📚 AS CCEA Business: Formulae and Theorems Quick Reference Handbook | AS CCEA 商务：公式定理速查手册
This handbook provides a concise collection of essential formulae and theorems you need to master for the AS CCEA Business examinations. Each section presents the key quantitative techniques and decision-making models, with clear explanations in both English and Chinese, designed for quick revision and deep understanding. Use it to reinforce your knowledge of break-even, contribution, ratio analysis, budgeting, investment appraisal, and more.
本手册收编了AS CCEA商务考试必须掌握的核心公式与定理。每个部分都展示了关键的定量方法和决策模型，并用中英双语清晰解释，专为快速复习和深入理解而设计。利用它来巩固盈亏平衡、贡献、比率分析、预算、投资评估等方面的知识。
1. Break-Even Analysis | 盈亏平衡分析
Break-even analysis identifies the output level where total revenue equals total costs. The break-even point (BEP) can be expressed in units or revenue.
盈亏平衡分析确定总收入等于总成本的产出水平。盈亏平衡点可以用产量或收入来表示。
Break-even point (units) = Fixed Costs / (Selling Price per unit – Variable Cost per unit)
Fixed costs (FC) are costs that do not change with output, e.g. rent. Variable cost per unit (VC) is the cost that varies directly with each unit produced. The denominator (P – VC) is the contribution per unit. This formula tells you how many units must be sold to cover all costs.
固定成本(FC)是不随产量变化的成本，如租金。单位可变成本(VC)是随每单位产量直接变动的成本。分母(P – VC)是单位贡献。该公式表明必须销售多少单位才能覆盖所有成本。
Break-even revenue = Break-even point (units) × Selling Price per unit
Alternatively, break-even revenue can be calculated by dividing fixed costs by the contribution margin ratio. It represents the sales income needed to break even.
盈亏平衡收入也可用固定成本除以贡献毛利率计算。它表示达到盈亏平衡所需的销售收入。
Margin of Safety = Actual Output – Break-even Output
The margin of safety shows the amount by which current sales exceed the break-even point. A higher margin of safety indicates lower risk. It can be expressed in units, revenue or as a percentage.
安全边际显示当前销售量超出盈亏平衡点的幅度。安全边际越高，风险越低。它可以用单位、收入或百分比表示。
2. Contribution and Profit | 贡献与利润
Contribution is the selling price minus the variable cost per unit. It is not profit, because it contributes towards covering fixed costs first; once fixed costs are covered, contribution becomes profit.
贡献是销售价格减去单位可变成本。它不是利润，因为它首先用于覆盖固定成本；一旦固定成本被覆盖，贡献就成为利润。
Contribution per unit = Selling Price per unit – Variable Cost per unit
This per-unit measure helps in pricing and profitability analysis. A positive contribution means the product is helping to pay for fixed costs.
单位贡献有助于定价和盈利能力分析。正的贡献意味着该产品正在帮助支付固定成本。
Total Contribution = Contribution per unit × Quantity Sold
Total contribution aggregates the contribution across all units sold. It is used to compute profit and break-even points.
总贡献是所有销售单位的贡献总和。它用于计算利润和盈亏平衡点。
Profit = Total Contribution – Total Fixed Costs
Once total contribution exceeds total fixed costs, the business earns a profit. If total contribution is less than fixed costs, the business makes a loss.
当总贡献超过总固定成本时，企业获利。如果总贡献少于固定成本，企业亏损。
3. Profitability Ratios | 盈利能力比率
Profitability ratios measure a business’s ability to generate profit relative to sales, assets or equity. They are essential for assessing financial health.
盈利能力比率衡量企业相对于销售收入、资产或权益的盈利生成能力。它们对于评估财务健康状况至关重要。
Gross Profit Margin = (Gross Profit / Sales Revenue) × 100%
Gross profit is sales revenue minus cost of goods sold. This ratio shows how efficiently a business turns raw materials into profit before operating expenses.
毛利润是销售收入减去已售商品成本。该比率显示企业在扣除营业费用之前将原材料转化为利润的效率。
Net Profit Margin = (Net Profit / Sales Revenue) × 100%
Net profit is the profit remaining after all expenses, including interest and tax. This ratio reveals the overall profitability of a company's operations.
