📚 AQA A-Level Business Year 13: Formula & Theorem Quick Reference Handbook | AQA A-Level 商务 Year 13：公式定理速查手册
Welcome to the Year 13 AQA Business Formula & Theorem Quick Reference Handbook. This resource consolidates every essential formula, ratio and decision-making technique required for your A-Level examinations, from basic profit calculations to critical path analysis. Use it for quick revision, classroom support and intensive daily practice to master quantitative applications in real business contexts.
欢迎使用 AQA A-Level 商务 Year 13 公式定理速查手册。本手册汇集了 A-Level 考试必需的全部基础公式、财务比率与决策技术，从基础利润计算到关键路径分析一应俱全。你可以用它快速复习、课堂辅助或高强度日常训练，彻底掌握商务情境中的量化应用。
1. Basic Financial Formulas | 基础财务公式
Revenue = Selling price per unit × Quantity sold
Revenue is the total income generated from normal trading activities before any costs are deducted. It forms the top line of the income statement and is driven by both price and volume.
收入是在扣除任何成本之前，企业正常经营活动所获得的总所得。它构成利润表的顶行，同时受价格和销量的驱动。
Total variable costs = Variable cost per unit × Output
Variable costs change directly with the level of production or sales, such as raw materials and direct labour. Total variable cost rises in proportion to output.
变动成本随产量或销量水平直接变化，如原材料和直接人工。总变动成本与产出成比例上升。
Total costs = Fixed costs + Total variable costs
Fixed costs, such as rent and salaries, remain constant over a period regardless of output. Total costs are the sum of all fixed and variable expenses.
固定成本（如租金和管理人员薪水）在一定期间内不随产量变化。总成本是全部固定支出与变动支出之和。
Profit = Total revenue – Total costs
Profit is the reward for risk-taking; it shows the surplus after all operating expenses are covered. A positive profit indicates financial success, while a loss signals that costs exceed revenue.
利润是对承担风险的回报；它反映扣除全部运营费用后的剩余。正值利润表示财务成功，亏损则意味着成本超过收入。
2. Profitability & Liquidity Ratios | 盈利能力与流动性比率
Gross profit margin = (Gross profit ÷ Revenue) × 100
Gross profit margin measures the percentage of revenue left after subtracting the cost of sales. A higher margin suggests efficient purchasing and production, or strong pricing power.
毛利率衡量扣除销售成本后剩余收入所占的百分比。较高的毛利率表明高效的采购与生产，或者企业拥有较强的定价权。
Operating profit margin = (Operating profit ÷ Revenue) × 100
Operating profit margin evaluates profitability after all operating expenses (including fixed overheads) are deducted, but before interest and tax. It indicates how well a business controls its core running costs.
营业利润率评价在扣除全部营业费用（含固定间接费用）但未扣除利息与税款之前的盈利水平。它显示企业对核心运营成本的控制能力。
Return on capital employed (ROCE) = (Operating profit ÷ Capital employed) × 100
ROCE expresses operating profit as a percentage of the total long-term funds invested in the business. Capital employed equals total equity plus non‑current liabilities. It is a key measure of managerial efficiency.
ROCE 将营业利润表达为投入企业长期资金总额的百分比。资本使用额等于股东权益加非流动负债。它是衡量管理效率的关键指标。
Current ratio = Current assets ÷ Current liabilities
The current ratio assesses whether a firm has enough short-term assets to cover its short-term debts. A ratio of between 1.5:1 and 2:1 is often considered healthy.
流动比率评估企业是否有足够短期资产覆盖短期负债。一般认为 1.5:1 至 2:1 的比率较为健康。
Acid test ratio = (Current assets – Inventories) ÷ Current liabilities
The acid test ratio removes inventories from current assets, offering a stricter measure of liquidity. It focuses on cash, receivables and other quickly convertible assets.
速动比率从流动资产中剔除存货，提供更严格的流动性衡量。它聚焦现金、应收账款及其他可迅速变现的资产。
3. Efficiency & Gearing Ratios | 效率比率与杠杆比率
Inventory turnover = Cost of goods sold ÷ Average inventories held
Inventory turnover shows how many times a business sells and replaces its stock over a period. A higher turnover signals efficient inventory management and strong sales.
