📚 Year 11 CIE Business Studies: Quick Reference Handbook of Formulas & Theorems | Year 11 CIE 商务：公式定理速查手册
This quick-reference guide brings together all the essential formulas, ratios and decision-making theorems covered in the Cambridge IGCSE Business Studies (0450) syllabus. Each entry is paired with a concise explanation to help you apply the formula in calculation, analysis and evaluation questions. Use the handbook to reinforce your understanding and improve your confidence with numerical and application tasks.
本速查手册汇集了剑桥 IGCSE 商务学（0450）课程涉及的所有核心公式、比率和决策定理。每一条公式都配有简要说明，帮助你在计算、分析和评价题中准确运用。利用本手册巩固理解，增强处理数字题和应用题的信心。
1. Revenue, Costs and Profit | 收入、成本与利润
Revenue is the income a business generates from selling goods or services. Total costs are the sum of all expenses incurred. Profit is the surplus when total revenue exceeds total costs.
收入是企业通过销售商品或服务获得的全部所得。总成本是所有费用的总和。当总收入超过总成本时，剩余的部分就是利润。
Total Revenue = Selling Price per unit × Quantity sold
A change in price or volume directly changes total revenue. Businesses must forecast demand carefully.
单价或销售数量的变化会直接影响总收入。企业必须谨慎预测需求。
Total Costs = Fixed Costs + Variable Costs
Fixed costs do not vary with output in the short run, while variable costs change directly with the level of production or sales.
固定成本在短期内不随产出变化，而变动成本则直接随生产或销售水平变化。
Profit = Total Revenue − Total Costs
Profit can be expressed as gross profit (revenue minus cost of sales) or net profit (after all overheads and interest).
利润可分为毛利（收入减销售成本）和净利（扣除所有间接费用和利息后）。
2. Break-even Analysis | 盈亏平衡分析
Break-even analysis identifies the level of sales at which total revenue equals total costs, resulting in neither profit nor loss. It is a vital planning tool.
盈亏平衡分析确定总收入等于总成本时的销售水平，此时既不盈利也不亏损。它是重要的规划工具。
Break-even point (units) = Fixed Costs ÷ (Selling Price per unit – Variable Cost per unit)
The denominator is called 'unit contribution'. It shows how much each unit sold contributes towards covering fixed costs.
分母称为“单位贡献”。它表示每销售一单位产品能用来补偿固定成本的金额。
Break-even point (revenue) = Break-even units × Selling Price per unit
= Fixed Costs ÷ Contribution margin ratio. The margin ratio is Unit Contribution ÷ Price.
另一种方法：盈亏平衡收入 = 固定成本 ÷ 贡献毛利率。贡献毛利率 = 单位贡献 ÷ 单价。
Margin of safety (units) = Actual or planned sales – Break-even sales
Margin of safety shows how much sales can fall before the business starts making a loss. A larger margin reduces risk.
安全边际显示销售量在亏损发生前可以下降的幅度。安全边际越大，风险越低。
3. Profitability Ratios | 盈利能力比率
Profitability ratios measure how effectively a business turns sales revenue into profit and how well it uses its capital.
盈利能力比率衡量企业将销售收入转化为利润的效率，以及运用资本的效益。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100%
A higher ratio indicates better control of direct costs and/or stronger pricing power. It is useful for comparing with competitors.
该比率越高，表明对直接成本的控制越好和/或定价能力越强。适合用于与竞争对手比较。
Net Profit Margin = (Net Profit before interest and tax ÷ Sales Revenue) × 100%
This ratio reflects overall expense management. A falling net margin may signal rising overheads or falling efficiency.
该比率反映总体费用管理水平。净利率下降可能表明间接费用上升或效率降低。
on Capital Employed (ROCE) = (Net Profit before interest and tax ÷ Capital Employed) × 100%
Capital employed is often defined as total assets minus current liabilities, or as non-current liabilities plus equity. ROCE shows the return generated on all long-term funds.
资本运用通常定义为总资产减流动负债，或非流动负债加所有者权益。ROCE 显示所有长期资金的回报率。
4. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet short-term obligations as they fall due. They are crucial for survival.
流动性比率评估企业按时偿还短期债务的能力。这对企业生存至关重要。
Current Ratio = Current Assets ÷ Current Liabilities
A ratio between 1.5 and 2 is often considered safe, but this depends on the industry. Very high ratio may indicate idle assets.
通常认为1.5至2之间的比率较为安全，但需视行业而定。过高的比率可能意味着资产闲置。
Acid Test Ratio = (Current Assets – Inventories) ÷ Current Liabilities
This strips out inventory, which is less liquid. A ratio of 1:1 is typically desirable, showing the firm can meet immediate debts.
该比率剔除了流动性较差的存货。1:1的比率通常较为理想，表明企业能立即偿付债务。
5. Efficiency Ratios | 效率比率
Efficiency ratios measure how well a business uses its assets and manages its working capital.
效率比率衡量企业使用资产和管理营运资本的效率。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
ory + Closing inventory) ÷ 2. A higher turnover means goods are being sold quickly, reducing storage costs and obsolescence risk.
