📚 Year 13 AQA Business: Formula & Theorem Quick Reference Handbook | AQA 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 guide compiles all the essential quantitative formulas, financial ratios, investment appraisal techniques, and strategic models you need to master for the AQA A-level Business examinations. Understanding and applying these tools accurately is crucial for analysing business performance, making strategic decisions, and securing top marks. Each section presents the formulas with clear explanations in both English and Chinese to reinforce your learning.
欢迎使用 Year 13 AQA 商务公式定理速查手册。本指南汇集了 AQA A-level 商务考试需要掌握的所有核心量化公式、财务比率、投资评估方法及战略模型。准确理解并应用这些工具，对于分析企业绩效、制定战略决策和取得高分至关重要。每一节都以中英双语提供清晰的公式解释，以强化你的学习效果。
1. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm's ability to generate profit relative to its sales, assets, and capital employed. They are vital for assessing the financial health and operational efficiency of a business from the perspective of shareholders and management.
盈利能力比率衡量企业相对于销售额、资产和运用资本的获利能力。这些比率从股东和管理层的角度评估企业的财务健康状况和运营效率至关重要。
The gross profit margin shows how much of each pound of revenue remains after covering the direct costs of producing goods or services. It reflects production and pricing efficiency.
毛利率显示每一英镑收入在覆盖生产商品或服务的直接成本后剩余多少。它反映了生产和定价效率。
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
The operating profit margin measures the percentage of revenue that remains after both direct costs and operating expenses (such as rent, salaries, and utilities) have been paid. It indicates how well the company controls its overall cost structure.
运营利润率衡量在支付直接成本和运营费用（如租金、薪资和公用事业费）后剩余收入的百分比。它表明公司控制整体成本结构的能力。
Operating Profit Margin (%) = (Operating Profit ÷ Revenue) × 100
The net profit margin takes into account all expenses, including interest and taxes, and reveals the ultimate percentage of revenue that remains as profit after all costs.
净利润率考虑了包括利息和税收在内的所有费用，揭示了扣除所有成本后最终留存为利润的收入百分比。
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
Return on Capital Employed (ROCE) is a fundamental measure of how efficiently a company uses its long-term capital to generate operating profit. It is often used to compare performance across companies and industries.
运用资本回报率 (ROCE) 是衡量公司如何有效利用其长期资本产生运营利润的基本指标。它常被用于比较不同公司和行业间的绩效。
ROCE (%) = (Operating Profit ÷ Capital Employed) × 100
Capital employed is calculated as total assets minus current liabilities, or as equity plus non-current liabilities.
运用资本计算公式为总资产减去流动负债，或者权益加上非流动负债。
2. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet its short-term obligations as they fall due. These ratios are critical indicators of financial stability, ensuring that the business can avoid cash flow crises.
流动性比率评估企业在到期时偿还短期债务的能力。这些比率是财务稳定性的关键指标，确保企业能够避免现金流危机。
The current ratio compares current assets to current liabilities, providing a broad measure of how well the firm can cover its short-term debts with assets expected to be converted into cash within one year.
流动比率将流动资产与流动负债进行比较，广泛衡量企业利用预计在一年内变现的资产覆盖短期债务的能力。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test ratio (quick ratio) is a stricter measure that excludes inventory, as stock may not be quickly convertible into cash. It focuses on the most liquid assets: cash, receivables, and short-term investments.
酸性测试比率（速动比率）是一种更严格的衡量标准，它排除了存货，因为库存可能无法快速变现。它关注最具有流动性的资产：现金、应收账款和短期投资。
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
3. Efficiency Ratios | 效率比率
Efficiency ratios, also called activity ratios, measure how well a company utilises its assets and manages its working capital. They provide insight into operational effectiveness, cash flow timing, and overall management performance.
效率比率，也称营运能力比率，衡量公司如何有效利用其资产并管理营运资金。它们提供了关于运营有效性、现金流时间安排和整体管理绩效的见解。
Inventory turnover indicates how many times a company sells and replaces its stock over a period. A higher turnover suggests efficient inventory management and strong sales.
存货周转率表示公司在一定时期内销售和补充库存的次数。较高的周转率意味着有效的库存管理和强劲的销售。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
Inventory turnover can also be expressed in days, showing the average time stock is held before being sold.
存货周转率也可以以天数表示，显示库存在销售前的平均持有时间。
Inventory Turnover (days) = (Average Inventory ÷ Cost of Sales) × 365
The trade receivables days ratio measures the average time it takes for a business to collect payments from its credit customers. Shorter collection periods improve cash flow.
应收账款周转天数衡量企业从赊销客户处收回款项的平均时间。较短的回收期可改善现金流。
Trade Receivables Days = (Trade Receivables ÷ Revenue) × 365
The trade payables days ratio shows how long, on average, a business takes to pay its suppliers. A longer payment period may help cash flow but could strain supplier relationships.
应付账款周转天数显示企业平均支付供应商货款所需的时间。较长的支付期可能有利于现金流，但可能损害供应商关系。
Trade Payables Days = (Trade Payables ÷ Cost of Sales) × 365
Asset turnover (or capital employed turnover) evaluates how effectively a company uses its total capital to generate sales. A higher figure indicates greater efficiency.
