Pre-U Edexcel Business: Formula & Theorem Quick Reference Handbook | Pre-U Edexcel 商务：公式定理速查手册

📚 Pre-U Edexcel Business: Formula & Theorem Quick Reference Handbook | Pre-U Edexcel 商务：公式定理速查手册

This handbook compiles the essential formulas, ratios, and key decision-making theorems required for the Pre-U Edexcel Business examination. Each entry is presented with a clear business definition and practical interpretation so that learners can move confidently from calculation to evaluation. Mastering these tools will sharpen your quantitative analysis and support high-level commentary on business performance, strategy, and financial health.

本手册汇总了 Pre-U Edexcel 商务考试所必需的核心公式、比率以及关键决策定理。每一条目都配有清晰的商业定义与实务解读，帮助学习者自信地从计算走向评估。掌握这些工具将强化你的定量分析能力，并为有关企业绩效、战略和财务健康的深度评论提供支撑。

1. Profit & Loss Fundamentals | 利润与亏损基础

Revenue is the total income generated from selling goods or services before any costs are deducted. It is calculated as selling price per unit multiplied by the quantity sold.

收入是在扣除任何成本之前，通过销售商品或服务所产生的总收入。它等于单位售价乘以销售数量。

Revenue = Price × Quantity

Gross profit measures the surplus after direct costs of production have been subtracted from revenue. It demonstrates how efficiently a business converts raw materials and direct labour into earnings.

毛利衡量的是从收入中扣除直接生产成本后的盈余，体现企业将原材料和直接人工转化为收益的效率。

Gross Profit = Revenue − Cost of Sales

Operating profit goes a step further by removing all operating expenses (such as rent, marketing, and administration) from gross profit. This reveals the profit generated from core business activities before interest and tax.

营业利润更进一步，从毛利中扣除所有运营费用（如租金、营销和行政管理），揭示剔除非核心收支前企业核心活动产生的利润。

Operating Profit = Gross Profit − Operating Expenses

Net profit is the final ‘bottom line’, taking into account all revenues and all costs, including interest and taxation. It is the amount available to shareholders or for reinvestment.

净利润是最终的“底线”，计入所有收入与全部成本（含利息与税款），是可分配给股东或用于再投资的金额。

Net Profit = Operating Profit − Interest − Tax

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2. Break-Even Analysis | 盈亏平衡分析

The break-even point represents the level of output at which total revenue equals total costs, producing neither profit nor loss. It is a vital planning tool for assessing risk and setting sales targets.

盈亏平衡点表示总收入等于总成本时的产出水平，此时既不盈利也不亏损。它是评估风险与制定销售目标的重要规划工具。

Break-Even Point (units) = Fixed Costs ÷ (Selling Price − Variable Cost per Unit)

Contribution per unit is the amount each unit sold contributes towards covering fixed costs and generating profit. It is found by subtracting variable cost per unit from the selling price.

单位贡献毛益是每售出一单位产品用以覆盖固定成本并创造利润的金额，由售价减去单位变动成本求得。

Contribution per Unit = Selling Price − Variable Cost per Unit

Total contribution extends this logic to the entire sales volume and is then compared against fixed costs. Any surplus after fixed costs becomes profit.

总贡献毛益将这一逻辑扩展到整体销量，并与固定成本进行比较；超出固定成本的部分即为利润。

Total Contribution = Contribution per Unit × Quantity Sold

Margin of safety shows the amount by which actual or budgeted sales can fall before the business reaches its break-even point, expressed in units or as a percentage of output.

安全边际表明实际或预算销售量在达到盈亏平衡点前可以下降的幅度，可以用单位数或占产出的百分比表示。

Margin of Safety = Actual Sales − Break-Even Sales

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3. Profitability Ratios | 盈利能力比率

Gross profit margin compares gross profit to revenue, indicating the percentage of sales revenue retained after covering direct costs. A higher margin suggests strong pricing power or efficient cost control in production.

