📚 Year 13 CIE Accounting: Formula & Theorem Quick Reference Handbook | Year 13 CIE 会计：公式定理速查手册
This handbook provides a concise yet thorough collection of the essential formulas, ratios, and theorems required for the Cambridge International A Level Accounting syllabus (9706). It is designed to help Year 13 students quickly review and consolidate their understanding of financial accounting and management accounting concepts ahead of assessment. Each section covers a core topic area, presenting formulas with plain‑English explanations followed immediately by a Chinese equivalent, ensuring clarity for bilingual learners.
本手册为剑桥国际 A Level 会计大纲 (9706) 汇集了必备的公式、比率与定理，内容简明全面。旨在帮助 Year 13 学生在评估前快速回顾并巩固财务会计与管理会计的核心概念。每个章节围绕一个重点主题，先以英文简明解释公式，随后附上对应的中文说明，让双语学习者一目了然。
1. Profitability Ratios | 盈利能力比率
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%. This ratio measures the percentage of sales revenue remaining after deducting the cost of goods sold. A higher margin indicates better control over direct production or purchasing costs.
毛利率 = (毛利 ÷ 营业收入) × 100%。该比率衡量扣除销货成本后销售收入留存的百分比。毛利率越高，说明企业对直接生产或采购成本的控制越强。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%. It shows how much of each dollar of sales is left after all expenses, including operating costs, interest, and taxes, have been covered.
净利率 = (净利润 ÷ 营业收入) × 100%。它显示每一元销售收入在支付包括营业费用、利息和税费在内的全部支出后所剩余的利润。
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%. Capital employed is typically calculated as Total Assets − Current Liabilities, or as Equity + Non‑current Liabilities. ROCE evaluates how efficiently a business uses its long‑term capital to generate profits.
已用资本回报率 (ROCE) = (营业利润 ÷ 已用资本) × 100%。已用资本通常按总资产 − 流动负债计算，或按权益 + 非流动负债计算。ROCE 用于评价企业运用长期资本创造利润的效率。
2. Liquidity Ratios | 流动性比率
Current Ratio = Current Assets ÷ Current Liabilities. This ratio shows a company’s ability to meet its short‑term obligations with its short‑term resources. A ratio between 1.5 and 2 is often considered satisfactory, but this depends on the industry.
流动比率 = 流动资产 ÷ 流动负债。该比率反映企业用短期资源偿还短期债务的能力。一般认为 1.5 至 2 之间的比率较为理想，但须结合行业特点判断。
Quick Ratio (Acid‑Test Ratio) = (Current Assets − Inventory) ÷ Current Liabilities. By removing inventory – often the least liquid current asset – this ratio gives a stricter test of immediate liquidity.
速动比率 (酸性测试比率) = (流动资产 − 存货) ÷ 流动负债。剔除通常流动性最低的存货后，该比率对即时流动性进行了更为严格的检验。
Inventory Turnover = Cost of Goods Sold ÷ Average Inventory. It measures how many times inventory is sold and replaced over a period. A higher turnover suggests efficient inventory management.
存货周转率 = 销货成本 ÷ 平均存货。衡量在一段时期内存货被售出及补充的次数。周转率越高，表明存货管理越高效。
Trade Receivables Collection Period = (Trade Receivables ÷ Credit Sales) × 365 days. This shows the average number of days it takes to collect debts from customers.
应收款项回收期 = (应收款项 ÷ 赊销额) × 365 天。该指标反映从客户处收回欠款的平均天数。
Trade Payables Payment Period = (Trade Payables ÷ Credit Purchases) × 365 days. It indicates how long, on average, a business takes to pay its suppliers.
应付款项支付期 = (应付款项 ÷ 赊购额) × 365 天。表明企业平均需多长时间支付供应商货款。
3. Efficiency and Gearing Ratios | 效率与杠杆比率
Non‑current Asset Turnover = Revenue ÷ Non‑current Assets. This ratio assesses how effectively a business uses its non‑current assets to generate sales.
