KS3 CAIE Business Formula & Theorem Quick Reference Handbook | KS3 CAIE 商务公式定理速查手册

📚 KS3 CAIE Business Formula & Theorem Quick Reference Handbook | KS3 CAIE 商务公式定理速查手册

This handbook provides a concise collection of essential business formulas and core economic theorems for KS3 CAIE Business students. Each entry is explained in plain English and followed by its Chinese translation, making revision quick and effective. Keep this guide handy to master the calculations and concepts that underpin successful business decision-making.

本手册为 KS3 CAIE 商务课程学生整理了必备的核心商务公式与基本经济定理。每一项均以简洁英文解释并附上中文翻译，方便快速复习，助你掌握支撑商业决策的计算与概念。

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1. The Revenue Formula | 收入公式

Total revenue is the income a business receives from selling its goods or services. It is calculated by multiplying the selling price per unit by the number of units sold. Revenue is a top-line figure that indicates the scale of sales before any costs are deducted.

总收入是企业销售商品或服务所获得的收入，它等于单位售价乘以销售数量。总收入是一项顶线指标，反映扣除任何成本之前的销售规模。

Total Revenue = Selling Price per Unit × Quantity Sold

总收入 = 单位售价 × 销售数量

If a business sells 200 cupcakes at $3 each, its total revenue is $600. Revenue can change if the price or the quantity sold changes, so it is a crucial number for forecasting and evaluating performance.

如果一家企业以每个 3 美元的价格卖出 200 个纸杯蛋糕，它的总收入就是 600 美元。价格或销量的变化都会引起收入变动，因此收入是预测和评估业绩的关键数据。

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2. Total Cost Formula | 总成本公式

Total cost represents all the expenses a business incurs in producing and delivering its goods or services. It is split into fixed costs, which stay the same regardless of output (e.g., rent), and variable costs, which change directly with the level of production (e.g., raw materials).

总成本代表企业生产和提供商品或服务所发生的全部费用。它分为固定成本（如租金，不随产量变化）和可变成本（如原材料，随产量直接变化）。

Total Cost = Total Fixed Cost + Total Variable Cost

总成本 = 总固定成本 + 总可变成本

Understanding total cost helps a business set prices and calculate profit. If fixed costs are $1,000 per month and variable costs are $2 per unit, producing 500 units means total variable cost is $1,000, giving a total cost of $2,000.

理解总成本有助于企业定价和计算利润。若月固定成本为 1,000 美元，单位可变成本为 2 美元，生产 500 件时总可变成本为 1,000 美元，总成本为 2,000 美元。

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3. Profit Calculation | 利润计算

Profit is the financial gain realised when revenue exceeds total costs over a period. It is the primary objective for most businesses and a key measure of success. A negative profit is called a loss.

利润是某一时期内收入超过总成本的那部分财务收益。它是大多数企业的主要目标，也是衡量成功的关键指标。负利润称为亏损。

Profit = Total Revenue – Total Cost

利润 = 总收入 – 总成本

A business with $10,000 revenue and $7,500 total cost makes a $2,500 profit. Monitoring profit helps owners decide whether to expand, invest, or cut costs. It is crucial to remember that cash and profit are not the same; a firm can be profitable but short on cash.

一家企业有 10,000 美元收入和 7,500 美元总成本，利润即为 2,500 美元。跟踪利润有助于业主决定是否扩张、投资或削减成本。务必记住现金与利润不是一回事，企业可以盈利但现金短缺。

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4. Break-even Point | 盈亏平衡点

The break-even point is the level of output at which total revenue exactly equals total cost, so the business makes neither profit nor loss. It is a vital planning tool, as it shows the minimum sales needed to avoid a loss. The formula uses fixed costs and the contribution per unit (selling price minus variable cost per unit).

盈亏平衡点是指总收入恰好等于总成本时的产出水平，此时企业既不盈利也不亏损。它是一个重要的规划工具，展示了避免亏损的最低销售量。该公式用到固定成本和单位边际贡献（售价减去单位可变成本）。

Break-even Output (units) = Total Fixed Costs ÷ (Selling Price per Unit – Variable Cost per Unit)

盈亏平衡产量（单位） = 总固定成本 ÷ (单位售价 – 单位可变成本)

For example, with fixed costs of $5,000, a selling price of $25, and a variable cost of $15 per unit, the break-even point is 5,000 ÷ (25 – 15) = 500 units. Selling more than 500 units generates profit; selling fewer results in a loss. Break-even analysis can be shown on a chart where the revenue and total cost lines intersect.

例如，固定成本 5,000 美元，售价 25 美元，单位可变成本 15 美元，盈亏平衡点为 5,000 ÷ (25 – 15) = 500 件。超过 500 件就产生利润，少于 500 件则亏损。盈亏平衡分析可在图表上表示，收入线与总成本线的交点即为平衡点。

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5. Profit Margin | 利润率

Profit margin expresses profit as a percentage of revenue, showing how much of every dollar earned translates into profit. It helps compare profitability across different-sized businesses or time periods. Two common margins are gross profit margin and net profit margin, but at KS3 level we focus on the overall profit margin.

利润率将利润表示为收入的百分比，显示出每赚取一美元中有多少转化为利润。它有助于比较不同规模企业或不同时期的盈利能力。常见的两大利润率是毛利率和净利率，但在 KS3 阶段我们聚焦于整体利润率。

Profit Margin = (Profit ÷ Revenue) × 100%

利润率 = (利润 ÷ 收入) × 100%

If a company has a profit of $6,000 and revenue of $30,000, its profit margin is (6,000 ÷ 30,000) × 100 = 20%. A higher margin indicates stronger control over costs or better pricing power. Businesses often try to improve margins by cutting unnecessary expenses or adding value to justify higher prices.

