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

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

This comprehensive quick-reference handbook collates every essential formula and key theorem required for Year 13 CIE A-Level Business. Designed as a revision aid, it ensures you can rapidly access profitability ratios, liquidity measures, investment appraisal techniques, decision trees and more. Each entry includes the formula in bold centre display and a concise English-Chinese explanation to reinforce understanding and application in examination contexts.

这本全面的速查手册汇集了Year 13 CIE A-Level 商务课程所需的所有基本公式和关键定理。作为复习助手，它能让你快速查阅盈利能力比率、流动性指标、投资评估方法、决策树等内容。每个条目都包含居中加粗的公式以及简明扼要的中英文解释，以帮助你在考试中强化理解和应用。

1. Profitability Ratios | 盈利能力比率

Profitability ratios assess a business’s ability to generate earnings relative to its sales, assets or equity. They are vital for comparing performance over time and against competitors.

盈利能力比率评估企业相对于其销售额、资产或股权的收益能力。它们对于跨期比较和与竞争对手的对标至关重要。

The return on capital employed (ROCE) evaluates how efficiently a firm uses its long-term capital. A higher ROCE indicates more effective use of funding.

资本回报率（ROCE）评价企业使用长期资本的效率。ROCE越高，说明资金运用越有效。

ROCE = (Profit from Operations ÷ Capital Employed) × 100

The gross profit margin reveals the percentage of sales revenue remaining after covering direct costs of sales. It indicates how well a business controls its production or purchasing costs.

毛利率揭示了销售收入扣除直接销售成本后剩余的百分比。它表明企业控制生产或采购成本的能力。

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

The net profit margin shows the proportion of revenue that becomes net profit after all expenses. It is a key measure of overall cost control and pricing strategy effectiveness.

净利率显示收入在扣除所有费用后转化为净利润的比例。它是衡量整体成本控制和定价策略有效性的关键指标。

Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100

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2. Liquidity Ratios | 流动性比率

Liquidity ratios measure the firm’s ability to meet short-term obligations. They highlight the cushion available to cover current liabilities using short-term assets.

流动性比率衡量企业偿还短期债务的能力。它们揭示了用短期资产覆盖流动负债的安全垫。

The current ratio compares total current assets to current liabilities. A ratio above 1 suggests sufficient short-term coverage, though industry norms vary.

流动比率将流动资产总额与流动负债进行比较。比率高于1表明短期覆盖充足，但行业标准各有不同。

Current Ratio = Current Assets ÷ Current Liabilities

The acid test (quick) ratio excludes inventories, offering a stricter liquidity test. It concentrates on assets that can be turned into cash quickly.

酸性测试（速动）比率排除存货，提供了更严格的流动性检验。它专注于能迅速变现的资产。

Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities

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3. Efficiency Ratios | 效率比率

Efficiency ratios examine how well a business manages its assets and liabilities in day-to-day operations. They reveal the speed of converting stock into sales and collecting cash from customers.

效率比率考察企业在日常运营中管理资产和负债的情况。它们揭示了将存货转化为销售和从客户收回现金的速度。

Inventory turnover shows how many times a firm sells and replaces its inventory in a period. A higher turnover often indicates strong demand and effective stock control.

存货周转率显示企业在一个时期内销售和补充存货的次数。周转率高通常表明需求强劲且存货控制有效。

Inventory Turnover = Cost of Sales ÷ Average Inventory

Trade receivables days (debtor days) measure the average time taken to collect cash from credit customers. Shorter periods improve cash flow.

应收账款周转天数衡量从赊销客户收回现金的平均时间。周转期越短，现金流越好。

Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365

Trade payables days (creditor days) indicate how long the business takes to pay its suppliers. A longer period may help cash flow but could strain supplier relationships.

应付账款周转天数表明企业支付供应商货款所需的时间。较长的周期有助于现金流，但可能影响供应商关系。

Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365

Asset turnover gauges the revenue generated per unit of assets. It shows how productively the firm uses its total asset base to drive sales.

