Pre-U AQA Business: Formula & Theorem Quick Reference Handbook | AQA 大学预科商务：公式定理速查手册

📚 Pre-U AQA Business: Formula & Theorem Quick Reference Handbook | AQA 大学预科商务：公式定理速查手册

Welcome to the Pre-U AQA Business Formula & Theorem Quick Reference Handbook. This concise guide compiles all essential quantitative formulas, ratios and decision-making tools required for AQA’s Pre-U Business specification. Use it to reinforce your revision and master the numerical aspects of business studies.

欢迎使用 AQA 大学预科商务公式定理速查手册。本简明指南汇编了 AQA 大学预科商务课程所需的所有基本定量公式、比率和决策工具。使用它可以巩固复习，掌握商务研究中的计算要点。

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1. Profitability Ratios | 盈利能力比率

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

This ratio shows the percentage of revenue remaining after paying for the direct costs of sales. It reflects a firm’s efficiency in managing production or purchasing, and its ability to add value.

该比率显示了扣除直接销售成本后剩余收入的百分比。它反映了企业生产或采购管理的效率以及增值能力。

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

It measures the proportion of revenue left after covering both cost of sales and operating expenses. A higher margin signals strong control over overheads and core operations.

它衡量了在覆盖销售成本和运营费用后剩余的收入比例。较高的利润率表明对间接费用和核心运营的控制得力。

Profit for the Year Margin = (Profit for the Year / Revenue) × 100

This is the final bottom-line margin after deducting interest, tax and any other one-off items. It shows overall profitability available to shareholders.

这是扣除利息、税款和所有一次性项目之后的最终底线利润率，反映可供股东分配的总体盈利水平。

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

ROCE evaluates how effectively a firm uses its long-term capital. Capital employed equals total equity plus non-current liabilities, or total assets minus current liabilities. It is a key performance indicator.

ROCE 评估企业使用长期资本的有效性。资本使用额等于总股本加非流动负债，或总资产减去流动负债。它是关键绩效指标之一。

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2. Liquidity Ratios | 流动性比率

Current Ratio = Current Assets / Current Liabilities

This ratio assesses whether a business has enough short-term assets to meet its short-term obligations. A ratio below 1 may signal liquidity problems, while an excessively high ratio could indicate inefficient asset use.

该比率评估企业是否有足够的短期资产偿还短期负债。比率低于 1 可能预示流动性问题，而过高的比率可能意味着资产利用效率低下。

Acid Test Ratio = (Current Assets – Inventory) / Current Liabilities

Also known as the quick ratio, it strips out inventory because stock may not be quickly converted into cash. A result of 1 or above is generally considered safe.

又名速动比率，它剔除了存货，因为库存可能无法迅速转化为现金。结果等于或大于 1 通常被认为是安全的。

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3. Efficiency Ratios | 效率比率

Inventory Turnover (Number of Days) = (Average Inventory / Cost of Sales) × 365

This shows the average length of time inventory is held before being sold. A lower number of days suggests efficient stock management and less tied-up capital.

它显示库存在售出前的平均持有时间。天数越低，表明库存管理越有效，占用的资本也越少。

Receivables Days = (Trade Receivables / Sales Revenue) × 365

It measures how long, on average, customers take to pay their invoices. A shorter collection period improves cash flow and reduces the risk of bad debts.

它衡量客户平均需要多长时间支付账单。较短的收款期可以改善现金流并降低坏账风险。

Payables Days = (Trade Payables / Cost of Sales) × 365

This ratio indicates how long a firm takes to pay its suppliers. A longer period can ease short-term cash pressure, but might damage relationships with creditors.

该比率表示企业支付供应商款项的平均天数。较长的付款期可以缓解短期现金压力，但可能损害与债权人的关系。

Asset Turnover = Revenue / Capital Employed (or Net Assets)

Asset turnover reveals how well a company uses its assets to generate sales. A higher figure means more revenue is being produced for every pound of capital invested.