毛利率将毛利与收入进行比较，显示扣除直接成本后留存的销售收入百分比。较高的毛利率表明较强的定价能力或生产效率。

Gross Profit Margin = (Gross Profit ÷ Revenue) × 100

Operating profit margin reveals the proportion of revenue remaining after all operating costs have been met. It is a purer measure of operational efficiency than the gross margin.

营业利润率揭示了在满足所有运营成本后收入留存的比例，是比毛利率更纯粹的运营效率衡量指标。

Operating Profit Margin = (Operating Profit ÷ Revenue) × 100

Net profit margin captures the final profitability after every expense, giving a complete picture of overall financial success.

净利润率则捕捉了扣减全部费用后的最终盈利能力，提供了整体财务成功的完整图景。

Net Profit Margin = (Net Profit ÷ Revenue) × 100

Return on capital employed (ROCE) is a fundamental efficiency indicator that compares operating profit to the long-term capital invested in the business. Investors expect ROCE to exceed the cost of borrowing.

已用资本回报率（ROCE）是一项基本效率指标，将营业利润与企业投入的长期资本进行比较。投资者期望 ROCE 超过借贷成本。

ROCE = (Operating Profit ÷ Capital Employed) × 100

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4. Liquidity Ratios | 流动性比率

The current ratio assesses a firm’s ability to meet short-term obligations with its current assets. A ratio between 1.5:1 and 2:1 is generally considered healthy, though norms vary by industry.

流动比率评估企业用流动资产偿还短期债务的能力。一般情况下 1.5:1 到 2:1 被视为健康，但行业间规范有所不同。

Current Ratio = Current Assets ÷ Current Liabilities

The acid test ratio (or quick ratio) provides a more stringent liquidity test by excluding inventories, which may be difficult to convert to cash quickly. A result close to 1:1 is often reassuring to short-term creditors.

酸性测试比率（速动比率）通过排除难以快速变现的存货，提供更严格的流动性检验。接近 1:1 的结果通常令短期债权人安心。

Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities

These liquidity measures must be interpreted carefully; a very high current ratio could also signal inefficient use of cash or excessive inventory holding.

对这些流动性指标的解读需谨慎：过高的流动比率也可能表明现金使用效率低下或库存积压过多。

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5. Efficiency & Activity Ratios | 效率与营运比率

Inventory turnover measures how many times a business sells and replaces its stock over a period. A higher turnover implies efficient stock management or strong demand, but too high a figure might risk stock-outs.

存货周转率衡量企业在一段时间内存货售出并补进的次数。较高的周转率意味着库存管理高效或需求强劲，但过高则可能导致断货风险。

Inventory Turnover = Cost of Sales ÷ Average Inventory

Trade receivables days (debtor days) estimates the average time customers take to pay. A lower number indicates effective credit control and healthier cash flow.

应收帐款周转天数（债权天数）估算客户付款的平均时间。数值越低，说明信用控制越有效，现金流越健康。

Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365

Trade payables days (creditor days) shows how long the business takes to settle invoices from suppliers. Extending this period can ease cash flow but may damage supplier relationships if stretched too far.

应付帐款周转天数（债务天数）显示企业结算供应商发票所需的时间。延长该周期可缓解现金流，但若拖得太久则可能损害供应商关系。

Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365

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6. Gearing & Capital Structure | 杠杆与资本结构

Gearing (leverage) measures the proportion of a business’s capital that comes from debt. High gearing increases financial risk because interest must be paid regardless of profit levels, yet it can also amplify returns when trading is strong.

杠杆比率衡量企业资本中来自债务的比例。高杠杆会增加财务风险，因为无论盈利水平如何都必须支付利息；但在贸易景气时也能放大回报。

Gearing (%) = (Non‑Current Liabilities ÷ Capital Employed) × 100

An alternative formulation includes total interest-bearing debt: (Long-term debt ÷ (Long-term debt + Equity)) × 100. Businesses with gearing above 50% are often regarded as highly geared, though this depends on sector norms.

