📚 AS OCR Business: Formula & Theorem Quick Reference Guide | AS OCR 商务：公式定理速查手册
This quick reference guide brings together the key formulas, ratios and decision-making theorems you need to master for the AS OCR Business examination. All formulas are stated using standard business notation with clear definitions. Each entry is paired with a concise Chinese translation to support bilingual learning and quick revision.
本速查手册汇总了你必须掌握的 AS OCR 商务关键公式、比率和决策定理。所有公式均采用标准商务符号并附有清晰定义。每个条目都配有简洁的中文翻译，助你双语学习与快速复习。
1. Break-even Analysis | 盈亏平衡分析
Break-even analysis helps a business determine the level of output or sales at which total revenue equals total costs, so the firm makes zero profit or loss. The fundamental relationships are: Total costs = Fixed costs + Variable costs; Total revenue = Selling price per unit × Quantity sold.
盈亏平衡分析帮助企业确定总收入等于总成本的产出或销售水平，此时利润为零。基本关系为：总成本 = 固定成本 + 变动成本；总收入 = 单位售价 × 销量。
The break-even point in units is calculated by dividing total fixed costs by the contribution per unit, where contribution per unit is selling price minus variable cost per unit.
以数量表示的盈亏平衡点等于总固定成本除以单位贡献，其中单位贡献等于售价减单位变动成本。
Break-even output (units) = Fixed Costs ÷ (Selling Price – Variable Cost per unit)
BEQ = FC ÷ (P – VC)
To express break-even in revenue terms, multiply break-even output by selling price per unit, or divide fixed costs by the contribution margin ratio.
要将盈亏平衡表示为销售额，可将盈亏平衡产量乘以单位售价，或使用固定成本除以贡献毛利比率。
Break-even revenue = Break-even output × P
Margin of safety measures how far actual output exceeds the break-even output, providing a buffer against unexpected downturns. It can be expressed in units or as a percentage.
安全边际衡量实际产出超出盈亏平衡产出的幅度，为意外下滑提供缓冲。可用数量或百分比表示。
Margin of safety (units) = Actual output – Break-even output
Margin of safety (%) = (Margin of safety ÷ Actual output) × 100
Theorems for break-even charts assume a linear total revenue line starting from the origin, a total cost line starting from the level of fixed costs, and that the break-even point is their intersection.
盈亏平衡图的基本定理假设总收入线从原点出发呈线性，总成本线从固定成本水平出发，盈亏平衡点为两线交点。
2. Contribution and Contribution Margin Ratio | 贡献与贡献毛利比率
Contribution is the amount left from sales revenue after deducting variable costs; it contributes towards covering fixed costs and generating profit. It is a cornerstone of marginal costing.
贡献是指销售收入扣除变动成本后剩余的部分，用于弥补固定成本并创造利润。它是边际成本法的基石。
Contribution per unit = Selling Price – Variable Cost per unit
Total contribution is the aggregate contribution available to cover fixed costs and produce profit.
总贡献是所有可用于弥补固定成本和创造利润的贡献之和。
Total Contribution = (P – VC) × Quantity sold
The contribution margin ratio (or contribution-sales ratio) expresses contribution as a percentage of sales revenue. It is vital for multi-product break-even calculations.
贡献毛利比率（或贡献销售比）将贡献表示为销售收入的百分比，它对多产品盈亏平衡计算至关重要。
Contribution Margin Ratio = (Contribution per unit ÷ Selling Price) × 100
A higher contribution margin ratio implies more of each sales pound is available to cover fixed costs. It is used to work out break-even revenue quickly.
贡献毛利比率越高，每英镑销售收入中可用于弥补固定成本的部分就越多。它可快速计算盈亏平衡销售额。
Break-even revenue = Fixed Costs ÷ Contribution Margin Ratio
3. Profit and Profitability Ratios | 利润与盈利能力比率
Profitability ratios measure how effectively a business generates profit from its sales and capital employed. Gross profit margin focuses on production efficiency and pricing strategy.
盈利能力比率衡量企业从销售收入和资本占用中创造利润的效率。毛利率侧重于生产效率和定价策略。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100
Gross profit is sales revenue minus cost of sales. A falling gross margin may indicate rising material costs or heavy discounting.
毛利是销售收入减去销售成本。毛利率下滑可能表明原材料上涨或大幅打折。
Net profit margin accounts for all business expenses, including overheads and interest, showing overall cost control.
