📚 OCR A Level Business: Formulas & Theorems Quick Reference Handbook | OCR A Level 商务：公式定理速查手册
Mastering quantitative methods is essential for success in Year 13 OCR Business. This quick reference handbook consolidates the key formulas and decision-making theorems you need to analyse financial performance, appraise investments, manage operations, and control budgets. Each entry is presented with a clear formula and a concise business interpretation, helping you move from calculation to insightful evaluation.
掌握定量方法是 Year 13 OCR 商务成功的关键。本速查手册汇集了分析财务绩效、评估投资项目、管理运营和控制预算所需的核心公式与决策定理。每个条目都配有清晰的公式和简明的商业解读，帮助你从计算走向有洞察力的评估。
1. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm's ability to generate profit relative to sales, assets, and equity. They are vital for assessing the overall financial health of a business from the perspective of shareholders and potential investors.
盈利能力比率衡量企业相对于销售收入、资产和所有者权益创造利润的能力。从股东和潜在投资者的角度评估企业整体财务健康状况时，这些比率至关重要。
The Gross Profit Margin reveals how efficiently a business converts raw materials and direct labour into revenue. It is calculated as:
毛利率反映企业将原材料和直接人工转化为收入的效率。计算公式为：
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
A falling gross margin may indicate rising input costs or pricing pressure, while a rising margin suggests strong cost control or premium pricing power.
毛利率下降可能表明投入成本上升或定价压力增大，而毛利率上升则意味着成本控制得当或拥有溢价定价能力。
The Operating Profit Margin accounts for all operating expenses and overheads, offering a more complete picture of core business performance:
营业利润率计入了所有营业费用和间接成本，能更全面地反映核心业务表现：
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100
This ratio is particularly useful for comparing businesses within the same industry because it strips out the effects of different financing structures and tax arrangements.
该比率特别适用于同行业内企业之间的比较，因为它剔除了不同融资结构和税务安排的影响。
Return on Capital Employed (ROCE) is often regarded as the ultimate test of profitability from an investor's viewpoint:
已用资本回报率（ROCE）常被视为从投资者角度衡量盈利能力的终极指标：
ROCE = (Operating Profit ÷ Capital Employed) × 100
Capital Employed = Total Equity + Non‑ he cost of borrowing indicates that the business is generating value for its shareholders.
已用资本 = 总权益 + 非流动负债。ROCE 高于借款成本表明企业正在为股东创造价值。
2. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm's ability to meet its short‑term obligations as they fall due. High liquidity reassures suppliers and lenders, whereas low liquidity can signal cash‑flow problems.
流动性比率评估企业履行到期短期债务的能力。高流动性能让供应商和债权人安心，而低流动性则可能预示现金流问题。
The Current Ratio compares current assets to current liabilities:
流动比率比较流动资产与流动负债：
Current Ratio = Current Assets ÷ Current Liabilities
A ratio above 1.5:1 is generally considered safe, but the ideal level varies by industry. Too high a ratio might indicate inefficient use of working capital, such as excessive inventory or idle cash.
比率高于 1.5:1 通常被视为安全，但理想水平因行业而异。比率过高可能表明营运资本利用效率低下，如存货过多或现金闲置。
The Acid Test Ratio (Quick Ratio) provides a stricter test by excluding inventory, which is often less liquid:
速动比率（酸性测试比率）通过剔除流动性较差的存货，提供了更严格的衡量：
Acid Test Ratio = (Current Assets - Inventories) ÷ Current Liabilities
A ratio of 0.8:1 to 1:1 is commonly cited as adequate, though firms with fast stock turnover can operate healthily with a lower figure.
常见的理想区间为 0.8:1 至 1:1，不过存货周转快的企业可以在较低的比率下依然保持健康运营。
3. Efficiency Ratios | 效率比率
Efficiency ratios show how well a business uses its assets and manages its working capital. They help pinpoint operational bottlenecks such as slow‑moving stock or delayed customer payments.
