📚 IGCSE AQA Business: Formula Summary Handbook | IGCSE AQA 商务：公式汇总手册
This handbook brings together all the essential quantitative formulas you will need for the IGCSE AQA Business exam. Understanding how to calculate and interpret these figures is a core skill, and mastering them will help you tackle both calculation questions and analysis tasks with confidence. Each section presents the key formulas, worked examples, and guidance on what the results mean for a business.
这本手册汇集了 IGCSE AQA 商务考试中所需的所有核心量化公式。掌握如何计算并解读这些数字是一项基本技能，熟练运用它们将帮助你从容应对计算题和分析题。每一节都提供了关键公式、示例计算以及对结果含义的解读，帮助你理解数字背后的商业意义。
1. Revenue, Total Costs and Profit | 收入、总成本和利润
Revenue (or turnover) is the money a business earns from selling its goods or services. The formula is straightforward: Revenue = Price per unit × Quantity sold. For example, if a bakery sells 2,000 loaves of bread at £1.50 each, revenue is £1.50 × 2,000 = £3,000. Revenue does not subtract costs, so it represents the top line of a business’s trading performance.
收入（或营业额）是企业通过销售商品或服务所获得的资金。基本公式为：收入 = 每单位售价 × 销售数量。例如，一家面包店以每块 1.50 英镑的价格售出 2,000 块面包，收入为 1.50 英镑 × 2,000 = 3,000 英镑。收入并未扣除成本，因此它代表了企业经营业绩的“顶线”。
Total costs are the sum of all fixed and variable costs. Fixed costs (e.g. rent, salaries) stay the same regardless of output, while variable costs (e.g. raw materials) change directly with the number of units produced. So, Total costs = Fixed costs + (Variable cost per unit × Quantity).
总成本是所有固定成本和变动成本之和。固定成本（如租金、固定薪资）无论产量多少都保持不变，而变动成本（如原材料）随产量变化直接增减。因此，总成本 = 固定成本 +（单位变动成本 × 数量）。
Profit is what remains after all costs are subtracted from revenue. The simple formula is: Profit = Total revenue − Total costs. A positive result is a profit; a negative result is a loss. Businesses must understand these calculations to set prices and plan production levels.
利润是收入扣除所有成本后的剩余部分。简单公式为：利润 = 总收入 − 总成本。正数结果为利润，负数结果为亏损。企业必须理解这些计算，才能合理定价并规划产量。
2. Break-even Point | 盈亏平衡点
The break-even point is the level of output at which total revenue exactly equals total costs, so the business makes neither a profit nor a loss. The formula used is: Break-even output = Fixed costs ÷ (Selling price per unit − Variable cost per unit). The denominator (price minus variable cost) is known as the contribution per unit.
盈亏平衡点是指总收入恰好等于总成本的产出水平，此时企业既不盈利也不亏损。所用的公式为：盈亏平衡产量 = 固定成本 ÷（单位售价 − 单位变动成本）。分母（售价减变动成本）被称为单位边际贡献。
For instance, if fixed costs are £10,000, the selling price is £25, and variable cost per unit is £15, then contribution per unit is £10. Break-even = 10,000 ÷ 10 = 1,000 units. This means the business must sell 1,000 units to cover all costs. Break-even analysis is a vital tool for decision-making about new product launches, pricing, and cost control.
例如，如果固定成本为 10,000 英镑，单位售价为 25 英镑，单位变动成本为 15 英镑，则单位边际贡献为 10 英镑。盈亏平衡产量 = 10,000 ÷ 10 = 1,000 件。这意味着企业必须售出 1,000 件产品才能覆盖全部成本。盈亏平衡分析是新产品上市、定价和成本控制决策的重要工具。
3. Margin of Safety | 安全边际
Once the break-even point is known, a business can calculate its margin of safety. This shows the amount by which actual sales can fall before the business starts making a loss. The formula is: Margin of safety = Actual output (or sales) − Break-even output.
