A-Level Business: Formula Summary Handbook | A-Level 商务：公式汇总手册

📚 A-Level Business: Formula Summary Handbook | A-Level 商务：公式汇总手册

Mastering quantitative analysis is essential for success in A-Level Business. This handbook brings together all the key formulas you need – from break-even and profitability to investment appraisal and productivity – with clear explanations and paired Chinese translations. Use it for revision, quick reference and exam practice.

掌握定量分析是 A-Level 商务考试成功的关键。本手册汇总了所有核心公式——从盈亏平衡、利润率到投资评估和生产率——并配以清晰的解释和中英对照。适合复习、速查和备考使用。

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1. Break-even Analysis | 盈亏平衡分析

Break-even analysis helps businesses determine the level of output needed to cover all costs. The break-even point is where total revenue equals total costs, resulting in neither profit nor loss.

盈亏平衡分析帮助企业确定覆盖全部成本所需的产量。盈亏平衡点指总收入等于总成本、既无利润也无亏损的状态。

The formula for break-even output (units) is:

盈亏平衡产量（单位）的公式为：

Break-even output = Fixed costs ÷ (Selling price per unit – Variable cost per unit)

You can also calculate break-even revenue by multiplying break-even output by the selling price per unit.

也可通过盈亏平衡产量乘以单位售价来计算盈亏平衡销售额。

Margin of safety shows how far sales can fall before a loss is made:

安全边际表明销售额在发生亏损前可以下降的幅度：

Margin of safety = Actual sales – Break-even sales

Target profit output adds desired profit to fixed costs in the numerator:

目标利润产量将期望利润加入分子中的固定成本：

Output for target profit = (Fixed costs + Target profit) ÷ (Selling price per unit – Variable cost per unit)

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2. Profit and Profitability Ratios | 利润与盈利能力比率

Profitability ratios assess a firm’s ability to generate earnings relative to sales, assets or equity. These ratios are vital for investors and managers alike.

盈利能力比率评估企业相对于销售额、资产或权益的盈利水平，对投资者和管理者都至关重要。

Gross profit margin measures the percentage of revenue remaining after deducting cost of sales:

毛利率衡量扣除销售成本后剩余收入的百分比：

Gross profit margin (%) = (Gross profit ÷ Revenue) × 100

Operating profit margin includes all operating expenses:

营业利润率包含所有营业费用：

Operating profit margin (%) = (Operating profit ÷ Revenue) × 100

Net profit margin accounts for all expenses, interest and tax:

净利润率涵盖所有费用、利息和税金：

Net profit margin (%) = (Net profit ÷ Revenue) × 100

Return on Capital Employed (ROCE) shows how efficiently a company uses its long-term capital to generate profit:

资本回报率 (ROCE) 显示企业如何高效利用长期资本创造利润：

ROCE (%) = (Operating profit ÷ Capital employed) × 100

Capital employed is usually total equity + non-current liabilities, or total assets – current liabilities.

资本占用通常为总权益 + 非流动负债，或总资产 – 流动负债。

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3. Liquidity Ratios | 流动性比率

Liquidity ratios evaluate a business’s ability to meet short-term obligations using its current assets. Poor liquidity can lead to insolvency even if the business is profitable.

流动性比率评估企业用流动资产偿还短期债务的能力。流动性差可能导致企业尽管盈利却无法偿付，从而资不抵债。

The current ratio compares current assets to current liabilities:

流动比率比较流动资产与流动负债：

Current ratio = Current assets ÷ Current liabilities

A ratio between 1.5 and 2 is generally considered healthy, though this varies by industry.

比率通常在 1.5 至 2 之间被认为是健康的，尽管因行业而异。

The acid test ratio (quick ratio) excludes inventory, which is less liquid:

酸性测试比率（速动比率）剔除了流动性较差的存货：

Acid test ratio = (Current assets – Inventories) ÷ Current liabilities

A ratio of 1 or above is typically desirable, indicating the firm can pay its short-term debts without selling inventory.

比率通常期望在 1 或以上，表明企业无需出售存货就能偿还短期债务。

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4. Efficiency Ratios | 效率比率

Efficiency ratios measure how well a business manages its resources, such as inventory, trade receivables and payables. Better efficiency often means lower costs and improved cash flow.

