📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
In the Cambridge International AS & A Level Accounting syllabus, a solid grasp of formulas, key ratios and underlying theorems is essential for success. This handbook brings together every vital equation you will need — from liquidity and profitability ratios to costing and variance analysis — presented in a clear, bilingual format so you can reinforce understanding in both English and Chinese. Use this as your go‑to checklist when revising for examinations or tackling case studies. Work through each section systematically, test your recall and practise applying the formulas to scenario‑based problems.
在剑桥国际 AS 与 A Level 会计课程大纲中，牢固掌握公式、关键比率和基本原理是取得成功的必要条件。本手册汇总了你将需要的每一项重要等式——从流动性与盈利能力比率到成本计算和差异分析——以清晰的双语对照形式呈现，帮助你用中英文同时加深理解。复习备考或攻克案例题时，可以把这本手册作为你的首选速查清单。系统性地消化每个小节，测试记忆，并在情景问题中反复练习应用这些公式。
1. Liquidity Ratios | 流动比率
Liquidity ratios measure a business’s ability to meet its short‑term obligations as they fall due. The two core liquidity ratios are the current ratio and the quick ratio (acid test). These ratios are calculated from the statement of financial position and are crucial for assessing working capital health.
流动比率衡量企业到期偿还短期债务的能力。两个核心流动性指标是流动比率和速动比率（酸性测试）。这些比率根据财务状况表计算，对于评估营运资金健康状况至关重要。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
Quick Ratio (Acid Test) = (Current Assets – Inventories) ÷ Current Liabilities
速动比率（酸性测试）=（流动资产 – 存货）÷ 流动负债
- The quick ratio excludes inventories because they are considered the least liquid current asset. A ratio of 1:1 is often regarded as a safe standard for the quick ratio, while a current ratio of around 2:1 is traditionally seen as healthy, but benchmarks vary by industry.
- 速动比率剔除存货，因为它被认为是流动性最差的流动资产。速动比率 1:1 通常被视为安全标准，而流动比率约 2:1 传统上被认为是健康的，但行业基准各不相同。
- Overly high liquidity ratios may indicate inefficient use of resources, while very low ratios signal potential cash flow problems.
- 流动比率过高可能表示资源使用效率低下，而过低的比率则预示潜在的现金流问题。
2. Profitability Ratios | 盈利能力比率
Profitability ratios evaluate how effectively a business generates profit relative to sales, assets and equity. These ratios help stakeholders judge the return they are receiving and the efficiency of cost control.
盈利能力比率评估企业相对于销售额、资产和权益创造利润的有效性。这些比率帮助利益相关者判断他们获得的回报以及成本控制的效率。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
毛利率 =（毛利 ÷ 营业收入）× 100%
Profit for the Year Margin (Net Profit Margin) = (Profit for the Year ÷ Revenue) × 100%
年度利润率（净利润率）=（年度利润 ÷ 营业收入）× 100%
Return on Capital Employed (ROCE) = (Profit from Operations ÷ Capital Employed) × 100%
已动用资本回报率（ROCE）=（经营利润 ÷ 已动用资本）× 100%
- Capital employed is usually calculated as total assets less current liabilities, or as equity plus non‑current liabilities. ROCE is sometimes called the primary profitability ratio because it shows how well the long‑term funds are being used.
- 已动用资本通常按总资产减流动负债计算，或按权益加非流动负债计算。ROCE 有时被称为首要盈利能力比率，因为它展示了长期资金的使用效果。
- A rising gross profit margin suggests better control of direct costs or stronger pricing power, while a falling net profit margin may indicate growing overheads.
- 毛利率上升表明直接成本控制更好或定价能力增强，而净利润率下降可能表明间接费用在增长。
3. Efficiency Ratios | 效率比率
Efficiency ratios reveal how well a business utilises its assets and manages its liabilities. They focus on turnover speeds for inventory, trade receivables and trade payables, giving insight into working capital management.
效率比率揭示企业利用资产和管理负债的情况。它们聚焦于存货、应收账款和应付账款的周转速度，提供对营运资金管理的洞察。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventories
存货周转率（次）= 销售成本 ÷ 平均存货
de Receivables Collection Period (days) = (Trade Receivables ÷ Credit Sales Revenue) × 365
应收账款回收期（天）=（应收账款 ÷ 赊销收入）× 365
Trade Payables Payment Period (days) = (Trade Payables ÷ Credit Purchases) × 365
应付账款支付期（天）=（应付账款 ÷ 赊购额）× 365
- turnover suggests efficient stock management, but excessively high turnover may risk stock‑outs.