一旦知道了盈亏平衡点，企业就可以计算其安全边际。它显示了实际销售量在达到盈亏平衡点之前还可以下降的空间。公式为：安全边际 = 实际产量（或销量） − 盈亏平衡产量。
For example, if the break-even output is 1,000 units and the business expects to sell 1,500 units, the margin of safety is 500 units. It can also be expressed as a percentage: (Margin of safety ÷ Actual sales) × 100. In this case, (500 ÷ 1,500) × 100 = 33.3%. A high margin of safety means the business is less likely to incur a loss if demand drops.
例如，盈亏平衡产量为 1,000 件，企业预计销售 1,500 件，则安全边际为 500 件。它也可以用百分比表示：（安全边际 ÷ 实际销量）× 100。本例中，（500 ÷ 1,500）× 100 = 33.3%。高安全边际意味着即使需求下降，企业也不容易发生亏损。
4. Gross and Net Profit Margins | 毛利率和净利率
Profit margins measure how much profit a business makes relative to its sales revenue, highlighting profitability and efficiency. Gross profit margin focuses on the direct costs of production. The formula is: Gross profit margin (%) = (Gross profit ÷ Revenue) × 100, where gross profit = Revenue − Cost of sales.
利润率衡量企业相对于销售收入所获得的利润，反映盈利能力和经营效率。毛利率关注生产的直接成本。公式为：毛利率（%）=（毛利润 ÷ 收入）× 100，其中毛利润 = 收入 − 销售成本。
If a business has revenue of £100,000 and cost of sales of £60,000, gross profit is £40,000. Gross profit margin = (40,000 ÷ 100,000) × 100 = 40%. This means 40% of revenue remains after covering direct costs to pay for other expenses and profit.
如果企业收入为 100,000 英镑，销售成本为 60,000 英镑，则毛利润为 40,000 英镑。毛利率 =（40,000 ÷ 100,000）× 100 = 40%。这意味着支付直接成本后，40% 的收入可用来支付其他费用并形成利润。
Net profit margin takes all expenses into account, including operating costs, interest, and tax. The formula is: Net profit margin (%) = (Net profit ÷ Revenue) × 100. Net profit = Gross profit − All other expenses. This ratio tells stakeholders how much of each pound of sales becomes final profit.
净利率则考虑了全部费用，包括运营成本、利息和税费。公式为：净利率（%）=（净利润 ÷ 收入）× 100，其中净利润 = 毛利润 − 所有其他费用。这个比率告诉利益相关者每一英镑的销售额最终有多少成为利润。
5. Average Rate of Return (ARR) | 平均收益率
The average rate of return is an investment appraisal method that calculates the average annual profit as a percentage of the initial investment cost. Step 1: Calculate the total profit over the project’s lifetime (total cash inflows minus initial outlay). Step 2: Divide the total profit by the number of years to find the average annual profit. Step 3: Use the formula: ARR (%) = (Average annual profit ÷ Initial investment) × 100.
平均收益率是一种投资评估方法，计算平均年利润占初始投资成本的百分比。第一步：计算项目生命期内的总利润（总现金流入减去初始支出）。第二步：将总利润除以年数，得到平均年利润。第三步：使用公式：ARR（%）=（平均年利润 ÷ 初始投资额）× 100。
For example, a machine costs £20,000 and is expected to generate total net cash inflows of £30,000 over 5 years. Total profit = £30,000 − £20,000 = £10,000. Average annual profit = £10,000 ÷ 5 = £2,000. ARR = (2,000 ÷ 20,000) × 100 = 10%. Businesses often compare the ARR with their target return to decide whether to proceed with the investment.
