📚 IB OCR Business Formula Handbook | IB OCR 商务公式汇总手册
This handbook brings together the essential quantitative formulas required for IB Business Management and OCR Business, from simple revenue calculations to investment appraisal and variance analysis. Having these formulas at your fingertips will help you tackle data‑response questions, construct sound business arguments, and perform quick checks under exam conditions.
本手册汇集了 IB 商务管理和 OCR 商务课程所需的核心定量公式，从简单的收入计算到投资评估和差异分析。将这些公式熟记于心能帮助你从容应对数据分析题、构建扎实的商业论证，并在考试中快速核查答案。
1. Revenue, Costs and Profit | 收入、成本与利润
Total Revenue (TR) is the income a business receives from selling its goods or services. It does not account for any costs yet.
Total Revenue = Price × Quantity Sold
总收入 (TR) 是企业通过销售商品或服务获得的收入，尚未扣除任何成本。公式为：总收入 = 价格 × 销售量。
Total Costs (TC) are the sum of all fixed and variable costs incurred in producing a given level of output.
Total Costs = Fixed Costs + Variable Costs
总成本 (TC) 是生产一定产量水平所发生的全部固定成本与变动成本之和。公式为：总成本 = 固定成本 + 变动成本。
Variable costs depend directly on output, so Total Variable Costs (TVC) = Variable Cost per Unit × Quantity Produced.
变动成本直接取决于产量，因此 总变动成本 (TVC) = 单位变动成本 × 产量。
Profit/Loss reveals whether revenue covers all costs. A negative result indicates a loss.
Profit = Total Revenue − Total Costs
利润/亏损 反映收入是否能够覆盖全部成本。结果为负则表示亏损。公式为：利润 = 总收入 − 总成本。
2. Contribution and Break-even Analysis | 贡献与盈亏平衡分析
Contribution per Unit shows how much each sale contributes towards covering fixed costs and, once they are covered, towards profit.
Contribution per Unit = Selling Price − Variable Cost per Unit
单位贡献 表示每销售一单位产品对覆盖固定成本所带来的贡献，在固定成本被覆盖后则贡献于利润。公式为：单位贡献 = 售价 − 单位变动成本。
Total Contribution can be calculated either as contribution per unit multiplied by output, or as total revenue minus total variable costs.
Total Contribution = Contribution per Unit × Output
总贡献 既可以用单位贡献乘以产量计算，也可以用总收入减去总变动成本求得。公式：总贡献 = 单位贡献 × 产量。
The Break-even Point (BEP) in units tells the business how many units it must sell to cover all costs exactly.
Break-even Output = Fixed Costs ÷ Contribution per Unit
以单位计量的盈亏平衡点 (BEP) 告诉企业必须销售多少单位才能恰好覆盖全部成本。公式：盈亏平衡产出 = 固定成本 ÷ 单位贡献。
The Break-even Point in revenue is useful for multi‑product businesses.
Break-even Revenue = Break-even Output × Selling Price
以金额计量的盈亏平衡点 对多产品企业尤其管用。公式：盈亏平衡收入 = 盈亏平衡产出 × 售价。
Margin of Safety measures the cushion between actual sales and break‑even sales.
Margin of Safety (units) = Actual Output − Break-even Output
安全边际 衡量实际销售与盈亏平衡销售之间的缓冲量。公式：安全边际（单位）= 实际产出 − 盈亏平衡产出。
3. Profitability Ratios | 盈利能力比率
Gross Profit Margin (GPM) assesses how efficiently a business converts raw materials into income, before overheads.
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
毛利率 (GPM) 衡量企业在扣除间接费用之前将原材料转化为收入的效率。公式：毛利率 = (毛利 ÷ 收入) × 100。
Operating Profit Margin (OPM) includes indirect costs and gives a clearer picture of trading performance.
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100
营业利润率 (OPM) 将间接费用也纳入考量，更清晰地反映经营绩效。公式：营业利润率 = (营业利润 ÷ 收入) × 100。
Operating profit is revenue minus cost of sales and operating expenses, and may also be called profit from operations.