非流动资产周转率 = 营业收入 ÷ 非流动资产。该比率衡量企业利用非流动资产创造销售收入的效率。
Gearing Ratio = (Non‑current Liabilities ÷ Capital Employed) × 100%, where capital employed is equity plus non‑current liabilities. It shows the proportion of a company’s long‑term funding that comes from debt. A high gearing ratio indicates higher financial risk.
杠杆比率 = (非流动负债 ÷ 已用资本) × 100%，其中已用资本为权益加上非流动负债。它显示企业长期资金中来源于债务的比例。杠杆率越高，财务风险越大。
Interest Cover = Operating Profit ÷ Finance Costs (Interest). This measures how many times a business can pay its interest charges out of its operating profit. A low interest cover signals difficulty in servicing debt.
利息保障倍数 = 营业利润 ÷ 融资成本 (利息)。衡量企业营业利润能覆盖利息支出的倍数。利息保障倍数低意味着偿债压力大。
4. Investment Appraisal | 投资评估
Payback Period = Number of full years before payback + (Unrecovered cost at start of year ÷ Net cash flow during the year). This method calculates how long it takes for an investment to recover its initial cost. Shorter payback periods are preferred.
投资回收期 = 投资收回前的完整年数 + (年初未收回成本 ÷ 当年净现金流)。该方法计算收回初始投资所需的时间，回收期越短越有利。
Accounting Rate of Return (ARR) = (Average Annual Operating Profit ÷ Average Investment) × 100%. Average investment is often calculated as (Initial cost + Residual value) ÷ 2. ARR is expressed as a percentage and compared with a target rate.
会计收益率 (ARR) = (平均年营业利润 ÷ 平均投资额) × 100%。平均投资额常按 (初始成本 + 残值) ÷ 2 计算。ARR 以百分比表示，并与目标收益率进行比较。
Net Present Value (NPV) = Σ (Net cash flow in year t × Discount factor for year t) − Initial investment. A positive NPV indicates that the project is expected to add value to the business. Discount factors are derived from the cost of capital.
净现值 (NPV) = 各年净现金流 × 对应年份折现系数的总和 − 初始投资。NPV 为正，表示该项目预期将增加企业价值。折现系数来自资本成本。
Internal Rate of Return (IRR) is the discount rate that makes the NPV equal to zero. It is usually found by interpolation: IRR = L% + [NPV at L% ÷ (NPV at L% − NPV at H%)] × (H% − L%), where L% gives a positive NPV and H% gives a negative NPV.
内部收益率 (IRR) 是使净现值为零的折现率。通常通过插值法求得：IRR = L% + [L%下的 NPV ÷ (L%下的 NPV − H%下的 NPV)] × (H% − L%)，其中 L% 给出正 NPV，H% 给出负 NPV。
5. Marginal and Absorption Costing | 边际成本法与吸收成本法
Marginal Costing: Contribution = Sales revenue − Variable costs. Profit = Total contribution − Fixed costs. Contribution per unit = Selling price per unit − Variable cost per unit. This method emphasises the behaviour of costs and is useful for short‑term decision‑making.
边际成本法：贡献 = 销售收入 − 变动成本。利润 = 总贡献 − 固定成本。单位贡献 = 单位售价 − 单位变动成本。该方法强调成本性态，在短期决策中尤为实用。
Break‑even Point (units) = Total Fixed Costs ÷ Contribution per Unit. At break‑even, total revenue equals total costs, resulting in zero profit.
盈亏平衡点 (数量) = 固定成本总额 ÷ 单位贡献。在盈亏平衡点，总收入等于总成本，利润为零。
Break‑even Point (dollar sales) = Total Fixed Costs ÷ (Contribution per Unit ÷ Selling Price per Unit), or alternatively = Total Fixed Costs ÷ C/S ratio. C/S ratio = (Contribution per unit ÷ Selling price per unit) × 100%.
盈亏平衡点 (金额) = 固定成本总额 ÷ (单位贡献 ÷ 单位售价)，或 = 固定成本总额 ÷ C/S 比率。C/S 比率 = (单位贡献 ÷ 单位售价) × 100%。
Margin of Safety = Actual or Budgeted Sales − Break‑even Sales. It indicates how much sales can fall before a business starts incurring a loss.