例如，一台机器成本为 20,000 英镑，预计在 5 年内产生的净现金流入总额为 30,000 英镑。总利润 = 30,000 英镑 − 20,000 英镑 = 10,000 英镑。平均年利润 = 10,000 英镑 ÷ 5 = 2,000 英镑。ARR =（2,000 ÷ 20,000）× 100 = 10%。企业通常将 ARR 与目标收益率进行比较，以决定是否进行该项投资。
6. Cash Flow Forecasting Formulas | 现金流量预测公式
A cash flow forecast is a plan for the cash inflows and outflows over a period. At the heart of it are two simple calculations. Net cash flow for a period = Total cash inflows − Total cash outflows. This can be positive or negative. Closing balance = Opening balance + Net cash flow. The closing balance of one period becomes the opening balance of the next.
现金流量预测是对某一时期内现金流入和流出的计划。其核心包含两个简单计算。某一期间的净现金流量 = 总现金流入 − 总现金流出。这一数值可能为正或负。期末余额 = 期初余额 + 净现金流量。一个期间的期末余额成为下一个期间的期初余额。
If a business starts a month with £5,000, receives £8,000 from customers, and pays out £6,000 in total costs, net cash flow is £8,000 − £6,000 = £2,000. Closing balance = £5,000 + £2,000 = £7,000. Monitoring these figures helps businesses avoid liquidity problems and arrange overdraft facilities in advance.
如果某企业月初余额为 5,000 英镑，从客户处收到 8,000 英镑，并支付总计 6,000 英镑的成本，则净现金流为 8,000 英镑 − 6,000 英镑 = 2,000 英镑。期末余额 = 5,000 英镑 + 2,000 英镑 = 7,000 英镑。监控这些数字有助于企业避免流动性问题，并提前安排透支额度。
7. Labour and Capital Productivity | 劳动和资本生产率
Productivity measures how efficiently inputs are converted into outputs. Labour productivity is output per worker over a given time. Formula: Labour productivity = Total output ÷ Number of employees. For example, if a factory produces 10,000 units in a week with 50 workers, labour productivity is 10,000 ÷ 50 = 200 units per worker per week. Improvements in productivity can lower unit costs and increase competitiveness.
生产率衡量投入转化为产出的效率。劳动生产率是指某一时期内每个工人的产出量。公式：劳动生产率 = 总产出 ÷ 员工人数。例如，如果一家工厂一周内用 50 名工人生产 10,000 件产品，则劳动生产率为 10,000 ÷ 50 = 200 件/工人/周。提高生产率可以降低单位成本，增强竞争力。
Capital productivity looks at the output generated per unit of capital (e.g. per machine). Formula: Capital productivity = Total output ÷ Number of machines (or value of capital). If the same factory uses 20 machines to produce those 10,000 units, capital productivity is 500 units per machine. Tracking these figures helps businesses identify inefficiencies and plan investments in training or new equipment.
资本生产率考察单位资本（如每台机器）的产出量。公式：资本生产率 = 总产出 ÷ 机器数量（或资本价值）。如果同一工厂使用 20 台机器生产 10,000 件产品，则资本生产率为每台机器 500 件。跟踪这些指标有助于企业发现低效环节，并规划对培训或新设备的投资。
8. Unit Costs | 单位成本
Unit cost (or average cost per unit) tells a business how much it spends to produce a single unit of output. The formula is: Unit cost = Total costs ÷ Quantity of output. Total costs include both fixed and variable costs. As output increases, fixed costs are spread over more units, so unit cost tends to fall – this is known as economies of scale.
单位成本（或每单位平均成本）告诉企业生产一件产品需要花费多少。公式为：单位成本 = 总成本 ÷ 产出数量。总成本包括固定成本和变动成本。随着产量增加，固定成本被分摊到更多产品上，因此单位成本往往会下降——这就是所谓的规模经济。
If total costs are £20,000 for producing 4,000 items, unit cost is £5. If production rises to 8,000 items and total costs become £32,000, unit cost falls to £4. A lower unit cost can mean higher profit margins or the ability to reduce prices while still making a profit.