另一种公式包含全部付息债务：(长期债务 ÷ (长期债务 + 权益)) × 100。杠杆率高于 50% 的企业通常被视为高杠杆，但这取决于行业惯例。

Interest cover indicates how easily a firm can pay interest charges from its operating profit. A ratio below 2 may raise concern among lenders.

利息保障倍数表明企业用营业利润支付利息费用的容易程度。若该比率低于 2，可能引起贷款方的担忧。

Interest Cover = Operating Profit ÷ Interest Payable

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7. Investment Appraisal: Payback & ARR | 投资评估：回收期与平均回报率

Payback period calculates the time needed for a project’s cumulative net cash inflows to equal the initial investment. It is simple and risk-focused but ignores the time value of money and returns beyond the payback point.

回收期计算的是项目累计净现金流入等于初始投资所需的时间。它简单且注重风险，但忽略了货币时间价值和回收期之后的回报。

Payback Period = Year before full recovery + (Unrecovered amount ÷ Cash flow in next year)

Average Rate of Return (ARR) measures an investment’s annual average profit as a percentage of the initial cost. It enables easy comparison with bank interest rates or target returns, though it is based on profit rather than cash flow.

平均回报率（ARR）衡量投资每年平均利润占初始成本的百分比，便于与银行利率或目标回报进行比较，但它基于利润而非现金流。

ARR = (Average Annual Profit ÷ Initial Investment) × 100

Managers should use both methods together: payback for liquidity risk, ARR for profitability assessment, and then supplement with discounted cash flow techniques for more rigorous analysis.

管理者应结合使用两者：回收期用于评估流动性风险，ARR 用于盈利评估，然后以贴现现金流量技术进行更严格的分析。

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8. Net Present Value (NPV) & Discounted Cash Flow | 净现值与贴现现金流量

Net Present Value discounts all future cash flows to their present value using a chosen discount rate (often the cost of capital). A positive NPV indicates that the project should increase shareholder wealth.

净现值使用选定的贴现率（通常是资本成本）将所有未来现金流量折现为现值。正的 NPV 表明该项目应能增加股东财富。

NPV = Σ (Net Cash Flowₜ ÷ (1 + r)ᵗ) − Initial Investment

The discount factor for a year is calculated as 1 ÷ (1 + r)ⁿ, where r is the discount rate and n is the year number. Pre-U candidates must be comfortable applying given discount factors from a provided table without recalculating them manually.

某一年的贴现因子计算公式为 1 ÷ (1 + r)ⁿ，其中 r 为贴现率，n 为年数。Pre-U 考生需熟练地运用给出的贴现系数表，而不是手动重新计算。

When comparing mutually exclusive projects, the project with the highest positive NPV is usually preferred, but managers should also consider non-financial factors, strategic fit, and capital rationing.

在比较互斥项目时，通常偏好 NPV 最高且为正的项目，但管理者还需考虑非财务因素、战略匹配度以及资本限额。

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9. Decision Trees & Expected Value | 决策树与期望值

Expected value combines the financial outcome of each possible option with its probability. It provides a weighted average payoff that supports rational choice under uncertainty.

期望值将每个可能选项的财务结果与其概率相结合，提供一个加权平均收益，支持不确定条件下的理性决策。

Expected Value = Σ (Probability × Payoff)

Net expected value subtracts the initial cost of an option from the total expected monetary value. A positive net figure suggests the option is worth pursuing, while a negative one advises against it.

净期望值从总期望货币值中减去选项的初始成本。正数表明该选项值得追求，负数则建议放弃。

Decision trees illustrate choices, chance events, probabilities, and payoffs in a branching diagram. They enable clear visual comparison of alternative strategies and encourage systematic risk assessment.

决策树以分支图的形式展示选项、机会事件、概率和回报，使替代策略的直观对比成为可能，并鼓励系统性的风险评估。

Candidates must remember that expected value is a long-run average and should be supplemented with sensitivity analysis, especially when probabilities are estimated subjectively.

