📚 Year 13 Cambridge Business: Formula & Theorem Quick Reference Handbook | A Level 商务公式定理速查手册
This quick reference handbook consolidates the essential formulas and quantitative techniques required for the Year 13 Cambridge Business examination. Mastering these formulas is critical for interpreting financial performance, evaluating investment projects, and making data-driven decisions.
本速查手册汇总了 Year 13 Cambridge 商务考试所必需的核心公式和定量技术。掌握这些公式对于解读财务表现、评估投资项目以及做出数据驱动的决策至关重要。
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, resulting in neither profit nor loss. It is a vital tool for planning and risk assessment.
盈亏平衡分析确定了总收入等于总成本、利润为零的产出水平。它是企业规划和风险评估的重要工具。
The contribution per unit is the amount each unit sold contributes towards covering fixed costs after variable costs are deducted. It is the building block of break-even calculations.
单位贡献毛利是扣除变动成本后，每售出一单位产品对覆盖固定成本的贡献额，是盈亏平衡计算的基础。
Contribution per unit = Selling Price per unit − Variable Cost per unit
The break-even output formula determines how many units must be sold to cover all costs. At this point, total contribution exactly equals fixed costs.
盈亏平衡点公式决定了需要销售多少单位才能覆盖所有成本。此时总贡献毛利恰好等于固定成本。
Break-even point (units) = Fixed Costs ÷ Contribution per unit
To express the break-even point in terms of sales revenue, use the contribution margin ratio. This is useful for multi-product firms.
若要用销售收入表示盈亏平衡点，可使用贡献毛利率。这对于多产品企业很有用。
Break-even point (revenue) = Fixed Costs ÷ (Contribution per unit / Selling Price)
The margin of safety indicates the cushion between actual sales and the break-even level. It shows how much sales can fall before losses occur.
安全边际表明实际销售量与盈亏平衡点之间的缓冲，揭示了在发生亏损之前销售量可以下降多少。
Margin of safety (units) = Actual output − Break-even output
To reach a target profit, the required output is calculated by adding the desired profit to fixed costs and dividing by contribution per unit.
为达成目标利润，将期望利润加至固定成本后除以单位贡献毛利，即可计算出所需产量。
Output for target profit = (Fixed Costs + Target Profit) ÷ Contribution per unit
2. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm's ability to generate earnings relative to sales, assets, and equity. They are key indicators of financial health and operational efficiency.
盈利能力比率衡量企业相对于销售额、资产和所有者权益创造利润的能力，是财务健康和运营效率的重要指标。
The gross profit margin shows the percentage of revenue remaining after accounting for the cost of goods sold. It reflects pricing and production efficiency.
毛利率反映了扣除销售成本后剩余收入的百分比，体现定价和生产效率。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
The operating profit margin reveals the profitability from core business activities before interest and tax. It excludes non-operating items.
营业利润率揭示了核心业务活动在扣除利息和税款前的盈利能力，排除了非经营项目。
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100%
Return on capital employed (ROCE) measures how efficiently a company generates profit from its long-term capital. It is a fundamental benchmark for investors.
资本运用回报率 (ROCE) 衡量公司利用长期资本创造利润的效率，是投资者的基本评估基准。
ROCE = (Operating Profit ÷ Capital Employed) × 100%
Capital employed is typically defined as total assets minus current liabilities, or as non-current liabilities plus shareholders' equity.
资本运用通常定义为总资产减去流动负债，或非流动负债加股东权益。
Capital Employed = Total Assets − Current Liabilities
3. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet its short-term obligations as they fall due. They are critical for solvency and day-to-day cash management.
流动性比率评估企业偿还到期短期债务的能力，对偿债能力和日常现金管理至关重要。
The current ratio compares total current assets to total current liabilities. A higher ratio suggests better liquidity, but excess may indicate idle assets.
流动比率将流动资产总额与流动负债总额进行比较。比率较高表明流动性较好，但过高可能意味着资产闲置。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test (quick) ratio excludes inventories from current assets, as inventories may not be easily convertible to cash. It is a stricter liquidity measure.
速动比率从流动资产中剔除存货，因为存货变现不易，是更严格的流动性衡量标准。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
4. Efficiency Ratios | 效率比率
Efficiency ratios indicate how well a company utilizes its assets and manages its liabilities. They focus on turnover of stock, receivables, and payables.
效率比率反映企业利用资产和管理负债的效率，重点关注存货、应收账款和应付账款的周转速度。
Inventory turnover shows how many times inventory is sold and replaced over a period. A higher turnover often indicates strong sales or effective inventory management.