若一家公司利润为 6,000 美元，收入为 30,000 美元，其利润率为 (6,000 ÷ 30,000) × 100 = 20%。更高的利润率表明成本控制更为有力或定价能力更强。企业常通过削减不必要开支或增加价值以支撑更高价格来提升利润率。

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6. Net Cash Flow | 净现金流

Net cash flow measures the difference between cash inflows (money coming into the business) and cash outflows (money leaving the business) over a specific period. It is crucial for ensuring a business can pay its bills on time. A positive cash flow means more cash is coming in than going out.

净现金流衡量的是特定时期内现金流入（进入企业的资金）与现金流出（离开企业的资金）之间的差额。它对于确保企业按时支付账单至关重要。正现金流表示流入多于流出。

Net Cash Flow = Total Cash Inflows – Total Cash Outflows

净现金流 = 现金流入总额 – 现金流出总额

A cash flow forecast uses this formula to predict future cash positions. Inflows may include sales revenue, loans, and owner’s capital; outflows include wages, rent, and materials. Even a profitable business can fail if it runs out of cash, so managing cash flow is essential for survival.

现金流量预测运用该公式来预测未来的现金状况。流入可包括销售收入、贷款和所有者资本；流出包括工资、租金和原材料。即便是盈利企业，如果现金耗尽也可能失败，因此管理现金流对生存至关重要。

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7. Added Value Formula | 增值公式

Added value is the difference between the selling price of a product and the cost of bought-in materials and components. It represents the increase in worth created during the production process. A business that adds more value can often charge higher prices or earn greater margins.

增值是产品售价与购入材料和零部件成本之间的差额，它代表了生产过程中创造的额外价值。能创造更多增值的企业通常可以收取更高价格或获得更大利润空间。

Added Value = Selling Price – Cost of Bought-in Materials and Components

增值 = 售价 – 购入材料和零部件成本

For example, a carpenter buys timber for $40 and builds a table sold for $150; the added value is $110. This excludes other costs like labour and rent, but it shows how much the business has increased the value of the inputs. Ways to boost added value include improving design, branding, or customer service.

例如，一位木匠花 40 美元购入木材并制作桌子以 150 美元售出，增值为 110 美元。这里并未包括人工和租金等其他成本，但它显示了企业对投入品增值了多少。提升增值的途径包括改进设计、品牌包装或客户服务。

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8. The Law of Demand | 需求定理

The Law of Demand states that, all other factors being equal, as the price of a good or service increases, the quantity demanded decreases, and vice versa. There is an inverse relationship between price and quantity demanded. This is one of the most fundamental principles in business and economics.

需求定理指出，在其他条件不变的情况下，商品或服务的价格上升时，需求量下降；价格下降时，需求量上升。价格与需求量之间存在反向关系。这是商务和经济学中最基本的原理之一。

When Price ↑, Quantity Demanded ↓ (ceteris paribus)

当价格 ↑，需求量 ↓（其他条件不变）

This relationship occurs because consumers’ purchasing power falls when prices rise, and they may switch to cheaper alternatives. Demand curves slope downwards from left to right. Factors such as advertising, income changes, and trends can shift the entire demand curve even if price stays constant.

出现这种关系是因为价格上涨时消费者购买力下降，他们可能转向更便宜的替代品。需求曲线从左向右下倾。广告、收入变化、潮流等因素即使价格不变，也可能使整条需求曲线发生移动。

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9. The Law of Supply | 供给定理

The Law of Supply states that, all other things being equal, an increase in price results in an increase in the quantity supplied. Producers are willing to supply more of a good when they can sell it at a higher price because the potential for profit is greater. There is a direct relationship between price and quantity supplied.

供给定理指出，在其他条件不变的情况下，价格上涨会导致供给量增加。生产者能够在更高价格下出售商品时，因潜在利润更大而愿意供应更多。价格与供给量之间存在正向关系。

When Price ↑, Quantity Supplied ↑ (ceteris paribus)

当价格 ↑，供给量 ↑（其他条件不变）

Supply curves slope upwards. If a bakery can sell loaves for $5 instead of $3, it has a stronger incentive to bake more. Market supply can be affected by production costs, technology, and government policies; these shift the supply curve, changing the quantity supplied at every price.

供给曲线向上倾斜。如果一家面包房能以 5 美元而非 3 美元卖出面包，它就有更大动力烘焙更多。生产成本、技术和政府政策等因素会影响市场供给，使供给曲线移动，从而改变每一价格下的供给量。

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10. Opportunity Cost Theorem | 机会成本定理

Opportunity cost is the value of the next best alternative foregone when a choice is made. Because resources are scarce, every decision involves a trade-off. This concept helps businesses and individuals weigh what they sacrifice when committing time, money, or effort to one option over another.

机会成本是指做出某一选择时所放弃的次优替代选项的价值。由于资源是稀缺的，每个决策都包含权衡取舍。这一概念帮助企业和个人衡量在将时间、金钱或精力投入某一选项时牺牲了什么。

Opportunity Cost = Value of the Next Best Alternative Given Up

机会成本 = 放弃的次优替代选项的价值

For example, if an entrepreneur invests $10,000 in a café rather than putting it in a savings account with 3% interest, the opportunity cost is the foregone interest (plus the lost security). Opportunity cost is not always monetary; it can be measured in time, enjoyment, or other benefits. It underpins the basic economic problem of scarcity and choice.

例如，一位企业家将 10,000 美元投资于一家咖啡馆，而不是存入年利率 3% 的储蓄账户，其机会成本就是放弃的利息（以及失去的安全性）。机会成本并不总是货币性的，它也可以用时间、乐趣或其他收益来衡量。它揭示了稀缺性与选择这一基本经济问题。

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Published by TutorHao | Business Revision Series | aleveler.com

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