📚 AS AQA Business: Formula & Theorem Quick Reference Handbook | AS AQA 商务：公式定理速查手册
This handbook delivers a concise yet comprehensive collection of every formula, ratio, and strategic model that AS AQA Business candidates must master. Use it to reinforce your quantitative skills, memorise key calculations, and quickly recall theorem-based frameworks during revision.
本手册简明扼要地汇编了 AS AQA 商务考生必须掌握的每一条公式、比率和战略模型。利用它巩固你的定量技能、牢记关键计算方法，并在复习时快速回忆基于定理的框架。
1. Profit & Contribution Formulas | 利润与贡献公式
Profit and contribution are the bedrock of financial analysis. Contribution helps managers understand how much each unit sold covers fixed costs and generates profit, while total profit reveals the overall financial health of a trading period.
利润与贡献是财务分析的基石。贡献帮助管理者了解每售出一单位产品能覆盖多少固定成本并创造利润，而总利润则揭示整个营业期的财务健康状况。
| Formula (English) | 中文公式 | Application Notes |
|---|---|---|
| Profit = Total Revenue – Total Costs | 利润 = 总收入 – 总成本 | Can be calculated as total profit or operating profit for a period. |
| Contribution per unit = Selling price – Variable cost per unit | 单位贡献 = 售价 – 单位可变成本 | Represents the amount available to cover fixed costs and then profit. |
| Total contribution = Contribution per unit × Quantity sold | 总贡献 = 单位贡献 × 销售数量 | Useful for comparing the overall earning power of different products. |
| Profit = Total contribution – Total fixed costs | 利润 = 总贡献 – 总固定成本 | Shows the direct link between contribution and profit. |
These formulas are the starting point for pricing decisions, cost control, and break-even analysis. A firm can use contribution to decide whether to accept a special order or discontinue a product line.
这些公式是定价决策、成本控制和盈亏平衡分析的起点。企业可以利用贡献来决定是否接受特殊订单或停止某个产品线。
2. Break-Even Analysis | 盈亏平衡分析
Break-even analysis identifies the output level where total revenue equals total costs, meaning the business neither makes a profit nor a loss. It is a vital tool for assessing risk and setting sales targets.
盈亏平衡分析确定总收入等于总成本时的产出水平，即企业既不盈利也不亏损。它是评估风险和设定销售目标的重要工具。
| Formula (English) | 中文公式 | Notes |
|---|---|---|
| Break-even point (units) = Total fixed costs / (Selling price per unit – Variable cost per unit) | 盈亏平衡点（单位）= 总固定成本 ÷ (单位售价 – 单位可变成本) | The denominator is the contribution per unit. |
| Break-even output (revenue) = Break-even units × Selling price per unit | 盈亏平衡收入 = 盈亏平衡单位 × 单位售价 | Shows the sales value needed to break even. |
| Margin of safety = Actual sales – Break-even sales | 安全边际 = 实际销售额 – 盈亏平衡销售额 | May be expressed in units, revenue, or as a percentage. |
| Profit at a given output = Margin of safety (units) × Contribution per unit | 给定产出的利润 = 安全边际（单位）× 单位贡献 | A quick check on targeted profit levels. |
Notice that the contribution per unit is the key driver. A high contribution ratio moves the break-even point lower, reducing risk. Managers will also evaluate the margin of safety to see how much sales can fall before losses occur.
请注意，单位贡献是关键驱动因素。高贡献率会使盈亏平衡点降低，从而减少风险。管理者还会评估安全边际，以了解在发生亏损之前销售额可以下降多少。
3. Profitability Ratios | 盈利率比率
Profitability ratios measure a firm’s ability to convert sales revenue into profit. They enable comparisons across time periods and between competitors, highlighting strengths in cost control and pricing power.
盈利率比率衡量企业将销售收入转化为利润的能力。它们可以跨时段和跨竞争对手进行比较，凸显成本控制和定价能力的优势。
| Ratio (English) | 中文比率 | Formula & Interpretation |
|---|---|---|
| Gross profit margin | 毛利率 | (Gross profit ÷ Revenue) × 100; measures profitability after deducting direct cost of sales. |
| Operating profit margin | 营业利润率 | (Operating profit ÷ Revenue) × 100; accounts for operating expenses. |
| Net profit margin (profit for the year margin) | 净利率（年度利润率） | (Net profit ÷ Revenue) × 100; the final margin after all expenses and interest. |
An increasing gross profit margin may indicate lower direct costs or higher selling prices, while a falling net profit margin signals rising overheads or finance costs. Always investigate changes by looking at the underlying components.
