📚 Year 12 AQA Business: Formula & Theorem Quick Reference Guide | AQA 商务：公式定理速查手册
This quick reference guide brings together every essential formula, ratio and key relationship you need for Year 12 AQA Business. Use it to revise calculations for financial performance, operations, marketing and human resources, and to understand the ‘theorems’ – the logic that links business data to decision making.
本速查手册汇集了 Year 12 AQA 商务所需的所有核心公式、比率与关键关系。用它来复习财务表现、运营、营销和人力资源中的计算，并理解那些把商业数据与决策连接起来的’定理’。
1. Revenue, Total Costs and Profit | 收入、总成本与利润
Revenue is the money coming in from sales. Total cost includes fixed and variable elements. Profit is what remains after deducting total costs from revenue – the fundamental measure of business success.
收入是销售带来的进账。总成本包含固定和变动两部分。利润是收入扣除总成本后剩余的部分，是衡量商业成功的根本指标。
Total revenue = Selling price per unit × Quantity sold
总收益 = 单位售价 × 销售量
Total costs are the sum of fixed costs, which do not change with output, and variable costs, which rise directly with output. Variable costs can be found by multiplying variable cost per unit by the number of units produced.
总成本是固定成本（不随产量变化）与变动成本（随产量直接上升）之和。变动成本可由单位变动成本乘以产量得出。
Total costs = Fixed costs + (Variable cost per unit × Quantity)
总成本 = 固定成本 + (单位变动成本 × 数量)
Profit (or loss) is the difference between total revenue and total costs. A positive figure indicates a profit; a negative figure signals a loss.
利润（或亏损）是总收益与总成本之差。正值代表盈利，负值表示亏损。
Profit = Total revenue − Total costs
利润 = 总收益 − 总成本
2. Contribution and Contribution per Unit | 贡献与单位贡献
Contribution shows how much revenue is ‘contributing’ towards fixed costs and profit after variable costs are covered. It is a cornerstone for break-even and pricing decisions.
贡献反映在覆盖变动成本后，收入能为固定成本和利润’贡献’多少。它是盈亏平衡和定价决策的基石。
Contribution = Total revenue − Total variable costs
贡献 = 总收益 − 总变动成本
Contribution per unit is the simpler, per-item version, crucial for calculating break-even output.
单位贡献是更简洁的单件版本，对计算盈亏平衡产量至关重要。
Contribution per unit = Selling price per unit − Variable cost per unit
单位贡献 = 单位售价 − 单位变动成本
3. Break-even Point and Margin of Safety | 盈亏平衡点与安全边际
The break-even point is the level of output where total revenue equals total costs, so the business makes neither a profit nor a loss. It is calculated using fixed costs and contribution per unit.
盈亏平衡点是总收益等于总成本的产量水平，此时企业既不盈利也不亏损。它用固定成本和单位贡献来计算。
Break-even output (units) = Fixed costs ÷ Contribution per unit
盈亏平衡产量（单位） = 固定成本 ÷ 单位贡献
Margin of safety measures how much output can fall before the business reaches break-even. It is often expressed in units or as a percentage.
安全边际衡量在达到盈亏平衡之前，产出还能下降多少。它通常以单位或百分比表示。
Margin of safety = Current output − Break-even output
安全边际 = 当前产量 − 盈亏平衡产量
To express margin of safety as a percentage: (Margin of safety ÷ Current output) × 100.
安全边际用百分比表示：(安全边际 ÷ 当前产量) × 100。
4. Profit Margins | 利润率
Profit margins reveal how effectively a firm is controlling costs and generating profit from revenue. The two main AQA margins are gross profit margin and net profit margin.
利润率揭示企业控制成本和从收入中创造利润的效率。AQA 主要的两个利润率是毛利率和净利率。
Gross profit = Revenue − Cost of sales
毛利 = 收入 − 销售成本
Gross profit margin = (Gross profit ÷ Revenue) × 100
毛利率 = (毛利 ÷ 收入) × 100
Net profit takes away all expenses, including operating costs and overheads. The net profit margin is a stronger indicator of overall profitability.
净利润扣除了包括运营成本和间接费用在内的所有开支。净利率是整体盈利能力更强的指标。
Net profit margin = (Net profit ÷ Revenue) × 100
净利率 = (净利润 ÷ 收入) × 100
5. Return on Capital Employed (ROCE) | 已用资本回报率
ROCE gauges the efficiency with which a business turns its invested capital into operating profit. It is a vital profitability ratio for comparing firms of different sizes.
ROCE 衡量企业把投入资本转化为经营利润的效率。它是比较不同规模企业时一个至关重要的盈利能力比率。
ROCE = (Operating profit ÷ Capital employed) × 100
已用资本回报率 = (经营利润 ÷ 已用资本) × 100
Capital employed can be calculated using the balance sheet: Total equity + Non-current liabilities, or Total assets − Current liabilities. Operating profit is often profit before interest and tax.
已用资本可通过资产负债表计算：总权益 + 非流动负债，或 总资产 − 流动负债。经营利润通常为息税前利润。
6. Liquidity Ratios | 流动性比率
Liquidity ratios measure a firm’s ability to meet short-term obligations. The two core ratios are the current ratio and the acid test ratio.
