Year 9 CAIE Business: Formula & Theorem Quick Reference Guide | 9年级CAIE商务：公式定理速查手册

📚 Year 9 CAIE Business: Formula & Theorem Quick Reference Guide | 9年级CAIE商务：公式定理速查手册

This quick-reference handbook brings together all the essential formulas and theorems you need for Year 9 CAIE Business Studies. From calculating profit to analysing cash flow, each concept is clearly defined with a worked example to help you cement your understanding before exams.

这本速查手册汇总了9年级CAIE商务课程所需的关键公式和定理。从利润计算到现金流分析，每个概念都配有清晰的定义和范例，帮助你在考试前巩固理解。

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1. Revenue Formula | 收入公式

Revenue (or sales revenue) is the total amount of money a business receives from selling its products or services in a given period. It is calculated using a simple multiplication.

收入（或销售收入）是企业在特定时期内通过销售产品或服务获得的总金额。它通过简单的乘法计算得出。

Revenue = Price per unit × Quantity sold

收入 = 单价 × 销售量

Price per unit (P) is the selling price of one item. Quantity sold (Q) is the number of units purchased by customers. Revenue does not subtract any costs — it is the ‘top line’ of a business.

单价（P）是每件商品的售价。销售量（Q）是顾客购买的数量。收入不扣除任何成本，它是企业的“顶线”。

Example: A bookshop sells 150 notebooks at $4 each. Revenue = 4 × 150 = $600.

示例：一家书店以每本4美元的价格售出150本笔记本。收入 = 4 × 150 = 600美元。

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2. Total Costs and Cost Types | 总成本与成本类型

Total costs are the full amount a business pays to produce and deliver its goods or services. They are split into two main types: fixed costs and variable costs.

总成本是企业为生产和提供商品或服务所支付的全部金额。它们分为两大类：固定成本和变动成本。

Total costs = Fixed costs + Variable costs

总成本 = 固定成本 + 变动成本

Fixed costs stay the same regardless of how many units are produced (e.g. rent, insurance, salaries of permanent staff). They must be paid even if output is zero.

固定成本不随产量变化（例如租金、保险、长期员工工资）。即使产量为零也必须支付。

Variable costs change directly with the level of output (e.g. raw materials, packaging, piece-rate wages). As you produce more, these costs rise proportionally.

变动成本直接随产量变动（例如原材料、包装、计件工资）。产量增加，这些成本按比例上升。

Example: A bakery has monthly fixed costs of $2,000 and variable costs of $1.50 per loaf. If it makes 1,000 loaves, total costs = 2,000 + (1.50 × 1,000) = $3,500.

示例：一家面包店每月固定成本2,000美元，每块面包的变动成本为1.50美元。如果生产1,000块面包，总成本 = 2,000 + (1.50 × 1,000) = 3,500美元。

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3. Profit Calculation | 利润计算

Profit is the financial gain a business makes once all costs have been deducted from revenue. It is the ultimate measure of success for most firms.

利润是企业在扣除所有成本后获得的财务收益。对大多数公司而言，它是衡量成功的最终指标。

Profit = Total revenue − Total costs

利润 = 总收入 − 总成本

If revenue exceeds total costs, the business makes a profit. If total costs are greater than revenue, it makes a loss.

如果收入大于总成本，企业就盈利；如果总成本大于收入，企业则亏损。

Gross profit focuses on the difference between revenue and the cost of making the product (cost of sales), while net profit subtracts all other expenses such as rent, salaries and marketing. For Year 9, you can start with the simple profit formula above.

毛利侧重于收入与产品制造成本（销售成本）之间的差额，而净利润则扣除租金、工资和营销等所有其他费用。对于9年级，你可以先从上述简单的利润公式开始。

Example: A hot-dog stall earns $800 in revenue. The hot dogs and buns cost $200, and the stall fee is $100. Profit = 800 − (200+100) = $500.

示例：一个热狗摊收入800美元，热狗和面包成本200美元，摊位费100美元。利润 = 800 − (200+100) = 500美元。

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4. Contribution per Unit | 单位贡献

Contribution is the amount left from the selling price after variable costs have been covered. It goes towards paying fixed costs and generating profit.

贡献是在扣除变动成本后售价剩余的金额。它用于支付固定成本并创造利润。

Contribution per unit = Selling price − Variable cost per unit

单位贡献 = 售价 − 单位变动成本

Once you know the contribution per unit, you can work out how many units need to be sold to cover all fixed costs. A higher contribution means each sale is more effective at boosting profit.