营业利润等于收入减去销售成本和营业费用，也称作经营利润。
Net Profit Margin (NPM) is the final measure after all costs, interest and tax.
Net Profit Margin = (Net Profit ÷ Revenue) × 100
净利率 (NPM) 是扣除所有成本、利息和税费后的最终指标。公式：净利率 = (净利润 ÷ 收入) × 100。
Return on Capital Employed (ROCE) shows the return generated from all long‑term funds employed in the business.
ROCE = (Operating Profit ÷ Capital Employed) × 100
已用资本回报率 (ROCE) 反映企业从所有长期投入资金中获得的回报。公式：ROCE = (营业利润 ÷ 已用资本) × 100。
Capital employed can be calculated as total equity + non‑current liabilities, or total assets − current liabilities.
已用资本可按总权益 + 非流动负债计算，也可按总资产 − 流动负债计算。
4. Liquidity Ratios | 流动性比率
Current Ratio indicates whether the business has enough short‑term assets to cover its short‑term debts.
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 反映企业的短期资产是否足以偿还短期债务。公式：流动比率 = 流动资产 ÷ 流动负债。
Acid Test Ratio (Quick Ratio) removes inventory, the least liquid current asset, to give a stricter liquidity test.
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
酸性测试比率（速动比率） 剔除了流动性最差的存货，提供了更为严格的流动性检验。公式：酸性测试比率 = (流动资产 − 存货) ÷ 流动负债。
Relevant in both IB and OCR, liquidity analysis is often paired with credit management and cash‑flow forecasting.
在 IB 与 OCR 课程中，流动性分析经常与信用管理和现金流预测结合考察。
5. Efficiency Ratios | 效率比率
Inventory Turnover (Stock Turn) measures how many times inventory is sold and replaced over a period.
Inventory Turnover = Cost of Sales ÷ Average Inventory
存货周转率 衡量一段时期内存货售出与补进的次数。公式：存货周转率 = 销售成本 ÷ 平均存货。
The average inventory period converts the ratio into days.
Average Inventory Period = (Average Inventory ÷ Cost of Sales) × 365
平均存货期 将周转率转化为天数。公式：平均存货期 = (平均存货 ÷ 销售成本) × 365。
Trade Receivables Days (Debtor Days) indicates the average time customers take to pay.
Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
应收账款周转天数 显示客户平均付款时间。公式：应收账款周转天数 = (应收账款 ÷ 赊销收入) × 365。
Trade Payables Days (Creditor Days) shows how long the business takes to pay its suppliers.
Payables Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 显示企业支付供应商货款的平均用时。公式：应付账款周转天数 = (应付账款 ÷ 赊购额) × 365。
Asset Turnover evaluates how effectively a business uses its assets to generate revenue.
Asset Turnover = Revenue ÷ Net Assets
资产周转率 评价企业利用资产创造收入的有效性。公式：资产周转率 = 收入 ÷ 净资产。
6. Gearing and Investor Ratios | 杠杆与投资者比率
Gearing Ratio expresses the proportion of a business’s funding that comes from long‑term debt. Higher gearing implies greater financial risk.
Gearing = (Non‑current Liabilities ÷ Capital Employed) × 100
杠杆比率（负债比率） 反映企业资金来源中来自长期债务的比例。比率越高，财务风险越大。公式：杠杆比率 = (非流动负债 ÷ 已用资本) × 100。
Some syllabi also use Gearing = Non‑current Liabilities ÷ (Total Equity + Non‑current Liabilities) × 100, which yields the same result when capital employed is defined appropriately.
部分教学大纲也使用 杠杆比率 = 非流动负债 ÷ (总权益 + 非流动负债) × 100，在合理定义已用资本的前提下结果相同。
Dividend Yield tells shareholders the cash return they receive relative to the share price.
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100
股息率 告诉股东相对于股价所获得的现金回报。公式：股息率 = (每股股息 ÷ 每股市价) × 100。
Earnings per Share (EPS) indicates how much profit is attributable to each ordinary share.