流动性比率衡量企业偿付短期到期债务的能力。两个核心比率是流动比率和速动比率（酸性测试）。
Current ratio = Current assets ÷ Current liabilities
流动比率 = 流动资产 ÷ 流动负债
The acid test ratio excludes inventories, offering a stricter test of immediate liquidity.
速动比率剔除了存货，对即时流动性的检验更为严格。
Acid test ratio = (Current assets − Inventories) ÷ Current liabilities
速动比率 = (流动资产 − 存货) ÷ 流动负债
7. Inventory Turnover | 存货周转率
This efficiency ratio indicates how many times a business sells and replaces its inventory over a period. A higher turnover suggests effective stock management.
这项效率比率显示企业在一段时间内存货销出与更新的次数。周转率越高，说明库存管理越有效。
Inventory turnover = Cost of sales ÷ Average inventories
存货周转率 = 销售成本 ÷ 平均存货
It is often expressed in days to help interpret the speed of stock movement.
通常也用天数表示，以便理解库存流动速度。
Inventory turnover (days) = (Average inventories ÷ Cost of sales) × 365
存货周转天数 = (平均存货 ÷ 销售成本) × 365
Average inventories = (Opening inventories + Closing inventories) ÷ 2.
平均存货 = (期初存货 + 期末存货) ÷ 2。
8. Payables and Receivables Days | 应付账款与应收账款天数
Receivables days (debtor days) show the average time a business takes to collect money from credit customers. Shorter periods improve cash flow.
应收账款天数（债务人天数）显示企业回收赊销款项的平均时间。周期越短，现金流越好。
Receivables days = (Trade receivables ÷ Revenue) × 365
应收账款天数 = (应收账款 ÷ 收入) × 365
Payables days (creditor days) measure how long a business takes to pay its suppliers. A longer period may help cash flow but could strain supplier relationships.
应付账款天数（债权人天数）衡量企业支付供应商货款的平均时间。周期更长可能有利于现金流，但可能对供应商关系造成压力。
Payables days = (Trade payables ÷ Cost of sales) × 365
应付账款天数 = (应付账款 ÷ 销售成本) × 365
9. Labour Productivity, Unit Costs, Absenteeism and Labour Turnover | 劳动生产率、单位成本、缺勤率与员工流失
Labour productivity measures output per worker. Higher productivity often lowers unit costs and improves competitiveness.
劳动生产率衡量每位员工的产出。更高的生产率往往能降低单位成本并提升竞争力。
Labour productivity = Output per period ÷ Number of employees
劳动生产率 = 每期产量 ÷ 员工人数
Unit cost (average cost) shows the total expense incurred to produce one unit of output.
单位成本（平均成本）显示生产一单位产出所发生的总费用。
Unit cost = Total costs ÷ Output
单位成本 = 总成本 ÷ 产量
Absenteeism and labour turnover are key HR metrics that reflect employee satisfaction and stability.
缺勤率和员工流失率是反映员工满意度与稳定性的关键人力资源指标。
Absenteeism (%) = (Number of days lost to absence ÷ Total possible working days) × 100
缺勤率 = (缺勤损失天数 ÷ 应出勤总天数) × 100
Labour turnover (%) = (Number of staff leaving ÷ Average number of staff) × 100
员工流失率 = (离职员工人数 ÷ 平均员工人数) × 100
10. Capacity Utilisation | 产能利用率
Capacity utilisation indicates the percentage of a firm’s maximum potential output that is currently being used. It helps assess operational efficiency and spare capacity.
产能利用率表示企业当前使用的最大潜在产出的百分比。它有助于评估运营效率和剩余产能。
Capacity utilisation (%) = (Actual output ÷ Maximum possible output) × 100
产能利用率 = (实际产量 ÷ 最大可能产量) × 100
11. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in price. It is essential for pricing strategy and predicting revenue effects.
PED 衡量需求量对价格变化的反应程度。它对定价策略和预测收入变动至关重要。
PED = % change in quantity demanded ÷ % change in price
需求价格弹性 = 需求量变动百分比 ÷ 价格变动百分比
Calculate percentage changes using the formula: (New value − Old value) ÷ Old value × 100. If PED > 1 demand is elastic; if PED < 1 demand is inelastic.
百分比变动公式：(新值 − 旧值) ÷ 旧值 × 100。当 PED > 1 时，需求有弹性；当 PED < 1 时，需求缺乏弹性。
12. Income Elasticity of Demand (YED) | 需求收入弹性
YED indicates how demand changes as consumer income changes. It helps classify goods and forecast market shifts during economic cycles.
YED 显示需求如何随消费者收入变化而变动。它有助于对商品进行分类，并在经济周期中预测市场变动。
YED = % change in quantity demanded ÷ % change in income
需求收入弹性 = 需求量变动百分比 ÷ 收入变动百分比
A positive YED indicates a normal good (luxury if YED > 1, necessity if between 0 and 1). A negative YED signals an inferior good.
YED 为正表明是正常品（若 YED > 1 为奢侈品，介于 0 到 1 之间为必需品）。YED 为负说明是劣等品。
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