📚 Year 10 CAIE Business: Formula & Theorem Quick Reference Handbook | CAIE 10年级商务：公式定理速查手册
This handbook brings together essential formulas and key theorems from the CAIE IGCSE Business (0450) syllabus for Year 10. Use it as a rapid revision tool to sharpen your calculation skills and deepen your understanding of business concepts before assessments.
本手册汇集了CAIE IGCSE商务（0450）十年级课程中最核心的公式与关键定理，可作为考前快速复习的工具，帮助你强化计算能力并深化对商业概念的理解。
1. Profit Formulas | 利润公式
Profit is the surplus remaining after total costs are deducted from total revenue. The two main types are gross profit and net profit.
利润是总收入扣除总成本后的盈余，主要有毛利和净利润两种。
Gross Profit = Sales Revenue − Cost of Sales
毛利 = 销售收入 − 销售成本
Gross profit shows the profit made on trading activities before other expenses are subtracted. Cost of sales often includes direct materials, packaging, and direct labour.
毛利反映出在扣除其他费用前，企业通过买卖活动赚取的利润。销售成本通常包括直接材料、包装成本和直接人工。
Net Profit = Gross Profit − Expenses
净利润 = 毛利 − 费用
Net profit is the final profit after all operating expenses, interest, and tax have been taken away. Expenses include rent, salaries, advertising, and depreciation.
净利润是扣除所有营业费用、利息和税费后的最终利润。费用项目有租金、工资、广告费和折旧等。
2. Break-even Analysis | 盈亏平衡分析
Break-even analysis helps businesses determine the number of units they must sell to cover all costs. At the break-even point, total revenue equals total costs, resulting in zero profit or loss.
盈亏平衡分析可以帮助企业确定需要销售多少单位产品才能覆盖全部成本。在盈亏平衡点，总收入等于总成本，利润为零。
The break-even output can be calculated using the formula:
盈亏平衡产出可通过以下公式计算：
Break-even Output = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
盈亏平衡产量 = 固定成本 ÷（单位售价 − 单位可变成本）
The expression (Selling Price per Unit − Variable Cost per Unit) is also known as the contribution per unit. A break-even chart visually shows the point where total revenue and total cost lines intersect.
（单位售价 − 单位可变成本）也称为单位边际贡献。盈亏平衡图能够直观展示总收入线与总成本线相交的那个点。
3. Revenue, Costs and Profit | 收入、成本与利润
Total revenue is the income a business generates from selling goods or services.
总收入是企业通过销售商品或服务所获得的收入。
Total Revenue = Selling Price per Unit × Quantity Sold
总收入 = 单位售价 × 销售量
Total costs are split into fixed costs (which do not vary with output) and variable costs (which change directly with output).
总成本分为固定成本（不随产量变化）和可变成本（随产量直接变化）。
Total Costs = Fixed Costs + Variable Costs
总成本 = 固定成本 + 可变成本
Profit can therefore be rewritten as:
因此利润也可以表示为：
Profit = Total Revenue − Total Costs
利润 = 总收入 − 总成本
4. Profitability Ratios | 盈利能力比率
Profitability ratios measure how well a business converts sales into profit. The two most common are gross profit margin and net profit margin.
盈利能力比率衡量企业将销售收入转化为利润的能力，最常用的是毛利率和净利润率。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100%
毛利率 =（毛利 ÷ 销售收入）× 100%
A high gross profit margin suggests the business keeps a large portion of sales after covering direct costs. It can be improved by raising prices or finding cheaper suppliers.
较高的毛利率意味着在支付直接成本后，企业保留了大部分的销售收入。企业可通过提价或寻找更便宜的供应商来改善毛利率。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100%
净利润率 =（净利润 ÷ 销售收入）× 100%
Net profit margin takes all expenses into account. It reveals how much of each dollar of sales becomes net profit.
净利润率考虑了所有费用，揭示了每一元销售收入中有多少变成了净利润。
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm’s ability to meet short-term debts as they fall due. The two key ratios are the current ratio and the acid test ratio.
流动性比率衡量企业偿还到期短期债务的能力，主要有流动比率和酸性测试比率。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
A current ratio between 1.5 and 2.0 is generally considered healthy. Too high a ratio may mean assets are not being used efficiently.
流动比率通常在1.5至2.0之间被视为健康。比率过高可能意味着资产未被有效利用。
Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities
酸性测试比率 =（流动资产 − 存货）÷ 流动负债
This stricter test excludes inventories because they are the hardest current asset to convert into cash quickly. A result of 1.0 or above is ideal.
这一更严格的测试剔除了存货，因为存货是流动资产中最难快速变现的。比率在1.0或以上较为理想。
6. Average Costs | 平均成本
Average costs show the cost of producing a single unit. Understanding this helps with pricing decisions.
平均成本表示生产单件产品的成本，理解它有助于定价决策。
Average Cost per Unit = Total Costs ÷ Total Output
单位平均成本 = 总成本 ÷ 总产量
As output rises, average fixed costs fall continuously because fixed costs are spread over more units. This relationship is crucial when studying economies of scale.
随着产量增加，平均固定成本不断下降，因为固定成本被分摊到更多单位上。这一关系在学习规模经济时至关重要。
The average cost curve typically has a U-shape due to the combination of falling average fixed costs and eventually rising average variable costs.
由于平均固定成本下降与最终上升的平均可变成本共同作用，平均成本曲线通常呈U形。
7. Productivity and Efficiency | 生产力与效率
Productivity measures the output produced per unit of input. Labour productivity is the most common measure in Year 10 business.
生产力衡量每单位投入所生产的产出，十年级商务中最常见的衡量指标是劳动生产率。
Labour Productivity = Total Output ÷ Number of Workers
劳动生产率 = 总产量 ÷ 员工人数
Higher productivity can lead to lower unit costs and greater competitiveness. It can be improved through training, better equipment, or motivation schemes.
