📚 Year 10 CAIE Business: Formula & Theorem Quick Reference Handbook | Year 10 CAIE 商务：公式定理速查手册
Welcome to the Year 10 CAIE Business Studies Formula & Theorem Quick Reference Handbook. This guide compiles essential formulas and key business concepts you must master for your IGCSE examinations. Each formula is presented with a clear explanation in both English and Chinese to support bilingual learning. Use this handbook to revise ratios, break-even analysis, cash flow budgeting, and profit calculations quickly and effectively.
欢迎使用 Year 10 CAIE 商务研究公式定理速查手册。本手册汇编了 IGCSE 考试中必须掌握的基本公式和关键商业概念。每个公式均附有中英文清晰解释，以支持双语学习。使用本手册可快速有效地复习比率、盈亏平衡分析、现金流预算和利润计算。
1. Revenue, Cost and Profit | 收入、成本与利润
Total revenue is the income a business earns 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.
总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收入，等于单位售价乘以销售数量。
Total Revenue = Price × Quantity
Total costs are the sum of fixed costs and variable costs. Fixed costs do not change with output in the short run (e.g. rent, salaries), while variable costs change directly with the level of production (e.g. raw materials, packaging).
总成本是固定成本与变动成本之和。固定成本在短期内不随产量变化（如租金、薪金），变动成本则直接随生产水平变动（如原材料、包装）。
Total Costs = Fixed Costs + Variable Costs
Profit is the surplus remaining after all costs have been subtracted from total revenue. A positive figure indicates a profit; a negative figure means the business is making a loss.
利润是从总收入中扣除所有成本后的盈余。正数表示盈利，负数表示企业处于亏损状态。
Profit = Total Revenue − Total Costs
2. Contribution and Break-even Point | 贡献毛利与盈亏平衡点
Contribution per unit measures how much each unit sold contributes towards covering fixed costs and, once fixed costs are covered, towards profit. It does not represent pure profit because fixed costs must still be paid.
单位贡献毛利衡量每售出一单位产品对覆盖固定成本所做的贡献，并在固定成本全部覆盖后为利润做贡献。它不代表纯利润，因为固定成本仍需支付。
Contribution per unit = Selling Price − Variable Cost per unit
Total contribution is the aggregate contribution from all units sold. It can be used to quickly find total profit by subtracting total fixed costs.
总贡献毛利是所有已售单位的贡献总和，减去总固定成本后可快速得出总利润。
Total Contribution = Contribution per unit × Quantity Sold
The break-even point is the level of output where total revenue equals total costs, so the business makes neither a profit nor a loss. Knowing this point helps managers set sales targets and make pricing decisions.
盈亏平衡点是总收入等于总成本时的产出水平，此时企业既不盈利也不亏损。了解该点有助于管理者设定销售目标和做出定价决策。
Break-even point (units) = Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)
3. Margin of Safety | 安全边际
Margin of safety shows the amount by which actual sales exceed the break-even level. It indicates the cushion a business has before it starts incurring losses. A larger margin of safety implies lower risk.
安全边际显示实际销售额超过盈亏平衡水平的数量，表明企业开始亏损前的缓冲空间。安全边际越大，意味着风险越低。
Margin of Safety (units) = Actual Sales (units) − Break-even Sales (units)
The margin of safety can also be expressed as a percentage of actual sales to make comparisons easier between different time periods or products.
安全边际也可以表示为实际销售额的百分比，以便在不同时期或产品之间进行比较。
Margin of Safety (%) = (Margin of Safety ÷ Actual Sales) × 100%
If a company produces 1,200 units, and its break-even output is 900 units, the margin of safety is 300 units. Sales could fall by 300 units before the firm becomes unprofitable.
如果一家公司生产 1,200 单位，其盈亏平衡产量为 900 单位，则安全边际为 300 单位。销量下降 300 单位后企业才会开始亏损。
4. Income Statement Key Calculations | 损益表关键计算
Gross profit is the profit made from core trading activities after deducting the direct cost of goods sold. It indicates how efficiently a business turns raw materials or purchases into revenue.
毛利是在扣除直接销售成本后从核心贸易活动中获得的利润，表明企业将原材料或采购转化为收入的效率。
Gross Profit = Sales Revenue − Cost of Sales
Net profit is the final profit after all other operating expenses (e.g. rent, advertising, salaries, interest) are subtracted from gross profit. For IGCSE, it is commonly expressed as gross profit minus overheads.
