📚 Pre-U CAIE Accounting: Formulae & Theorems Quick Reference | Pre-U CAIE 会计：公式定理速查手册
This quick reference handbook compiles the essential formulas, theorems, and key principles for the Cambridge Pre-U Accounting syllabus. It serves as a rapid revision tool, covering financial accounting, management accounting, and investment appraisal. Use it to reinforce your understanding and boost exam confidence.
本速查手册汇编了剑桥Pre-U会计课程中的核心公式、定理和关键原理，可作为快速复习工具，涵盖财务会计、管理会计与投资评估。通过手册巩固理解，提升考试信心。
1. The Accounting Equation and the Balance Sheet | 会计等式与资产负债表
The fundamental accounting equation is the bedrock of double-entry bookkeeping and must always remain in balance.
基本会计等式是复式记账的基石，必须始终保持平衡。
Assets = Liabilities + Equity
这一等式揭示了企业资源与对这些资源的要求权之间的关系。
The expanded accounting equation shows how profit, drawings, and capital interact over an accounting period.
扩展会计等式揭示了一个会计期间内利润、提款和资本之间的互动关系。
Assets = Liabilities + Opening Capital + (Revenue − Expenses) − Drawings
该等式是编制资产负债表和利润表的核心逻辑。
2. Profitability Ratios | 盈利能力比率
Gross profit margin measures the percentage of revenue retained after covering the cost of sales.
毛利率衡量销售收入扣除销售成本后留存的百分比。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
该比率越高，企业保留的毛利空间越大。
Net profit margin indicates overall profitability after all operating expenses and costs are deducted.
净利率反映扣除所有经营费用和成本后的整体盈利能力。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
投资者和管理者利用净利率评估成本控制效率。
Return on capital employed (ROCE) evaluates how efficiently a business generates profit from its total capital base.
已用资本回报率评价企业利用其全部资本获取利润的效率。
ROCE = (Operating Profit ÷ Capital Employed) × 100%
Capital employed is typically defined as total assets less current liabilities, or equity plus non-current liabilities.
已用资本通常定义为总资产减去流动负债，或所有者权益加非流动负债。
3. Liquidity and Efficiency Ratios | 流动性与效率比率
The current ratio assesses a firm's ability to meet short-term obligations using its current assets.
流动比率评估企业利用流动资产偿还短期债务的能力。
Current Ratio = Current Assets ÷ Current Liabilities
一般安全值约为1.5:1至2:1，但行业差异显著。
The quick ratio (acid-test) provides a stricter liquidity test by excluding inventory, which may not be easily converted to cash.
速动比率排除不易变现的存货，提供了更严格的流动性检验。
Quick Ratio = (Current Assets − Inventory) ÷ Current Liabilities
Inventory turnover shows how many times inventory is sold and replaced over a period.
存货周转率显示一定期间内存货被售出和重置的次数。
Inventory Turnover = Cost of Sales ÷ Average Inventory
Trade receivables collection period indicates the average time taken to collect debts from credit customers.
应收账款周转天数表示向赊销客户收回欠款的平均天数。
Receivables Collection Period = (Trade Receivables ÷ Credit Sales) × 365
Trade payables payment period reflects how long the business takes to pay its suppliers.
应付账款周转天数反映企业向供应商付款的平均时间。
Payables Payment Period = (Trade Payables ÷ Credit Purchases) × 365
4. Gearing and Investor Ratios | 杠杆及投资者比率
Gearing ratio measures the proportion of a company's capital provided by debt, indicating financial risk.
杠杆比率衡量企业资本中债务融资的比例，反映财务风险。
Gearing = (Non-current Liabilities ÷ (Equity + Non-current Liabilities)) × 100%
高杠杆意味着更大的固定利息负担，但可能在景气时放大股东回报。
Interest cover indicates how comfortably operating profit covers finance costs.
利息保障倍数表明营业利润覆盖财务费用的充裕程度。
Interest Cover = Operating Profit ÷ Finance Costs
Earnings per share (EPS) shows the profit attributable to each ordinary share in issue.
每股收益表示每张发行在外的普通股所应占的利润。
EPS = (Net Profit − Preferred Dividends) ÷ Weighted Average Number of Ordinary Shares
Price/earnings (P/E) ratio compares the market price to earnings, indicating growth expectations.
市盈率比较市场价格与盈利，反映市场对企业增长的预期。
P/E Ratio = Market Price per Share ÷ EPS
Dividend yield expresses the annual dividend as a percentage of the current share price.
股息率将年度股息表示为当前股价的百分比。
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%
5. Depreciation Methods | 折旧方法
Depreciation systematically allocates the depreciable amount of a non-current asset over its useful life.
折旧是将非流动资产的应折旧金额在其使用寿命内系统分摊的过程。
Straight-line method charges an equal amount each year.
直线法每年计提等额折旧。
Annual Depreciation = (Cost − Residual Value) ÷ Useful Life
This method matches cost evenly to each period of use.
该方法使成本均匀地匹配于每个使用期间。
Reducing balance method applies a constant percentage to the net book value each year.
余额递减法每年对账面净值应用固定百分比。
Annual Depreciation = Net Book Value × Depreciation Rate
The rate is often calculated as 1 − (Residual Value ÷ Cost)1/n, though a given percentage may be used.
折旧率常用公式 1 − (残值/成本)的n次方根计算，但考题常直接给出百分比。
Sum-of-the-years'-digits (SYD) method is a more accelerated depreciation technique.
年数总和法是一种更为加速的折旧方法。
Annual Depreciation = (Cost − Residual Value) × (Remaining Life ÷ SYD)
YD equals the total of digits for each year of useful life, e.g. 5 years → 5+4+3+2+1 = 15.
