Year 12 WJEC Business: Quick-Reference Formulas and Theorems Handbook | Year 12 WJEC 商务：公式定理速查手册

📚 Year 12 WJEC Business: Quick-Reference Formulas and Theorems Handbook | Year 12 WJEC 商务：公式定理速查手册

Welcome to your essential formula handbook tailored for the Year 12 WJEC Business specification. Whether you are calculating profit margins, analysing break-even points, or evaluating investment decisions, these formulas form the backbone of your quantitative toolkit. Master them not just for the exam, but to develop a sharper financial intuition that will serve you in any business context.

欢迎使用为你量身定制的 Year 12 WJEC 商务公式速查手册。无论你是在计算利润率、分析盈亏平衡点，还是在评估投资决策，这些公式都是你定量分析工具的核心基础。掌握它们不仅是为了考试，更是为了培养在任何商业情境中都能派上用场的敏锐财务直觉。

1. Revenue, Costs and Profit Basics | 收入、成本与利润基础

Total Revenue (TR) = Price per unit (P) × Quantity sold (Q)

Total revenue represents the inflow of money from selling goods or services before any costs are subtracted. It is the top line of an income statement and drives every subsequent performance measure.

总收入（TR）= 单位售价（P）× 销售量（Q）。总收入代表在扣除任何成本之前，从销售商品或服务中流入的现金，是利润表的首行，驱动所有后续的业绩衡量。

Total Costs (TC) = Total Fixed Costs (TFC) + Total Variable Costs (TVC)

Fixed costs, such as rent, do not change with output in the short run. Variable costs, such as raw materials, rise proportionally with production. Separating them is crucial for contribution and break-even analysis.

总成本（TC）= 总固定成本（TFC）+ 总可变成本（TVC）。固定成本（如租金）在短期内不随产量变化；可变成本（如原材料）随产量同比例上升。将两者分开对于贡献和盈亏平衡分析至关重要。

Profit = Total Revenue − Total Costs

Profit is the reward for risk-taking and efficiency. It is the absolute difference between revenue and total costs, serving as the simplest measure of financial success.

利润 = 总收入 − 总成本。利润是对承担风险和提高效率的回报，是收入与总成本之间的绝对差额，也是衡量财务成功的最简单指标。

Average Cost per unit = Total Costs ÷ Quantity produced

Average cost helps businesses set prices and evaluate efficiency. It falls as fixed costs are spread over more units until diseconomies of scale set in.

单位平均成本 = 总成本 ÷ 生产数量。平均成本帮助企业定价和评估效率，随着固定成本被分摊到更多产品上会下降，直到规模不经济出现。

---

2. Contribution and Break-Even Analysis | 贡献与盈亏平衡分析

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

Contribution is the amount each unit sold contributes towards covering fixed costs and then generating profit. It is the engine behind break-even calculations.

单位贡献 = 单位售价 − 单位可变成本。贡献是每售出一件产品为覆盖固定成本并进而产生利润所做出的金额贡献，是盈亏平衡计算的核心动力。

Total Contribution = Total Revenue − Total Variable Costs, or Contribution per unit × Quantity sold

Total contribution shows the aggregate surplus available to cover fixed costs. Once fixed costs are fully covered, every additional unit’s contribution becomes pure profit.

总贡献 = 总收入 − 总可变成本，或 单位贡献 × 销售量。总贡献显示了可用于覆盖固定成本的总盈余，一旦固定成本被完全覆盖，每多卖一单位，其贡献就全部转为利润。

Break-even output (units) = Total Fixed Costs ÷ Contribution per unit

Break-even point = FC ÷ (P − VC per unit)

Break-even output tells you how many units must be sold to make zero profit or loss. It is a vital target for startups and for evaluating the safety of a business plan.

盈亏平衡产量（单位） = 总固定成本 ÷ 单位贡献，即 盈亏平衡点 = FC ÷ (P − 单位VC)。它告诉你必须卖出多少件产品才能实现零利润，是初创企业和评估商业计划安全性的关键目标。

Margin of Safety = Actual (or forecast) sales − Break-even sales

The margin of safety shows how much sales can drop before the business starts losing money. A high margin of safety reduces risk and gives room to experiment.

安全边际 = 实际（或预计）销售量 − 盈亏平衡销售量。安全边际表明在开始亏损之前销量可以下降多少，高安全边际降低了风险，提供了试验空间。

---

3. Profit Margins and Profitability Ratios | 利润率与盈利能力比率

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

Gross profit margin reveals how efficiently a business turns raw materials and direct labour into profit. A declining margin might signal rising supplier costs or aggressive discounting.

毛利率 =（毛利 ÷ 收入）× 100%。毛利率揭示了企业将原材料和直接人工转化为利润的效率，毛利率下降可能暗示供应商成本上升或激进的折扣策略。

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

Operating profit margin takes into account both direct costs and operating expenses such as salaries and marketing. It measures the core business profitability before interest and tax.