净利润是扣除所有费用（包括利息和税款）后的剩余利润。该比率揭示了公司整体运营的盈利能力。
Return on Capital Employed (ROCE) = (Net Profit / Capital Employed) × 100%
Capital employed is total equity plus non-current liabilities, or total assets minus current liabilities. ROCE evaluates how effectively a business uses its long-term funds to generate profit.
资本运用额是总权益加非流动负债，或总资产减去流动负债。ROCE评估企业如何有效利用其长期资金创造利润。
4. Liquidity Ratios | 流动比率
Liquidity ratios assess a firm's ability to meet its short-term obligations. Adequate liquidity prevents cash flow crises.
流动比率评估企业履行短期义务的能力。充足的流动性可以防止现金流危机。
Current Ratio = Current Assets / Current Liabilities
Current assets include cash, receivables and inventory that can be converted to cash within one year. Current liabilities are debts due within one year. A ratio above 1 indicates the business can cover its short-term debts; a figure of around 1.5-2 is often considered healthy.
流动资产包括现金、应收账款和可在一年内变现的存货。流动负债是指一年内到期的债务。比率大于1表明企业可以偿还短期债务；1.5至2之间通常被视为健康水平。
Acid Test (Quick) Ratio = (Current Assets – Inventory) / Current Liabilities
Inventory is excluded because it may not be quickly converted into cash. This ratio provides a stricter test of liquidity. A ratio of 1 or above is generally acceptable.
存货被排除，因为它可能无法快速变现。该比率提供了更严格的流动性测试。通常比率在1或以上是可接受的。
5. Efficiency Ratios | 效率比率
Efficiency ratios examine how well a business manages its resources, especially inventory and trade receivables/payables.
效率比率考察企业管理资源（特别是存货和应收/应付账款）的能力。
Inventory Turnover = Cost of Goods Sold / Average Inventory
agement. It can also be expressed in days: (Average Inventory / Cost of Goods Sold) × 365.
该比率表明存货在一定时期内的销售和重置次数。周转率越高，表明存货管理越高效。也可以用天数表示：(平均存货 / 已售货物成本) × 365。
Trade Receivables Days = (Trade Receivables / Credit Sales) × 365
This shows the average number of days it takes a business to collect money from credit customers. A lower figure implies effective credit control.
这显示了企业从赊销客户处收回款项的平均天数。数值越小，说明信用管控越有效。
Trade Payables Days = (Trade Payables / Credit Purchases) × 365
This measures the average time a business takes to pay its suppliers. A longer period may improve cash flow but could damage supplier relationships.
这衡量企业平均需要多长时间支付供应商货款。较长的支付期可能改善现金流，但可能损害与供应商的关系。
6. Costs and Revenues | 成本与收益
Understanding the structure of costs and revenues is fundamental for pricing, production and profit planning.
理解成本和收益的构成对于定价、生产和利润规划至关重要。
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
riable cost rises in direct proportion to output: TVC = Variable Cost per unit × Quantity.
总固定成本不随产量变化。总可变成本与产量成正比：TVC = 单位可变成本 × 数量。
Average Cost (AC) = Total Cost / Quantity
Average cost is the cost per unit of output. It declines as output rises if fixed costs are spread over more units, but may eventually rise due to diseconomies of scale.
平均成本是每单位产出的成本。如果固定成本被分摊到更多单位上，平均成本随着产量增加而下降，但最终可能因规模不经济而上升。
Total Revenue (TR) = Selling Price per unit × Quantity Sold
Total revenue is the income from selling a product. Average revenue (AR) equals TR / Quantity, which is the price per unit.
总收益是销售产品的收入。平均收益 (AR) 等于总收益/数量，即单位价格。
7. Budgets and Variance | 预算与差异
Budgeting involves setting financial targets, while variance analysis compares actual performance with budgeted figures to identify deviations.