安全边际 = 实际或预算销售额 − 盈亏平衡销售额。它表明在亏损发生前销售额可以下降的幅度。
Target Profit Volume = (Total Fixed Costs + Target Profit) ÷ Contribution per Unit. This formula calculates the number of units that must be sold to achieve a desired profit.
目标利润销量 = (固定成本总额 + 目标利润) ÷ 单位贡献。该公式计算为实现预期利润所需销售的件数。
Absorption Costing: Total production cost = Direct materials + Direct labour + Variable production overheads + Fixed production overheads. Profit is calculated after recovering all manufacturing costs through cost of goods sold. Under/over‑absorbed overheads may arise when actual production differs from budgeted.
吸收成本法：总生产成本 = 直接材料 + 直接人工 + 变动制造费用 + 固定制造费用。利润在通过销售成本回收全部制造成本后计算。当实际产量与预算量不同时，可能出现制造费用吸收不足或吸收过度。
6. Standard Costing and Variance Analysis | 标准成本法与差异分析
Direct Material Price Variance = (Standard Price − Actual Price) × Actual Quantity Purchased. A favourable variance occurs when the actual price is lower than standard.
直接材料价格差异 = (标准价格 − 实际价格) × 实际采购量。当实际价格低于标准价格时产生有利差异。
Direct Material Usage Variance = (Standard Quantity for Actual Output − Actual Quantity Used) × Standard Price. This measures efficiency in material consumption.
直接材料用量差异 = (实际产量下的标准用量 − 实际用量) × 标准价格。用于衡量材料消耗的效率。
Direct Labour Rate Variance = (Standard Rate per Hour − Actual Rate per Hour) × Actual Hours Worked.
直接人工工资率差异 = (标准小时工资率 − 实际小时工资率) × 实际工作小时数。
Direct Labour Efficiency Variance = (Standard Hours for Actual Output − Actual Hours Worked) × Standard Rate per Hour.
直接人工效率差异 = (实际产量下的标准工时 − 实际工作小时数) × 标准小时工资率。
Variable Overhead Expenditure Variance = (Standard Variable Overhead Rate × Actual Hours) − Actual Variable Overhead Cost.
变动制造费用开支差异 = (标准变动制造费用率 × 实际小时数) − 实际变动制造费用成本。
Variable Overhead Efficiency Variance = (Standard Hours for Actual Output − Actual Hours) × Standard Variable Overhead Rate.
变动制造费用效率差异 = (实际产量下的标准工时 − 实际小时数) × 标准变动制造费用率。
Fixed Overhead Expenditure Variance = Budgeted Fixed Overhead − Actual Fixed Overhead.
固定制造费用开支差异 = 预算固定制造费用 − 实际固定制造费用。
Sales Volume Profit Variance = (Actual Sales Units − Budgeted Sales Units) × Standard Profit per Unit (under absorption costing) or Standard Contribution per Unit (under marginal costing).
销售量利润差异 = (实际销售数量 − 预算销售数量) × 单位标准利润 (吸收成本法下) 或单位标准贡献 (边际成本法下)。
Sales Price Variance = (Actual Selling Price − Standard Selling Price) × Actual Sales Quantity.
销售价格差异 = (实际售价 − 标准售价) × 实际销售数量。
7. Budgeting | 预算编制
Cash Budget Format: Opening cash balance + Cash receipts (from sales, receivables, etc.) − Cash payments (purchases, wages, overheads, capital expenditure, etc.) = Closing cash balance. The cash budget focuses solely on cash inflows and outflows, not on accrual‑based income.
现金预算格式：期初现金余额 + 现金收入 (来自销售、应收款项等) − 现金支付 (采购、工资、间接费用、资本支出等) = 期末现金余额。现金预算仅关注现金流入与流出，而非权责发生制下的收益。
Flexible Budget: A flexible budget adjusts variable costs for the actual level of activity. Flexed budget allowance for a variable cost = Original budget cost × (Actual output ÷ Budgeted output). Fixed costs remain unchanged within the relevant range. Comparison against a flexed budget provides more meaningful variances.