效率比率显示企业利用资产和管理营运资本的效率，有助于发现运营瓶颈，如存货滞销或客户延迟付款。
Inventory Turnover measures how many times a firm sells and replaces its stock over a period:
存货周转率衡量企业在一定时期内卖出和补充存货的次数：
Inventory Turnover = Cost of Sales ÷ Average Inventories
A high turnover indicates strong sales or effective stock control; a low turnover may point to overstocking or obsolescence. Sometimes it is expressed in days:
高周转率表明销售强劲或库存控制有效；低周转率则可能指向存货积压或过时。有时以天数表示：
Inventory Turnover (days) = (Average Inventories ÷ Cost of Sales) × 365
Trade Receivable Days (debtor days) measure how quickly customers settle their invoices:
应收账款周转天数（债务人天数）衡量客户结算发票的速度：
Trade Receivable Days = (Trade Receivables ÷ Revenue) × 365
A low number improves cash flow, whereas a rising figure might signal poor credit control or financial stress among customers.
较低的天数能改善现金流，而天数上升可能表明信用控制不力或客户面临财务压力。
Trade Payable Days (creditor days) indicate how long a business takes to pay its suppliers:
应付账款周转天数（债权人天数）显示企业支付供应商货款的时长：
Trade Payable Days = (Trade Payables ÷ Cost of Sales) × 365
Stretching payables can ease short‑term cash pressure, but doing so excessively may damage supplier relationships and result in lost discounts.
延长付款可以缓解短期现金压力，但过度拖延可能损害供应商关系并丧失折扣机会。
Asset Turnover gauges how effectively a business generates revenue from its asset base:
资产周转率衡量企业从资产基础中创造收入的有效性：
Asset Turnover = Revenue ÷ Net Assets
A high asset turnover implies capital intensity is used efficiently, which is particularly important in capital‑heavy industries.
高资产周转率意味着资本密集度运用高效，这在资本密集型行业中尤为重要。
4. Gearing Ratio and Interest Cover | 杠杆比率与利息覆盖倍数
Gearing (leverage) shows the proportion of a firm's capital that comes from long‑term debt compared with equity. It is a key measure of financial risk.
杠杆比率（齿轮比率）显示企业资本中长期债务与权益的比例，是衡量财务风险的关键指标。
Gearing Ratio = (Non‑current Liabilities ÷ Capital Employed) × 100
Capital Employed = Total Equity + Non‑current Liabilities. A ratio above 50% highly geared, implying greater risk because interest must be paid regardless of profits.
已用资本 = 总权益 + 非流动负债。比率超过 50% 被视为高杠杆，意味着更高的风险，因为无论利润如何，利息都必须支付。
Interest Cover measures how comfortably a firm can pay its interest charges from operating profit:
利息覆盖倍数衡量企业用营业利润支付利息费用的轻松程度：
Interest Cover = Operating Profit ÷ Finance Costs
A cover of less than 2 suggests vulnerability to interest rate rises or profit downturns. Lenders often look for a cover of 3 or more when assessing creditworthiness.
覆盖倍数低于 2 意味着对利率上升或利润下降敏感且脆弱。债权人在评估信用时通常期望覆盖倍数达到 3 或以上。
5. Investment Appraisal: Payback and ARR | 投资评估：回收期与会计收益率
Investment appraisal techniques help managers decide whether long‑term projects are financially viable. Payback and Accounting Rate of Return (ARR) are two straightforward methods frequently examined.
投资评估技术帮助管理者判断长期项目在财务上是否可行。回收期法和会计收益率法是两种常考的直接方法。
Payback Period calculates the time needed for the initial investment to be recovered from net cash inflows:
回收期计算从净现金流入回收初始投资所需的时间：
Payback Period = Point at which cumulative net cash flow turns positive
For uneven cash flows, identify the year before full recovery, then add the fraction (Remaining amount ÷ Cash flow in the next year). Shorter payback is preferred because it reduces risk.
对于不均匀的现金流，先找到完全回收前一年，再加上未回收金额 ÷ 次年现金流这一分数。较短的回收期更受青睐，因为能降低风险。
Accounting Rate of Return (ARR) expresses average annual profit as a percentage of the initial investment (or average investment):
会计收益率将平均年度利润表示为初始投资（或平均投资额）的百分比：
ARR = (Average Annual Profit ÷ Initial Investment) × 100
sh flows - Total depreciation) ÷ Number of years. ARR is compared against a target rate set by the business. It recognises profitability but ignores the time value of money.
平均年度利润 = (总净现金流 - 总折旧) ÷ 年数。ARR 与公司设定的目标收益率进行比较。该方法考虑了盈利能力，但忽略了货币的时间价值。
6. Investment Appraisal: Net Present Value (NPV) | 投资评估：净现值
NPV discounts all future cash flows to their present value using a chosen discount rate, reflecting the time value of money and project risk.