资产周转率（或运用资本周转率）评估公司如何有效利用其总资本产生销售额。数值越高表明效率越高。
Asset Turnover = Revenue ÷ Capital Employed
4. Gearing and Investor Ratios | 杠杆与股东比率
Gearing ratios examine the proportion of a business's capital that is financed by long-term debt, highlighting financial risk. Investor ratios give shareholders and potential investors tools to evaluate returns and market performance.
杠杆比率考察企业资本中由长期债务融资的比例，突显财务风险。股东比率则为股东和潜在投资者提供评估回报和市场表现的工具。
The gearing ratio measures the extent to which a firm is funded by debt. A highly geared firm faces higher fixed interest obligations, which can amplify both gains and losses.
杠杆比率衡量公司由债务提供资金的程度。高杠杆公司面临更高的固定利息义务，这可能放大收益和损失。
Gearing (%) = (Non-current Liabilities ÷ Capital Employed) × 100
Interest cover shows the company's ability to pay interest from its operating profits. A low cover ratio may signal difficulty in servicing debt.
利息覆盖率显示公司利用运营利润支付利息的能力。较低的覆盖率可能表明偿债困难。
Interest Cover = Operating Profit ÷ Interest Payable
Earnings per share (EPS) indicates the profit attributable to each outstanding ordinary share, serving as a key indicator of profitability from an equity holder's perspective.
每股收益 (EPS) 表明每股发行在外的普通股所对应的利润，是从权益持有人角度衡量盈利能力的关键指标。
Earnings Per Share = (Net Profit − Preference Dividends) ÷ Number of Ordinary Shares
Dividend yield measures the cash return an investor receives as a percentage of the share's market price. It is important for income-focused shareholders.
股息率衡量投资者收到的现金回报占股票市场价格的百分比。这对于关注收入的股东很重要。
Dividend Yield (%) = (Dividend per Share ÷ Share Price) × 100
The price/earnings (P/E) ratio compares the market price of a share to its earnings, indicating market confidence. A high P/E suggests investors expect future growth.
市盈率 (P/E) 将股票市场价格与其收益进行比较，反映市场信心。高市盈率表明投资者预期未来增长。
P/E Ratio = Share Price ÷ Earnings per Share
5. Investment Appraisal: Payback and ARR | 投资评估：回收期与会计回报率
Investment appraisal techniques help businesses decide whether to proceed with capital projects. Payback period and Accounting Rate of Return (ARR) are relatively simple methods that focus on liquidity and profitability respectively.
投资评估技术帮助企业决定是否推进资本项目。回收期和会计回报率 (ARR) 是分别关注流动性和盈利能力的相对简单的方法。
The payback period calculates the time required for the cumulative net cash inflows to equal the initial investment. Projects with shorter payback are generally preferred as they reduce risk and improve liquidity. The method involves identifying the year before full recovery and then interpolating any fraction of the next year needed.
回收期计算累计净现金流入等于初始投资所需的时间。回收期较短的项目通常更受欢迎，因为它们能降低风险并改善流动性。该方法包括确定完全回收的前一年，然后插值计算还需要下一年的部分时间。
= Year before full recovery + (Unrecovered cost at start of year ÷ Cash flow during year)
ARR measures the average annual profit generated by an investment as a percentage of the initial investment (or average investment). It is based on accounting profit rather than cash flow, making it familiar to users of financial statements. The formula using average investment is often preferred by AQA.
ARR 衡量投资产生的平均年利润占初始投资（或平均投资）的百分比。它基于会计利润而非现金流，因此对财务报表使用者而言易于理解。AQA 通常倾向于使用平均投资的公式。
ARR (%) = (Average Annual Profit ÷ Average Investment) × 100
Average investment is computed as (Initial cost + Residual value) ÷ 2.
平均投资计算为（初始成本 + 残值）÷ 2。
6. Investment Appraisal: Net Present Value (NPV) | 投资评估：净现值 (NPV)
Net Present Value (NPV) is a discounted cash flow technique that considers the time value of money. It converts all future cash flows to their present value using a chosen discount rate and then subtracts the initial investment. A positive NPV indicates the project should increase shareholder wealth.
净现值 (NPV) 是一种考虑货币时间价值的折现现金流方法。它使用选定的折现率将所有未来现金流转换为现值，然后减去初始投资。正的 NPV 表明该项目应增加股东财富。
To calculate NPV, multiply each year's net cash flow by the corresponding discount factor provided in the examination, sum these present values, and then deduct the initial investment cost. You may need to handle multiple years and varying cash flows.
要计算 NPV，将每年的净现金流乘以考试中提供的相应折现因子，将这些现值加总，然后减去初始投资成本。你可能需要处理多年和变化的现金流。
NPV = Σ (Net Cash Flow in period t × Discount Factor for period t) − Initial Investment
A higher discount rate reduces the present value of future cash flows, making it harder for longer-term projects to show a positive NPV. NPV is widely regarded as the most robust investment appraisal method because it directly links to the objective of maximising shareholder wealth.
较高的折现率会降低未来现金流的现值，使长期项目更难显示正的 NPV。NPV 被广泛认为是最可靠的投资评估方法，因为它直接与股东财富最大化的目标相关联。
7. Break-even Analysis and Contribution | 盈亏平衡分析与贡献
Break-even analysis determines the level of output at which total revenue equals total costs, resulting in neither profit nor loss. It is a crucial
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