Formula & Theorems Quick Reference Handbook | 公式定理速查手册

📚 Formula & Theorems Quick Reference Handbook | 公式定理速查手册

This comprehensive quick reference handbook compiles essential formulas, ratios, and theorems for the CCEA Pre-U Accounting specification. Whether you are tackling financial statements, management accounting, or investment appraisal, these tools will support accurate analysis and decision-making. Keep this guide handy for revision and practice.

这本全面的速查手册汇编了CCEA Pre-U会计课程的核心公式、比率和定理。无论你是在处理财务报表、管理会计还是投资评估，这些工具都有助于准确分析和决策。请将本指南放在手边以供复习和练习。

1. Profitability Ratios | 盈利能力比率

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

This ratio expresses gross profit as a percentage of revenue, indicating the efficiency of production and pricing. A higher margin suggests better control over cost of sales.

该比率以百分比表示毛利占收入的比例，反映生产和定价效率。较高的毛利率意味着更好地控制了销售成本。

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

It measures the percentage of revenue remaining after covering operating expenses, revealing the profitability of core business activities before interest and tax.

它衡量扣除运营费用后剩余收入的百分比，反映息税前核心业务活动的盈利能力。

Net Profit Margin = (Net Profit after Tax ÷ Revenue) × 100%

This indicator shows the final profit generated per unit of revenue after all expenses and taxes. It is a comprehensive measure of overall profitability.

该指标显示了扣除所有费用和税款后每单位收入产生的最终利润，是衡量整体盈利能力的综合指标。

Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%

Capital Employed is usually defined as Total Assets minus Current Liabilities, or Equity plus Non-current Liabilities. ROCE assesses how efficiently a firm uses its long-term funds to generate operating profit.

资本运用通常定义为总资产减去流动负债，或权益加上非流动负债。ROCE评估企业如何有效利用其长期资金产生营业利润。

Return on Equity (ROE) = (Net Profit after Tax ÷ Shareholders’ Equity) × 100%

ROE measures the return generated on ordinary shareholders’ investment. It is a key driver of shareholder value.

ROE衡量普通股股东投资所产生的回报，是股东价值的关键驱动因素。

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2. Liquidity Ratios | 流动性比率

Current Ratio = Current Assets ÷ Current Liabilities

This ratio tests a company’s ability to meet its short-term obligations using current assets. A ratio above 1 indicates positive working capital, but excessively high values may suggest inefficient use of assets.

该比率测试企业使用流动资产偿还短期债务的能力。比率大于1表明营运资本为正，但过高的数值可能意味着资产使用效率低下。

Quick Ratio (Acid Test) = (Current Assets − Inventory) ÷ Current Liabilities

It refines the current ratio by excluding inventory, the least liquid current asset. This ratio reveals whether a firm can cover its immediate liabilities without selling inventory.

它通过排除流动性最差的流动资产——存货，来优化流动比率。该比率揭示了企业能否在不出售存货的情况下清偿即时负债。

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3. Efficiency Ratios | 效率比率

Inventory Turnover = Cost of Sales ÷ Average Inventory

Average Inventory = (Opening Inventory + Closing Inventory) ÷ 2. This measures how many times inventory is sold and replaced over a period. Alternatively, use Inventory Turnover Days = (Average Inventory ÷ Cost of Sales) × 365.

平均存货 = (期初存货 + 期末存货) ÷ 2。它衡量存货在一定时期内被销售和补货的次数。也可使用存货周转天数 = (平均存货 ÷ 销售成本) × 365。

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

This ratio indicates the average number of days it takes a company to collect cash from credit customers. Shorter periods signal efficient credit control.

该比率表示公司从赊销客户处收回现金的平均天数。较短的回收期表明信用控制有效。

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

It shows the average time taken to pay suppliers. Longer periods may improve cash flow but can strain supplier relationships.

它显示支付供应商的平均时间。较长的支付期可改善现金流，但可能影响与供应商的关系。

Asset Turnover = Revenue ÷ Capital Employed (or Total Assets)

Asset turnover measures the revenue generated per unit of capital employed. A higher figure indicates more efficient use of assets to generate sales.

