📚 IB CCEA Business: Formula Summary Handbook | IB CCEA 商务：公式汇总手册
This handbook brings together every essential formula you need for IB Business Management and CCEA Business Studies. Mastery of these quantitative tools empowers you to analyse financial health, forecast outcomes, and justify strategic decisions with confidence. The following sections present each formula with clear definitions, practical examples, and bilingual explanations.
本手册汇集了 IB 商务管理和 CCEA 商务研究所需的每一个关键公式。掌握这些定量工具，您将能够自信地分析财务健康状况、预测结果并证明战略决策的合理性。以下各节提供了每个公式的清晰定义、实用示例和中英双语解释。
1. Break-even Analysis | 盈亏平衡分析
Break-even analysis identifies the level of output at which total revenue equals total costs, so the business makes neither profit nor loss. The break-even quantity (BEQ) is calculated by dividing total fixed costs by the contribution per unit.
BEQ = FC ÷ (P − V)
盈亏平衡分析确定了总收入等于总成本的产出水平，此时企业既不盈利也不亏损。盈亏平衡产量（BEQ）等于总固定成本除以每单位贡献毛利。
Contribution per unit is the amount each unit sold contributes towards covering fixed costs and generating profit. It is found by subtracting the variable cost per unit from the selling price.
Contribution per unit = P − V
每单位贡献毛利是每售出一单位产品对覆盖固定成本和创造利润的贡献额。它等于售价减去每单位可变成本。
Total contribution then equals the unit contribution multiplied by the number of units sold. This is useful for short-term decision making.
Total Contribution = (P − V) × Q
总贡献毛利等于每单位贡献乘以销售数量，这对于短期决策很有用。
The margin of safety shows how far actual sales can fall before the business incurs a loss. It is the difference between actual output and break-even output.
Margin of Safety = Actual Output − Break-even Output
安全边际显示了实际销售量在达到亏损之前可以下降的幅度，即实际产出与盈亏平衡产出之差。
- FC = Total Fixed Costs / 总固定成本
- P = Selling Price per unit / 每单位售价
- V = Variable Cost per unit / 每单位可变成本
- Q = Quantity sold / 销售数量
2. Profit, Margins and ROCE | 利润、利润率与已用资本回报率
Gross profit is the surplus remaining after deducting the cost of goods sold (COGS) from sales revenue. It measures the core trading profitability.
Gross Profit = Sales Revenue − Cost of Sales
毛利润是从销售收入中扣除销售成本（COGS）后的盈余，衡量核心交易的盈利能力。
Net profit is the final profit after all operating expenses, interest and tax have been subtracted. It reflects the overall efficiency of the business.
Net Profit = Gross Profit − Expenses
净利润是扣除所有运营费用、利息和税金后的最终利润，反映了企业的整体效率。
Mark-up expresses gross profit as a percentage of the cost of sales. It helps set selling prices.
Mark-up = (Gross Profit ÷ Cost of Sales) × 100%
加成率将毛利润表示为销售成本的百分比，有助于制定售价。
Gross profit margin shows the percentage of sales revenue turned into gross profit. A higher margin indicates better control of production costs.
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100%
毛利率表示转化为毛利润的销售收入百分比，毛利率越高说明生产成本控制越好。
Net profit margin reveals what percentage of revenue remains as net profit. It is a key profitability gauge.
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100%
净利润率揭示了收入中以净利润保留下来的百分比，是一个关键的盈利指标。
Return on Capital Employed (ROCE) assesses how efficiently a business uses its long-term capital to generate operating profit.
ROCE = (Operating Profit ÷ Capital Employed) × 100%
已用资本回报率（ROCE）评估企业使用长期资本产生运营利润的效率。
3. Liquidity and Efficiency Ratios | 流动性与效率比率
The current ratio measures a firm’s ability to meet short-term obligations. A value between 1.5 and 2 is often considered healthy.