年数总和等于使用年限各年数字之和，如5年总和为5+4+3+2+1=15。
6. Inventory Valuation | 存货估值
Inventory must be valued at the lower of cost and net realisable value (NRV) as per the prudence concept.
根据稳健性原则，存货应按成本与可变现净值孰低计量。
Valuation = Lower of (Cost, NRV)
NRV = estimated selling price − estimated costs to completion − estimated selling costs.
可变现净值 = 估计售价 − 估计完工成本 − 估计销售费用。
FIFO (first-in, first-out) assumes the earliest inventory is sold first; closing inventory is valued at recent costs.
先进先出法假定最早购入的存货最先售出；期末存货按近期成本计价。
LIFO (last-in, first-out) assumes the latest inventory is sold first; closing inventory reflects older costs.
后进先出法假定最后购入的存货最先售出；期末存货反映较早成本。（注：IFRS已不允许）
AVCO (weighted average cost) calculates a single average cost per unit after each purchase or periodically.
加权平均法在每次进货后或定期计算单一平均单位成本。
Average Cost per Unit = Total Cost of Inventory ÷ Total Units
This cost is then used to value issues and closing inventory.
该成本随后用于计量发出存货和期末存货。
7. Costing and Break-Even Analysis | 成本计算与盈亏平衡分析
Contribution per unit is the excess of selling price over variable cost, contributing to fixed costs and profit.
单位贡献毛益是售价超过变动成本的部分，用于弥补固定成本并形成利润。
Contribution per Unit = Selling Price − Variable Cost per Unit
Break-even point in units is the sales volume at which total contribution equals total fixed costs.
盈亏平衡点销售量是指总贡献毛益等于总固定成本时的销售数量。
Break-even (units) = Total Fixed Costs ÷ Contribution per Unit
Break-even revenue can be found using the contribution to sales (C/S) ratio.
盈亏平衡金额可利用贡献毛益率计算。
Break-even Revenue = Total Fixed Costs ÷ C/S Ratio
C/S ratio = (Contribution per Unit ÷ Selling Price) × 100% or (Total Contribution ÷ Total Revenue) × 100%.
贡献毛益率 = (单位贡献毛益÷售价)×100% 或 (总贡献毛益÷总收入)×100%。
Margin of safety represents the extent by which actual sales exceed break-even sales.
安全边际反映实际销售额超过盈亏平衡销售额的程度。
Margin of Safety = Actual Sales − Break-even Sales
xtends break-even: required units = (Fixed Costs + Target Profit) ÷ Contribution per Unit.
目标利润分析在盈亏平衡基础上延伸：所需销量 = (固定成本+目标利润) ÷ 单位贡献毛益。
8. Investment Appraisal Techniques | 投资评估方法
Payback period measures how long it takes to recoup the initial investment from net cash flows.
投资回收期衡量从净现金流量中收回初始投资所需的时间。
For equal annual cash flows: Payback = Initial Investment ÷ Annual Net Cash Inflow.
若年现金流量相等：回收期 = 初始投资 ÷ 年净现金流入。
Accounting rate of return (ARR) uses average accounting profit to gauge return.
会计收益率利用平均会计利润衡量回报。
ARR = (Average Annual Profit ÷ Initial Investment) × 100%
Alternatively, average investment can be used in the denominator: (Initial Investment + Residual Value) ÷ 2.
分母也可采用平均投资额：(初始投资+残值) ÷ 2。
Net present value (NPV) discounts future cash flows to their present value and subtracts the initial outlay.
净现值法将未来现金流折现，再减去初始投资额。
NPV = Sum of Discounted Future Net Cash Flows − Initial Investment
A positive NPV indicates the project should be accepted; negative NPV signals rejection.
净现值为正表明项目可接受；负值则应拒绝。
Internal rate of return (IRR) is the discount rate that makes NPV equal to zero.
内含报酬率是使净现值等于零的折现率。
Decision rule: accept if IRR > cost of capital. Linear interpolation is often used to estimate IRR.
决策规则：若内含报酬率大于资本成本，则接受。通常使用线性内插法估算。
9. Standard Costing and Variance Analysis | 标准成本法与差异分析
Variance analysis compares actual costs and revenues to standard (budgeted) figures to aid management control.
差异分析将实际成本与收入同标准(预算)数据比较，以辅助管理控制。
Material price variance (MPV) captures the effect of paying a different price than expected.
材料价格差异捕捉支付价格与预期不同的影响。
MPV = (Actual Price − Standard Price) × Actual Quantity Purchased
Material usage variance (MUV) isolates the effect of using more or less material than allowed.
材料用量差异反映用量超过或少于标准用量的影响。
MUV = (Actual Quantity Used − Standard Quantity for Actual Output) × Standard Price
Labour rate variance follows a similar logic for labour pay rates.
人工工资率差异遵循类似逻辑。
Labour Rate Variance = (Actual Rate − Standard Rate) × Actual Hours Worked
Labour efficiency variance measures productivity differences.
人工效率差异衡量生产效率差异。
ur Efficiency Variance = (Actual Hours − Standard Hours for Actual Output) × Standard Rate
Fixed overhead variances include expenditure and volume variances. Volume variance can be further split into capacity and efficiency components.
固定制造费用差异包括支出差异和产量差异。产量差异可进一步分为生产能力差异和效率差异。
10. Cash Flow Statements | 现金流量表
The statement of cash flows classifies cash movements into operating, investing, and financing activities.
现金流量表将现金流动分类为经营活动、投资活动和筹资活动。
The indirect method starts with profit before tax and adjusts for non-cash items and changes in working capital.
间接法从税前利润开始，调整非现金
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