弹性预算：弹性预算根据实际活动水平调整变动成本。某项变动成本的弹性预算额度 = 原预算成本 × (实际产量 ÷ 预算产量)。固定成本在相关范围内保持不变。与弹性预算进行比较能够得出更有意义的差异。
8. Depreciation and Inventory Valuation | 折旧与存货估值
Straight‑line Depreciation = (Cost − Residual Value) ÷ Useful Life. The same amount of depreciation is charged each year.
直线折旧法 = (成本 − 残值) ÷ 使用年限。每年计提相同金额的折旧。
Reducing Balance Depreciation = Net Book Value at beginning of year × Depreciation Rate. This method charges a higher depreciation expense in earlier years.
余额递减折旧法 = 年初账面净值 × 折旧率。该方法在早期计提较高的折旧费用。
Sum‑of‑Years’ Digits: Depreciation fraction = Remaining life ÷ Sum of the years’ digits. The sum is calculated as n(n+1)/2 for an asset with n years of life. Annual depreciation = (Cost − Residual value) × the fraction for that year.
年数总和法：折旧分数 = 剩余使用年限 ÷ 年数总和。年数总和对于使用寿命为 n 年的资产为 n(n+1)/2。年折旧额 = (成本 − 残值) × 该年分数。
FIFO (First‑In, First‑Out): The earliest purchased inventory is assumed to be sold first. Closing inventory is valued at the most recent costs. In times of rising prices, FIFO results in lower cost of goods sold and higher closing inventory value.
FIFO (先进先出法)：假设最早购入的存货最先售出。期末存货按最近的成本计价。物价上升时，FIFO 导致较低的销货成本和较高的期末存货价值。
AVCO (Average Cost): Weighted average cost per unit = Total cost of goods available for sale ÷ Total units available. Both cost of goods sold and closing inventory are valued at this weighted average cost after each purchase or at the period end.
AVCO (加权平均成本法)：加权平均单位成本 = 可售商品总成本 ÷ 可售商品总数量。每次购货后或期末，销货成本和期末存货均按该加权平均成本计价。
9. Partnership and Company Accounting | 合伙与公司会计
Appropriation of Partnership Profit: Profit for the year − Interest on drawings + Interest on partners’ capitals − Partners’ salaries = Residual profit shared in the profit‑sharing ratio.
合伙企业利润分配：年度利润 − 提款利息 + 合伙人资本利息 − 合伙人薪资 = 剩余利润按利润分成比例分配。
Goodwill Calculation: Goodwill is often the excess of the purchase consideration over the fair value of net assets acquired. For admission or retirement of a partner, goodwill may be valued using average super‑profit method: Super profit = Average maintainable profit − (Normal rate of return × Capital employed). Goodwill = Super profit × Number of years’ purchase.
商誉计算：商誉通常为购买对价超过所收购净资产公允价值的差额。对于合伙人入伙或退伙，商誉可按平均超额利润法估值：超额利润 = 可维持的平均利润 − (正常回报率 × 已用资本)。商誉 = 超额利润 × 购买年数。
Rights Issue and Bonus Issue: In a rights issue, shares are offered to existing shareholders at a discount. Theoretical ex‑rights share price = (Market value of shares before issue + Cash raised) ÷ Total shares after the issue. A bonus issue capitalises reserves to issue free shares; there is no cash inflow, and the number of shares increases while the share price falls proportionally.
配股与红股发行：配股中，股票以折扣价向现有股东发售。理论除权股价 = (发行前股份市值 + 筹集的现金) ÷ 发行后股份总数。红股发行将储备金转增股本以派发免费股份，无现金流入，股份数量增加而股价按比例下降。
Earnings per Share (EPS) = (Net Profit − Preference Dividends) ÷ Weighted Average Number of Ordinary Shares. EPS is a key indicator of a company’s profitability on a per‑share basis.
每股收益 (EPS) = (净利润 − 优先股股息) ÷ 普通股加权平均股数。EPS 是衡量公司每股盈利能力的关键指标。
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%. It shows the return a shareholder receives in the form of dividends relative to the share’s market value.
股息收益率 = (每股股息 ÷ 每股市价) × 100%。反映股东以股息形式获得的回报与股票市价之间的关系。
10. Statement of Cash Flows (Indirect Method) | 现金流量表 (间接法)
Under the indirect method, cash flow from operating activities starts with profit before tax and adjusts for non‑cash items (depreciation, amortisation, profit/loss on disposal of non‑current assets), changes in working capital (increase/decrease in inventories, receivables, payables), and interest and tax paid. The result is net cash from operating activities.