净现值使用选定的贴现率将所有未来现金流折算为现值，反映货币的时间价值和项目风险。
NPV = Σ [Net Cash Flowₜ ÷ (1 + r)ᵗ] - Initial Investment
indicates that the project should be accepted because it adds shareholder value. A negative NPV suggests rejection.
其中 r = 贴现率（以小数表示），t = 年份。正的 NPV 表明项目应被接受，因为它增加了股东价值；负的 NPV 则建议拒绝。
When choosing between mutually exclusive projects, the one with the higher NPV is preferred. The main challenge is selecting an appropriate discount rate; many firms use their weighted average cost of capital (WACC) plus a risk premium.
在互斥项目之间进行选择时，优先选择 NPV 更高的项目。主要难点在于选择合适的贴现率；许多企业使用加权平均资本成本并加上风险溢价。
0 → accept; NPV < 0 → reject; NPV = 0 → marginal, may accept if strategic benefits exist.
决策规则：NPV > 0 → 接受；NPV < 0 → 拒绝；NPV = 0 → 边际项目，存在战略利益时可考虑接受。
7. Decision Trees | 决策树
Decision trees map out the choices, possible outcomes, probabilities, and financial consequences of a decision, enabling a logical comparison of alternatives under risk.
决策树梳理出决策中的各项选择、可能结果、概率和财务后果，使企业能够在风险下逻辑清晰地比较不同方案。
Expected value is the weighted average payoff of a node:
期望值是某一节点的加权平均收益：
Expected Value = Σ (Probability × Net Payoff)
Net gain of an option is calculated by subtracting the initial cost from the total expected value:
一个方案的净收益通过总期望值减去初始成本计算：
Net Gain = Total Expected Value - Initial Cost
Managers choose the option with the highest net gain. Decision trees also encourage thinking about probabilities and encourage contingency planning, though estimates can be subjective.
管理者选择净收益最高的方案。决策树还能促使管理者思考概率并鼓励应急规划，尽管概率和收益的估计可能带有主观性。
8. Critical Path Analysis (CPA) | 关键路径分析
Critical Path Analysis identifies the longest sequence of dependent activities that determines the minimum project duration. It highlights tasks that cannot be delayed without extending the whole project.
关键路径分析确定决定项目最短工期的、最长的一连串依赖活动，指出哪些任务不能延迟，否则将延长整个项目。
Earliest Start Time (EST) is found through a forward pass:
最早开始时间通过正向推算得出：
EST = Earliest completion time of all preceding activities
Latest Finish Time (LFT) is found through a backward pass from the project end:
最晚完成时间通过从项目终点逆向推算得出：
LFT = Minimum LFT of following activities minus their duration
Float (slack) shows how much an activity can be delayed without affecting the project finish date:
浮动时间（时差）表示某项活动可延迟多久而不影响项目完成日期：
Float = LFT - Duration - EST
Activities with zero float lie on the critical path. Managers focus resources on these to avoid costly overruns.
浮动时间为零的活动处于关键路径上。管理者将资源集中在这些活动上，以避免代价高昂的延期。
9. Break‑even Analysis | 盈亏平衡分析
Break‑even analysis determines the output level at which total revenue equals total costs. It supports decisions on pricing, cost control, and target profits.
盈亏平衡分析确定总收入等于总成本时的产出水平，为定价、成本控制和目标利润决策提供支持。
Contribution per unit is the amount each unit sold contributes towards fixed costs and profit:
单位贡献毛益是每售出一单位产品用以弥补固定成本和创造利润的金额：
Contribution per Unit = Selling Price - Variable Cost per Unit
Break‑even Point (in units) is then:
盈亏平衡点（以数量表示）的计算公式为：
Break‑even Output = Total Fixed Costs ÷ Contribution per Unit
Break‑even revenue = Break‑ Selling Price. The Margin of Safety indicates how far sales can fall before losses occur:
盈亏平衡收入 = 盈亏平衡产量 × 售价。安全边际显示在出现亏损之前销售额可以下降的幅度：
Margin of Safety = Actual Output - Break‑even Output
A high margin of safety suggests resilience, while a narrow one signals vulnerability to demand fluctuations.