净利率囊括所有业务支出，包括间接费用和利息，反映整体成本控制力。
Net Profit Margin = (Net Profit Before Tax ÷ Sales Revenue) × 100
Return on Capital Employed (ROCE) is a central ratio linking profit to the long-term capital invested in the business. It measures the return generated from every pound tied up in the firm.
运用资本回报率（ROCE）是联系利润与企业长期投入资本的核心比率，衡量每英镑占用资本所创造的回报。
ROCE = (Operating Profit ÷ Capital Employed) × 100
Capital employed is typically total equity plus non-current liabilities, or total assets less current liabilities. A strong ROCE must exceed the cost of borrowing.
运用资本通常等于总权益加上非流动负债，或总资产减流动负债。满意的 ROCE 必须超过借贷成本。
4. Liquidity and Efficiency Ratios | 流动性与效率比率
Liquidity ratios assess a firm’s ability to meet short-term obligations. The current ratio compares all current assets to current liabilities.
流动性比率衡量企业偿还短期债务的能力。流动比率将所有流动资产与流动负债进行对比。
Current Ratio = Current Assets ÷ Current Liabilities
A ratio above 1.5 is often regarded as safe, but norms vary by industry. Too high a ratio may suggest inefficient use of cash or inventory build-up.
比率超过 1.5 通常被视为安全，但行业标准各异。比率过高可能暗示现金或存货低效运用。
The acid test ratio (quick ratio) is a stricter measure, excluding inventory which is less readily convertible to cash.
酸性测试比率（速动比率）更为严格，排除了不易迅速变现的存货。
Acid Test Ratio = (Current Assets – Inventory) ÷ Current Liabilities
Efficiency ratios reveal how well a business manages its inventory and trade receivables. Inventory turnover shows the speed of stock sales.
效率比率揭示企业管理存货和应收账款的成效。存货周转率表示存货销售速度。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
Average inventory is (Opening inventory + Closing inventory) ÷ 2. A low turnover may indicate obsolete stock, while a high turnover suggests strong demand.
平均存货 =（期初存货 + 期末存货）÷ 2。周转率低可能意味过时存货，高周转则反映强劲需求。
Trade receivables days (debtor days) measures the average time taken by credit customers to settle invoices.
应收账款周转天数衡量赊销客户平均支付发票所需时间。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
Trade payables days (creditor days) shows how long the business takes to pay its suppliers, a key cash flow tool.
应付账款周转天数反映企业支付供应商款项的平均时间，是关键的现金流工具。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
5. Operational Performance Metrics | 运营绩效指标
Labour productivity measures output per employee and is a sign of workforce efficiency and training effectiveness.
劳动生产率衡量每名员工的产出，是劳动力效率与培训成效的重要信号。
Labour Productivity = Total Output ÷ Number of Employees
Capacity utilisation shows the extent to which a firm’s productive capacity is being used, directly affecting unit fixed costs.
产能利用率反映企业生产能力的利用程度，直接影响单位固定成本。
Capacity Utilisation (%) = (Actual Output ÷ Maximum Possible Output) × 100
A high utilisation rate spreads fixed costs thinly but risks overworking assets; low utilisation indicates idle resources and higher unit costs.
高利用率可摊薄固定成本但存在过度使用的风险；低利用率暗示资源闲置和单位成本升高。
Absenteeism rate tracks the percentage of scheduled work time lost through employee absence and can signal morale or health issues.
缺勤率追踪因员工缺勤而损失的计划工时占比，能反映士气或健康问题。
Absenteeism (%) = (Total Absence Days ÷ Total Worked Days) × 100
Labour turnover rate indicates the proportion of employees who leave over a period, often linked to recruitment and retention costs.
员工流失率指在一定时期内离职员工的比例，常与招聘和留任成本相关。
Labour Turnover (%) = (Number of Staff Leaving ÷ Average Number of Staff) × 100
6. Market and Sales Metrics | 市场与销售指标
Market growth measures the percentage increase in the total size of a market over a period. It helps firms spot opportunities and plan marketing budgets.
市场增长率衡量市场总规模在一定时期内的百分比增幅，帮助企业发现机会并规划营销预算。
Market Growth (%) = [(Market Size This Period – Market Size Last Period) ÷ Market Size Last Period] × 100
Market share reflects a company’s sales as a proportion of total market sales, indicating competitive standing.
市场份额反映企业销售额占市场总销售额的比重，表明其竞争地位。
Market Share (%) = (Firm’s Sales Revenue ÷ Total Market Sales Revenue) × 100
Sales growth compares a firm’s own revenue change across periods, useful for evaluating internal strategies.
