📚 Pre-U Cambridge Business: Formulae and Theorems Quick Reference Handbook | Pre-U Cambridge 商务：公式定理速查手册
This handbook provides a concise summary of the essential quantitative formulae and business theorems required for the Cambridge Pre-U Business syllabus. It is designed for quick revision and exam preparation, covering break-even analysis, investment appraisal, financial ratios, costing methods, elasticity, and human resource metrics. Each formula is accompanied by a brief explanation and its business application.
本手册汇总了剑桥 Pre-U 商务课程所需的关键量化公式和商务定理，便于快速复习和备考。内容涵盖盈亏平衡分析、投资评估、财务比率、成本计算、弹性概念和人力资源指标，每个公式均附有简要说明和商业应用场景。
1. Break-Even Analysis | 盈亏平衡分析
Break-even analysis determines the level of sales at which total revenue equals total costs, resulting in zero profit. The fundamental concept is contribution per unit = Selling Price – Variable Cost per Unit. Contribution goes towards covering fixed costs and then generating profit.
盈亏平衡分析用于确定总收入等于总成本、利润为零的销售水平。基本概念是 单位贡献 = 售价 – 单位变动成本。贡献首先用于弥补固定成本，之后形成利润。
The break-even point in units is: BEP (units) = Fixed Costs / Contribution per Unit. The break-even revenue is: BEP (value) = BEP (units) × Selling Price. These formulae help businesses assess the viability of a product or investment.
盈亏平衡产量公式为：BEP（单位） = 固定成本 / 单位贡献。盈亏平衡销售额为：BEP（金额） = BEP（单位）× 售价。这些公式帮助企业评估产品项目的可行性。
Margin of Safety = Actual Sales – Break-even Sales (in units or revenue). It shows how much sales can fall before a loss occurs. A higher margin of safety indicates lower risk.
安全边际 = 实际销售量 – 盈亏平衡销售量（以单位或金额计）。它表示在发生亏损之前销售量可以下降的幅度。安全边际越高，风险越低。
To achieve a specific target profit, the required output is: Target Output = (Fixed Costs + Target Profit) / Contribution per Unit. Break-even analysis can also be extended to a break-even chart showing the total cost and total revenue lines.
要达到特定的目标利润，所需产量为：目标产量 = (固定成本 + 目标利润) / 单位贡献。盈亏平衡分析还可通过绘制总成本与总收入线的盈亏平衡图加以扩展。
2. Investment Appraisal | 投资评估
Payback Period measures the time taken for an investment to generate enough net cash flow to recover its initial cost. Shorter payback is preferred. It does not consider time value of money or cash flows after payback.
回收期衡量投资产生的净现金流收回初始成本所需的时间。回收期越短越好。它不考虑资金的时间价值或回收期后的现金流。
Average Rate of Return (ARR) = (Average Annual Profit / Initial Investment) × 100%. Some variants use average investment. ARR expresses returns as a percentage and can be compared to a target rate, but ignores timing of cash flows.
平均收益率 (ARR) = (平均年利润 / 初始投资) × 100%。部分计算采用平均投资额。ARR 以百分比表示回报，可与目标收益率比较，但忽略了现金流的时机。
Net Present Value (NPV) = Σ [Cash Flowₜ × Discount Factorₜ] – Initial Investment, where Discount Factor = 1 / (1 + r)ⁿ, ‘r’ is the discount rate and ‘n’ the year. A positive NPV indicates a project adds value. NPV recognises the time value of money and all future cash flows.
净现值 (NPV) = Σ [现金流ₜ × 贴现因子ₜ] – 初始投资，其中 贴现因子 = 1 / (1 + r)ⁿ，’r’ 为贴现率，’n’ 为年份。NPV 为正表明项目增加价值。NPV 认可资金的时间价值和全部未来现金流。
3. Profitability Ratios | 盈利性比率
Gross Profit Margin (GPM) = (Gross Profit / Revenue) × 100%. It measures the percentage of revenue left after paying for direct costs of goods sold. A higher margin suggests stronger pricing power or better control of production costs.
毛利率 (GPM) = (毛利 / 收入) × 100%。它衡量支付直接销售成本后剩余收入的比例。较高的毛利率表明较强的定价能力或更佳的生产成本控制。
Net Profit Margin (NPM) = (Net Profit / Revenue) × 100%. Net profit is profit after all expenses, including interest and tax. NPM reflects overall cost efficiency and is crucial for comparing performance over time or between competitors.
净利率 (NPM) = (净利润 / 收入) × 100%。净利润是扣除全部费用（包括利息和税款）后的利润。NPM 反映整体成本效率，对于跨期或竞争者之间的绩效比较至关重要。
Return on Capital Employed (ROCE) = (Operating Profit / Capital Employed) × 100%. Capital employed is usually total equity plus non-current liabilities or total assets minus current liabilities. ROCE is a fundamental measure of how efficiently a business uses its long-term funding to generate profit.
运用资本回报率 (ROCE) = (营业利润 / 运用资本) × 100%。运用资本通常为总权益加非流动负债，或总资产减去流动负债。ROCE 是衡量企业如何有效利用长期资金创造利润的核心指标。
4. Liquidity and Working Capital Ratios | 流动性与营运资本比率
Current Ratio = Current Assets / Current Liabilities. It indicates a firm’s ability to meet its short-term debts. A ratio above 1 suggests sufficient current assets, but an excessively high ratio may signal inefficient use of cash or inventory.