如果生产 4,000 件产品的总成本为 20,000 英镑，则单位成本为 5 英镑。如果产量提高到 8,000 件，总成本变为 32,000 英镑，则单位成本降至 4 英镑。较低的单位成本意味着更高的利润率，或能够在降价的同时仍实现盈利。
9. Market Share and Market Growth | 市场份额和市场增长
Market share measures a company’s sales as a proportion of the total market sales. Formula: Market share (%) = (Company’s sales ÷ Total market sales) × 100. If a smartphone brand sells 2 million units in a market where total sales are 20 million units, its market share is (2 ÷ 20) × 100 = 10%. An increasing market share indicates a stronger competitive position.
市场份额衡量一家公司的销售额占市场总销售额的比例。公式：市场份额（%）=（公司销售额 ÷ 市场总销售额）× 100。如果某智能手机品牌在一个总销量为 2,000 万部的市场中售出 200 万部，则其市场份额为（2 ÷ 20）× 100 = 10%。市场份额的增长表明竞争地位在加强。
Market growth shows how the size of the whole market is changing over time. Formula: Market growth (%) = [(Market size this period − Market size last period) ÷ Market size last period] × 100. For example, if the market was worth £500 million last year and £550 million this year, growth = [(550 − 500) ÷ 500] × 100 = 10%. These measures help businesses set realistic sales targets and decide whether to enter or exit markets.
市场增长反映整个市场规模随时间的变化情况。公式：市场增长率（%）= [（本期市场规模 − 上期市场规模） ÷ 上期市场规模] × 100。例如，去年市场规模为 5 亿英镑，今年为 5.5 亿英镑，则增长率 = [（550 − 500） ÷ 500] × 100 = 10%。这些指标有助于企业制定切实可行的销售目标，并决定进入或退出哪些市场。
10. Liquidity Ratios (Current & Acid Test) | 流动比率和速动比率
Liquidity ratios assess a firm’s ability to pay short-term debts as they fall due. The current ratio compares all current assets to all current liabilities. Formula: Current ratio = Current assets ÷ Current liabilities. A ratio of 1.5:1 to 2:1 is often considered healthy. For instance, if current assets are £90,000 and current liabilities are £50,000, the ratio is 1.8:1 – the business has £1.80 in current assets for every £1 of short-term debt.
流动比率评估企业到期偿还短期债务的能力。流动比率将全部流动资产与全部流动负债进行比较。公式：流动比率 = 流动资产 ÷ 流动负债。一般认为 1.5:1 到 2:1 的比率是健康的。例如，如果流动资产为 90,000 英镑，流动负债为 50,000 英镑，则比率为 1.8:1——即每一英镑的短期债务对应 1.80 英镑的流动资产。
The acid test ratio (or quick ratio) is a stricter measure because it excludes stock (inventory), which may take time to sell. Formula: Acid test ratio = (Current assets − Stock) ÷ Current liabilities. If stock is £20,000 in the above example, the acid test ratio = (90,000 − 20,000) ÷ 50,000 = 1.4:1. This shows the business could still cover its immediate debts even if stock could not be quickly turned into cash. A ratio below 1:1 could signal a liquidity problem.
速动比率（酸性测试比率）是一种更为严格的衡量标准，因为它剔除了可能需要时间才能售出的存货。公式：速动比率 =（流动资产 − 存货）÷ 流动负债。在上例中，如果存货为 20,000 英镑，则速动比率 =（90,000 − 20,000）÷ 50,000 = 1.4:1。这表明即使存货无法迅速变现，企业仍有能力支付即期债务。比率低于 1:1 可能预示存在流动性问题。
Finally, working capital itself is the difference between current assets and current liabilities: Working capital = Current assets − Current liabilities. Positive working capital means the firm has enough short-term resources to fund its day-to-day operations.
最后，营运资金本身是流动资产与流动负债的差额：营运资金 = 流动资产 − 流动负债。正的营运资金意味着企业有足够的短期资源来支持其日常运营。
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