更高的生产力可以降低单位成本、增强竞争力。通过培训、改进设备或激励计划都能提高生产力。
Efficiency relates to how well resources are used to minimise waste. The formula for capacity utilisation is also useful:
效率涉及资源被利用以最小化浪费的程度。产能利用率的公式也很有用：
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100%
产能利用率 =（实际产量 ÷ 最大可能产量）× 100%
8. Cash Flow Forecasting | 现金流量预测
Cash flow forecasting helps a business predict future cash inflows and outflows to avoid liquidity problems. The key figures are net cash flow, opening balance, and closing balance.
现金流量预测有助于企业预估未来的现金流入与流出，从而避免流动性问题，核心数字包括净现金流、期初余额和期末余额。
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
The closing balance for one month becomes the opening balance for the next month:
某个月的期末余额会成为下个月的期初余额：
Closing Balance = Opening Balance + Net Cash Flow
期末余额 = 期初余额 + 净现金流
A negative closing balance over several months signals potential insolvency. Businesses can respond by arranging an overdraft, delaying payments, or speeding up cash receipts.
连续几个月出现负期末余额预示着潜在破产风险。企业可以采取安排透支、延迟付款或加快收款等措施应对。
9. Law of Demand and Supply | 需求与供给定律
The law of demand states that, ceteris paribus, as price rises, quantity demanded falls. The law of supply says that as price rises, quantity supplied increases.
需求定律指出，在其他条件不变时，价格上升，需求量下降；供给定律则说明，价格上升，供给量增加。
These relationships are fundamental to market analysis. A demand curve slopes downward; a supply curve slopes upward.
这些关系是市场分析的基础。需求曲线向下倾斜，供给曲线向上倾斜。
The equilibrium price occurs where quantity demanded equals quantity supplied. Disequilibrium leads to excess supply (surplus) or excess demand (shortage).
均衡价格出现在需求量等于供给量之处。非均衡会导致超额供给（盈余）或超额需求（短缺）。
Price elasticity of demand (PED) is often introduced in Year 10 using the simple formula:
十年级通常会引入需求价格弹性（PED）的简单公式：
PED = Percentage Change in Quantity Demanded ÷ Percentage Change in Price
需求价格弹性 = 需求量变动百分比 ÷ 价格变动百分比
10. Economies and Diseconomies of Scale | 规模经济与不经济
Economies of scale are cost advantages a business gains as it grows. Average cost per unit falls when output increases.
规模经济是企业随着规模增长而获得的成本优势，产量增加时单位平均成本下降。
Internal economies of scale include purchasing economies (bulk buying discounts), technical economies (specialised machinery), financial economies (lower interest rates), marketing economies, and managerial economies.
内部规模经济包括采购经济（批量购买折扣）、技术经济（专用机械）、财务经济（更低利率）、营销经济和管理经济。
Diseconomies of scale occur when a business becomes too large and average costs begin to rise. Causes include communication problems, poor coordination, and low worker motivation.
规模不经济指企业规模过大导致平均成本上升，原因包括沟通不畅、协调失效和员工积极性下降。
The relationship can be tested with the break-even or average cost formulas learned earlier.
这一关系可以结合此前所学的盈亏平衡或平均成本公式进行检验。
11. Contribution and Margin of Safety | 边际贡献与安全边际
Contribution is the amount each unit sold contributes towards covering fixed costs and then generating profit.
边际贡献是指每售出一单位产品，可用于覆盖固定成本并创造利润的金额。
Contribution per Unit = Selling Price per Unit − Variable Cost per Unit
单位边际贡献 = 单位售价 − 单位可变成本
Total contribution can be used to calculate profit: Total Contribution − Fixed Costs = Profit.
总边际贡献可以用来计算利润：总边际贡献 − 固定成本 = 利润。
Margin of safety shows how far sales can fall before the business reaches its break-even point. It is a vital measure of risk.
安全边际显示销售量可以下降到何种程度而不至于达到盈亏平衡点，是衡量风险的重要指标。
Margin of Safety = Actual Sales − Break-even Sales
安全边际 = 实际销售量 − 盈亏平衡销售量
A higher margin of safety indicates a lower risk of making a loss if demand drops unexpectedly.
安全边际越高，意味着即便需求意外下滑，企业发生亏损的风险也越低。
12. Other Key Formulas | 其他关键公式
Several additional formulas are useful for decision-making and appear frequently in IGCSE Business papers.
以下额外公式对决策颇有帮助，在IGCSE商务试卷中也经常出现。
Working Capital = Current Assets − Current Liabilities
营运资金 = 流动资产 − 流动负债
Working capital shows the liquid funds available for day-to-day operations. A positive working capital is necessary for short-term survival.
营运资金反映企业日常运营可用的流动资金。保持正的营运资金对短期生存非常必要。
Profit = Total Contribution − Fixed Costs
利润 = 总边际贡献 − 固定成本
For businesses holding inventory, the cost of goods sold (COGS) equation is also tested:
对于持有存货的企业，销售成本（COGS）的计算公式也会考查：
Cost of Sales = Opening Inventory + Purchases − Closing Inventory
销售成本 = 期初存货 + 采购 − 期末存货
Average rate of return (ARR) is introduced in some Year 10 syllabuses to compare investment projects:
部分十年级教学大纲还会引入平均收益率（ARR）以比较投资项目：
ARR = (Average Annual Profit ÷ Initial Cost of Investment) × 100%
平均收益率 =（平均年利润 ÷ 初始投资成本）× 100%
Remember that these formulas must be applied carefully, with all amounts expressed in the same time period.
请注意，应用这些公式时所有金额必须取自同一时间段。
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