一旦知道单位贡献，你就能算出需要销售多少单位才能覆盖所有固定成本。贡献越高，每笔销售对利润的推动作用就越大。

Example: A phone case sells for $12, and the variable cost (material, packaging) is $5. Contribution per unit = 12 − 5 = $7.

示例：一个手机壳售价12美元，变动成本（材料、包装）为5美元。单位贡献 = 12 − 5 = 7美元。

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5. Break-even Point | 盈亏平衡点

The break-even point is the level of output where total revenue equals total costs — the business makes neither a profit nor a loss. It is a vital planning tool.

盈亏平衡点是指总收入等于总成本的产出水平——企业既不盈利也不亏损。它是一个至关重要的规划工具。

Break-even output = Fixed costs ÷ Contribution per unit

盈亏平衡产量 = 固定成本 ÷ 单位贡献

You can also find the break-even point in sales value by multiplying the break-even output by the selling price. The margin of safety shows how far actual sales can fall before the business reaches break-even.

你也可以通过将盈亏平衡产量乘以售价，计算出以销售额表示的盈亏平衡点。安全边际显示实际销售额在降至盈亏平衡点之前还能承受多大的降幅。

Margin of safety = Actual output − Break-even output

安全边际 = 实际产量 − 盈亏平衡产量

Example: Fixed costs are $2,000, the selling price is $50, and variable cost per unit is $30. Contribution = 50 − 30 = $20. Break-even = 2,000 ÷ 20 = 100 units. If the business sells 140 units, the margin of safety is 40 units.

示例：固定成本2,000美元，售价50美元，单位变动成本30美元。贡献 = 50 − 30 = 20美元。盈亏平衡产量 = 2,000 ÷ 20 = 100件。如果实际销售140件，安全边际为40件。

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6. Gross Profit Margin | 毛利率

Gross profit margin measures how much of every dollar of revenue remains after covering the direct costs of making the product. It is expressed as a percentage.

毛利率衡量每美元收入在扣除产品直接成本后还剩下多少。它以百分比表示。

Gross profit margin = (Gross profit ÷ Revenue) × 100%

毛利率 = (毛利 ÷ 收入) × 100%

Gross profit = Revenue − Cost of sales. Cost of sales includes items like raw materials and direct labour. A high gross profit margin means the business keeps more from each sale to pay overheads.

毛利 = 收入 − 销售成本。销售成本包括原材料和直接人工等项目。毛利率高意味着企业能从每笔销售中保留更多资金来支付间接费用。

Example: A café has revenue of $50,000 and cost of sales (coffee beans, milk, pastries) of $30,000. Gross profit = 50,000 − 30,000 = $20,000. Gross profit margin = (20,000 ÷ 50,000) × 100 = 40%.

示例：一家咖啡馆收入50,000美元，销售成本（咖啡豆、牛奶、糕点）为30,000美元。毛利 = 50,000 − 30,000 = 20,000美元。毛利率 = (20,000 ÷ 50,000) × 100 = 40%。

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7. Net Profit Margin | 净利率

Net profit margin shows the percentage of revenue left after all business expenses have been deducted. It gives a truer picture of overall profitability.

净利率显示扣除所有业务费用后收入的剩余百分比。它能更真实地反映整体盈利能力。

Net profit margin = (Net profit ÷ Revenue) × 100%

净利率 = (净利润 ÷ 收入) × 100%

Net profit = Gross profit − Other operating expenses (e.g. rent, salaries, advertising, interest, tax). A business can have a healthy gross margin but a low net margin if overheads are high.

净利润 = 毛利 − 其他营业费用（如租金、工资、广告、利息、税收）。如果间接费用高昂，企业可能毛利率良好但净利率很低。

Example: Continuing from the café, operating expenses (rent, wages, utilities) total $10,000. Net profit = 20,000 − 10,000 = $10,000. Net profit margin = (10,000 ÷ 50,000) × 100 = 20%.

示例：承接上例，咖啡馆的营业费用（租金、工资、水电）合计10,000美元。净利润 = 20,000 − 10,000 = 10,000美元。净利率 = (10,000 ÷ 50,000) × 100 = 20%。

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8. Market Share and Market Growth | 市场份额与市场增长

Market share tells you how much of the total market a business controls. Market growth shows whether the whole market is expanding or shrinking.