平均存货 = （期初存货 + 期末存货）÷ 2。周转次数越高，说明商品售出越快，降低仓储成本和过时风险。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
This reveals how long, on average, customers take to pay. A shorter period improves cash flow.
这揭示客户平均付款所需天数。天数越短，现金流越好。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
This shows how long the business takes to pay suppliers. A longer period can help cash flow but may damage supplier relationships.
这显示企业支付供应商的平均天数。期限较长可以改善现金流，但可能损害与供应商的关系。
6. Working Capital and Cash Flow | 营运资本与现金流
Working capital is the day-to-day finance needed for running the business. Cash flow is the movement of cash in and out.
营运资本是企业日常经营所需的资金。现金流是现金的流入和流出。
Working Capital = Current Assets − Current Liabilities
A positive working capital is necessary to avoid liquidity crises. It can be managed through stock, debtor and creditor control.
保持正的营运资本对于避免流动性危机十分必要。可通过控制存货、应收账款和应付账款来管理。
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
A cash flow forecast uses projected figures to estimate the closing bank balance: Closing Balance = Opening Balance + Net Cash Flow. It helps identify periods of potential overdraft.
现金流量预测使用预计数字估算期末银行存款余额：期末余额 = 期初余额 + 净现金流量。这有助于识别可能发生透支的期间。
7. Productivity Formulas | 生产率公式
Productivity measures the efficiency of input use. Higher productivity reduces unit costs and can improve competitiveness.
生产率衡量投入的使用效率。生产率越高，单位成本越低，并可能提高竞争力。
Labour Productivity = Total Output per period ÷ Number of Employees
Businesses can raise labour productivity through training, better equipment or motivation methods. Rise in productivity may lead to higher wages without inflationary pressure.
企业可通过培训、更新设备或激励手段提高劳动生产率。生产率提高可在不引发通胀压力的情况下带来更高工资。
Unit Cost = Total Costs ÷ Total Output
Falling unit costs allow a firm to lower prices or increase profit margins. Economies of scale contribute to lower unit costs.
单位成本下降使企业可以降低价格或提升利润率。规模经济有助于降低单位成本。
8. Marketing Metrics | 营销指标
Marketing metrics help a business understand its competitive position and the effectiveness of its strategies.
营销指标帮助企业了解自身的竞争地位和策略的有效性。
Market Share (%) = (Firm's Sales ÷ Total Market Sales) × 100%
Market share is a key indicator of market power. An increase suggests successful branding or pricing strategies.
市场份额是衡量市场力量的关键指标。份额上升表明品牌或定价策略成功。
Market Growth (%) = (Change in Market Size ÷ Original Market Size) × 100%
A growing market attracts new entrants; a declining market may require consolidation or innovation. Sales growth formula uses the same logic for the firm's own sales.
增长的市场吸引新进入者；萎缩的市场可能需要整合或创新。企业销售额增长率也采用相同逻辑计算。
9. External Influences: Interest, Exchange Rates and Taxation | 外部影响：利率、汇率与税收
External economic variables affect costs, demand and profitability. Decision makers must understand these formulas to predict impacts.
外部经济变量影响成本、需求和利润。决策者必须理解这些公式，以预测其影响。
Interest Cost (simple) = Loan Principal × Annual Interest Rate × Time (years)
Higher interest rates increase borrowing costs and can reduce investment. Lower rates stimulate demand but may reduce saving.
利率上升增加借款成本，可能减少投资。利率下降刺激需求，但可能减少储蓄。
t price: Price in home currency = Price in foreign currency × Exchange Rate (home/foreign)
When the home currency depreciates, imports become more expensive and exports become cheaper abroad. The reverse is true for appreciation.
本币贬值时，进口变贵而出口在国际市场变便宜。升值时则相反。
Tax Payable = Taxable Profit × Tax Rate
Higher corporation tax reduces retained profit available for reinvestment or dividends. Businesses may adjust prices or cut costs to maintain after-tax profit.
企业所得税提高会减少可用于再投资或分红的留存利润。企业可能调整价格或削减成本以维持税后利润。
10. Interpreting Break-even Charts and Decision-making | 盈亏平衡图解读与决策
A break-even chart visually presents the relationships among costs, revenue and volume. Key intersection points support pricing, output and investment decisions.
盈亏平衡图直观呈现成本、收入和数量之间的关系。图中关键交点辅助定价、产量和投资决策。
The point where the total revenue line crosses the total cost line is the break-even point. To the right of this point the business earns profit; to the left it incurs a loss. The distance between the revenue and total cost lines at any output level indicates the profit or loss.
总收入线与总成本线的交叉点就是盈亏平衡点。在该点右侧，企业盈利；左侧则亏损。任意产量水平上收入线与总成本线的垂直距离表示利润或损失。
A rise in fixed costs shifts the total cost line upward, pushing the break-even point to the right. A higher selling price tilts the revenue line steeper, reducing the break-even volume. Managers use this sensitivity to assess 'what-if' scenarios, such as changes in rent, wages or competitor pricing.
固定成本上升使总成本线上移，推动盈亏平衡点右移。更高的售价使收入线更陡，降低盈亏平衡销量。管理者利用这种敏感性评估诸如租金、工资或竞争对手定价变化等“假设”情景。
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