流动比率 = 流动资产 / 流动负债。它表明企业偿还短期债务的能力。比率高于 1 通常表示流动资产充足，但过高可能意味着现金或存货使用低效。
Acid Test (Quick) Ratio = (Current Assets – Inventories) / Current Liabilities. By excluding inventories – the least liquid current asset – this ratio provides a more stringent test of immediate liquidity. A value of around 1 is often considered safe.
酸性测试（速动）比率 = (流动资产 – 存货) / 流动负债。由于剔除了流动性最差的流动资产——存货，该比率对即时流动性给出了更严格的衡量。通常认为接近 1 较为安全。
Working Capital = Current Assets – Current Liabilities. Positive working capital means the business has enough short-term assets to cover short-term obligations. Management of receivable, payable and inventory turnover directly impacts working capital requirements.
营运资本 = 流动资产 – 流动负债。营运资本为正值意味着企业拥有足够的短期资产以覆盖短期债务。应收、应付及存货周转的管理直接影响营运资本需求。
5. Efficiency Ratios | 效率比率
Inventory Turnover = Cost of Sales / Average Inventory. It measures how many times inventory is sold and replaced over a period. A high turnover suggests efficient inventory management; too high may risk stock-outs.
存货周转率 = 销售成本 / 平均存货。它衡量一个时期内存货售出并替换的次数。高周转率表明存货管理高效；过高则可能面临缺货风险。
Trade Receivables Days = (Trade Receivables / Credit Sales) × 365. This ratio indicates the average number of days it takes to collect debts from customers. Shorter periods improve cash flow, while longer periods may signal poor credit control.
应收帐款天数 = (应收帐款 / 赊销收入) × 365。该比率表示从客户处收回债务所需的平均天数。天数越短，现金流越好；过长可能表明信用控制不力。
Trade Payables Days = (Trade Payables / Credit Purchases) × 365. It shows how long, on average, a business takes to pay its suppliers. Lengthening this period can conserve cash but may damage supplier relationships.
应付帐款天数 = (应付帐款 / 赊购额) × 365。它显示企业平均用多长时间支付供应商款项。延长支付期可保留现金，但可能损害供应商关系。
Asset Turnover = Revenue / Net Assets (or Capital Employed). It measures sales generated per unit of net assets. A higher ratio indicates more efficient use of the firm’s asset base.
资产周转率 = 收入 / 净资产（或运用资本）。它衡量每单位净资产所产生的销售收入。比率越高，表明资产利用效率越高。
6. Investor (Shareholder) Ratios | 投资者（股东）比率
Earnings per Share (EPS) = (Net Profit – Preference Dividends) / Number of Ordinary Shares in Issue. EPS is a key indicator of a company’s profitability on a per-share basis and influences share price.
每股收益 (EPS) = (净利润 – 优先股股息) / 已发行普通股数。EPS 是衡量公司每股盈利的关键指标，会影响股价。
Price/Earnings (P/E) Ratio = Market Price per Share / EPS. It expresses market confidence: a high P/E may indicate growth expectations, while a low P/E may suggest undervaluation or limited growth prospects.
市盈率 (P/E) = 每股市价 / 每股收益。它反映市场信心：高市盈率可能表明增长预期，低市盈率可能暗示估值偏低或增长前景有限。
Dividend Yield = (Dividend per Share / Market Price per Share) × 100%. This shows the shareholder’s cash return on the current market price. Income-oriented investors favour a higher yield.
股息收益率 = (每股股息 / 每股市价) × 100%。它显示股东按当前市价获得的现金回报。注重收入的投资者偏好较高收益率。
Dividend Cover = EPS / Dividend per Share. It measures how many times the company’s earnings cover its dividend payments. A higher cover suggests the dividend is more sustainable.
股息保障倍数 = 每股收益 / 每股股息。它衡量公司盈利覆盖股息支付的倍数。倍数越高，股息可持续性越强。
7. Costing and Contribution | 成本计算与贡献毛利
Full (Absorption) Costing allocates all production costs – both fixed and variable – to units of output. It ensures each product absorbs a share of overheads but can lead to over- or under-absorption if estimated activity levels are inaccurate.
完全（吸收）成本法将全部生产成本——包括固定和变动——分配至产出单位。它能确保每件产品吸收一部分间接费用，但如果预计活动水平不准确，可能导致多吸收或少吸收。
Marginal Costing charges only variable costs to units, treating fixed costs as period costs. The key metric is Contribution = Selling Price – Variable Cost per Unit. This approach aids decision-making on pricing, special orders and make-or-buy choices.
边际成本法仅将变动成本计入产品，固定成本作为期间费用处理。关键指标是 贡献毛利 = 售价 – 单位变动成本。这种方法有助于定价、特殊订单以及自制或外购决策。
Total Contribution = Contribution per Unit × Number of Units Sold. Profit is then Total Contribution – Total Fixed Costs. When selling multiple products, a weighted average contribution can be used.
总贡献毛利 = 单位贡献 × 销售数量。利润即为 总贡献 – 总固定成本。销售多种产品时，可采用加权平均贡献毛利。
8. Budgeting and Variance Analysis | 预算与差异分析
Published by TutorHao | Pre-U 商务 Revision Series | aleveler.com更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导