市场份额告诉你一家企业在整个市场中控制了多大比例。市场增长则显示整个市场是在扩张还是萎缩。

Market share = (Company’s sales ÷ Total market sales) × 100%

市场份额 = (企业销售额 ÷ 市场总销售额) × 100%

Market growth = (Change in market size ÷ Original market size) × 100%

市场增长 = (市场规模变化量 ÷ 原始市场规模) × 100%

Change in market size = Market size this year − Market size last year. Both measures are crucial for strategy: a growing market may attract new competitors, while a shrinking market can pressure profits.

市场规模变化量 = 今年市场规模 − 去年市场规模。这两个指标对战略至关重要：增长的市场可能吸引新的竞争者，而萎缩的市场会挤压利润。

Example: A phone brand sells 2 million units in a market where total sales are 10 million units. Market share = (2m ÷ 10m) × 100 = 20%. If the total market was 9 million units last year, market growth = ((10m − 9m) ÷ 9m) × 100 ≈ 11.1%.

示例：某手机品牌售出200万部，而市场总销量为1,000万部。市场份额 = (200万 ÷ 1,000万) × 100 = 20%。如果去年市场总规模为900万部，市场增长 = ((1,000万 − 900万) ÷ 900万) × 100 ≈ 11.1%。

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9. Cash Flow and Net Cash Flow | 现金流与净现金流

Cash flow is the movement of money into and out of a business. It is not the same as profit — a profitable business can still run out of cash.

现金流是企业资金的流入与流出。它不同于利润——盈利的企业仍然可能出现现金短缺。

Net cash flow = Total cash inflows − Total cash outflows

净现金流 = 总现金流入 − 总现金流出

Cash inflows include sales revenue, money from loans, and capital introduced. Cash outflows cover wages, raw materials, rent, loan repayments, and taxes.

现金流入包括销售收入、贷款资金和业主投入资本。现金流出涵盖工资、原材料、租金、偿还贷款和税款。

Closing cash balance = Opening balance + Net cash flow

期末现金余额 = 期初余额 + 净现金流

Example: A florist starts the month with $300 in the bank. Cash inflows from sales total $1,200. Outflows for flowers, rent and salaries are $1,000. Net cash flow = 1,200 − 1,000 = $200. Closing balance = 300 + 200 = $500.

示例：一家花店月初有300美元银行存款，当月销售收入现金流入共计1,200美元，采购鲜花、租金和工资等流出1,000美元。净现金流 = 1,200 − 1,000 = 200美元。期末余额 = 300 + 200 = 500美元。

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10. Liquidity Ratios: Current and Acid Test | 流动性比率：流动比率与速动比率

Liquidity ratios measure a firm’s ability to pay its short-term debts. The two most common are the current ratio and the acid test (quick) ratio.

流动性比率衡量企业偿还短期债务的能力。最常用的两个是流动比率和速动（酸性测试）比率。

Current ratio = Current assets ÷ Current liabilities

流动比率 = 流动资产 ÷ 流动负债

Acid test ratio = (Current assets − Inventories) ÷ Current liabilities

速动比率 = (流动资产 − 存货) ÷ 流动负债

Current assets include cash, receivables and inventory; current liabilities are debts due within one year. A current ratio of around 1.5:1 to 2:1 is usually considered safe. The acid test ratio is stricter because it removes inventory, which may take time to sell. A result close to 1:1 is often desirable.

流动资产包括现金、应收账款和存货；流动负债是一年内到期的债务。流动比率约在1.5:1至2:1通常被认为安全。速动比率更为严格，因为它剔除了可能需要较长时间才能变现的存货。接近1:1的结果往往是理想的。

Example: A business has current assets of $50,000 (including $15,000 inventory) and current liabilities of $30,000. Current ratio = 50,000 ÷ 30,000 = 1.67:1. Acid test = (50,000 − 15,000) ÷ 30,000 = 35,000 ÷ 30,000 ≈ 1.17:1. Both suggest the business can meet its short-term obligations.

示例：一家企业拥有流动资产50,000美元（其中包含15,000美元存货），流动负债30,000美元。流动比率 = 50,000 ÷ 30,000 = 1.67:1。速动比率 = (50,000 − 15,000) ÷ 30,000 = 35,000 ÷ 30,000 ≈ 1.17:1。两者都表明该企业能够履行其短期债务。

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