资产周转率显示企业利用资产创造销售的能力。数值越高，意味着每投入一英镑资本所带来的收入越多。

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4. Gearing and Financial Structure | 杠杆与财务结构比率

Gearing Ratio = (Non-Current Liabilities / (Total Equity + Non-Current Liabilities)) × 100

Gearing measures the proportion of a firm’s capital that comes from debt. A high gearing ratio increases financial risk because interest must be paid regardless of profit levels.

杠杆比率衡量企业资本中来源于债务的比例。高杠杆会增加财务风险，因为无论利润如何都必须支付利息。

Interest Cover = Operating Profit / Interest Payable

This ratio shows how easily a business can pay interest on its outstanding debt from its operating earnings. A value below 2 is often seen as a warning sign.

利息覆盖率反映企业用营业利润支付未偿债务利息的难易程度。数值低于 2 通常被视为警示信号。

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5. Market and Shareholder Ratios | 市场与股东比率

Earnings Per Share (EPS) = (Profit for the Year – Preference Dividends) / Number of Issued Ordinary Shares

EPS indicates the amount of profit attributable to each ordinary share. It is a fundamental measure of a company’s profitability from a shareholder’s perspective.

每股收益表示每张普通股对应的利润额，从股东角度衡量公司盈利能力的核心指标。

Price/Earnings Ratio (P/E) = Market Price Per Share / Earnings Per Share

The P/E ratio shows what the market is willing to pay for each unit of earnings. A high P/E suggests strong future growth expectations.

市盈率表明市场愿意为每一单位收益支付的价格。高市盈率暗示对未来增长的强烈预期。

Dividend Yield = (Dividend Per Share / Market Price Per Share) × 100

This ratio measures the cash return a shareholder receives relative to the share price. It is important for income-focused investors.

股息率衡量股东获得的现金回报相对于股价的比例，对关注收益的投资者非常重要。

Dividend Cover = Earnings Per Share / Dividend Per Share

Dividend cover shows how many times the profit for the year covers the dividend payment. A higher cover indicates greater capacity to sustain or grow dividends.

股息覆盖倍数显示年度利润能够支付股息的倍数。覆盖倍数越高，说明维持或增加股息的能力越强。

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6. Break-even Analysis | 盈亏平衡分析

Break-even Output (Units) = Total Fixed Costs / Contribution Per Unit

This formula calculates the number of units a firm must sell to cover all costs, where contribution per unit equals selling price minus variable cost per unit.

该公式计算企业为覆盖所有成本而必须销售的产品数量，其中单位贡献等于售价减去单位变动成本。

Margin of Safety (Units) = Actual (or Budgeted) Output – Break-even Output

The margin of safety shows how far sales can fall before the business starts making a loss. A larger margin reduces risk.

安全边际表示在开始亏损之前销售量可以下降的幅度。安全边际越大，风险越低。

Target Profit Output (Units) = (Total Fixed Costs + Target Profit) / Contribution Per Unit

This extends the break-even concept to find the output level required to achieve a desired amount of profit.

该公式将盈亏平衡概念扩展，用于求为实现特定目标利润所需的产量水平。

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7. Investment Appraisal | 投资评估

Payback Period = Number of Years (and Months) to Recover Initial Investment Cost

Payback measures the time needed for cumulative net cash inflows to equal the initial outlay. While simple, it ignores the time value of money and cash flows after payback.

投资回收期衡量累计净现金流入等于初始投资所需的时间。虽然简单，但它忽略了货币时间价值和回收后的现金流量。

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

ARR compares the average accounting profit generated by a project with the average capital tied up. It provides a percentage return but ignores the timing of profits.

ARR 将项目产生的平均会计利润与平均占用资本进行比较，给出百分比回报，但忽略了利润的时间分布。

Net Present Value (NPV) = Σ (Net Cash Flow ₙ / (1 + Discount Rate)ⁿ) – Initial Investment

NPV discounts all future cash flows to today’s value. A positive NPV means the project should theoretically add value to the business and is worth pursuing.

