📚 Cambridge A2 Accounting Formula & Theorem Quick Reference | 剑桥A2会计公式定理速查手册
This quick-reference guide brings together the essential formulas, ratios and logical relationships required in Year 13 Cambridge International A Level Accounting. Use it to revise interpretation of financial statements, cost and management accounting, investment appraisal, budgeting and consolidated accounts. Every entry is presented in paired English and Chinese paragraphs for clarity and bilingual learning.
本速查手册汇集了剑桥国际A Level会计Year 13阶段所有重要的公式、比率和逻辑关系，涵盖财务报表解释、成本与管理会计、投资评估、预算以及合并报表等内容。每个条目均以中英配对的形式呈现，便于双语理解和复习。
1. Profitability Ratios | 盈利能力比率
Gross profit margin measures the percentage of revenue that exceeds the cost of sales. It is a primary indicator of trading success.
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
毛利润率衡量收入中超过销售成本的百分比，是衡量交易成果的首要指标。
Net profit margin (often profit for the year) expresses the final profit after all expenses relative to revenue.
Net Profit Margin = (Profit for the Year ÷ Revenue) × 100%
净利润率（通常使用年度利润）表示扣除所有费用后最终利润占收入的比重。
Return on capital employed evaluates the overall return generated from the total long-term capital invested in the business.
ROCE = (Profit before Interest and Tax ÷ Capital Employed) × 100%
已动用资本回报率衡量企业通过长期资本所创造的总体回报。资本通常定义为非流动负债加权益。
Return on equity focuses on the return attributable to ordinary shareholders.
ROE = (Profit after Tax and Preference Dividends ÷ Total Equity) × 100%
净资产收益率衡量归属于普通股股东的回报，通常高于ROCE时才增加股东财富。
2. Liquidity and Efficiency Ratios | 流动性与效率比率
The current ratio tests the ability of the business to meet its short-term obligations using current assets.
Current Ratio = Current Assets ÷ Current Liabilities
流动比率测试企业使用流动资产偿还短期债务的能力，通常以倍数表示。
The acid-test (quick) ratio excludes inventories from current assets to give a stricter measure of immediate liquidity.
Acid-Test Ratio = (Current Assets – Inventory) ÷ Current Liabilities
速动比率将存货从流动资产中剔除，提供更严格的即时流动性衡量标准。
Inventory turnover (times) shows how many times inventory is sold and replaced in a period.
Inventory Turnover = Cost of Sales ÷ Average Inventory
存货周转次数反映一定时期内存货被销售和补充的次数。
Trade receivables days indicates the average credit period taken by credit customers.
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
应收账款周转天数表明赊销客户平均占用信用的天数。
Trade payables days measures the average time taken to pay suppliers.
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数衡量企业支付供应商的平均期限。
Working capital cycle combines inventory days, receivables days and payables days into one cash-to-cash cycle.
Working Capital Cycle = Inventory Days + Receivables Days – Payables Days
营运资金周期将存货天数、应收天数和应付天数结合，反映现金到现金的循环时长。
3. Investment and Gearing Ratios | 投资与杠杆比率
Earnings per share (EPS) measures the profit attributable to each ordinary share in issue.
EPS = (Profit after Tax – Preference Dividends) ÷ Weighted Average Ordinary Shares
每股收益衡量每一普通股应占的利润份额，是评价盈利能力的核心指标。
The price/earnings (P/E) ratio links the market price of a share to its earnings, reflecting growth expectations.
P/E Ratio = Market Price per Share ÷ Earnings per Share
市盈率将每股市价与每股收益联系起来，反映了市场对公司未来增长的预期。
Dividend yield expresses the cash return on investment for a shareholder, relative to market price.
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%
股息率表示股东从现金股息中获得的回报占市价的百分比。
Dividend cover measures how many times the current year’s profit could pay the proposed dividend.
Dividend Cover = Profit for the Year ÷ Total Dividend
股利保障倍数显示本年度利润能够支付拟派发股利的倍数。
Gearing ratio indicates the proportion of capital employed that is financed by interest-bearing debt.
Gearing = (Non-current Debt ÷ Capital Employed) × 100%
杠杆比率揭示长期付息债务在已动用资本中所占的比例。高杠杆意味着财务风险较大。
Interest cover shows the number of times profit can cover the interest charge.
Interest Cover = Profit before Interest and Tax ÷ Interest Payable
利息保障倍数反映利润可覆盖利息费用的倍数，越低则偿债风险越高。
4. Cost-Volume-Profit Analysis | 成本数量利润分析
Contribution per unit is the selling price less all variable costs; it contributes towards fixed costs and profit.
Contribution per Unit = Selling Price – Variable Cost per Unit
单位边际贡献等于售价减去全部变动成本，用于补偿固定成本并产生利润。
The break-even point in units is the number of units that must be sold to cover all fixed costs.
Break-even (units) = Total Fixed Costs ÷ Contribution per Unit
盈亏平衡销量是指恰好覆盖全部固定成本所需售出的产品数量。
Break-even revenue uses the contribution-to-sales ratio to find the revenue needed to break even.