资产周转率衡量每单位资本运用产生的收入。数值越高，说明资产在产生销售方面的利用效率越高。

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4. Investment Ratios | 投资比率

Earnings per Share (EPS) = (Net Profit after Tax − Preference Dividends) ÷ Weighted Average Number of Ordinary Shares

EPS shows the profit attributable to each ordinary share. It is a fundamental measure of a company’s profitability from an equity holder’s perspective.

EPS显示了归属于每一普通股的利润。它是从股权持有人角度衡量公司盈利能力的根本指标。

Price/Earnings Ratio (P/E) = Market Price per Share ÷ Earnings per Share

The P/E ratio reflects the market’s expectations of future earnings growth. A higher P/E often indicates optimism about the company’s prospects.

市盈率反映了市场对未来盈利增长的预期。较高的市盈率通常表明市场对公司的前景持乐观态度。

Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%

This ratio measures the cash return an investor receives on the market price of a share. It is important for income-focused investors.

该比率衡量投资者从每股市价中获得的现金回报，对于注重收入的投资者很重要。

Dividend Cover = Earnings per Share ÷ Dividend per Share

Dividend cover indicates the number of times profit covers the dividend payment, showing the sustainability of dividends and the proportion of profits retained for reinvestment.

股利保障倍数表示利润覆盖股利支付的程度，反映股利的可持续性以及用于再投资的留存利润比例。

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5. Costing Formulas | 成本核算公式

Prime Cost = Direct Material + Direct Labour + Direct Expenses

Prime cost aggregates all directly traceable costs of production. It serves as the basis for calculating total production cost by adding factory overheads.

主要成本汇总了所有可直接追溯的生产成本，是加上制造费用后计算总生产成本的依据。

Production Overhead Absorption Rate = Budgeted Overheads ÷ Budgeted Level of Activity

Activity can be measured in labour hours, machine hours, or units. This rate is used to allocate fixed production overheads to cost units in traditional absorption costing.

活动量可按人工小时、机器小时或产量衡量。在传统吸收成本法中，该费率用于将固定制造费用分配到成本核算单位。

Contribution per Unit = Selling Price − Variable Cost per Unit

Contribution is the amount each unit sold contributes towards covering fixed costs and generating profit. It is the central concept in marginal costing.

每件产品的贡献额是指销售一件产品所带来用于弥补固定成本和产生利润的金额。它是边际成本法中的核心概念。

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

The break-even point is the sales volume at which total revenue equals total costs, resulting in zero profit. It is a crucial tool for planning and risk assessment.

盈亏平衡点是指总收入等于总成本、利润为零的销售量。它是规划和风险评估的关键工具。

Break-even Point (sales value) = Fixed Costs ÷ (Contribution to Sales Ratio)

where C/S Ratio = Contribution per Unit ÷ Selling Price. This expresses break-even in monetary terms, useful when multiple products are sold.

其中C/S比率 = 单位贡献额 ÷ 售价。这以货币形式表示盈亏平衡点，在多产品销售时很有用。

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

Margin of safety indicates the extent to which sales can fall before losses are incurred. A higher margin implies lower risk.

安全边际表明在出现亏损之前销售额可以下降的幅度。较高的安全边际意味着较低的风险。

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6. Budgeting and Variance Analysis | 预算与差异分析

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

This variance isolates the effect of selling a different volume than planned on profit. It uses standard contribution (or standard profit margin under absorption costing).

此差异分离了实际销售量与计划销售量不同对利润的影响。它使用标准贡献额（或吸收成本法下的标准利润率）。

Sales Price Variance = (Actual Price − Standard Price) × Actual Quantity

It measures the profit impact due to differences between actual and standard selling prices.

它衡量由于实际售价与标准售价差异而对利润产生的影响。

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

A favourable variance occurs when materials are purchased for less than the standard price. It assesses the purchasing department’s performance.

当材料采购价格低于标准价格时，产生有利差异。它用于评估采购部门的绩效。

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

This variance reveals the efficiency of material usage. More material used than standard leads to an adverse variance.