预算涉及设定财务目标，而差异分析将实际表现与预算数字进行比较，以找出偏差。
Variance = Actual Figure – Budgeted Figure
A positive variance for costs indicates an overspend (adverse), while a positive variance for revenue indicates higher-than-expected income (favourable). A negative variance for costs is favourable because costs were lower than planned.
成本的有利差异是负值（实际低于预算），收入的有利差异是正值（实际高于预算）。成本的超支差异为正值（不利），收入的差异为负值则不利。
Managers analyse variances to take corrective actions. For example, a significant adverse material variance might signal wastage or price increases.
管理者分析差异以采取纠正措施。例如，重大的不利材料差异可能表明浪费或价格上涨。
8. Investment Appraisal | 投资评估
Investment appraisal techniques help businesses evaluate the potential returns of long-term projects. At AS level, two primary methods are payback period and average rate of return.
投资评估技术帮助企业评估长期项目的潜在回报。在AS水平，两种主要方法是投资回收期和平均回报率。
Payback Period = Initial Investment / Annual Net Cash Inflow
When annual cash inflows are even, this simple formula gives the number of years to recover the initial cost. For uneven cash flows, cumulative inflows are calculated until the initial outlay is recovered.
当年净现金流入相等时，这个简单公式给出了收回初始成本的年数。对于不均衡的现金流，需计算累计流入直到初始投资被收回。
Average Rate of Return (ARR) = (Average Annual Profit / Initial Investment) × 100%
Average annual profit is the total profit over the project’s life divided by the number of years. Some variants use average investment instead of initial investment. ARR expresses return as a percentage, making it easy to compare with other projects.
平均年利润是项目寿命期内总利润除以年数。有些变体使用平均投资额。ARR以百分比表示回报，便于与其他项目比较。
9. Capacity and Productivity | 产能与生产率
Capacity refers to the maximum possible output of a business. Productivity measures how efficiently inputs are converted into outputs.
产能指企业可能的最大产出。生产率衡量将投入转化为产出的效率。
Capacity Utilisation = (Actual Output / Maximum Possible Output) × 100%
This percentage shows how much of the available capacity is being used. Low utilisation suggests idle resources, while very high utilisation may lead to overworking machinery and staff.
该百分比显示有多少可用产能正在被使用。利用率低表明资源闲置，而利用率过高可能导致机器和员工过度劳累。
Labour Productivity = Total Output / Number of Employees
Productivity can be improved through training, better equipment or motivation. Higher productivity typically lowers unit costs.
生产率可以通过培训、更优设备或激励来提高。较高的生产率通常会降低单位成本。
Unit Cost (Average Cost) = Total Costs / Output
Relating productivity to costs, a rise in productivity spreads total costs over more units, reducing the unit cost and potentially increasing competitiveness.
将生产率与成本联系起来，生产率的提高将总成本分摊到更多单位，降低单位成本并可能增强竞争力。
10. Decision Trees and Expected Value | 决策树与期望值
Decision trees are a visual tool for making complex decisions under uncertainty. Each branch represents a possible outcome with a probability and a financial payoff.
决策树是在不确定性下做出复杂决策的可视化工具。每个分支代表可能的结果，并附有概率和财务回报。
) = (Probability of Outcome × Payoff) + ... (summed for all possible outcomes of a choice)
ue is the weighted average of potential payoffs. For example, if a product launch has a 60% chance of a £50,000 profit and a 40% chance of a £10,000 loss, the EV is (£50,000 × 0.6) + (–£10,000 × 0.4) = £30,000 – £4,000 = £26,000.
期望值是潜在回报的加权平均值。例如，若产品推出有60%机会盈利50,000英镑，40%机会损失10,000英镑，EV为(£50,000 × 0.6) + (–£10,000 × 0.4) = £30,000 – £4,000 = £26,000。
Net Expected Value = Expected Value – Initial Cost of Decision
To choose between options, calculate the net expected value for each. The option with the highest positive net EV is preferred. This technique accounts for both risk and return.
在选项之间进行选择时，计算每个选项的净期望值。净期望值最高的选项优先考虑。该技术兼顾了风险与回报。
Published by TutorHao | Business Revision Series | aleveler.com
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