Break-even Revenue = Total Fixed Costs ÷ C/S Ratio
盈亏平衡收入使用边际贡献率来计算达到盈亏平衡所需要的销售收入总额。
The C/S ratio expresses contribution as a percentage of sales and helps with multi-product analysis.
C/S Ratio = (Contribution per Unit ÷ Selling Price) × 100%
边际贡献率将单位边际贡献表示为售价的百分比，有助于分析多产品情形。
Margin of safety shows how much sales can fall before the business reaches its break-even point.
Margin of Safety = Actual Sales – Break-even Sales (units or revenue)
安全边际衡量实际销售量高于盈亏平衡点的幅度，可用数量或收入表示。
Target profit volume adds desired profit to fixed costs and divides by contribution per unit.
Target Sales (units) = (Fixed Costs + Target Profit) ÷ Contribution per Unit
目标利润销量将目标利润计入分子，求出达到目标利润所需的销量。
5. Absorption vs Marginal Costing Profit Reconciliation | 吸收成本法与边际成本法利润调节
Under absorption costing, fixed production overheads are included in inventory valuation, whereas under marginal costing they are treated as period costs. The difference in profit arises solely from the change in inventory levels multiplied by the fixed overhead absorption rate per unit.
Profit Difference = (Closing Inventory – Opening Inventory) × Fixed Overhead Rate per Unit
在吸收成本法下，固定生产间接费用计入存货价值；而在边际成本法下，固定生产间接费用被视为期间费用。利润的差异完全由存货数量的变化乘以每单位固定间接费用吸收率决定。
When production exceeds sales, inventory increases and absorption costing reports a higher profit than marginal costing.
当产量大于销量时，存货增加，吸收成本法下的利润会高于边际成本法下的利润。
When sales exceed production, inventory decreases and marginal costing reports a higher profit.
当销量大于产量时，存货减少，边际成本法下的利润反而更高。
The reconciliation statement is often required in multi-period scenarios to align the two profit figures.
跨期决策时常需要编制利润调节表，使两种成本法下的利润数字相互衔接。
6. Standard Costing Variances: Materials & Labour | 标准成本差异：材料与人工
Total direct material variance can be split into price and usage sub-variances. The price variance is calculated at the time of purchase using actual quantity purchased.
Material Price Variance = (Standard Price – Actual Price) × Actual Quantity Purchased
直接材料总差异可分为价格差异和用量差异。材料价格差异按采购时计算，使用实际采购数量。
Material usage variance compares the actual quantity used with the standard quantity allowed for actual production, valued at standard price.
Material Usage Variance = (Standard Quantity for Actual Output – Actual Quantity Used) × Standard Price
材料用量差异将实际用量与实际产量允许的标准用量进行比较，并以标准价格计价。
Labour rate variance isolates the effect of paying a different actual rate per hour compared to the standard rate, for the actual hours worked.
Labour Rate Variance = (Standard Rate – Actual Rate) × Actual Hours Worked
人工工资率差异反映实际支付的小时工资率与标准工资率之间的差异，按实际工时计算。
Labour efficiency variance measures the productivity of labour by comparing actual hours worked with standard hours allowed for actual production.
Labour Efficiency Variance = (Standard Hours for Actual Output – Actual Hours Worked) × Standard Rate
人工效率差异通过比较实际工时与实际产量允许的标准工时，评估人工的生产效率。
Variable overhead variances follow exactly the same logic: expenditure and efficiency sub-variances.
Variable Overhead Expenditure Variance = (Standard Rate – Actual Rate) × Actual Hours
变动间接费用差异结构相同，分为开支差异和效率差异，均以标准分配率为基础计算。
7. Standard Costing Variances: Fixed Overheads & Sales Margins | 标准成本差异：固定间接费用与销售利润差异
Fixed production overhead total variance is the difference between actual fixed overhead and absorbed fixed overhead. It is analysed into expenditure and volume variances.
Fixed Overhead Expenditure Variance = Budgeted Fixed Overhead – Actual Fixed Overhead
固定生产间接费用总差异为实际固定间接费用与已吸收固定间接费用之间的差额，可拆分为开支差异和产量差异。
The volume variance shows over- or under-absorption caused by producing a different number of units than budgeted.
Fixed Overhead Volume Variance = (Actual Production Units – Budgeted Production Units) × Standard Fixed Overhead Rate per Unit
产量差异揭示由于实际产量与预算产量不一致而导致的过度吸收或吸收不足。
Sales margin price variance quantifies the effect of selling products at a price different from the standard selling price, valued at actual sales units.
Sales Price Variance = (Actual Price – Standard Price) × Actual Quantity Sold
销售价格差异衡量实际售价偏离标准售价对利润的影响，按实际销量计算。
Sales volume profit variance measures the impact on profit of selling a different quantity than budgeted, using the standard profit per unit.