营业利润率 =（营业利润 ÷ 收入）× 100%。营业利润率同时考虑了直接成本和营业费用（如工资和营销），衡量的是息税前核心业务的盈利能力。

Net Profit Margin = (Net Profit after tax ÷ Revenue) × 100%

Net profit margin is the ultimate bottom line. It shows what percentage of every pound earned remains as profit after all costs, interest, and tax have been paid.

净利率 =（税后净利润 ÷ 收入）× 100%。净利率是最终盈亏底线，显示出每赚取一英镑，在支付所有成本、利息和税金后，有多少比例保留为利润。

Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%

ROCE measures the return generated on the total capital invested in the business. Capital employed is typically calculated as total equity plus non-current liabilities, or total assets minus current liabilities.

资本回报率（ROCE）=（营业利润 ÷ 动用资本）× 100%。ROCE 衡量的是投入企业的总资本所产生的回报，动用资本通常计算为总权益加非流动负债，或总资产减流动负债。

---

4. Liquidity Ratios | 流动性比率

Current Ratio = Current Assets ÷ Current Liabilities

The current ratio tests whether a business has enough short-term assets to cover its short-term debts. A ratio below 1 often signals a liquidity crisis; above 2 might indicate idle assets.

流动比率 = 流动资产 ÷ 流动负债。流动比率测试企业是否有足够的短期资产来偿还短期债务，比率低于1通常预示流动性危机，高于2则可能表明资产闲置。

Acid Test (Quick) Ratio = (Current Assets − Inventory) ÷ Current Liabilities

By removing inventory, which can be hard to liquidate quickly, the acid test ratio offers a stricter view of immediate liquidity. A value of 0.8–1.0 is often considered healthy.

速动比率（酸性测试）=（流动资产 − 存货）÷ 流动负债。通过削除可能难以快速变现的存货，速动比率提供了更严格的即时流动性视角，0.8–1.0 通常被认为是健康的。

---

5. Efficiency Ratios | 效率比率

Inventory Turnover = Cost of Sales ÷ Average Inventory

This ratio shows how many times a business sells and replaces its stock in a period. A higher turnover indicates effective inventory management, but excessive speed may risk stockouts.

存货周转率 = 销售成本 ÷ 平均存货。该比率显示企业在一个时期内存货的销售和更换次数，较高的周转率表明存货管理有效，但过快可能带来缺货风险。

Inventory Turnover Period (days) = (Average Inventory ÷ Cost of Sales) × 365

Expressed in days, this tells you how long, on average, stock sits before being sold. Sectors like fresh food will have very low day figures.

存货周转天数 =（平均存货 ÷ 销售成本）× 365。以天数表示，它告诉你存货在被售出前平均存放多久，诸如新鲜食品行业的天数会非常低。

Trade Receivable Days = (Trade Receivables ÷ Revenue) × 365

This metric reveals the average number of days customers take to pay. Lower days improve cash flow but may require stricter credit control.

应收账款周转天数 =（应收账款 ÷ 收入）× 365。该指标揭示客户平均支付所需天数，较低的天数能改善现金流，但可能需要更严格的信用控制。

Trade Payable Days = (Trade Payables ÷ Cost of Sales) × 365

Payable days show how long a business takes to pay its suppliers. Extending this period can help cash flow, but may damage supplier relationships if abused.

应付账款周转天数 =（应付账款 ÷ 销售成本）× 365。应付天数显示企业支付供应商所需的平均时间，延长该期间有助于现金流，但若滥用可能损害供应商关系。

---

6. Budgeting and Variance Analysis | 预算编制与差异分析

Variance = Actual figure − Budgeted figure

A positive variance for revenue means more money came in than planned, which is favourable. For costs, a positive variance means actual costs were higher than budget, which is adverse.

差异 = 实际数值 − 预算数值。对收入而言，正差异意味着实际收入比计划多，属于有利差异；对成本而言，正差异表示实际成本高于预算，属于不利差异。

Favourable variance (F) indicates a better-than-expected result for profit; Adverse variance (A) indicates a worse-than-expected result.

Budgets are essential control tools. By breaking variances into sales volume, price, material usage, and labour rate components, managers can pinpoint exactly where performance deviates from plan.

有利差异（F）表示对利润而言结果优于预期；不利差异（A）表示结果差于预期。预算是最基本的控制工具，通过将差异分解为销量差异、价格差异、材料用量差异和工资率差异等，管理者可以精准定位实际业绩与计划的偏离之处。

---

7. Investment Appraisal Techniques | 投资评价方法

Payback Period = Time taken for net cash inflows to equal the initial investment

When cash flows are even, payback = Initial investment ÷ Annual net cash flow. Shorter payback periods reduce risk and free capital for other projects.

回收期 = 净现金流入累积等于初始投资所需的时间。当现金流均匀时，回收期 = 初始投资 ÷ 年净现金流。较短的回收期降低了风险，并使资金得以释放用于其他项目。

Average Rate of Return (ARR) = (Average annual profit ÷ Average investment) × 100%

Average investment is often calculated as (Initial investment + Residual value) ÷ 2. ARR compares the project’s annual profitability with the capital tied up, expressed as a percentage.