资产周转率衡量每单位资产产生的收入。它表明企业利用总资产基础创造销售的生产效率。

Asset Turnover = Sales Revenue ÷ Total Assets

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4. Gearing Ratio | 杠杆比率

The gearing ratio assesses a company’s long-term financial structure by comparing debt to total capital employed. High gearing means greater financial risk because interest must be paid regardless of profit levels.

杠杆比率通过比较债务与总占用资本来评估企业的长期财务结构。杠杆比率高意味着更大的财务风险，因为无论利润如何都必须支付利息。

It is calculated as the proportion of long-term borrowings in the total of long-term borrowings and shareholders’ equity. Many analysts focus on the percentage of capital financed by debt.

它的计算方法是长期借款占长期借款与股东权益合计的比例。许多分析师关注由债务融资的资本百分比。

Gearing Ratio = (Long-term Borrowings ÷ (Long-term Borrowings + Shareholders’ Equity)) × 100

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5. Shareholder & Investor Ratios | 股东与投资比率

Shareholder ratios help investors evaluate the returns and risk associated with owning shares. They connect share price, dividends and earnings to support investment decisions.

股东比率帮助投资者评估持股的回报和风险。它们将股价、股息和盈利联系在一起，以支持投资决策。

Dividend per share (DPS) represents the total dividend paid to shareholders divided by the number of ordinary shares issued. It is the cash return earned by each share.

每股股息（DPS）代表支付给股东的股息总额除以已发行普通股数量。它是每股获得的现金回报。

DPS = Total Dividends Paid ÷ Number of Ordinary Shares

Dividend yield expresses the annual dividend as a percentage of the current market share price. It shows the income return relative to the share’s value.

股息率将年度股息表示为当前市场股价的百分比。它显示了相对于股票价值的收入回报。

Dividend Yield = (DPS ÷ Market Share Price) × 100

Dividend cover measures how many times profits could cover the dividend payment. A higher cover suggests safer dividends and more retained profit for reinvestment.

股息保障倍数衡量利润能够覆盖股息支付的倍数。保障倍数越高，股息越安全，留存利润用于再投资也越多。

Dividend Cover = Profit after Tax ÷ Total Dividends

Earnings per share (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.

每股收益（EPS）显示归属于每一普通股的利润。它是从股东角度衡量公司盈利能力的基本指标。

EPS = (Profit after Tax − Preference Dividends) ÷ Number of Ordinary Shares

The price/earnings (P/E) ratio compares the market price per share to the EPS. It indicates how much investors are willing to pay for each unit of current earnings, reflecting growth expectations.

市盈率（P/E）比较每股市价与每股收益。它表明投资者愿意为当前每一单位盈利支付多少价格，反映了增长预期。

P/E Ratio = Market Price per Share ÷ EPS

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6. Contribution and Break-even Analysis | 贡献与盈亏平衡分析

Contribution and break-even tools help managers to cover fixed costs and plan for profits. They are essential for short-term decision making and sensitivity testing.

贡献和盈亏平衡工具有助于管理者覆盖固定成本并规划利润。它们对于短期决策和敏感性测试至关重要。

Contribution per unit is the amount each unit sold contributes towards fixed costs and profit after covering variable costs.

单位贡献是每售出一单位产品在覆盖变动成本后，对固定成本和利润的贡献额。

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

Total contribution scales this up and is used to calculate profit: Profit = Total Contribution − Total Fixed Costs.

总贡献将单位贡献加总，并用于计算利润：利润 = 总贡献 − 总固定成本。

Total Contribution = Contribution per Unit × Quantity Sold

The break-even output is the level of sales at which total revenue equals total costs. It provides a crucial benchmark for survival and profit planning.

盈亏平衡产量是总收入等于总成本的销售水平。它为生存和利润规划提供了关键基准。

Break-even Output = Total Fixed Costs ÷ Contribution per Unit

The margin of safety shows how far actual sales can fall before losses occur. It is a buffer expressed in units or revenue.

安全边际反映实际销售在发生亏损前可下降的幅度。它是一个用数量或收入表示的缓冲。

Margin of Safety (units) = Actual Output − Break-even Output

To achieve a target profit, managers can calculate the required output level by adding target profit to fixed costs before dividing by contribution per unit.