存货周转率显示一定时期内存货被销售和替换的次数。周转率较高通常表明销售强劲或存货管理高效。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
Inventory turnover can also be expressed in days, reflecting the average number of days items stay in stock.
存货周转天数反映了存货平均滞留天数。
Inventory Turnover Period (days) = (Average Inventory ÷ Cost of Sales) × 365
Trade receivables days measure the average time taken by customers to settle debts. Shorter periods improve cash flow.
应收账款周转天数衡量客户平均付款时间，期限越短现金流越好。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
Trade payables days show how long the business takes to pay its suppliers. Balancing this with cash flow needs is essential.
应付账款周转天数显示企业付款给供应商的平均时间，平衡现金流需求至关重要。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
5. Gearing and Investor Ratios | 杠杆与投资比率
Gearing ratios examine the proportion of a company's capital that comes from debt. High gearing indicates higher financial risk but also potential for higher returns to equity holders.
杠杆比率考察公司资本中来自债务的比例。高杠杆意味着较高的财务风险，但也可能为股东带来更高回报。
Gearing Ratio = (Interest-bearing Debt ÷ (Equity + Interest-bearing Debt)) × 100%
Interest cover gauges the ability to pay interest from operating profits. A ratio below 1 suggests the firm cannot meet its interest obligations from earnings.
利息保障倍数衡量运营利润支付利息的能力。比率低于1意味着企业无法从盈利中偿还利息。
Interest Cover = Operating Profit ÷ Interest Payable
Earnings per share (EPS) is the profit attributable to each ordinary share. It is a key determinant of share price.
每股收益 (EPS) 是归属于每一普通股的利润，是股价的关键决定因素。
EPS = Profit after Tax ÷ Number of Ordinary Shares
Dividend per share (DPS) shows the actual dividend paid per share. Combined with the market price, it yields the dividend yield.
每股股息 (DPS) 显示每股实际支付的股息，结合市价得出股息收益率。
Dividend Yield = (DPS ÷ Market Price per Share) × 100%
The price/earnings (P/E) ratio reflects the market's confidence in the company's future. A higher P/E suggests anticipated growth.
市盈率 (P/E) 反映市场对公司未来的信心，较高的市盈率暗示预期的增长。
P/E Ratio = Market Price per Share ÷ EPS
6. Investment Appraisal Methods | 投资评价方法
Investment appraisal helps businesses decide whether to undertake long-term projects. The three main techniques are payback period, accounting rate of return (ARR), and net present value (NPV).
投资评价帮助企业决定是否进行长期项目，主要有三种方法：回收期、会计收益率 (ARR) 和净现值 (NPV)。
The payback period is the time required to recoup the initial investment from project cash flows. It measures liquidity and risk, ignoring the time value of money.
回收期是从项目现金流中收回初始投资所需的时间，衡量流动性和风险，但忽略了货币时间价值。
Payback Period = Initial Outlay ÷ Annual Net Cash Flow (if equal flows)
For uneven cash flows, cumulative net cash flows are summed until the initial investment is recovered.
若现金流不均匀，则累计净现金流直至收回初始投资。
ARR compares the average annual profit to the average investment, expressed as a percentage. It uses accounting profit rather than cash flow.
ARR 将年平均利润与平均投资额进行比较，用百分比表示，使用的是会计利润而非现金流。
ARR = (Average Annual Profit ÷ Average Investment) × 100%
Average Investment = (Initial Cost + Scrap Value) ÷ 2
NPV discounts all future cash flows back to their present value using a discount rate, then subtracts the initial investment. A positive NPV indicates a viable project.
NPV 使用折现率将所有未来现金流折现回现值，再减去初始投资。正净现值表示项目可行。
NPV = Σ [Net Cash Flowₜ ÷ (1 + r)ᵗ] − Initial Cost
The profitability index is a variation that relates the present value of inflows to the initial investment, useful for ranking projects when capital is limited.
获利指数是净现值的一种变形，将未来现金流入现值与初始投资相联系，在资本受限时有助于项目排序。
Profitability Index = Present Value of Future Cash Flows ÷ Initial Investment
7. Decision Trees | 决策树
A decision tree maps out potential choices and possible outcomes, incorporating probabilities and financial values to support decision-making under uncertainty.
决策树以图形方式展示备选方案和可能的结果，结合概率和财务数值，支持不确定条件下的决策。
For each chance node, the expected monetary value (EMV) is calculated by multiplying each outcome's value by its probability and summing the results.