该差异揭示了材料使用的效率。实际用料超过标准将产生不利差异。

Labour Rate Variance = (Standard Rate − Actual Rate) × Actual Hours Worked

It captures the difference between the budgeted labour rate and the actual rate paid.

它反映了预算人工费率与实际支付费率之间的差额。

Labour Efficiency Variance = (Standard Hours for Actual Production − Actual Hours Worked) × Standard Rate

This measures workforce productivity. Taking more hours than standard to produce actual output gives an adverse variance.

这衡量了劳动力生产率。生产实际产出所用工时超过标准工时会带来不利差异。

Fixed Overhead Expenditure Variance = Budgeted Fixed Overheads − Actual Fixed Overheads

It simply compares budgeted and actual fixed overhead spending.

它简单地比较预算固定制造费用与实际支出。

Fixed Overhead Volume Variance = (Actual Output − Budgeted Output) × Standard Fixed Overhead Rate per Unit

This arises only under absorption costing and reflects the over- or under-absorption of fixed overheads due to production volume deviation.

该差异仅出现在吸收成本法下，反映由于产量偏差导致的固定制造费用多分配或少分配。

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7. Investment Appraisal Methods | 投资评估方法

Payback Period = Initial Investment ÷ Annual Cash Inflow (for uniform cash flows)

Payback calculates the time required to recoup the initial outlay from net cash flows. It is simple but ignores the time value of money and post-payback cash flows.

回收期计算从净现金流中收回初始投资所需的时间。它简单易懂，但忽略了货币时间价值和回收期后的现金流。

Accounting Rate of Return (ARR) = (Average Annual Profit ÷ Average Investment) × 100%

Average Investment is typically (Initial Investment + Scrap Value) ÷ 2. ARR evaluates profitability as a percentage of the book value of the invested capital.

平均投资额通常为 (初始投资 + 残值) ÷ 2。ARR以投资资本账面价值的百分比来评估盈利能力。

Net Present Value (NPV) = Σ (CFₙ ÷ (1 + r)ⁿ) − I₀

where CFₙ = net cash flow in year n, r = discount rate, I₀ = initial investment. Positive NPV indicates that the project adds value to the firm.

其中CFₙ = 第n年净现金流，r = 折现率，I₀ = 初始投资。正NPV表明该项目为公司增加价值。

Internal Rate of Return (IRR) ≈ L + [NPV_L ÷ (NPV_L − NPV_H)] × (H − L)

IRR is the discount rate at which NPV equals zero. It is estimated by linear interpolation between two rates, L (lower) and H (higher), giving positive (NPV_L) and negative (NPV_H) NPVs respectively.

IRR是使净现值为零的折现率。它通过在两个折现率L（较低，NPV为正）和H（较高，NPV为负）之间线性插值来估算。

Profitability Index = Present Value of Future Cash Flows ÷ Initial Investment

A profitability index greater than 1 indicates acceptance. It shows the return per unit of investment in present-value terms.

盈利能力指数大于1表示接受该项目。它以现值形式显示每单位投资所产生的回报。

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8. Working Capital Management | 营运资本管理

Working Capital = Current Assets − Current Liabilities

This basic equation determines the short-term financial health of a business. Negative working capital may signal liquidity problems.

此基本等式决定了企业的短期财务健康状况。负营运资本可能预示着流动性问题。

Operating Cycle = Inventory Days + Receivable Days − Payable Days

The operating cycle measures the time taken from paying for inventory to receiving cash from sales. A shorter cycle minimises the need for external finance.

经营周期衡量从支付存货到收到销售现金所需的时间。较短的周期可最大限度地减少对外部融资的需求。

Cash Conversion Efficiency = Revenue ÷ Working Capital

This ratio, though less common in textbooks, helps gauge how effectively working capital is being used to generate revenue.

该比率虽不常见于教科书，但有助于衡量营运资本用于创造收入的有效性。

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9. Financial Statement Equations | 财务报表等式

Accounting Equation: Assets = Liabilities + Equity

This is the foundation of double-entry bookkeeping. Every transaction preserves this equality.

这是复式记账的基础。每笔交易都保持

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