为实现目标利润，管理者可通过将目标利润加到固定成本上再除以单位贡献，计算出所需产量水平。

Output for Target Profit = (Total Fixed Costs + Target Profit) ÷ Contribution per Unit

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7. Decision Trees | 决策树

Decision trees map out different choices and their likely outcomes in a structured diagram. They use probability and financial values to identify the option with the highest expected monetary return.

决策树通过结构化图表展示不同选择及其可能的结果。它们利用概率和财务价值来确定预期货币回报最高的选项。

The expected value of a decision combines the probability of each outcome with its associated payoff. It is the weighted-average return used to compare alternatives.

决策的期望值将每种结果的概率与其相关回报相结合。它是用于比较备选方案的加权平均回报。

Expected Value = Probability of Outcome × Monetary Value of Outcome

The net gain of a decision deducts the initial cost of choosing that option from the total expected value. It reveals the true financial benefit after accounting for the investment required.

决策的净收益是从总期望值中扣除选择该选项的初始成本。它揭示了考虑所需投资后的真实财务收益。

Net Gain = Expected Value − Decision Cost

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8. Investment Appraisal | 投资评估

Investment appraisal techniques allow firms to evaluate the profitability and risk of major capital projects. They help decide whether to accept or reject potential long-term investments.

投资评估方法让企业能够评价重大资本项目的盈利能力和风险。它们有助于决定是接受还是拒绝潜在的长线投资。

The payback period calculates how long it takes to recover the initial investment from net cash inflows. A shorter payback is generally preferred as it reduces uncertainty.

投资回收期计算从净现金流入中收回初始投资所需的时间。回收期越短通常越受青睐，因为它降低了不确定性。

Payback Period = Initial Investment ÷ Annual Net Cash Flow (if uniform)

The average rate of return (ARR) measures the yearly accounting profit as a percentage of the investment. It uses profit figures rather than cash flows.

平均收益率（ARR）衡量年度会计利润占投资的百分比。它使用利润数据而非现金流。

ARR = (Average Annual Profit ÷ Initial Investment) × 100

Net present value (NPV) discounts all future cash flows to today’s values and subtracts the initial cost. It accounts for the time value of money, where a positive NPV signals value creation.

净现值（NPV）将所有未来现金流折现为今天的价值并减去初始成本。它考虑了货币的时间价值，正NPV表示创造价值。

NPV = Σ (Net Cash Flow in Year t × Discount Factor for Year t) − Initial Outlay

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9. Labour and Operational Efficiency | 劳动生产率与效率指标

Operational efficiency ratios monitor workforce performance and capacity usage. They are critical for productivity improvements and cost control.

运营效率比率监控劳动力表现和产能利用。它们对于提高生产率和控制成本至关重要。

Labour productivity identifies output produced per employee over a given period. It is a core measure of workforce effectiveness.

劳动生产率是指在既定时期内每位员工生产的产品。它是衡量员工效率的核心指标。

Labour Productivity = Total Output per Period ÷ Number of Employees

Labour turnover tracks the rate at which staff leave the business. High turnover can raise recruitment costs and indicate dissatisfaction.

劳动力流失率跟踪员工离职的速度。高流失率会增加招聘成本并暗示不满情绪。

Labour Turnover = (Number of Staff Leaving ÷ Average Number of Staff) × 100

Absenteeism measures the proportion of working time lost due to employee absence. Managing it helps maintain smooth operations.

缺勤率衡量因员工缺勤而损失的工作时间比例。管理好缺勤有助于维持运营顺畅。

Absenteeism = (Number of Absent Days ÷ Total Possible Working Days) × 100

Capacity utilisation compares actual output to the maximum possible output. It indicates how close the firm is to operating at full potential.

产能利用率将实际产量与最大可能产量进行比较。它表明企业接近满负荷运营的程度。

Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100

Unit (average) cost represents the total cost of producing one item. Lower unit costs can lead to higher profit margins if selling prices are maintained.

单位（平均）成本代表生产一件产品的总

Published by TutorHao | Year 13 商务 Revision Series | aleveler.com

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