对于每个机会节点，预期货币价值 (EMV) 是将每个结果的数值乘以概率并求和得出。
EMV = Σ (Probability × Outcome)
The decision maker then subtracts any direct costs associated with the decision branch and selects the alternative with the highest net EMV.
然后决策者减去与该决策分支相关的直接成本，选择预期净货币价值最高的方案。
Net Gain = EMV − Decision Cost
8. Critical Path Analysis | 关键路径分析
Critical path analysis (CPA) identifies the longest sequence of dependent activities within a project. It determines the minimum completion time and highlights which tasks cannot be delayed.
关键路径分析 (CPA) 确定项目中依赖活动的最长序列，从而找出最短完工时间并标示出不可延误的任务。
The forward pass calculates the earliest start time (EST) and earliest finish time (EFT) for each activity, moving from left to right.
顺推法从左到右计算每个活动的最早开始时间 (EST) 和最早完成时间 (EFT)。
EFT = EST + Duration
The backward pass calculates the latest finish time (LFT) and latest start time (LST) by working right to left from the project end.
逆推法从项目终点由右向左计算最晚完成时间 (LFT) 和最晚开始时间 (LST)。
LST = LFT − Duration
Total float is the amount of time an activity can be delayed without affecting the overall project duration. Activities on the critical path have zero float.
总浮动时间是一项活动可被延误但不影响整个项目工期的时量。关键路径上的活动浮动时间为零。
Total Float = LFT − EFT, or LST − EST
9. Budgets and Variance Analysis | 预算与差异分析
Budgets are financial plans that quantify targets. Variance analysis compares actual performance against budgeted figures to identify and investigate deviations.
预算是量化目标的财务计划。差异分析将实际业绩与预算数据进行比较，以识别和调查偏差。
A total sales variance can be split into sales volume variance and sales price variance to understand the sources of difference.
总销售差异可分解为销售量差异和销售价格差异，以了解差异来源。
me Variance = (Actual Volume − Budgeted Volume) × Standard Profit or Contribution per unit
Sales Price Variance = (Actual Price − Budgeted Price) × Actual Volume
On the cost side, material and labour variances are analysed through price and usage/efficiency components.
在成本方面，材料和人工差异通过价格与用量/效率因素进行分析。
Material Price Variance = (Actual Price − Standard Price) × Actual Quantity Purchased
e Material Usage Variance = (Actual Quantity Used − Standard Quantity for Actual Output) × Standard Price
Labour Rate Variance = (Actual Rate − Standard Rate) × Actual Hours
ur Labour Efficiency Variance = (Actual Hours − Standard Hours for Actual Output) × Standard Rate
Variances are labelled as adverse (A) when they reduce expected profit and favourable (F) when they increase it.
当差异减少预期利润时标记为逆差 (A)，增加利润时标记为顺差 (F)。
10. Costs, Revenues and Contribution | 成本、收入与贡献毛利
A firm's cost structure underpins pricing and output decisions. Understanding how costs behave at different levels of output is fundamental.
企业的成本结构是定价和产量决策的基础，理解成本在不同产出水平下的变化规律十分基本。
Total costs are the sum of fixed costs, which do not vary with output in the short run, and variable costs, which change directly with output.
总成本是短期内不随产量变化的固定成本与随产量直接变动的变动成本之和。
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average cost per unit declines when fixed costs are spread over more output, illustrating economies of scale.
单位平均成本随产量增加而下降，反映了固定成本分摊带来的规模经济效应。
Average Cost (AC) = Total Cost ÷ Output
Marginal cost is the additional cost of producing one extra unit. It is central to profit-maximising output decisions.
边际成本是多生产一单位产品所增加的成本，是利润最大化产量决策的核心。
Marginal Cost (MC) = Change in Total Cost ÷ Change in Output
Total revenue and marginal revenue guide pricing and output. Profit is maximised where marginal revenue equals marginal cost.
总收入与边际收入指导定价和产量，当边际收入等于边际成本时利润最大。
Total Revenue (TR) = Price × Quantity
Marginal Revenue (MR) = Change in Total Revenue ÷ Change in Quantity
The profit or loss of a business is simply total revenue minus total cost. Contribution analysis connects sales volume directly to profit.
企业的利润或亏损就是总收入减去总成本。贡献毛利分析将销售量与利润直接挂钩。
Profit = Total Revenue − Total Cost, or (Contribution per unit × Units) − Fixed Costs
Total Contribution = Total Revenue − Total Variable Costs
Published by TutorHao | Cambridge Business Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图