销售增长率比较企业自身收入的跨期变化，有助于评价内部战略。
Sales Growth (%) = [(Current Period Sales – Previous Period Sales) ÷ Previous Period Sales] × 100
These metrics often underpin strategic models such as the Boston Matrix, where market growth and relative market share classify products.
这些指标常支撑波士顿矩阵等战略模型，用市场增长率与相对市场份额对产品进行分类。
7. Decision Trees and Expected Value | 决策树与期望值
A decision tree is a diagrammatic aid that maps out different strategic options, possible outcomes and their probabilities. It encourages logical decision making under risk.
决策树是一种图示辅助工具，勾勒出不同战略选项、可能结果及其概率，鼓励在风险下做出合乎逻辑的决策。
The expected value of a course of action is the weighted average payoff, calculated by multiplying each monetary outcome by its probability and summing the results.
某个行动方案的期望值是加权平均回报，计算方法是将每个货币结果乘以其概率，然后加总。
Expected Value = Σ (Probability × Payoff)
If a decision node has several branches, calculate the net expected value by subtracting associated costs from the expected gross return.
如果决策节点有好几个分支，计算净期望值时需用预期总回报减去相关成本。
Net Expected Value = Total Expected Revenue – Associated Cost
The preferred option is normally the one with the highest positive net expected value. However, qualitative factors and risk attitude must also be considered.
通常选择正净期望值最高的方案，但还须考虑定性因素及决策者的风险态度。
8. Investment Appraisal Methods | 投资评估方法
Investment appraisal techniques help firms assess whether long-term projects will generate acceptable returns. The Average Rate of Return (ARR) compares average annual profit to the initial investment cost as a percentage.
投资评估方法帮助企业判断长期项目能否产生可接受的回报。平均收益率（ARR）用百分比比较平均年度利润与初始投资成本。
ARR = (Average Annual Profit ÷ Initial Investment) × 100
Average annual profit is total profit over the project life divided by number of years. A higher ARR suggests a more attractive project, but ARR ignores timing of returns.
平均年度利润是项目周期内总利润除以年数。ARR 越高项目越有吸引力，但它忽略回报的时序。
The payback period computes the time required for net cash inflows to recover the initial outlay. It is simple and highlights liquidity risk.
回收期计算净现金流入收回初始支出所需的时间，方法简单并凸显流动性风险。
Payback Period = Initial Investment ÷ Annual Net Cash Flow (when constant)
For unequal cash flows, cumulative cash flow is tracked until the investment is fully paid back. Shorter payback reduces uncertainty.
若现金流不均，则跟踪累计现金流直到全额收回投资。较短的回收期可降低不确定性。
9. Cash Flow Management | 现金流量管理
Net cash flow is the difference between cash inflows and outflows over a period and is the lifeblood of a business’s day-to-day survival.
净现金流是某一期间现金流入与流出的差额，是企业日常生存的命脉。
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
Closing balance forecasts are built sequentially: start with the opening balance, add net cash flow, and the result is the closing balance, which becomes the next period’s opening balance.
期末余额预测是序贯构建的：以初期余额为起点，加上净现金流，得到期末余额，并成为下一期的期初余额。
Closing Balance = Opening Balance + Net Cash Flow
A cash-flow forecast relies on the theorem that a business can identify periods of surplus or deficit and take pre-emptive action, such as arranging overdrafts or delaying payments.
现金流量预测依赖的基本定理是：企业可以识别盈余或赤字时段并采取预防措施，如安排透支或延迟付款。
10. Core Cost and Revenue Calculations | 核心成本与收入计算
Understanding cost behaviour is essential for profit planning. Variable costs change directly with output, while fixed costs remain unchanged within a relevant range.
理解成本性态对利润规划至关重要。变动成本随产出直接变动，固定成本在相关范围内保持不变。
Total Cost = Fixed Costs + (Variable Cost per unit × Quantity)
Average cost, or unit cost, is obtained by dividing total cost by output. As output rises, average fixed cost falls through economies of scale.
平均成本（单位成本）等于总成本除以产量。随着产量上升，平均固定成本因规模经济而降低。
Average Cost = Total Cost ÷ Output
Total revenue is the income from selling goods or services. The intersection of total revenue and total cost lines on a break-even chart determines the break-even point.
总收入是销售产品或服务的收入。盈亏平衡图上总收入线与总成本线的交点决定了盈亏平衡点。
Total Revenue = Selling Price × Quantity Sold
Profit is the positive difference between total revenue and total cost. When total revenue is less than total cost, a loss occurs.
利润是总收入与总成本之间的正差额。当总收入低于总成本时，便会出现亏损。
Profit = Total Revenue – Total Cost
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