考生须记住期望值是长期平均值，尤其在概率为主观估计时，应辅以敏感性分析。

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10. Market & Demand Analysis | 市场与需求分析

Market share quantifies a business’s sales as a percentage of total market sales. It is a key indicator of competitive position and brand strength.

市场份额将企业的销售额量化为市场总销售额的百分比，是竞争地位和品牌实力的关键指标。

Market Share = (Firm’s Sales ÷ Total Market Sales) × 100

Market growth compares the change in market size over a period. It helps businesses decide whether to invest in a growing sector or exit a declining one.

市场增长率比较一段时间内市场规模的变化，帮助企业决定是投资于增长行业还是退出萎缩行业。

Market Growth (%) = ((Market Size₂ − Market Size₁) ÷ Market Size₁) × 100

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. A PED value greater than 1 indicates elastic demand; less than 1 indicates inelastic demand.

需求价格弹性（PED）衡量需求量对价格变化的反应程度。PED 值大于 1 表示弹性需求，小于 1 表示非弹性需求。

PED = (% Change in Quantity Demanded) ÷ (% Change in Price)

Income elasticity of demand (YED) follows a similar logic with respect to consumer income. A positive YED suggests a normal good; a negative YED indicates an inferior good.

需求收入弹性（YED）针对消费者收入采用类似逻辑。正 YED 表明是正常商品，负 YED 则是低档商品。

YED = (% Change in Quantity Demanded) ÷ (% Change in Income)

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11. Capacity Utilization & Productivity | 产能利用率与生产率

Capacity utilization shows the proportion of maximum possible output that is actually achieved. Low utilization may indicate idle resources, while figures above 90% can strain operations and lead to overtime costs.

产能利用率显示实际产出占最大可能产出的比例。利用率低可能表明资源闲置，而超过 90% 则可能使运营承压并导致加班成本。

Capacity Utilization = (Actual Output ÷ Maximum Possible Output) × 100

Labour productivity measures output per employee over a given time frame. Improving productivity is essential for cost competitiveness and usually requires investment in training or technology.

劳动生产率衡量给定时间内每位员工的产出。提升生产率对于成本竞争力至关重要，通常需要培训或技术投资。

Labour Productivity = Total Output ÷ Number of Employees

Unit cost (average cost) is derived by dividing total costs by output. Falling unit costs as volume rises indicate economies of scale, while rising unit costs beyond a certain point suggest diseconomies.

单位成本（平均成本）由总成本除以产出得出。随着规模扩大而下降的单位成本表明规模经济，而超出某点后上升的成本则意味着规模不经济。

Unit Cost = Total Costs ÷ Output

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12. Variance Analysis & Budgetary Control | 差异分析与预算控制

A variance is the difference between a budgeted figure and the actual result. Favourable variances improve profit (e.g., revenue higher than budget or costs lower), while adverse variances reduce profit.

差异是预算数字与实际结果之间的差额。有利差异改善利润（如收入高于预算或成本低于预算），不利差异则降低利润。

Variance = Actual − Budget (stated as favourable or adverse)

Sales volume variance highlights the profit impact of selling a different quantity than planned; it is calculated using standard contribution per unit.

销售数量差异突出实际销量与计划数量不同对利润的影响，使用标准单位贡献毛益计算。

Sales Volume Variance = (Actual Quantity − Budgeted Quantity) × Standard Contribution per Unit

Material price variance isolates the effect of paying a different price for raw materials, while material usage variance captures efficiency in material consumption. Together they explain the total material cost variance.

材料价格差异分离出原材料实际支付价格不同的影响，而材料用量差异则捕捉材料消耗的效率。二者共同解释总材料成本差异。

Variance analysis should trigger investigation into causes, enabling corrective action. It is not simply about praising or blaming managers but about continuous improvement in planning and control.

差异分析应促使调查原因以便采取纠正措施。它并非简单地表扬或指责管理人员，而是关乎规划与控制的持续改进。

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