较高的安全边际表明抗风险能力强，安全边际狭窄则表明容易受需求波动影响。
Target profit output can be found by adding desired profit to fixed costs:
目标利润产量可通过将期望利润加入固定成本来计算：
Output for Target Profit = (Fixed Costs + Target Profit) ÷ Contribution per Unit
10. Budgets and Variance Analysis | 预算与差异分析
Budgets set financial targets, and variance analysis compares actual outcomes with budgeted figures to highlight areas needing management attention.
预算设定财务目标，差异分析将实际结果与预算数字进行比较，以突出需要管理层关注的领域。
A variance is favourable (F) if it increases profit and adverse (A) if it reduces profit:
如果偏差增加了利润，则为有利差异；如果减少了利润，则为不利差异：
Variance = Actual Figure - Budgeted Figure
For revenue, a positive variance is favourable; for costs, a positive variance is adverse. Sub‑variances can be broken down into price and volume components, especially in manufacturing.
对于收入，正差异是有利的；对于成本，正差异是不利的。偏差还可分解为价格差异和数量差异，尤其在制造业中运用广泛。
Sales Volume Variance isolates the effect of selling a different quantity than planned:
销售数量差异分离出实际销量与计划销量不同所带来的影响：
s Volume Variance = (Actual Quantity - Budgeted Quantity) × Standard Contribution per Unit
Sales Price Variance captures the impact of charging a different price:
销售价格差异反映实际售价与预算售价不同产生的影响：
Sales Price Variance = (Actual Price - Budgeted Price) × Actual Quantity Sold
Interpreting variances requires managers to investigate root causes rather than simply labelling figures as ‘good’ or ‘bad’.
解读差异需要管理者探究根本原因，而不是简单地给数字贴上“好”或“坏”的标签。
11. Elasticities of Demand | 需求弹性
Elasticity measures responsiveness. Price, income, and cross elasticities help firms forecast the impact of pricing changes, economic cycles, and competitors' actions on demand.
弹性衡量反应程度。价格弹性、收入弹性和交叉弹性帮助企业预测价格变动、经济周期和竞争对手行为对需求的影响。
Price Elasticity of Demand (PED):
需求的价格弹性：
PED = (% Change in Quantity Demanded) ÷ (% Change in Price)
If |PED| > 1, demand is elastic (revenue rises when price falls). If |PED| < 1, demand is inelastic (revenue rises when price rises). Unitary elasticity leaves revenue unchanged.
若 |PED| > 1，需求富有弹性（降价使收入增加）；若 |PED| < 1，需求缺乏弹性（提价使收入增加）。单位弹性下收入不变。
Income Elasticity of Demand (YED):
需求的收入弹性：
YED = (% Change in Quantity Demanded) ÷ (% Change in Income)
Positive YED indicates a normal good; negative YED indicates an inferior good. Luxury goods typically have YED > 1, making them very sensitive to economic cycles.
正的 YED 表示正常商品；负的 YED 表示低档商品。奢侈品的 YED 通常大于 1，对经济周期非常敏感。
Cross Elasticity of Demand (XED):
需求的交叉弹性：
XED = (% Change in Quantity Demanded of Good A) ÷ (% Change in Price of Good B)
A positive XED signals substitute goods; a negative XED signals complements. Near‑zero XED suggests independent products.
正的 XED 表示替代品；负的 XED 表示互补品。接近零的 XED 表明产品之间关系不大。
12. Stock Control: Economic Order Quantity (EOQ) | 库存控制：经济订货量
The EOQ model determines the optimal order size that minimises total inventory costs, balancing ordering costs against holding costs.
经济订货量模型确定使总库存成本最小的最优订货批量，在订货成本与持有成本之间取得平衡。
EOQ = √2 × Annual Demand × Order Cost ÷ Holding Cost per Unit per Year
Assumptions include constant demand, immediate delivery, and no quantity discounts. In reality, businesses adjust reorder levels to include buffer stock, but EOQ remains a helpful starting point for managing inventory.
该模型假设需求恒定、即时交货且无数量折扣。现实中，企业会调整再订货水平并预留安全库存，但 EOQ 仍是有用的库存管理起点。
Managers also calculate the reorder level to ensure stock arrives before it runs out:
管理者还会计算再订货水平，确保库存耗尽前新货到达：
Reorder Level = Maximum Lead Time × Maximum Usage
Combining EOQ with a well‑judged reorder level and buffer stock allows a business to maintain service levels without tying up excessive working capital.
将 EOQ 与合理的再订货水平和安全库存相结合，企业就能在维持服务水平的同时，避免占用过多营运资本。
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