效率比率衡量企业管理资源（如存货、应收账款和应付账款）的能力。效率越高通常意味着成本更低、现金流更佳。

Inventory turnover (stock turnover) shows how many times inventory is sold and replaced over a period:

存货周转率表示一段时间内存货售出和补进的次数：

Inventory turnover = Cost of sales ÷ Average inventory

Alternatively, inventory turnover in days:

或以天数表示的存货周转期：

Inventory turnover (days) = (Average inventory ÷ Cost of sales) × 365

Trade receivables days (debtor days) indicates the average time taken to collect money from credit customers:

应收账款周转天数反映从赊销客户收回款项的平均时间：

Receivables days = (Trade receivables ÷ Credit sales) × 365

Trade payables days (creditor days) measures how long a business takes to pay its suppliers:

应付账款周转天数衡量企业向供应商付款的平均时长：

Payables days = (Trade payables ÷ Credit purchases) × 365

Asset turnover shows revenue generated per pound of assets employed:

资产周转率显示单位资产所产生的收入：

Asset turnover = Revenue ÷ Net assets (or capital employed)

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5. Investment Appraisal | 投资评估

Investment appraisal techniques help businesses decide whether long-term projects are financially worthwhile. The three main methods are payback period, average rate of return (ARR) and net present value (NPV).

投资评估方法帮助企业判断长期项目在财务上是否可行。三种主要方法是回收期法、平均收益率法 (ARR) 和净现值法 (NPV)。

Payback period calculates how long it takes for an investment to recover its initial cost from net cash inflows. When cash flows are even, the formula is:

回收期计算投资从净现金流入中收回初始成本所需的时间。当年均现金流均等时，公式为：

Payback period = Initial investment ÷ Annual net cash inflow

For uneven cash flows, the cumulative cash flow method is used.

当现金流不均等时，采用累积现金流法。

Average Rate of Return (ARR) measures the annual average profit as a percentage of the initial investment:

平均收益率 (ARR) 衡量年均利润占初始投资额的百分比：

ARR (%) = (Total net profit during project life ÷ Number of years) ÷ Initial investment × 100

Net Present Value (NPV) discounts future cash flows to their present value using a discount factor. The NPV is the sum of discounted net cash flows minus the initial investment. Although the formula involves discount factors, the concept is:

净现值 (NPV) 利用贴现因子将未来现金流折现为现值。净现值等于各期折现净现金流之和减去初始投资。虽然具体计算涉及贴现表，其概念为：

NPV = Σ (Net cash flow_t × Discount factor_t) – Initial investment

A positive NPV indicates that the project should be accepted.

净现值为正表明项目可行。

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6. Capacity Utilisation and Productivity | 产能利用率与生产率

Capacity utilisation measures the proportion of maximum possible output that is actually achieved. Productivity measures output per unit of input, commonly labour productivity.

产能利用率衡量实际产出占最大可能产出的比例。生产率衡量单位投入所带来的产出，常用的是劳动生产率。

Capacity utilisation formula:

产能利用率公式：

Capacity utilisation (%) = (Actual output ÷ Maximum possible output) × 100

High utilisation spreads fixed costs over more units but may strain resources; low utilisation implies spare capacity and higher unit costs.

产能利用率高可将固定成本摊薄到更多单位，但可能使资源紧张；利用率低则意味着存在闲置产能和更高的单位成本。

Labour productivity measures output per worker or per hour worked:

劳动生产率衡量每位员工或每工作小时的产出：

Labour productivity = Total output ÷ Number of employees (or total hours worked)

Unit cost (average cost per unit) is crucial for pricing and competitiveness:

单位成本（平均每单位成本）对定价和竞争力至关重要：

Unit cost = Total production costs ÷ Number of units produced

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7. Employee Performance | 员工绩效

Monitoring employee performance through quantitative metrics helps businesses identify HR problems and improve workforce planning. Key formulas include labour turnover, absenteeism rate, and labour cost per unit.

通过量化指标监控员工绩效有助于企业发现人力资源问题并改进劳动力规划。关键公式包括员工流失率、缺勤率和单位劳动成本。

Labour turnover measures the rate at which staff leave and are replaced:

员工流失率衡量员工离职和补充的速率：

Labour turnover (%) = (Number of staff leaving in a period ÷ Average number of staff) × 100

Absenteeism rate shows the proportion of scheduled working time lost due to absence:

缺勤率显示因缺勤而损失的计划工作时间的比例：

Absenteeism rate (%) = (Total number of absence days ÷ Total possible working days) × 100

Labour cost per unit can be used alongside productivity data:

单位劳动成本可与生产率数据结合使用：

Labour cost per unit = Total labour costs ÷ Total output

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8. Gearing and Capital Structure | 杠杆比率与资本结构

Gearing (leverage) indicates the proportion of a business’s capital that comes from debt. High gearing means higher financial risk due to fixed interest commitments, but it can amplify returns on equity when profits are strong.