- 存货周转率也可用天数表示：（平均存货 ÷ 销售成本）× 365。高周转率表明库存管理高效，但过高的周转率可能导致缺货风险。
- The collection period should be compared with the credit terms offered to customers; if it is significantly longer, the business may have poor credit control.
- 回收期应与给予客户的信用条款进行比较；如果明显更长，企业可能存在信用控制不佳的问题。
4. Investment Ratios | 投资比率
Investment ratios are used by shareholders and potential investors to assess the performance and value of a company’s shares. Key ratios include earnings per share, price‑earnings ratio and dividend yield, often examined in the context of limited companies.
投资比率被股东和潜在投资者用来评估公司股票的表现和价值。关键比率包括每股收益、市盈率和股息率，常在有限公司的背景下考查。
Earnings per Share (EPS) = (Profit for the Year – Preference Dividends) ÷ Number of Ordinary Shares in Issue
每股收益（EPS）=（年度利润 – 优先股股息）÷ 已发行普通股股数
Price‑Earnings (P/E) Ratio = Market Price per Share ÷ Earnings per Share
市盈率（P/E）= 每股市价 ÷ 每股收益
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%
股息率 =（每股股息 ÷ 每股市价）× 100%
- EPS shows the theoretical profit attributable to each ordinary share. It is a fundamental driver of share price.
- EPS 显示理论上归属于每一普通股的利润。它是股价的基本驱动力。
- A high P/E ratio may indicate the market expects high future growth, while a low P/E might suggest undervaluation or limited prospects.
- 高市盈率可能表明市场预期未来高增长，而低市盈率可能暗示估值偏低或前景有限。
5. Costing Formulas | 成本计算公式
Costing techniques — particularly marginal costing — are central to decision‑making. Formulas for contribution, break‑even point and margin of safety enable managers to plan production levels, set prices and evaluate profitability at different volumes.
成本计算技术——尤其是边际成本法——是决策的核心。贡献、盈亏平衡点和安全边际的公式使管理者能够规划生产水平、设定价格并评估不同产量下的盈利能力。
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 = Total Sales Revenue – Total Variable Costs
总贡献 = 销售总收入 – 总变动成本
Break‑Even Point (units) = Total Fixed Costs ÷ Contribution per Unit
盈亏平衡点（单位）= 总固定成本 ÷ 单位贡献
Break‑ Point (sales value) = (Total Fixed Costs ÷ Contribution per Unit) × Selling Price per Unit
盈亏平衡点（销售额）=（总固定成本 ÷ 单位贡献）× 单位售价
Margin of Safety (units) = Actual Sales Units – Break‑Even Sales Units
安全边际（单位）= 实际销售量 – 盈亏平衡销售量
- ntribution to sales (C/S) ratio is: (Contribution per Unit ÷ Selling Price per Unit) × 100% It indicates the proportion of each sale that contributes towards fixed costs and profit.
- 贡献销售比（C/S 比）为：（单位贡献 ÷ 单位售价）× 100%。它表示每一笔销售中用于弥补固定成本和创造利润的比例。
- Margin of safety can be expressed as a percentage: (Margin of Safety ÷ Actual Sales) × 100%.
- 安全边际可用百分比表示：（安全边际 ÷ 实际销售量）× 100%。
6. Inventory Valuation | 存货估值
Inventories must be valued at the lower of cost and net realisable value (NRV). Cost can be determined using methods such as first‑in, first‑out (FIFO) or average cost (AVCO). These methods affect reported profit and inventory values in the statement of financial position.
存货必须按成本与可变现净值（NRV）孰低计价。成本可以采用先进先出法（FIFO）或平均成本法（AVCO）等方法确定。这些方法会影响利润表和财务状况表中存货的价值。
Cost of Sales = Opening Inventory + Purchases – Closing Inventory
销售成本 = 期初存货 + 采购 – 期末存货
FIFO: The earliest purchased items are assumed to be issued or sold first. Closing inventory consists of the most recent purchases, reflecting current prices more closely.
FIFO（先进先出法）： 假设最早购入的存货最先被发出或售出。期末存货由最近购入的批次组成，更贴近当前价格。
AVCO: A weighted average cost per unit is recalculated after each purchase. The average cost is then used to value issues and closing inventory.