NPV 将所有未来现金流折现为当前价值。正值 NPV 意味着项目理论上会为企业增加价值，值得进行。

Expected Monetary Value (EMV) = Σ (Probability × Net Payoff)

Used in decision trees, EMV multiplies each possible outcome by its probability and sums the results. It helps managers choose the option with the highest expected financial return.

用于决策树的期望货币值，将每个可能结果乘以概率后加总，帮助管理者选择期望财务回报最高的方案。

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8. Elasticities | 弹性

Price Elasticity of Demand (PED) = % Change in Quantity Demanded / % Change in Price

PED measures the responsiveness of demand to a price change. If the absolute value is greater than 1, demand is price elastic; if less than 1, it is inelastic. This affects total revenue decisions.

PED 衡量需求量对价格变化的反应程度。若绝对值大于 1，需求富有弹性；小于 1 则缺乏弹性。这会影响总收入决策。

Income Elasticity of Demand (YED) = % Change in Quantity Demanded / % Change in Income

YED indicates whether a good is normal (positive elasticity) or inferior (negative elasticity). Luxury goods typically have a YED greater than 1.

YED 显示商品是正常品（弹性为正）还是劣等品（弹性为负）。奢侈品的 YED 通常大于 1。

Cross-Price Elasticity of Demand (XED) = % Change in Quantity Demanded of Good A / % Change in Price of Good B

XED shows the relationship between two products. A positive XED indicates substitutes, while a negative XED suggests complements. It helps in strategic pricing and product placement.

XED 反映两种产品的关系。正值表示替代品，负值表示互补品，有助于企业制定定价和产品组合战略。

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9. Contribution and Cost Formulas | 贡献与成本公式

Contribution Per Unit = Selling Price Per Unit – Variable Cost Per Unit

Contribution is the surplus each unit generates to first cover fixed costs and then provide profit. It is central to break-even and margin analysis.

贡献是每单位产品产生的用于首先覆盖固定成本然后提供利润的盈余，是盈亏平衡和边际分析的核心。

Total Contribution = Contribution Per Unit × Quantity Sold

Total contribution represents the total amount available to pay fixed costs and earn profit. Once fixed costs are deducted, whatever remains is profit.

总贡献代表可用于支付固定成本并获取利润的总金额。扣除固定成本后的剩余部分即为利润。

Profit = Total Contribution – Total Fixed Costs

This restates the profit equation in terms of contribution. It highlights how profit changes with volume, as variable costs move proportionally with output.

该方程式以贡献形式重新表述利润，凸显利润如何随产量变化，因为变动成本与产量成比例变动。

Total Costs = Total Fixed Costs + (Variable Cost Per Unit × Quantity)

Understanding the cost structure allows managers to forecast total expenses at different output levels and set appropriate prices.

理解成本结构可以让管理者预测不同产量下的总费用，并制定合适的价格。

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10. Productivity and Capacity | 生产率与产能利用率

Labour Productivity = Total Output Per Period / Number of Employees

This measures the output per worker in a given time frame. Higher productivity reduces unit labour costs and can improve competitiveness.

该指标衡量单位时间内每位员工的产出。较高的生产率可降低单位劳动力成本，提升竞争力。

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

Capacity utilisation shows how much of a firm’s productive potential is being used. Operating too close to 100 % may strain resources; too low a rate may waste fixed costs.

产能利用率显示企业生产潜力的使用程度。过度接近 100 % 可能令资源紧张；比率过低则可能浪费固定成本。

Unit Cost (Average Cost) = Total Cost / Units of Output

Unit cost falls as output rises if fixed costs are spread over more units. It is a critical benchmark for pricing, profitability and economies of scale analysis.

当固定成本被更多产量分摊时，单位成本会下降，这是定价、盈利能力以及规模经济分析的重要基准。

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Published by TutorHao | Business Revision Series | aleveler.com

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