📚 AS WJEC Business: Formula & Theorem Quick Reference Handbook | AS WJEC 商务：公式定理速查手册
This handbook consolidates every essential formula, equation and key theorem that you need to apply in AS WJEC Business. Use it to check your quantitative skills, revise for structured questions and build confidence in numerical reasoning. Each section presents the idea in English first, followed by its Chinese equivalent, so you can learn bilingually while meeting the assessment objectives.
本手册汇总了AS WJEC商务课程中所有必须掌握的重要公式、方程和关键定理。你可以用它来检验自己的计算技能、复习结构化问题，并建立对数值推理的信心。每个小节先用英文陈述概念，再给出中文对应，这样既能实现双语学习，又能满足考评目标。
1. Break-even Analysis | 盈亏平衡分析
Break-even analysis identifies the level of output at which total revenue equals total costs, meaning the business makes neither a profit nor a loss. The central formula uses fixed costs and contribution per unit.
盈亏平衡分析可以确定总收入等于总成本的产量水平，此时企业既不盈利也不亏损。核心公式涉及固定成本和单位贡献。
Break-even output (units) = Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)
盈亏平衡产量（单位）= 固定成本 ÷（单位售价 − 单位变动成本）。
盈亏平衡点（单位）= 固定成本 ÷ 单位贡献
You can also express the break-even point in sales revenue by multiplying the break-even output by the selling price.
你也可以用盈亏平衡产量乘以售价，得出盈亏平衡销售额。
Break-even revenue = Break-even output × Selling Price per unit
盈亏平衡收入 = 盈亏平衡产量 × 单位售价。
The margin of safety shows how far actual sales can drop before reaching the break-even point: Margin of safety = Actual output – Break-even output. This is a vital risk indicator in financial planning.
安全边际反映实际销售可以下降多少才会触及盈亏平衡点：安全边际 = 实际产量 – 盈亏平衡产量。这是财务规划中重要的风险指标。
2. Contribution & Profit | 贡献与利润
Contribution refers to the amount each unit sold contributes towards covering fixed costs and then generating profit. It is the foundation for break-even and profit planning.
贡献是指每售出一单位产品，为覆盖固定成本并创造利润所提供的金额。它是盈亏平衡和利润规划的基础。
Contribution per unit = Selling Price per unit − Variable Cost per unit
单位贡献 = 单位售价 − 单位变动成本。
Total contribution is simply the unit contribution multiplied by the number of units sold.
总贡献等于单位贡献乘以销售数量。
Total Contribution = Contribution per unit × Quantity sold
总贡献 = 单位贡献 × 销售数量。
Profit (or loss) can be derived directly from contribution statements: Profit = Total Contribution − Fixed Costs. When total contribution equals fixed costs, the business is at break-even point.
利润（或亏损）可以直接从贡献表中得出：利润 = 总贡献 − 固定成本。当总贡献等于固定成本时，企业处于盈亏平衡点。
3. Profit Margins | 利润率
Profit margins measure how much profit is generated from sales. The gross profit margin focuses on direct trading activities, while the net profit margin accounts for all expenses.
利润率衡量企业从销售中赚取了多少利润。毛利率聚焦于直接贸易活动，而净利润率则涵盖所有费用。
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
毛利率 (%) =（毛利润 ÷ 收入）× 100。
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
净利润率 (%) =（净利润 ÷ 收入）× 100。
The mark-up is a different concept, showing profit as a percentage of cost of sales, often used in pricing decisions.
加成率是另一个概念，显示利润占销售成本的百分比，常用于定价决策。
Mark-up (%) = (Gross Profit ÷ Cost of Sales) × 100
加成率 (%) =（毛利润 ÷ 销售成本）× 100。
Comparing these margins over time or with competitors helps assess operational efficiency and cost control.
对比不同时期的这些利润率，或与竞争对手比较，有助于评估运营效率和成本控制。
4. Liquidity Ratios | 流动性比率
Liquidity ratios assess a business’s ability to meet its short-term obligations using current assets. The current ratio and acid test ratio are the two most common measures.
流动性比率评估企业运用流动资产履行短期义务的能力。流动比率和酸性测试比率是最常用的两个指标。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债。
The ideal current ratio is often said to be between 1.5 and 2, although this varies by industry.
理想的流动比率通常被认为在1.5到2之间，但因行业不同而有差异。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
酸性测试比率 =（流动资产 − 存货）÷ 流动负债。
This stricter test of liquidity excludes inventories, which may not be quickly converted into cash. A result of at least 1 is generally reassuring.
这一更严格的流动性检验剔除了存货，因为存货不一定能快速转换为现金。一般达到1或以上会让人放心。
5. Efficiency Ratios | 效率比率
Efficiency ratios reveal how well a business manages its assets and liabilities. Inventory turnover, trade receivable days and trade payable days are particularly important for working capital management.
效率比率展示企业如何管理其资产和负债。存货周转率、应收账款周转天数和应付账款周转天数对营运资金管理尤为重要。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventories
存货周转率（次）= 销售成本 ÷ 平均存货。
A higher inventory turnover suggests stock is sold quickly, reducing holding costs.
存货周转率越高，表明存货售出越快，可降低持有成本。
Trade Receivable Days = (Trade Receivables ÷ Credit Sales Revenue) × 365
应收账款周转天数 =（应收账款 ÷ 赊销收入）× 365。
Trade Payable Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 =（应付账款 ÷ 赊购额）× 365。
Comparing receivable days with payable days can indicate potential cash flow gaps. A business generally wants to collect faster than it pays.