AVCO（平均成本法）： 每次采购后重新计算加权平均单位成本，然后用平均成本对发出和期末存货进行计价。
Net Realisable Value (NRV) = Estimated Selling Price – Estimated Costs to Completion and Selling
可变现净值（NRV）= 估计售价 – 估计完工及销售费用
- In CIE examinations, both periodic and perpetual AVCO may be required; the periodic weighted average is computed at the end of the period, while perpetual AVCO updates after every receipt.
- 在 CIE 考试中，可能要求计算定期和永续 AVCO；定期加权平均在期末计算，而永续 AVCO 在每次收货后更新。
7. Depreciation Methods | 折旧方法
Depreciation spreads the cost of a non‑current asset over its useful life. The two common methods are the straight‑line method and the reducing (diminishing) balance method. The choice of method impacts the annual depreciation charge and the carrying amount of the asset.
折旧将非流动资产的成本在其使用寿命内分摊。两种常见的方法是直线法和余额递减法。方法的选择会影响每年的折旧费用和资产的账面金额。
Straight‑Line Depreciation per Year = (Cost – Residual Value) ÷ Useful Life
年直线法折旧额 =（成本 – 残值）÷ 使用年限
Reducing Balance Depreciation = Carrying Amount at Start of Year × Depreciation Rate (%)
余额递减法折旧 = 年初账面金额 × 折旧率（%）
- The straight‑line method charges an equal amount each year, making it suitable for assets that provide even benefits, such as buildings. The reducing balance method charges more depreciation in the early years, which suits assets that lose value quickly, like vehicles.
- 直线法每年计提等额折旧，适用于提供均匀利益的资产，如建筑物。余额递减法在早期计提更多折旧，适用于快速贬值的资产，如车辆。
- If an asset is revalued, depreciation is subsequently based on the revalued amount over its remaining useful life.
- 如果资产被重估，折旧随后基于重估金额在剩余使用年限内计提。
8. Working Capital Management | 营运资金管理
Working capital is the capital available for day‑to‑day operations. Managing the cash conversion cycle is vital to liquidity. The working capital cycle formula links inventory, receivables and payables days.
营运资金是可用于日常经营的资本。管理现金转换周期对流动性至关重要。营运资金周期公式将存货、应收账款和应付账款天数联系起来。
Working Capital = Current Assets – Current Liabilities
营运资金 = 流动资产 – 流动负债
Working Capital Cycle (days) = Inventory Turnover Days + Receivables Collection Days – Payables Payment Days
营运资金周期（天）= 存货周转天数 + 应收账款回收天数 – 应付账款支付天数
- of Sales) × 365. A shorter cycle means cash is tied up for less time, improving liquidity.
- 存货周转天数 =（平均存货 ÷ 销售成本）× 365。周期越短，现金占用时间越少，流动性改善。
- Overtrading occurs when a business expands beyond its working capital resources, leading to severe liquidity problems even when profitable.
- 当企业扩张超出其营运资金资源时，会发生过度交易，导致即使盈利也出现严重的流动性问题。
9. The Accounting Equation and Double Entry | 会计等式与复式记账
The accounting equation is the foundation of the double‑entry system. It ensures that the statement of financial position always balances and that every transaction has a dual effect.
会计等式是复式记账系统的基础。它确保财务状况表始终平衡，且每笔交易都有双重影响。
Assets = Capital + Liabilities
资产 = 资本 + 负债
Assets = (Opening Capital + Profit – Drawings) + Liabilities
资产 =（期初资本 + 利润 – 提款）+ 负债
- The expanded form shows how profit earned during the period increases the owner’s equity, while drawings reduce it. This relationship underpins the preparation of the income statement and the statement of financial position.
- 扩展形式显示了期间内赚取的利润如何增加所有者权益，而提款则减少权益。这一关系构成利润表和财务状况表编制的基础。
- s replaced by share capital and reserves: Assets = Share Capital + Reserves + Liabilities.
- 对于有限公司，资本被股本和储备所取代：资产 = 股本 + 储备 + 负债。
10. Cash Flow Statements | 现金流量表
The statement of cash flows classifies cash inflows and outflows into operating, investing and financing activities. While not a single formula, the structure can be condensed into key equations that are regularly tested.