杠杆比率表示企业资本中来源于债务的比例。高杠杆意味着因固定利息支出而面临较高的财务风险，但在利润强劲时可以放大股东回报。

The most common gearing formula is:

最常见的杠杆比率公式为：

Gearing (%) = (Non-current liabilities ÷ Capital employed) × 100

Alternatively, some definitions use total debt ÷ total equity. Key thresholds: above 50% is generally considered high, although acceptable levels vary by industry.

也有定义使用总债务 ÷ 总权益。关键阈值：通常认为超过 50% 即为高杠杆，但可接受水平因行业而异。

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9. Costing and Contribution | 成本核算与贡献毛利

Understanding cost behaviour is fundamental to decision-making. Contribution per unit helps businesses analyse the profitability of individual products and make short-term decisions.

理解成本行为是决策的基础。单位贡献毛利帮助企业分析单个产品的盈利能力并做出短期决策。

Total costs split into fixed and variable:

总成本分为固定成本和变动成本：

Total cost = Fixed costs + (Variable cost per unit × Number of units)

Contribution per unit is the amount each unit contributes towards fixed costs and profit:

单位贡献毛利指每单位产品用于覆盖固定成本和创造利润的金额：

Contribution per unit = Selling price per unit – Variable cost per unit

Total contribution can be used to quickly calculate overall profit:

总贡献毛利可用于快速计算整体利润：

Profit = Total contribution – Fixed costs

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10. Inventory Management | 库存管理

Efficient inventory management balances the costs of holding stock against the risk of stock-outs. The Economic Order Quantity (EOQ) model, though more advanced, calculates the optimal order size to minimise total inventory costs.

高效的库存管理需要平衡持有成本与缺货风险。经济订货量 (EOQ) 模型虽然较进阶，但可计算最优订货批量以最小化总库存成本。

For A-Level, a simplified approach is often used, but the classic EOQ formula is:

A-Level 层面常使用简化方法，但经典的 EOQ 公式为：

EOQ = √ (2 × Annual demand × Order cost ÷ Holding cost per unit)

Lead time, re-order level and buffer stock are also key concepts that interact with quantitative planning.

前置时间、再订货水平和安全库存也是与定量计划密切相关的关键概念。

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11. Key Formula Quick Reference Table | 关键公式速查表

The table below summarises the most essential formulas grouped by topic for rapid revision.

下表按主题汇总了最核心的公式，便于快速复习。

Category 类别	Formula 公式
Break-even output	Fixed costs ÷ (Price – Variable cost per unit)
Margin of safety	Actual sales – Break-even sales
Gross profit margin	(Gross profit ÷ Revenue) × 100
Operating profit margin	(Operating profit ÷ Revenue) × 100
Net profit margin	(Net profit ÷ Revenue) × 100
ROCE	(Operating profit ÷ Capital employed) × 100
Current ratio	Current assets ÷ Current liabilities
Acid test ratio	(Current assets – Inventories) ÷ Current liabilities
Inventory turnover days	(Average inventory ÷ Cost of sales) × 365
Receivables days	(Trade receivables ÷ Credit sales) × 365
Payables days	(Trade payables ÷ Credit purchases) × 365
Payback period (even cash flows)	Initial investment ÷ Annual net cash inflow
ARR	(Average annual profit ÷ Initial investment) × 100
Capacity utilisation	(Actual output ÷ Maximum possible output) × 100
Labour productivity	Total output ÷ Number of employees
Labour turnover	(Number leaving ÷ Average staff) × 100
Gearing	(Non-current liabilities ÷ Capital employed) × 100
Contribution per unit	Selling price – Variable cost per unit
Total cost	Fixed costs + (Variable cost per unit × Quantity)

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12. Final Tips for Exam Success | 考试高分策略

Always show your working clearly in calculation questions – even if the final answer is wrong, you can still earn method marks. Memorise the formulas but, more importantly, understand their meaning and when to use them. Practise past paper questions regularly to reinforce application.

计算题中务必清晰展示解题步骤——即使最终答案错误，仍可获得过程分。熟背公式，但更重要的是理解其含义及适用情形。定期练习历年考题以加强应用能力。

Interpret your results in context. A ratio is meaningless unless compared with past data, competitor benchmarks or industry averages. Link quantitative findings to qualitative analysis for higher-level evaluation marks.

将计算结果置于情境中解读。比率若未与历史数据、竞争对手基准或行业平均值比较则毫无意义。将定量发现与定性分析相联系，可获得更高层次的评价分。

Published by TutorHao | Business Revision Series | aleveler.com

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