存货周转率显示企业在一段时期内售出并重置存货的次数。周转率越高，表明存货管理越高效，销售越强劲。
Receivables days = (Receivables ÷ Revenue) × 365
This ratio calculates the average number of days customers take to pay. A lower figure improves cash flow; a rising trend may indicate lenient credit control.
该比率计算客户平均付款天数。数值越低越有利于现金流；上升趋势则可能预示信用控制偏松。
Payables days = (Payables ÷ Cost of sales) × 365
Payables days measure how long a business takes to pay its suppliers. Extending payment periods conserves cash but may harm supplier relationships.
应付账款天数衡量企业向供应商付款的平均时长。延长付款期可保留现金，但可能损害供应商关系。
Asset turnover = Revenue ÷ Net assets
Asset turnover indicates how effectively a business uses its assets to generate revenue. A higher ratio suggests better asset utilisation.
资产周转率显示企业利用资产产生收入的效率。比率越高，表明资产利用效果越好。
Gearing = (Non‑current liabilities ÷ Total equity + Non‑current liabilities) × 100
Gearing reveals the proportion of a firm’s long-term capital that comes from debt. High gearing above 50% is often viewed as risky, though it can boost returns when trading is profitable.
杠杆比率揭示企业长期资本中来自债务的比例。高于 50% 的高杠杆通常被视为有风险，但在盈利良好时可放大回报。
4. Investment Appraisal Methods | 投资评估方法
Payback period = Time taken for cumulative net cash inflows to equal initial investment
Payback period measures how long it takes to recover the original cost of a project. Shorter payback means lower risk and faster liquidity recovery.
投资回收期衡量收回项目原始成本所需的时间。回收期越短，意味着风险越低、资金回收越快。
Average rate of return (ARR) = (Average annual profit ÷ Average investment) × 100
ARR evaluates profitability by comparing the average annual return to the average value of the investment. A higher ARR indicates a more attractive project.
ARR 通过比较平均年收益与平均投资价值来评估盈利性。ARR 越高，项目吸引力越大。
Net present value (NPV) = Σ (Net cash inflow in period t × Discount factor for period t) – Initial investment
NPV discounts future cash flows to their present value and subtracts the initial cost. A positive NPV means the project should be accepted, as it adds shareholder value.
NPV 将未来现金流折现为现值后扣除初始成本。若 NPV 为正，项目应被接受，因为它增加了股东价值。
Discount factor = 1 ÷ (1 + r)ⁿ where r = discount rate, n = year
Each year’s net cash flow is multiplied by its discount factor to reflect the time value of money. The discount rate usually reflects the cost of capital or risk premium.
每年的净现金流乘以其折现系数，以反映货币的时间价值。折现率通常体现资本成本或风险溢价。
5. Decision Trees & Expected Value | 决策树与期望值
Expected value = Σ (Probability of outcome × Monetary value of outcome)
Expected value is the weighted average of possible payoffs, using probabilities as weights. It helps managers choose between uncertain options by quantifying risk.
期望值是以概率为权重的可能结果的加权平均值。它通过量化风险帮助管理者在不同确定程度的选项间抉择。
Net gain = Expected value – Initial cost of decision
Net gain subtracts the immediate expenditure of a decision node from its expected value. A positive net gain suggests the decision is financially worthwhile.
净收益从决策节点的期望值中扣除即时支出。若净收益为正，表明该决策在财务上值得采纳。
6. Break-Even & Contribution | 盈亏平衡与贡献
Contribution per unit = Selling price per unit – Variable cost per unit
Contribution is the amount each unit sold contributes towards covering fixed costs and generating profit. It is the foundation of break-even and marginal costing analysis.
单位贡献是指每销售一单位产品对弥补固定成本和创造利润的贡献额。它是盈亏平衡与边际成本分析的基石。
Break-even output = Fixed costs ÷ Contribution per unit
Break-even output is the number of units a business must sell to cover all total costs. At this level, profit is zero and any additional sales begin to generate a margin.
盈亏平衡产量是企业为覆盖全部总成本所必须售出的单位数量。在该水平上利润为零，超出部分的销售开始产生利润。
Margin of safety = Actual output – Break-even output
Margin of safety shows how far sales can fall before the business reaches its break-even point. A larger margin provides greater comfort against downturns.
安全边际显示销售可以下降多少而企业仍未达到盈亏平衡点。较大的安全边际能更好地抵御市场下滑。
7. Budgeting & Variance Analysis | 预算与差异分析
Variance = Actual figure – Budgeted figure
A variance measures the difference between the actual outcome and the budget. Managers use this information to investigate deviations and take corrective action.
