📚 Year 9 CAIE Business: Formula and Theorem Quick Reference Handbook | Year 9 CAIE 商务：公式定理速查手册
Welcome to your essential quick reference guide for Year 9 CAIE Business. This handbook collects all the key formulas and important business principles you need to master for your assessments. Use it to revise effectively and solve business problems with confidence.
欢迎阅读 Year 9 CAIE 商务必备速查手册。本手册汇集了你需要掌握的所有关键公式和重要商务原理，助你高效复习，自信解决商业问题。
1. Sales Revenue | 销售收入
Sales revenue is the income a business receives from selling its products or services. It does not consider costs and is often called ‘turnover’. The basic formula is: Sales Revenue = Selling Price × Quantity Sold.
销售收入是企业通过销售产品或服务获得的收入，不考虑成本，常被称为’营业额’。基本公式为：销售收入 = 销售价格 × 销售数量。
If a stationery shop sells 150 notebooks at $3 each, its sales revenue equals $3 × 150 = $450. A higher revenue does not always mean higher profit, as costs also matter.
如果一家文具店以每本 3 美元的价格卖出 150 本笔记本，其销售收入为 3 × 150 = 450 美元。收入高并不一定意味着利润高，因为成本同样重要。
2. Fixed Costs and Variable Costs | 固定成本与可变成本
Costs are classified by how they behave when output changes. Fixed costs stay the same regardless of production volume (e.g., rent, insurance). Variable costs change directly with output (e.g., raw materials, packaging).
成本根据产量变化时的表现进行分类。固定成本不随生产数量变化（如租金、保险）。可变成本直接随产量变化（如原材料、包装）。
Understanding this split is crucial for break‑even analysis. Total Fixed Costs (TFC) remain constant, while Total Variable Costs (TVC) = Variable Cost per Unit × Output.
理解这一划分对盈亏平衡分析至关重要。总固定成本 (TFC) 保持不变，而总可变成本 (TVC) = 单位可变成本 × 产量。
3. Total Costs | 总成本
Total costs combine all fixed and variable expenses a business incurs to produce a given level of output. The formula is: Total Costs (TC) = Total Fixed Costs (TFC) + Total Variable Costs (TVC).
总成本是企业在某一产量水平下发生的全部固定和可变费用之和。公式为：总成本 (TC) = 总固定成本 (TFC) + 总可变成本 (TVC)。
For example, if a bakery pays $800 rent and $2 per cake for ingredients, producing 300 cakes gives TFC = $800, TVC = $2 × 300 = $600, so TC = $1,400. Controlling total costs is essential for maximising profit.
例如，一家面包店支付 800 美元租金，每个蛋糕原料成本 2 美元，生产 300 个蛋糕时，TFC = 800 美元，TVC = 2 × 300 = 600 美元，因此 TC = 1400 美元。控制总成本对利润最大化至关重要。
4. Profit | 利润
Profit is the surplus remaining after total costs are subtracted from sales revenue. A business aims to make a profit to survive and grow. The formula is: Profit = Sales Revenue − Total Costs.
利润是销售收入扣除总成本后的剩余。企业以盈利为目标以生存和发展。公式为：利润 = 销售收入 − 总成本。
If sales revenue is $5,000 and total costs are $4,200, the profit is $800. Profit can be increased by raising revenue, cutting costs, or both. A loss occurs when total costs exceed revenue.
若销售收入为 5000 美元，总成本为 4200 美元，则利润为 800 美元。提高收入、削减成本或两者结合均可增加利润。当总成本超过收入时便出现亏损。
5. Break-even Point | 盈亏平衡点
The break-even point is the output level at which total revenue equals total costs, meaning the business makes neither a profit nor a loss. The formula is: Break-even Output = Total Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit).
盈亏平衡点是指总收入等于总成本时的产量水平，此时企业既不盈利也不亏损。公式为：盈亏平衡产量 = 总固定成本 ÷ (单位售价 − 单位可变成本)。
The denominator (Selling Price − Variable Cost per Unit) is called the contribution per unit. If a business has TFC = $1,000, sells at $10, and variable cost is $6 per unit, break-even output = $1,000 ÷ ($10 − $6) = 250 units.