在间接法下，经营活动现金流量从税前利润出发，调整非现金项目 (折旧、摊销、非流动资产处置利得/损失)、营运资本变动 (存货、应收、应付的增减) 以及已付利息和税款，最终得出经营活动现金净流量。
Key Adjustments:
主要调整：
Add back depreciation and amortisation; deduct gains on disposal; add losses on disposal. Increase in inventory: deduct; decrease in inventory: add. Increase in trade receivables: deduct; decrease: add. Increase in trade payables: add; decrease: deduct. Interest paid and income tax paid are often shown separately under IAS 7 or appropriate local standards.
加回折旧与摊销；扣减处置利得；加回处置损失。存货增加：扣减；存货减少：加回。应收款项增加：扣减；减少：加回。应付款项增加：加回；减少：扣减。已付利息和已付所得税通常根据 IAS 7 或适用的当地准则单独列示。
Cash flows from investing activities include purchase and disposal of non‑current assets, interest received, and dividends received. Cash flows from financing activities include proceeds from issuing shares, loans received, repayment of borrowings, and dividends paid.
投资活动现金流量包括购买和处置非流动资产、收到的利息和股息。筹资活动现金流量包括发行股份所得、借款所得、偿还借款和支付股息。
11. Consolidated Financial Statements | 合并财务报表
Goodwill on Acquisition: Consideration transferred + Fair value of non‑controlling interest (if measured at fair value) + Fair value of previously held equity interest (for step acquisitions) − Fair value of net assets acquired. Any excess is recognised as goodwill.
收购商誉：转移的对价 + 非控股权益的公允价值 (若按公允价值计量) + 先前持有权益的公允价值 (适用于分步收购) − 所收购净资产的公允价值。差额确认为商誉。
Non‑controlling Interest (NCI): NCI at the reporting date = NCI at acquisition + NCI share of post‑acquisition retained earnings and other reserves. The parent’s share of subsidiary’s post‑acquisition profits is added to consolidated retained earnings.
非控股权益 (NCI)：报告日 NCI = 收购日 NCI + NCI 在收购后留存收益及其他公积金中的份额。母公司享有的子公司收购后利润份额计入合并留存收益。
Intra‑group Transactions: Sales between group companies must be eliminated from consolidated revenue and cost of sales. Unrealised profit in closing inventory is removed by deducting it from the inventory value and from consolidated profit. Intra‑group payables and receivables are cancelled. Dividends paid by a subsidiary to the parent are eliminated.
集团内部交易：集团内部公司之间的销售必须从合并收入和销售成本中抵销。期末存货中未实现利润应从存货价值和合并利润中扣除。集团内部应收应付款项相互抵销。子公司支付给母公司的股利应予消除。
12. Ethical Principles and Accounting Concepts | 伦理原则与会计概念
While not formulas in the strictly numerical sense, the CIE syllabus requires understanding of fundamental principles that support all accounting work. The accruals concept states that transactions are recorded in the period to which they relate, not when cash is received or paid. The going concern concept assumes the business will continue operating for the foreseeable future. Prudence requires that assets and income are not overstated and liabilities and expenses are not understated. Consistency demands that the same accounting methods are applied from one period to the next. Materiality allows trivial items to be treated in a simpler way.
尽管以下内容并非严格意义上的数学公式，但 CIE 大纲要求学生理解支撑所有会计工作的基本概念。权责发生制概念规定交易在其所属期间记录，而非在现金收付时记录。持续经营概念假设企业在可预见的未来将继续运营。审慎性要求不得高估资产和收益，也不得低估负债和费用。一致性要求不同期间采用相同的会计方法。重要性原则允许对不重要的项目采取简便处理方式。
These concepts form the theoretical foundation for the more quantitative formulas, ensuring that the numbers produced are relevant, reliable, comparable, and understandable.
这些概念构成了定量公式的理论基础，确保所产生的数字具有相关性、可靠性、可比性和可理解性。
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