Sales Volume Profit Variance = (Actual Units Sold – Budgeted Units Sold) × Standard Profit per Unit
销售数量利润差异反映实际销量与预算销量不同所导致的利润差异，以单位标准利润为基础。
When using marginal costing, the volume variance is valued at standard contribution per unit instead of profit.
在边际成本法下，销售数量差异则使用每单位标准边际贡献，而非标准利润。
8. Capital Investment Appraisal: Payback, ARR & NPV | 投资评估：回收期、会计报酬率与净现值
Payback period calculates the time required for the net cash inflows from an investment to recoup the initial outlay.
Payback = Year before full recovery + (Unrecovered Amount ÷ Cash Inflow in Next Year)
回收期计算投资项目产生的净现金流入收回初始投资额所需的时间。
Accounting rate of return uses average annual accounting profit (after depreciation) as a percentage of the initial investment.
ARR = (Average Annual Profit ÷ Initial Investment) × 100%
会计报酬率以平均每年会计利润（扣除折旧后）占初始投资的百分比表示。
Net present value discounts all future cash flows at the cost of capital and subtracts the initial investment. A positive NPV means the project is financially acceptable.
NPV = Σ [Cash Flowₜ × (1 + r)⁻ᵗ] – Initial Investment
净现值以资本成本为折现率，将未来各期现金流折现后减去初始投资。NPV为正即表明项目在财务上可以接受。
Discount factors can be taken from present value tables. The general single-period factor is (1 + r)⁻ⁿ.
折现系数可从现值表查询。通用单期折现因子为(1 + r)⁻ⁿ。
9. Internal Rate of Return and Profitability Index | 内部收益率与盈利指数
IRR is the discount rate that makes the NPV equal to zero. It is estimated by linear interpolation between two rates that give a positive and a negative NPV.
IRR = L + [NPVₗ ÷ (NPVₗ – NPVₕ)] × (H – L)
内部收益率是使净现值为零的折现率，通常通过插值法在两个贴现率之间估算。L为较低贴现率，H为较高贴现率。
The profitability index (PI) shows the value created per unit of investment, often used when capital is rationed.
Profitability Index = Present Value of Future Cash Flows ÷ Initial Investment
盈利指数显示每单位投资所创造的价值，在资本限额下用于优选方案。指数大于1即可接受。
When ranking mutually exclusive projects under capital rationing, the profitability index helps identify the best combination of projects.
在资金限额下对互斥项目进行排序时，盈利指数有助于确定最佳的项目组合。
10. Budgeting: Key Operational Budget Formulas | 预算：关键业务预算公式
The production budget converts sales volume into required production units after adjusting for inventory of finished goods.
Required Production = Budgeted Sales + Desired Closing Finished Goods – Opening Finished Goods
生产预算通过调整成品库存，将预算销售量转换为所需生产量。
The material purchases budget calculates the quantity of raw materials to buy after considering desired closing raw material inventory.
terial Purchases (units) = Material Required for Production + Desired Closing Raw Material – Opening Raw Material
材料采购预算在考虑原材料期末库存后，计算需采购的原材料数量。
A cash budget determines the closing cash balance by listing all inflows and outflows over the period.
Closing Cash = Opening Cash + Total Receipts – Total Payments
现金预算按期初现金加本期现金流入减本期现金流出，得出期末现金余额。
When preparing a cash budget, non-cash items such as depreciation are excluded. Only cash movements are recorded.
编制现金预算时，折旧等非现金项目应予剔除，仅记录现金流量。
11. Incomplete Records: Mark-up and Margin | 不完整记录：加成率与毛利率
When full records are not kept, gross profit can be estimated using a constant relationship between sales, cost of sales and gross profit. Mark-up is the profit expressed as a percentage of cost of sales.
Mark-up = (Gross Profit ÷ Cost of Sales) × 100%
在不完整记录下，可以利用销售收入、销售成本和毛利之间的固定关系估算毛利。加成率是以销售成本为基数的利润率。
Margin (gross margin) expresses gross profit as a percentage of sales. It is always smaller than the corresponding mark-up.
Margin = (Gross Profit ÷ Sales) × 100%
毛利率是以销售收入为基数的利润率，其数值始终小于对应的加成率。
To convert mark-up to margin: Margin = Mark-up ÷ (100% + Mark-up) × 100%. Conversely, Mark-up = Margin ÷ (100% – Margin) × 100%.
Margin % = (Mark-up % ÷ (100 + Mark-up %)) × 100%
将加成率转换为毛利率：毛利率 = 加成率 ÷ (1 + 加成率) × 100%。反向换算也是可行的。
Closing inventory can be estimated using sales and margin to derive cost of goods sold, then the cost of goods available for sale less cost of sales gives the closing inventory. This is critical when stock is lost or destroyed.
Estimated Closing Inventory = Opening Inventory + Purchases – (Sales × (100% – Margin%))
期末存货可通过期初存货加购货，减去按销售和毛利率估算的销售成本来推算，这对认定存货损失尤为关键。
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