Current Ratio = Current Assets ÷ Current Liabilities
流动比率衡量企业偿还短期债务的能力，1.5至2之间的数值通常被认为是健康的。
The acid test ratio (quick ratio) is a stricter measure of liquidity, as it excludes stock which may not be quickly converted into cash.
Acid Test Ratio = (Current Assets − Stock) ÷ Current Liabilities
酸性测试比率（速动比率）是更严格的流动性指标，因为它排除了可能无法快速变现的存货。
Rate of inventory turnover indicates how many times stock is sold and replaced over a period. A higher figure suggests efficient stock management.
Inventory Turnover = Cost of Sales ÷ Average Stock
存货周转率显示在一个时期内库存售出并更新的次数，数值越高表明库存管理越高效。
Debtor days (days sales outstanding) measure the average credit period taken by customers.
Debtor Days = (Trade Receivables ÷ Credit Sales) × 365
应收账款天数（DSO）衡量客户的平均信用期。
Creditor days measure the average time a business takes to pay its suppliers.
Creditor Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款天数衡量企业支付供应商款项的平均时间。
4. Investment Appraisal | 投资评估
Payback period is the time needed for an investment to recoup its initial cost from net cash flows. It is calculated cumulatively; do not use a simple formula — prefer a cash flow table.
投资回收期是指从净现金流中收回初始投资成本所需的时间。它通过累积计算，通常使用现金流量表而非简单公式。
Average Rate of Return (ARR) evaluates an investment’s yearly profitability as a percentage of the initial outlay. The IB formula uses initial investment, not average investment.
ARR = (Average Annual Profit ÷ Initial Investment) × 100%
平均回报率（ARR）将投资的年度盈利能力表示为初始支出的百分比。IB 课程使用初始投资而非平均投资。
Net Present Value (NPV) discounts all future cash flows to today’s value and subtracts the initial cost. A positive NPV means the project should be accepted.
NPV = Σ (NCFₜ ÷ (1 + r)ᵗ) − I₀
净现值（NPV）将所有未来现金流折现为当前价值并减去初始成本。NPV 为正表示项目应被接受。
- NCFₜ = Net cash flow in year t / 第 t 年净现金流
- r = discount rate (cost of capital) / 折现率（资本成本）
- I₀ = initial investment / 初始投资
5. Elasticity | 弹性
Price elasticity of demand (PED) shows how responsive quantity demanded is to a change in price. It is usually negative but expressed as an absolute value.
PED = %ΔQd ÷ %ΔP
需求价格弹性（PED）显示需求量对价格变化的反应程度，通常为负值但以绝对值表示。
Income elasticity of demand (YED) measures the sensitivity of demand to changes in consumer income. Normal goods have positive YED, while inferior goods have negative YED.
YED = %ΔQd ÷ %ΔY
需求收入弹性（YED）衡量需求对消费者收入变化的敏感度。正常品具有正收入弹性，低档品则为负。
Cross elasticity of demand (XED) indicates how demand for one good reacts to a price change in another good. Complements have negative XED, substitutes positive.
XED = %ΔQd(A) ÷ %ΔP(B)
需求交叉弹性（XED）显示一种商品的需求如何随另一种商品价格变化而反应。互补品为负，替代品为正。
Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in price.
PES = %ΔQs ÷ %ΔP
供给价格弹性（PES）衡量供给量对价格变化的反应程度。
6. Productivity and Capacity Utilization | 生产力与产能利用率
Labour productivity measures the output produced per worker. It is a vital indicator of workforce efficiency.
Labour Productivity = Total Output ÷ Number of Employees
劳动生产率衡量每个工人生产的产出，是衡量劳动力效率的关键指标。
Capital productivity assesses how well a firm uses its fixed assets to generate output.
Capital Productivity = Output ÷ Capital Employed
Published by TutorHao | IB 商务 Revision Series | aleveler.com 更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply