Year 13 CIE Accounting: Formula & Theorem Quick Reference Handbook

📚 Year 13 CIE Accounting: Formula & Theorem Quick Reference Handbook | 公式定理速查手册

This article is a comprehensive quick-reference guide for Year 13 CIE Accounting students, consolidating all essential formulas, theorems, and analytical frameworks required for the A Level syllabus. It covers profitability, liquidity, efficiency, investment appraisal, costing methods, budgeting, and more. Each section is structured to present the key formulae first in English, followed immediately by the Chinese explanation, ensuring clarity for bilingual learners. Use this handbook to reinforce your revision and ensure you are fully prepared for both the structured and multiple-choice components of the examination.

本文是Year 13 CIE会计学生的综合速查手册，汇总了A Level考纲要求的所有核心公式、定理和分析框架。涵盖盈利能力、流动性、效率、投资评估、成本核算方法、预算编制等内容。每个小节先以英文列出关键公式，紧接中文解释，确保双语学习清晰明了。请用这本手册巩固复习，确保为考试中的结构化题目和选择题做好万全准备。

1. Profitability Ratios | 盈利比率

A firm’s ability to generate profit relative to sales, assets, or equity is measured by profitability ratios. The key ratios include Gross Profit Margin, Operating Profit Margin, and Return on Capital Employed (ROCE). The formula for Gross Profit Margin is:

企业相对于销售额、资产或权益产生利润的能力通过盈利比率衡量。关键比率包括毛利率、经营利润率以及已用资本回报率。毛利率的公式为：

Gross Profit Margin = (Gross Profit / Revenue) × 100%

Operating Profit Margin captures profit after operating expenses but before interest and tax:

经营利润率衡量扣除营业费用后但未扣除利息和税款的利润：

Operating Profit Margin = (Operating Profit / Revenue) × 100%

ROCE is a fundamental measure of how efficiently capital is used. The formula is:

已用资本回报率是衡量资本使用效率的基本指标。公式为：

ROCE = (Profit before Interest and Tax / (Total Assets − Current Liabilities)) × 100%

Alternatively, ROCE can be expressed as (PBIT / Capital Employed), where Capital Employed = Equity + Non-current Liabilities.

也可将ROCE表示为（息税前利润/已用资本），其中已用资本=权益+非流动负债。

Profit margins should be analysed alongside industry benchmarks and historical trends. A declining gross margin may signal rising input costs or discounting strategies.

利润率应与行业基准和历史趋势一起分析。毛利率下降可能表明投入成本上升或折扣策略。

2. Liquidity Ratios | 流动比率

Liquidity ratios assess a business’s ability to meet short-term obligations. The two primary indicators are the Current Ratio and the Quick Ratio (Acid-test Ratio).

流动比率评估企业偿还短期债务的能力。两个主要指标是流动比率和速动比率（酸性测试比率）。

Current Ratio = Current Assets / Current Liabilities

A ratio between 1.5 and 2.0 is often considered healthy, but this varies by industry.

比率在1.5至2.0之间通常被认为是健康的，但取决于行业。

Quick Ratio = (Current Assets − Inventory) / Current Liabilities

The quick ratio excludes inventory because it is not always easily convertible to cash. A value of 1 or above is generally satisfactory.

速动比率剔除存货，因为存货并不总能轻易变现。通常数值大于或等于1是令人满意的。

It is essential to examine the composition of current assets; a high proportion of receivables may mask underlying collection problems.

必须审查流动资产的构成；应收账款比例过高可能掩盖潜在的收款问题。

3. Efficiency Ratios | 效率比率

Efficiency ratios indicate how well an entity manages its resources. Key formulas include Inventory Turnover, Receivables Collection Period, and Payables Payment Period.

效率比率显示企业管理资源的效率。关键公式包括存货周转率、应收账款收款期和应付账款付款期。

Inventory Turnover (times) = Cost of Sales / Average Inventory

Alternatively, in days: (Average Inventory / Cost of Sales) × 365.

或者以天数表示：（平均存货/销售成本）× 365。

Receivables Collection Period = (Trade Receivables / Credit Sales) × 365

This shows the average number of days to collect debts. A shorter period is usually desirable.

这表示收回债务的平均天数。较短的期限通常是理想的。

Payables Payment Period = (Trade Payables / Credit Purchases) × 365

Extending this period conserves cash but may strain supplier relationships.

延长付款期可保留现金，但可能损害供应商关系。

Total Asset Turnover = Revenue / Total Assets further assesses how effectively assets generate sales.

总资产周转率=销售收入/总资产，进一步评估资产创造销售的有效性。

4. Investment Appraisal | 投资评估

Investment appraisal techniques help evaluate capital projects. The three main methods are Payback Period, Accounting Rate of Return (ARR), and Net Present Value (NPV).

投资评估技术有助于评估资本项目。三种主要方法是回收期、会计回报率（ARR）和净现值（NPV）。

Payback Period = Initial Investment / Annual Net Cash Inflow

For uneven cash flows, cumulative cash flows are used until the initial outlay is recovered.

若现金流不均匀，使用累计现金流直至收回初始投入。

ARR = (Average Annual Profit / Average Investment) × 100%

Average Investment is often (Initial Cost + Scrap Value) / 2. ARR ignores the time value of money.

平均投资通常为（初始成本+残值）/2。ARR忽略了货币的时间价值。

NPV = Σ (Cash Inflowₜ / (1 + r)ᵗ) − Initial Investment

Where r is the discount rate and t is the time period. A positive NPV indicates the project should be accepted.

其中r是贴现率，t为时期。正净现值表明项目应被接受。

The Internal Rate of Return (IRR) is the discount rate that makes NPV = 0. It can be approximated by linear interpolation.

内部收益率（IRR）是使净现值为零的贴现率，可通过线性插值近似求出。

5. Break-even Analysis | 盈亏平衡分析

Break-even analysis determines the level of sales needed to cover total costs. The break-even point is where total contribution equals fixed costs.

盈亏平衡分析确定需覆盖总成本的销售水平。盈亏平衡点即总贡献等于固定成本的点。

Break-even Point (units) = Fixed Costs / Contribution per Unit

Contribution per Unit = Selling Price − Variable Cost per Unit.

单位贡献=售价−单位变动成本。

Break-even Revenue = Fixed Costs / Contribution Margin Ratio

Contribution Margin Ratio = (Selling Price − Variable Cost) / Selling Price.

贡献毛利率=（售价−变动成本）/售价。

The margin of safety indicates how much sales can fall before losses occur:

安全边际表示在亏损发生前销售额可以下降的幅度：

Margin of Safety = (Actual Sales − Break-even Sales) / Actual Sales × 100%

Break-even charts visually represent cost-volume-profit relationships and are useful for decision-making.

盈亏平衡图直观展示成本-数量-利润关系，对决策有帮助。

6. Marginal Costing and Absorption Costing | 边际成本法与吸收成本法

Marginal costing charges only variable costs to units produced, treating fixed costs as period costs. The inventory value includes only variable production costs.

边际成本法仅将变动成本计入产品单位，固定成本视为期间成本。存货价值只包括变动生产成本。

Marginal Cost = Direct Materials + Direct Labour + Variable Overheads

Absorption costing, however, allocates all production costs (fixed and variable) to units. A predetermined overhead absorption rate (OAR) is used:

然而，吸收成本法将所有生产成本（固定和变动）分配至产品单位。使用预定的制造费用吸收率（OAR）：

OAR = Budgeted Fixed Overheads / Budgeted Activity Level

The difference in profit between the two methods is due to movement in inventory levels. If inventory rises, absorption costing profit exceeds marginal costing profit, and vice versa.

两种方法之间的利润差异源于存货水平变动。如果存货增加，吸收成本法利润大于边际成本法利润，反之亦然。

Reconciliation formula:

调节公式：

Absorption Profit − Marginal Profit = Change in Inventory × Fixed OAR per Unit

7. Budgeting and Variances | 预算与差异

Budgets are financial plans for a future period. Variance analysis compares budgeted figures with actual results. Key variances include material, labour, and overhead variances.

预算是未来期间的财务计划。差异分析将预算数字与实际结果比较。关键差异包括材料、人工和制造费用差异。

Sales Volume Variance = (Actual Sales Volume − Budgeted Sales Volume) × Standard Profit per Unit

Material price variance measures the impact of paying a different price for materials:

材料价格差异衡量支付不同材料价格的影响：

Material Price Variance = (Standard Price − Actual Price) × Actual Quantity Purchased

Material usage variance focusses on efficiency in using materials:

材料用量差异关注材料使用效率：

Material Usage Variance = (Standard Quantity for Actual Production − Actual Quantity Used) × Standard Price

Labour rate and efficiency variances are similar. All variances are labelled ‘F’ for favourable or ‘A’ for adverse, and they are essential for responsibility accounting.

人工工资率差异和效率差异类似。所有差异标注“F”（有利）或“A”（不利），它们对责任会计至关重要。

8. Depreciation Methods | 折旧方法

Depreciation systematically allocates the cost of a non-current asset over its useful life. The two main methods are straight-line and reducing balance.

折旧系统地将非流动资产成本在其使用寿命内分摊。两种主要方法是直线法和余额递减法。

Straight-line: Annual Depreciation = (Cost − Residual Value) / Useful Life

This method assumes equal benefit from the asset each year.

该方法假设每年从资产获得相等的效益。

Reducing Balance: Depreciation Rate = 1 − ⁿ√(Residual Value / Cost)

Where n is the number of years. The depreciation charge declines each year.