平均报酬率（ARR）=（平均年利润 ÷ 平均投资额）× 100%。平均投资额通常计算为（初始投资 + 残值）÷ 2。ARR 将项目的年盈利能力与投入资本进行比较，以百分比表达。

Net Present Value (NPV) = Σ [CFₜ ÷ (1 + r)ᵗ] − I₀

NPV = Sum of discounted future cash flows − Initial investment

NPV accounts for the time value of money by discounting future cash inflows. A positive NPV means the project is expected to add value to the business and should be accepted.

净现值（NPV）= Σ [CFₜ ÷ (1 + r)ᵗ] − I₀。NPV 通过对未来现金流入进行折现，考虑了货币的时间价值。NPV 为正意味着项目预期会为企业增加价值，应予接受。

---

8. Decision Trees and Expected Value | 决策树与期望值

Expected Value (EV) = Σ (Probability × Payoff)

When facing uncertainty, a decision tree maps options, probabilities, and financial outcomes. Multiply each possible payoff by its probability and sum the results to find the expected monetary value of a decision node.

期望值（EV）= Σ（概率 × 回报）。面对不确定性时，决策树可以映射选项、概率和财务结果。将每个可能的回报乘以其发生概率并求和，即可得到某个决策节点的期望货币价值。

Net Gain from a Decision = Expected Value − Initial cost of that option

The decision rule is to choose the option with the highest expected value or net gain, provided the business is risk-neutral. Decision trees also allow sensitivity analysis by altering probabilities.

决策的净收益 = 期望值 − 该选项的初始成本。决策规则是选择期望值或净收益最高的选项，前提是企业是风险中性的。决策树还能通过调整概率进行敏感性分析。

---

9. Cash Flow Management Metrics | 现金流量管理指标

Net Cash Flow = Total Cash Inflows − Total Cash Outflows

A net cash flow position can be positive or negative for a given period. Persistent negative net cash flows drain reserves and threaten solvency, even if the business is profitable on paper.

净现金流量 = 总现金流入 − 总现金流出。在某一给定期间，净现金流量可以为正或为负。持续的负净现金流量会耗尽储备，即使企业账面上有利润，也会威胁到偿债能力。

Closing Balance = Opening Balance + Net Cash Flow

This simple formula is the backbone of a cash flow forecast. It reveals the cash position at the end of a month or year, helping managers plan for overdrafts or short-term investments.

期末余额 = 期初余额 + 净现金流量。这一简单公式是现金流量预测的基础，显示出在月末或年末的现金状况，帮助管理者计划透支或短期投资。

---

10. Comprehensive Formula Quick-Reference Table | 核心公式速查总表

The table below brings together all the key formulas covered in this handbook. Use it for last-minute revision and to check your understanding of each measure’s purpose.

下表汇集了本手册中涵盖的所有核心公式，可用于考前最后冲刺复习，并检查你对各指标目的的理解。

Formula Name | 公式名称	Equation | 公式
Total Revenue | 总收入	TR = P × Q
Total Costs | 总成本	TC = TFC + TVC
Profit | 利润	Profit = TR − TC
Contribution per unit | 单位贡献	Contribution per unit = P − VC per unit
Break-even output | 盈亏平衡产量	B/E (units) = TFC ÷ (P − VC per unit)
Margin of Safety | 安全边际	Actual Sales − Break-even Sales
Gross Profit Margin | 毛利率	(Gross Profit ÷ Revenue) × 100%
Operating Profit Margin | 营业利润率	(Operating Profit ÷ Revenue) × 100%
Net Profit Margin | 净利率	(Net Profit ÷ Revenue) × 100%
ROCE | 资本回报率	(Operating Profit ÷ Capital Employed) × 100%
Current Ratio | 流动比率	Current Assets ÷ Current Liabilities
Acid Test Ratio | 速动比率	(Current Assets − Inventory) ÷ Current Liabilities
Inventory Turnover | 存货周转率	Cost of Sales ÷ Average Inventory
Trade Receivable Days | 应收账款天数	(Receivables ÷ Revenue) × 365
Trade Payable Days | 应付账款天数	(Payables ÷ Cost of Sales) × 365
Variance | 差异	Actual − Budget (F or A)
Payback Period (even) | 回收期（均匀）	Initial Investment ÷ Annual Net Cash Flow
ARR | 平均报酬率	(Avg Annual Profit ÷ Avg Investment) × 100%
NPV | 净现值	Σ [CFₜ ÷ (1+r)ᵗ] − I₀
Expected Value | 期望值	Σ (Probability × Payoff)
Net Cash Flow | 净现金流量	Total Inflows − Total Outflows
Closing Balance | 期末余额	Opening Balance + Net Cash Flow

---

Published by TutorHao | Business Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）