EPS = (Net Profit − Preference Dividends) ÷ Number of Ordinary Shares
每股收益 (EPS) 表示每一普通股所对应的利润。公式：EPS = (净利润 − 优先股股息) ÷ 普通股股数。
Price/Earnings (P/E) Ratio is a market‑based measure reflecting confidence in future earnings.
P/E Ratio = Market Price per Share ÷ Earnings per Share
市盈率 (P/E) 是一个基于市场的衡量指标，反映投资者对未来盈利的信心。公式：市盈率 = 每股市价 ÷ 每股收益。
7. Investment Appraisal Methods | 投资评估方法
Payback Period is the time taken for an investment to recover its initial cost from net cash inflows. When annual cash flows are constant:
Payback Period = Initial Investment ÷ Annual Net Cash Flow
回收期 是指用净现金流入收回初始投资额所需的时间。当年现金流均等时：回收期 = 初始投资额 ÷ 年净现金流量。
If cash flows vary, payback is found by accumulating net cash flows year by year until the initial outlay is recovered.
如果每年现金流量不同，则需逐年累计净现金流量，直至初始投资被完全收回。
Average Rate of Return (ARR) expresses average annual profit as a percentage of the initial investment. It uses profit, not cash flow.
ARR = (Average Annual Profit ÷ Initial Investment) × 100
平均收益率 (ARR) 将平均年度利润表示为初始投资额的百分比。注意这里使用的是利润而非现金流量。公式：ARR = (平均年度利润 ÷ 初始投资额) × 100。
Average annual profit is typically (total profit from the project ÷ number of years).
平均年度利润通常为（项目总利润 ÷ 年数）。
Net Present Value (NPV) discounts all future cash flows to their present value and subtracts the initial investment. It takes the time value of money into account.
NPV = Σ (Net Cash Flowₜ × Discount Factorₜ) − Initial Investment
净现值 (NPV) 将未来所有现金流量折现到当前价值，再减去初始投资额，考虑了货币的时间价值。公式：NPV = Σ (第 t 年净现金流量 × 第 t 年折现因子) − 初始投资。
The discount factor can be found using the formula 1 ÷ (1 + r)ᵗ, where r is the cost of capital and t is the year number.
折现因子可通过公式 1 ÷ (1 + r)ᵗ 计算，其中 r 为资本成本，t 为年份序号。
8. Budgeting and Variance Analysis | 预算与差异分析
Variance is the difference between budgeted and actual figures. A favourable variance improves profit; an adverse variance worsens it.
Variance = Actual Result − Budgeted Figure
差异 是指预算数与实际数之间的差额。有利差异提高利润，不利差异降低利润。公式：差异 = 实际结果 − 预算数字。
Sales Volume Variance focuses purely on the effect of selling a different quantity than planned.
Sales Volume Variance = (Actual Quantity − Budgeted Quantity) × Standard Profit per Unit
销售量差异 仅关注因实际销售量与预算不同所产生的影响。公式：销售量差异 = (实际销量 − 预算销量) × 单位标准利润。
Sales Price Variance isolates the impact of charging a different price.
Sales Price Variance = (Actual Price − Budgeted Price) × Actual Quantity Sold
销售价格差异 单独反映实际售价与预算售价不同所带来的影响。公式：销售价格差异 = (实际售价 − 预算售价) × 实际销售量。
Both IB and OCR expect students to interpret variances and suggest possible causes rather than just calculate them.
IB 和 OCR 都要求学生解读差异并提出可能的原因，而不仅仅是计算差异。
9. Productivity, Capacity and Inventory | 生产力、产能与库存
Labour Productivity compares output to the number of employees or hours worked.
Labour Productivity = Total Output ÷ Number of Employees (or Hours Worked)
劳动生产率 将产出与员工人数或工作小时数进行比较。公式：劳动生产率 = 总产出 ÷ 员工人数（或工作小时数）。
Capacity Utilisation shows how much of the maximum possible output is actually being used.