现金流量表将现金流入和流出分为经营活动、投资活动和融资活动。虽然不是单一公式，但其结构可以浓缩为常考的关键等式。
Net Cash Flow from Operating Activities = Cash Receipts from Customers – Cash Paid to Suppliers and Employees – Interest Paid – Tax Paid
经营活动净现金流量 = 从客户收到的现金 – 支付给供应商和员工的现金 – 支付的利息 – 支付的税款
Net Cash Used in Investing Activities = Purchase of Non‑current Assets – Proceeds from Sale of Non‑current Assets + Interest Received + Dividends Received
投资活动所用净现金 = 购买非流动资产 – 出售非流动资产收入 + 收到的利息 + 收到的股息
Net Cash from Financing Activities = Proceeds from Issue of Shares + New Borrowings – Repayment of Borrowings – Dividends Paid
融资活动净现金 = 发行股票收入 + 新增借款 – 偿还借款 – 支付的股息
f the three categories above, plus Cash and Cash Equivalents at the start, equals at the end.
现金净增加/减少 = 上述三类之和，加上期初现金及现金等价物，等于期末余额。
- In indirect method operating activities, we start with profit before tax and adjust for non‑cash items and changes in working capital.
- 在间接法下，经营活动从税前利润开始，调整非现金项目和营运资金变动。
11. Financial Statement Analysis and Ratios Framework | 财务报表分析与比率框架
Beyond individual ratios, examiners expect you to weave ratios together in a coherent analysis. This requires understanding the relationships among profitability, liquidity, efficiency and investment measures. The DuPont framework can be useful here, even if not explicitly named in CIE exams.
除了单个比率，考官期望你将比率结合起来进行连贯的分析。这需要理解盈利能力、流动性、效率和投资指标之间的关系。杜邦分析框架在此很有用，即使 CIE 考试中不一定明确提及。
ROCE can be decomposed as: Operating Profit Margin × Asset Turnover
ROCE 可分解为：经营利润率 × 资产周转率
Asset Turnover = Revenue ÷ Capital Employed (or Total Assets less Current Liabilities)
资产周转率 = 营业收入 ÷ 已动用资本（或总资产减流动负债）
- A business with a low profit margin but high asset turnover (e.g. supermarkets) can achieve a satisfactory ROCE, while one with high margins and low turnover (e.g. luxury goods) can achieve the same. This decomposition helps identify performance drivers.
- 一家利润率低但资产周转率高的企业（如超市）可以实现令人满意的 ROCE，而一家利润率高、周转率低的企业（如奢侈品）也能达到同样的效果。这种分解有助于识别业绩驱动因素。
- When analysing, always compare ratios with prior periods, industry averages and budgeted figures to form meaningful conclusions.
- 分析时，始终将比率与前期、行业平均水平和预算数字进行比较，以形成有意义的结论。
12. Budgeting and Variance Analysis | 预算与差异分析
Budgeting is a planning tool, and variance analysis compares actual performance against the budget. Variances are labelled as favourable (F) if they improve profit, or adverse (A) if they reduce profit. Standard costing variances for materials, labour and overheads are essential at A Level.
预算是一种规划工具，差异分析将实际业绩与预算进行比较。如果差异提高利润，则标记为有利 差异（F），如果减少利润则为不利差异（A）。直接材料、直接人工和制造费用的标准成本差异分析在 A Level 中至关重要。
Sales Volume Variance = (Actual Quantity Sold – Budgeted Quantity Sold) × Standard Profit per Unit
销售数量差异 =（实际销售量 – 预算销售量）× 单位标准利润
Material Price Variance = (Standard Price – Actual Price) × Actual Quantity Purchased
材料价格差异 =（标准价格 – 实际价格）× 实际采购量
Material Usage Variance = (Standard Quantity for Actual Output – Actual Quantity Used) × Standard Price
材料用量差异 =（实际产量的标准用量 – 实际用量）× 标准价格
Labour Rate Variance = (Standard Rate – Actual Rate) × Actual Hours Paid
工资率差异 =（标准工资率 – 实际工资率）× 实际支付工时
Labour Efficiency Variance = (Standard Hours for Actual Output – Actual Hours Worked) × Standard Rate
人工效率差异 =（实际产量的标准工时 – 实际工作工时）× 标准工资率
- Total cost variances can be split into price/rate and usage/efficiency components for both materials and labour. Fixed overhead variances (expenditure and volume) are also tested.
- 总成本差异可分为价格/工资率部分和用量/效率部分，适用于材料和人工。固定制造费用差异（支出差异和产量差异）也会考到。
- If actual performance is better than budgeted profit, then variances adding to profit are favourable. Variances are often linked to possible causes such as bulk discounts (favourable material price) or poor quality materials (adverse material usage).
- 如果实际业绩优于预算利润，则增加利润的差异为有利差异。差异通常与可能的原因相关联，例如批量折扣（有利的材料价格差异）或劣质材料（不利的材料用量差异）。
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