分母（售价 − 单位可变成本）称为单位贡献。如果企业 TFC = 1000 美元，售价为 10 美元，单位可变成本为 6 美元，则盈亏平衡产量 = 1000 ÷ (10 − 6) = 250 单位。
6. Margin of Safety | 安全边际
The margin of safety shows how much sales can fall before the business reaches its break-even point. It measures risk. The formula is: Margin of Safety = Actual Output (or Sales) − Break-even Output (or Sales).
安全边际显示企业销售额最多可下降多少才会达到盈亏平衡点，用于衡量风险。公式为：安全边际 = 实际产量（或销售额）− 盈亏平衡产量（或销售额）。
It can be expressed in units or as a percentage: Margin of Safety (%) = (Current Output − Break-even Output) ÷ Current Output × 100. A higher margin of safety means lower risk.
安全边际可用数量或百分比表示：安全边际 (%) = (当前产量 − 盈亏平衡产量) ÷ 当前产量 × 100。安全边际越高，风险越低。
7. Contribution per Unit | 单位贡献
Contribution per unit is the amount each unit sold contributes towards covering fixed costs and then generating profit. The formula is: Contribution per Unit = Selling Price per Unit − Variable Cost per Unit.
单位贡献是每售出一单位产品为覆盖固定成本进而创造利润所做的贡献。公式为：单位贡献 = 单位售价 − 单位可变成本。
If a burger is sold for $5 and its variable cost is $2, the contribution per unit is $3. Once total contribution covers all fixed costs, any remaining contribution becomes profit.
若一个汉堡售价 5 美元，可变成本 2 美元，则单位贡献为 3 美元。一旦总贡献覆盖了全部固定成本，剩余贡献即为利润。
8. Total Contribution and Profit using Contribution | 总贡献与利用贡献计算利润
Total contribution is the contribution earned from all units sold. It can be used as a shortcut to find profit. Total Contribution = Contribution per Unit × Quantity Sold.
总贡献是所有售出产品产生的贡献总和，可作为计算利润的快捷方式。总贡献 = 单位贡献 × 销售数量。
Then profit is found by: Profit = Total Contribution − Total Fixed Costs. This is especially useful when revenue and variable costs are not displayed separately, helping managers make quick decisions.
利润可依此计算：利润 = 总贡献 − 总固定成本。当收入和可变成本未分开列示时，该方法尤为有用，帮助管理者快速决策。
9. Gross Profit Margin | 毛利率
Gross profit is the profit a business makes after deducting the direct cost of goods sold from sales revenue. The margin shows gross profit as a percentage of revenue. Gross Profit Margin (%) = (Gross Profit ÷ Sales Revenue) × 100, where Gross Profit = Sales Revenue − Cost of Sales.
毛利是销售收入扣除销售直接成本后的利润。毛利率显示毛利占收入的百分比。毛利率 (%) = (毛利 ÷ 销售收入) × 100，其中毛利 = 销售收入 − 销售成本。
For instance, if revenue is $120,000 and cost of sales is $90,000, gross profit is $30,000, and gross profit margin = ($30,000 ÷ $120,000) × 100 = 25%. A higher margin indicates better control over direct costs.
举例：收入 120,000 美元，销售成本 90,000 美元，则毛利为 30,000 美元，毛利率 = (30,000 ÷ 120,000) × 100 = 25%。比率越高，表明直接成本控制越好。
10. Net Profit Margin | 净利率
Net profit margin takes all expenses into account, giving a fuller picture of profitability. Net Profit Margin (%) = (Net Profit ÷ Sales Revenue) × 100, where Net Profit = Gross Profit − Expenses (overheads, administration, etc.).
净利率考虑了所有费用，更全面地反映盈利能力。净利率 (%) = (净利润 ÷ 销售收入) × 100，其中净利润 = 毛利 − 各项费用（经常费用、行政费用等）。
A business with revenue of $200,000, gross profit of $60,000 and total expenses of $35,000 has net profit of $25,000, giving a net profit margin of 12.5%. Comparing this over time or with competitors shows whether a business is managing its overheads well.
一家企业收入 200,000 美元，毛利 60,000 美元，总费用 35,000 美元，净利润为 25,000 美元，净利率 12.5%。纵向与横向比较该比率，可以判断企业是否有效管理其间接费用。
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