将应收账款天数与应付账款天数进行比较，可以揭示潜在的现金流缺口。企业通常希望能比付款更快地收款。
6. Budgeting & Variance Analysis | 预算与差异分析
Budgets are financial plans for the future, and variance analysis compares actual results with budgeted figures. Variances can be favourable (F) or adverse (A).
预算是对未来的财务计划，差异分析则将实际结果与预算数据进行比较。差异可分为有利差异 (F) 和不利差异 (A)。
Variance = Actual figure − Budgeted figure
差异 = 实际值 − 预算值。
For revenue or profit, a positive variance is favourable; for costs, a positive variance (actual cost higher than budget) is adverse.
对收入或利润而言，正差异为有利；对成本而言，正差异（实际成本高于预算）则为不利。
Managers analyse variances to identify areas needing corrective action, such as overspending on materials or lower-than-expected sales.
管理者通过分析差异来确定需要采取纠正措施的领域，例如材料超支或销售低于预期。
Budgets themselves are built from multiple estimates: sales budget, production budget, cash budget, etc. The master budget summarises all of them.
预算本身由多项预估构成：销售预算、生产预算、现金预算等。总预算则是对它们的汇总。
7. Investment Appraisal | 投资评估
Investment appraisal techniques help businesses decide whether a long-term project is worth pursuing. Two key methods in AS WJEC Business are payback period and average rate of return (ARR).
投资评估技术帮助企业决定某长期项目是否值得开展。AS WJEC商务中的两个关键方法是投资回收期和平均回报率 (ARR)。
Payback Period = Time taken for net cash inflows to equal the initial investment cost
投资回收期 = 净现金流入等于初始投资成本所需的时间。
For constant annual cash flows: Payback = Initial Investment ÷ Annual Net Cash Flow. For uneven flows, cumulative cash flow must be calculated year by year.
若年现金流恒定：回收期 = 初始投资额 ÷ 年净现金流。若现金流不均，则需逐年计算累计现金流。
ARR (%) = (Average Annual Profit ÷ Initial Investment) × 100
平均回报率 (%) =（年均利润 ÷ 初始投资额）× 100。
Average annual profit is total profit over the project life divided by the number of years. ARR ignores the time value of money, but it is widely used because it expresses return as a percentage.
年均利润是项目期内的总利润除以年数。ARR忽略了货币的时间价值，但由于其用百分比表达回报率而被广泛使用。
8. Key Accounting Equations | 关键会计等式
The accounting equation is the bedrock of the balance sheet and ensures the books always balance. It can be expressed in two classic forms.
会计等式是资产负债表的基石，确保账簿始终平衡。它有两种经典的表达形式。
Assets = Liabilities + Equity
资产 = 负债 + 所有者权益。
Equity = Assets − Liabilities
所有者权益 = 资产 − 负债。
This equation underpins every double-entry transaction. For a sole trader, equity represents the owner’s capital plus retained profits minus drawings.
这一等式支撑着每一次复式记账。对个体工商户而言，权益代表业主资本加留存利润减提款。
Working capital (net current assets) is another critical concept: Working Capital = Current Assets − Current Liabilities. Positive working capital is needed for day-to-day liquidity.
营运资金（净流动资产）是另一个关键概念：营运资金 = 流动资产 − 流动负债。日常流动性需要正向营运资金。
9. Costs, Revenue & Break-even Chart Concepts | 成本、收入与盈亏平衡图概念
Understanding cost behaviour helps in constructing break-even charts and making short-term decisions. Total costs are split into fixed and variable components.
理解成本性态有助于绘制盈亏平衡图并做出短期决策。总成本分为固定成本和变动成本两部分。
Total Cost = Fixed Costs + (Variable Cost per unit × Output)
总成本 = 固定成本 +（单位变动成本 × 产量）。
Total Revenue = Selling Price per unit × Quantity sold
总收入 = 单位售价 × 销售数量。
Break-even charts plot these lines. The point where the total revenue line crosses the total cost line is the break-even point. The angle of incidence between the total revenue and total cost lines reflects the rate of profit contribution after break-even – a wider angle signals higher profitability.
盈亏平衡图描绘这些线条。总收入线与总成本线相交之处即为盈亏平衡点。两条线之间的夹角（入射角）反映出盈亏平衡后的利润贡献速度——夹角越大，表示盈利能力越强。
The margin of safety can also be read from the chart as the horizontal distance between actual output and break-even output.
安全边际也可以从图中读取，即实际产量与盈亏平衡产量之间的水平距离。
10. Cash Flow & Working Capital Rules | 现金流与营运资金法则
Cash flow is the movement of money into and out of a business. A cash flow forecast estimates future receipts and payments to predict the closing bank balance each month.
现金流是企业资金的流入与流出。现金流预测预估未来的收入和支出，以预测每个月的期末银行存款余额。
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
净现金流 = 现金流入总额 − 现金流出总额。
Closing Balance = Opening Balance + Net Cash Flow
期末余额 = 期初余额 + 净现金流。
A profitable business can still run into liquidity problems if cash inflows lag behind outflows – a core theorem for working capital management.
即使是盈利的企业，如果现金流入滞后于流出，也可能遇到流动性问题——这是营运资金管理的一个核心定律。
The cash conversion cycle is the total time from paying for inventory to collecting cash from sales. A shorter cycle improves liquidity.
现金转换周期是从支付存货到收回销售现金的总时长。周期越短，流动性越好。
Cash Conversion Cycle = Inventory Days + Receivable Days − Payable Days
现金转换周期 = 存货周转天数 + 应收账款天数 − 应付账款天数。
All these components interconnect; for instance, reducing inventory days or extending payment terms can release cash for the business.
所有这些要素相互关联；例如，缩短存货天数或延长付款期限都能为企业释放现金。
Published by TutorHao | Business Revision Series | aleveler.com
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