差异衡量实际结果与预算之间的差额。管理者利用该信息调查偏差并采取纠正措施。
Favourable variance occurs when actual profit is higher than budgeted or actual costs are lower. Adverse variance is the opposite.
A favourable revenue variance means actual sales exceeded expectations, boosting profit. An adverse cost variance indicates spending was higher than planned, reducing overall profit.
有利差异出现在实际利润高于预算或实际成本低于预算时。有利收入差异意味着实际销售超出预期，增加了利润；不利成本差异则表明支出高于计划，侵蚀了整体利润。
8. Labour Productivity, Capacity & Unit Costs | 劳动生产率、产能与单位成本
Labour productivity = Total output ÷ Number of employees
Labour productivity measures output per worker over a given period. Improvements can arise from training, technology or better motivation, directly reducing unit costs.
劳动生产率衡量一定时期内每位员工的产出。改进可源于培训、技术或更好的激励，直接降低单位成本。
Unit cost (average cost) = Total costs ÷ Total output
Unit cost tells management how much it costs to produce one item on average. Falling unit costs often lead to higher profit margins or more competitive pricing.
单位成本告诉管理层平均生产一件产品需要花费多少。单位成本下降通常带来更高的利润率或更强的定价竞争力。
Capacity utilisation = (Actual output ÷ Maximum possible output) × 100
Capacity utilisation shows the percentage of a firm’s potential output that is actually being used. High utilisation spreads fixed costs; too near 100% risks bottlenecks and quality issues.
产能利用率显示企业潜在产出中实际被使用的百分比。高利用率摊薄了固定成本，但过于接近 100% 则可能引起瓶颈和质量问题。
9. Key Marketing Metrics | 核心市场指标
Market share = (Company sales ÷ Total market sales) × 100
Market share reflects a business’s portion of total industry demand. Rising share may indicate competitive strength, brand loyalty or a successful marketing mix.
市场份额反映企业在行业总需求中所占的比重。份额上升可能表明竞争优势、品牌忠诚或成功的营销组合。
Market size = Total sales volume or total sales value in a market
Market size can be measured by units or revenue. Knowing market size helps firms assess growth opportunities and allocate resources effectively.
市场规模可按销售数量或销售价值衡量。了解市场规模有助于企业评估增长机会并有效配置资源。
Market growth = (Change in market size ÷ Original market size) × 100
Market growth indicates whether a market is expanding or contracting. Businesses in growing markets may pursue penetration strategies; declining markets demand consolidation or diversification.
市场增长率显示市场是在扩张还是收缩。处于增长市场的企业可采用渗透策略；衰退市场则要求巩固或多元化。
Price elasticity of demand (PED) = (% change in quantity demanded) ÷ (% change in price)
PED measures the responsiveness of demand to a price change. Inelastic goods (PED < 1) allow price rises to raise revenue; elastic goods (PED > 1) favour price cuts to boost volume.
PED 衡量需求对价格变化的反应程度。缺乏弹性的商品（PED < 1）提价可增加收入；富有弹性的商品（PED > 1）适合降价促量。
Income elasticity of demand (YED) = (% change in demand) ÷ (% change in income)
YED shows how demand responds to changes in consumer income. Luxury goods typically have high positive YED, while inferior goods have negative YED.
YED 显示需求如何随消费者收入变化。奢侈品通常有较高的正 YED，而低档品则为负 YED。
10. Critical Path Analysis (CPA) | 关键路径分析
Earliest start time (EST) = EST of preceding activity + Duration of preceding activity
EST is calculated by performing a forward pass through the network diagram. Where two activities converge, the highest forward value is selected.
EST 通过在网络图中执行正向遍历来计算。当两项活动汇合时，选择最大的正向值。
Latest finish time (LFT) = LFT of following activity – Duration of following activity
LFT is found through a backward pass from the project’s end node. Where two activities split, the smallest backward value is chosen.
LFT 通过从项目终点进行反向遍历求得。当两项活动分流时，选择最小的反向值。
Float = LFT – Duration – EST
Float represents the spare time available for a non‑critical activity without delaying the whole project. Critical path activities have zero float.
浮动时间代表非关键活动在不延迟整个项目的前提下可用的松弛时间。关键路径上的活动浮动时间为零。
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