其中n为年数。折旧费用逐年递减。

Accounting entries: debit Depreciation Expense, credit Accumulated Depreciation. The carrying amount (NBV) = Cost − Accumulated Depreciation.

会计分录：借记折旧费用，贷记累计折旧。账面净值（NBV）=成本−累计折旧。

If an asset is revalued, subsequent depreciation is based on the revalued amount.

如果资产重估，后续折旧基于重估金额。

9. Inventory Valuation | 存货计价

Inventory is valued at the lower of cost and net realisable value (NRV). Cost can be determined by First-In, First-Out (FIFO) or Average Cost (AVCO).

存货按成本与可变现净值（NRV）孰低计价。成本可采用先进先出法（FIFO）或加权平均成本法（AVCO）确定。

Under FIFO, the earliest purchased items are assumed to be sold first, leaving the latest costs in closing inventory.

在先进先出法下，假设最早购入的物品最先售出，期末存货包含最近的成本。

AVCO calculates a weighted average cost after each purchase: Average Cost = Total Cost of Goods Available / Total Units Available.

加权平均法在每次采购后计算加权平均成本：平均成本=可供销售商品总成本/可供销售总数量。

NRV = Estimated Selling Price − Costs to Complete − Costs to Sell. If NRV < Cost, a write-down is required.

可变现净值=估计售价−完工成本−销售费用。若NRV < 成本，需计提跌价准备。

The choice of method affects reported profit and asset values, especially in periods of changing prices.

方法的选择会影响报告的利润和资产价值，尤其在价格变动时期。

10. Working Capital Management | 营运资金管理

Working capital = Current Assets − Current Liabilities. Efficient management balances liquidity and profitability. The cash operating cycle is a crucial indicator.

营运资金=流动资产−流动负债。高效管理平衡流动性和盈利能力。现金周转期是关键指标。

Cash Operating Cycle = Inventory Days + Receivable Days − Payable Days

A shorter cycle means the business recovers cash more quickly. Strategies include reducing inventory levels, accelerating collections, and extending payment terms with suppliers.

周期越短，企业回收现金越快。策略包括降低存货水平、加速收款和延长对供应商的付款期限。

Overtrading occurs when a business expands too rapidly without adequate long-term funding, leading to severe liquidity problems even if profitable.

过度交易发生在企业扩张过快而没有足够长期资金时，即使盈利也会出现严重流动性问题。

Ratios such as the working capital cycle and current ratio should be monitored regularly to avoid insolvency.

应定期监控营运资金周转期和流动比率等比率，以避免资不抵债。

11. Ratio Analysis Framework | 比率分析框架

Interpreting ratios requires a structured framework. Users (management, investors, lenders) have different perspectives. Ratios are grouped into profitability, liquidity, efficiency, gearing, and investment.

解释比率需要一个结构化框架。使用者（管理层、投资者、债权人）有不同视角。比率分为盈利、流动性、效率、杠杆和投资类别。

Gearing Ratio = (Long-term Debt / (Long-term Debt + Equity)) × 100%

Or alternatively: (Long-term Debt / Equity) × 100%.

或：长期债务/权益 × 100%。

Interest cover = Profit before Interest and Tax / Interest Expense assesses the ability to service debt. A value less than 2 is risky.

利息保障倍数=息税前利润/利息费用，评估偿还债务的能力。低于2倍存在风险。

Earnings per Share (EPS) = (Profit after Tax − Preference Dividends) / Number of Ordinary Shares. It is a key stock market ratio.

每股收益（EPS）=（税后利润−优先股股息）/普通股股数，是关键的股市比率。

Price/Earnings (P/E) ratio = Market Price per Share / EPS. It reflects market expectations of future growth.

市盈率（P/E）=每股市价/每股收益，反映市场对未来增长的预期。

12. Key Accounting Equations | 关键会计等式

The fundamental accounting equation underpins all financial statements:

基本会计等式支撑所有财务报表：

Assets = Liabilities + Equity

The expanded equation includes income and expenses:

扩展等式包括收入和费用：

Assets = Liabilities + Equity + (Revenue − Expenses)

Within costing, the following relationships hold:

在成本核算中，存在以下关系：

Prime Cost = Direct Materials + Direct Labour + Direct Expenses

Total Production Cost = Prime Cost + Production Overheads

For a manufacturing account, Cost of Goods Manufactured = Opening WIP + Total Production Cost − Closing WIP.

对于制造业账户，产成品成本=期初在产品+总生产成本−期末在产品。

Finally, the statement of profit or loss summarises:

最后，损益表概括：

Gross Profit = Revenue − Cost of Sales

Profit for the Year = Gross Profit − Operating Expenses − Interest − Tax

These core equations provide the foundation for preparing and understanding financial statements.

这些核心等式为编制和理解财务报表提供了基础。

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Year 13 CIE Accounting: Formula & Theorem Quick Reference Handbook | 公式定理速查手册