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100
产能利用率 显示实际产出占最大可能产出的比例。公式：产能利用率 = (实际产出 ÷ 最大可能产出) × 100。
Unit Cost (Average Cost) helps a business price products and assess cost‑cutting initiatives.
Unit Cost = Total Costs ÷ Output
单位成本（平均成本） 有助于企业为产品定价并评估降本措施。公式：单位成本 = 总成本 ÷ 产出。
Economic Order Quantity (EOQ) minimises the combined costs of holding and ordering inventory, although it is more common in IB HL and some OCR quantitative tasks.
EOQ = √[(2 × Annual Demand × Ordering Cost) ÷ Holding Cost per Unit]
经济订货批量 (EOQ) 最小化了持有存货与订货的总成本，常见于 IB HL 以及 OCR 部分定量任务。公式：EOQ = √[(2 × 年需求量 × 每次订货成本) ÷ 单位持有成本]。
10. Decision‑making Tools | 决策工具
Decision Trees calculate expected monetary values (EMV) to help choose between options under uncertainty.
Expected Value = Probability × Financial Outcome
决策树 通过计算预期货币价值 (EMV) 帮助在不确定条件下选择方案。公式：预期价值 = 概率 × 财务结果。
The Net Expected Value of a decision is the sum of expected values at a chance node minus the cost of that decision.
Net Expected Value = Σ (Probabilityₙ × Payoffₙ) − Decision Cost
决策的净预期价值 等于某个机会节点上各预期价值之和减去该决策的成本。公式：净预期价值 = Σ (概率ₙ × 收益ₙ) − 决策成本。
Price Elasticity of Demand (PED) is vital for pricing decisions, though examined more in IB than OCR standalone, yet still relevant.
PED = % Change in Quantity Demanded ÷ % Change in Price
需求价格弹性 (PED) 对定价决策至关重要，虽在 IB 中单独考查更多，但对 OCR 同样具有关联性。公式：PED = 需求量变化百分比 ÷ 价格变化百分比。
When PED is greater than 1, demand is elastic; less than 1, it is inelastic. Elasticity informs total revenue predictions.
当 PED 大于 1 时需求富有弹性；小于 1 时缺乏弹性。弹性信息有助于预测总收入的变化。
11. Cash Flow and Working Capital | 现金流与营运资金
Net Cash Flow is the difference between cash inflows and outflows in a period, not to be confused with profit.
Net Cash Flow = Cash Inflows − Cash Outflows
净现金流 是某一期间现金流入与流出的差额，不要与利润混淆。公式：净现金流 = 现金流入 − 现金流出。
Closing Cash Balance is carried forward to the start of the next period.
Closing Balance = Opening Balance + Net Cash Flow
期末现金余额 结转至下一期间的期初。公式：期末余额 = 期初余额 + 净现金流。
Working Capital (Net Current Assets) measures the short‑term health of a business.
Working Capital = Current Assets − Current Liabilities
营运资金（净流动资产） 衡量企业的短期健康程度。公式：营运资金 = 流动资产 − 流动负债。
12. Market Share, Growth and Added Value | 市场份额、增长与附加值
Market Share tracks a firm’s sales relative to the whole market. It can be based on volume or value.
Market Share = (Firm’s Sales ÷ Total Market Sales) × 100
市场份额 跟踪企业销售相对于整体市场的占比，可按销量或价值计算。公式：市场份额 = (企业销售额 ÷ 市场总销售额) × 100。
Market Growth indicates how the overall market size is changing, useful for product portfolio analysis.
Market Growth = (Change in Market Size ÷ Original Market Size) × 100
市场增长率 显示整体市场规模的变动情况，对产品组合分析很有用。公式：市场增长率 = (市场规模变动量 ÷ 原市场规模) × 100。
Added Value is the difference between the selling price and the cost of bought‑in materials and components. It is a simple but strategic concept.
Added Value = Sales Revenue − Cost of Bought‑in Materials
附加值 是售价与外购材料及零部件成本之间的差额，看似简单却具有战略意义。公式：附加值 = 销售收入 − 外购材料成本。
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