毛利率上升可能表明直接成本降低或售价提高，而净利率下降则预示着间接费用或融资成本上升。始终通过审视基本组成部分来探究变化原因。
4. Liquidity Ratios | 流动性比率
Liquidity refers to the ability of a business to pay its short-term debts as they fall due. The current ratio and acid test ratio are the two most common measures, revealing the buffer of liquid assets available.
流动性是指企业按时偿还短期债务的能力。流动比率和速动比率是最常用的两项指标，揭示可用的流动资产缓冲。
| Ratio (English) | 中文比率 | Formula & Guidance |
|---|---|---|
| Current ratio | 流动比率 | Current assets ÷ Current liabilities Ideal range depends on industry; typically 1.5 : 1 to 2 : 1 is healthy. |
| Acid test ratio (quick ratio) | 速动比率（酸性测试比率） | (Current assets – Inventory) ÷ Current liabilities Excludes inventory as it is less liquid; a result of 1 : 1 is often satisfactory. |
A current ratio that is too low may indicate insolvency risk, whereas an excessively high ratio suggests that cash could be used more productively rather than sitting idle. The acid test provides a stricter assessment of immediate liquidity.
流动比率过低可能表明存在资不抵债的风险，而过高则意味着现金可以用于更有生产力的用途而不是闲置。速动比率则对即时流动性做出了更严格的评估。
5. Efficiency & Operational Ratios | 效率与运营比率
Efficiency ratios show how well a business manages its resources, from inventory and trade receivables to capacity and workforce output. They are critical for working capital management and productivity improvement.
效率比率显示企业如何管理其资源，从存货和应收账款到产能和劳动力产出。它们对于营运资本管理和提高生产力至关重要。
| Ratio (English) | 中文比率 | Formula |
|---|---|---|
| Inventory turnover (days) | 存货周转天数 | (Average inventory ÷ Cost of sales) × 365 |
| Receivables days (debtor days) | 应收账款天数 | (Trade receivables ÷ Revenue) × 365 |
| Payables days (creditor days) | 应付账款天数 | (Trade payables ÷ Cost of sales) × 365 |
| Capacity utilisation | 产能利用率 | (Actual output ÷ Maximum possible output) × 100 |
| Labour productivity | 劳动生产率 | Output per period ÷ Number of employees |
Long inventory and receivables days tie up cash, while a short payables period may strain supplier relationships. Capacity utilisation above 90% can cause bottlenecks; below 80% may indicate wasted resources.
较长的存货和应收账款天数会占用现金，而较短的应付账款期限可能给供应商关系带来压力。产能利用率超过90%可能导致瓶颈；低于80%则可能表明资源浪费。
6. Average Rate of Return (ARR) | 平均回报率
The Average Rate of Return is an investment appraisal technique that expresses the average annual profit of a project as a percentage of the initial investment. It is straightforward and widely used to compare competing projects.
平均回报率是一种投资评估方法，它将项目的平均年利润表示为初始投资的百分比。它简单明了，被广泛用于比较相互竞争的项目。
ARR = (Average annual profit / Initial investment) × 100
To calculate average annual profit, add up the total profits over the project’s life and divide by the number of years. A project is usually acceptable if its ARR exceeds a target rate set by the business.
要计算平均年利润，需将项目生命周期内的总利润相加再除以年数。如果项目的ARR超过企业设定的目标回报率，该项目通常会被接受。
ARR ignores the timing of cash flows, which is its main limitation. Nevertheless, AS candidates must be able to compute it accurately and discuss its advantages, such as simplicity and use of familiar profit data.
ARR 忽略现金流入的时间，这是它的主要局限。尽管如此，AS考生必须能够准确计算并讨论其优点，比如简单性和使用人们熟悉的利润数据。
7. Decision Trees & Expected Monetary Value | 决策树与期望货币价值
Decision trees structure choices by mapping out possible outcomes and their probabilities. Expected monetary value (EMV) converts uncertainty into a financial figure, aiding rational decision-making.
决策树通过描绘可能的结果及其概率来构建选择。期望货币价值 (EMV) 将不确定性转化为财务数字，有助于理性决策。
Expected value = Probability of outcome × Financial outcome
Net expected gain = Total expected
Published by TutorHao | AS 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