow
- Example: A cafe has an opening balance of £4 000, total inflows of £9 500 and total outflows of £8 200 in January. Net cash flow = £9 500 – £8 200 = £1 300. Closing balance = £4 000 + £1 300 = £5 300.
示例：一家咖啡店 1 月期初余额为 4 000 英镑，当月现金总流入为 9 500 英镑，总流出为 8 200 英镑。净现金流 = 9 500 – 8 200 = 1 300 英镑。期末余额 = 4 000 + 1 300 = 5 300 英镑。
9. Current Ratio (Working Capital Ratio) | 流动比率（营运资本比率）
The current ratio tests whether a business has enough short-term assets to cover its short-term liabilities. A result between 1.5:1 and 2:1 is often considered healthy, but the ideal level varies by industry.
流动比率用来测试企业是否有足够的短期资产来偿付其短期负债。该比率在 1.5:1 至 2:1 之间通常被视为健康，但理想水平因行业而异。
Current Ratio = Current Assets ÷ Current Liabilities
- Example: Current assets total £60 000 and current liabilities total £40 000, giving a current ratio of 1.5:1. This means for every £1 of short-term debt, the business has £1.50 in current assets.
示例：流动资产合计 60 000 英镑，流动负债合计 40 000 英镑，流动比率为 1.5:1。这意味着每 1 英镑的短期债务，企业有 1.50 英镑的流动资产作为保障。
10. Acid Test Ratio (Quick Ratio) | 速动比率（酸性测试比率）
The acid test ratio is a stricter measure of liquidity because it excludes stock (inventory) from current assets. Stock may take time to sell and is not instantly convertible to cash. The formula is:
速动比率是一种更严格的流动性衡量指标，因为它将存货从流动资产中剔除。存货可能需要时间才能售出，无法立即转化为现金。其公式为：
Acid Test Ratio = (Current Assets – Stock) ÷ Current Liabilities
- Example: A retailer has current assets of £80 000 including £30 000 worth of stock. Current liabilities are £50 000. Acid test ratio = (£80 000 – £30 000) ÷ £50 000 = 1:1. The business can just cover its short-term debts without selling any stock.
示例：一家零售商拥有流动资产 80 000 英镑，其中存货价值 30 000 英镑，流动负债为 50 000 英镑。速动比率 = (80 000 – 30 000) ÷ 50 000 = 1:1。企业在不依赖存货销售的情况下刚好能偿付短期债务。
11. Average Rate of Return (ARR) | 平均回报率
ARR is used to assess the profitability of an investment project. It compares the average annual profit generated by the project to the initial investment cost, giving a percentage figure that helps businesses compare different investment options.
平均回报率用于评价投资项目的盈利能力。它将项目产生的平均年利润与初始投资成本进行比较，得出一个百分比，帮助企业对比不同投资方案。
ARR = (Average Annual Profit ÷ Cost of Investment) × 100
- Example: A firm invests £40 000 in new machinery. The total profit over the machine’s 5‑year life is projected to be £50 000. Average annual profit = £50 000 ÷ 5 = £10 000. ARR = (£10 000 ÷ £40 000) × 100 = 25%.
示例：某企业投资 40 000 英镑购买新设备，预计该设备 5 年使用寿命内产生的总利润为 50 000 英镑。平均年利润 = 50 000 ÷ 5 = 10 000 英镑，ARR = (10 000 ÷ 40 000) × 100 = 25%。
12. Market Share and Sales Growth | 市场份额与销售增长
Market share expresses a firm’s sales as a percentage of the total sales in its market. It is a key indicator of a business’s competitive position. Sales growth measures the percentage increase (or decrease) in sales over time, often used to monitor performance.
市场份额用企业销售额占市场总销售额的百分比来表示，是衡量企业竞争地位的关键指标。销售增长则衡量销售额随时间变化的百分比增幅（或降幅），常用于监控业绩。
Market Share = (Firm's Sales ÷ Total Market Sales) × 100
Sales Growth (%) = [(Sales This Year – Sales Last Year) ÷ Sales Last Year] × 100
- Example – Market Share: A fitness app generates £2 million in sales in a market worth £40 million. Its market share = (£2m ÷ £40m) × 100 = 5%.
- Example – Sales Growth: Sales rise from £150 000 last year to £180 000 this year. Sales growth = [(£180 000 – £150 000) ÷ £150 000] × 100 = 20%.
市场占比示例：某健身应用程序在总规模为 4 000 万英镑的市场中实现销售额 200 万英镑，其市场份额 = (200 万 ÷ 4 000 万) × 100 = 5%。
销售增长示例：销售额从去年的 150 000 英镑上升到今年的 180 000 英镑，销售增长率 = [(180 000 – 150 000) ÷ 150 000] × 100 = 20%。
Published by TutorHao | Business Revision Series | aleveler.com
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