净利润是从毛利中扣除所有其他营业费用（如租金、广告、薪金、利息）后的最终利润。在 IGCSE 中通常表示为毛利减去间接费用。
Net Profit = Gross Profit − Expenses
Retained profit (a part of net profit) can be reinvested in the business to fund growth, while the rest may be paid out as dividends to shareholders.
留存利润（净利润的一部分）可再投资用于企业发展，其余部分可作为股息派发给股东。
5. Gross Profit Margin | 毛利率
Gross profit margin expresses gross profit as a percentage of revenue. It reveals how much of each pound or dollar of sales is left after covering direct costs. A rising margin often results from higher prices or lower cost of sales.
毛利率将毛利表示为收入的百分比，揭示了在覆盖直接成本后每单位销售额剩余多少。毛利率上升通常源于售价提高或销售成本降低。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
For example, if a business has a gross profit of £40,000 and revenue of £100,000, the gross profit margin is 40%. This means for every £1 of sales, 40p is gross profit.
例如，某企业毛利为 40,000 英镑，收入为 100,000 英镑，则毛利率为 40%。这意味着每 1 英镑销售收入中有 40 便士是毛利。
Comparing gross profit margin with competitors or previous periods helps assess whether the business is managing its direct costs effectively.
将毛利率与竞争对手或往年数据比较，有助于评估企业管理直接成本的效率。
6. Net Profit Margin | 净利率
Net profit margin indicates the percentage of revenue remaining as net profit after all expenses. A high net margin suggests strong control over both direct and indirect costs.
净利率表示收入在扣除所有费用后剩余为净利润的百分比。较高的净利率表明企业对直接和间接成本均有良好的控制。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
If revenue is £200,000 and net profit is £30,000, the net profit margin is 15%. This ratio is especially useful for assessing overall profitability and long-term viability.
若收入为 200,000 英镑，净利润为 30,000 英镑，则净利率为 15%。该比率对于评估整体盈利能力和长期生存能力尤其有用。
7. Return on Capital Employed (ROCE) | 资本回报率
ROCE measures how efficiently a business generates profit from the long-term capital invested by owners and lenders. It is one of the most widely used profitability indicators.
ROCE 衡量企业利用所有者和债权人投入的长期资本产生利润的效率，是最广泛使用的盈利指标之一。
ROCE = (Net Profit ÷ Capital Employed) × 100%
Capital employed is typically calculated as total assets minus current liabilities, or as non-current liabilities plus shareholders’ equity. It represents all long-term sources of finance.
资本占用通常计算为总资产减去流动负债，或非流动负债加所有者权益，代表所有长期资金来源。
A business with a 12% ROCE earns £0.12 of operating profit for every £1 of capital employed. Investors compare ROCE with interest rates to decide if funds are well used.
若某企业 ROCE 为 12%，则每 1 英镑占用资本产生 0.12 英镑的经营利润。投资者将 ROCE 与利率比较，以判断资金是否运用得当。
8. Liquidity Ratios (Current & Acid Test) | 流动比率与速动比率
The current ratio measures a firm’s ability to meet short-term obligations using its current assets. A ratio between 1.5 and 2 is often regarded as healthy, though it varies by industry.
流动比率衡量企业使用流动资产偿还短期债务的能力。一般认为介于 1.5 至 2 之间较为健康，但会因行业而异。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test (quick) ratio is a stricter liquidity measure because it excludes inventories. Inventory can be difficult to turn into cash quickly, so removing it gives a clearer picture of immediate liquidity.
速动比率（酸性测试比率）是更严格的流动性指标，因为它排除了存货。存货可能难以快速变现，剔除后可以更清晰地反映即时流动性。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
A very low acid test ratio (e.g. below 0.5) could signal cash flow problems, whereas an excessively high ratio may suggest idle cash that could be invested elsewhere.
速动比率极低（如低于 0.5）可能预示现金流问题，而过高的比率则表明存在闲置现金，可考虑另行投资。
9. Cash Flow Forecasting | 现金流预算
Net cash flow is the difference between total cash inflows and total cash outflows over a specific period. A positive net cash flow means more cash came in than went out.
净现金流是某一特定时期内现金流入总额与现金流出总额之差。正值表示现金流入大于流出。
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
The closing balance for any period is found by adding the net cash flow to the opening balance. This closing balance becomes the next period’s opening balance.
任何期间的期末现金余额等于期初余额加上净现金流，该期末余额成为下一期间的期初余额。
Closing Balance = Opening Balance + Net Cash Flow
Cash flow forecasts help managers anticipate shortages and arrange overdrafts or short-term finance in advance. They are vital for maintaining liquidity and avoiding failure.
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