📚 Year 11 CAIE Business: Formula & Theorem Quick Reference Handbook | Year 11 CAIE 商务：公式定理速查手册
This quick reference handbook compiles all essential formulas, ratios and key arithmetic theorems from the CAIE IGCSE Business Studies (0450) syllabus. It has been designed specifically for Year 11 learners who need to practise numerical skills and memorise calculations for Revenue, Break‑even, Profitability, Liquidity and Workforce performance. Keep it close during revision and use it to build confidence with numbers.
本速查手册汇编了 CAIE IGCSE 商务学 (0450) 课程中的所有核心公式、比率和关键计算定理，专为 Year 11 学生设计。无论你需要练习收入、盈亏平衡、盈利能力、流动性还是劳动力指标的计算，都可以随时查阅本手册，在复习过程中建立对数字的信心。
1. Revenue, Cost & Profit | 收入、成本与利润
Revenue is the income a business receives from selling its products or services. Understanding how revenue, costs and profit connect is the foundation of financial decision‑making. Fixed costs do not change with output, whereas variable costs vary directly with production volume.
收入是企业通过销售产品或服务获得的资金。理解收入、成本和利润之间的联系是财务决策的基础。固定成本不随产量变化，而变动成本与产量直接成正比。
The simplest way to compute the money coming into the business is to multiply the selling price per unit by the quantity sold.
计算企业资金流入最简单的方法是将单位售价乘以销售数量。
Total Revenue = Price × Quantity
Total costs are the sum of all fixed costs (such as rent and salaries) and total variable costs (such as raw materials that change with output).
总成本是所有固定成本（如租金和薪金）和总变动成本（如随产量变化的原材料）之和。
Total Costs = Fixed Costs + Variable Costs
Overall profit (or loss) is the difference between total revenue and total costs. It shows whether the business has covered all its expenses.
总利润（或亏损）是总收入与总成本之间的差额，反映企业是否涵盖了所有支出。
Profit = Total Revenue – Total Costs
Gross profit focuses on direct trade: it subtracts the cost of sales (materials/direct labour) from sales revenue, revealing the money left to pay overheads.
毛利关注直接交易：从销售收入中减去销售成本（材料/直接人工），显示剩余可用于支付间接费用的资金。
Gross Profit = Sales Revenue – Cost of Sales
Net profit goes a step further by deducting all other operating expenses and interest from gross profit, giving the final ‘bottom line’ profit.
净利润则更进一步，从毛利中扣除所有其他营业费用和利息，得出最终的“底线”利润。
Net Profit = Gross Profit – Total Expenses
2. Break‑even Analysis | 盈亏平衡分析
Break‑even analysis helps a business identify the quantity of sales needed to cover total costs – the point where profit is zero. The contribution per unit is the amount each sale contributes towards fixed costs after variable costs are paid.
盈亏平衡分析帮助企业确定覆盖总成本所需的销售量——即利润为零的点。单位贡献是指每售出一件产品在支付变动成本后为固定成本贡献的金额。
Contribution per unit = Selling Price per unit – Variable Cost per unit
The break‑even point in units is found by dividing total fixed costs by the contribution per unit. Once you know this number, you can convert it into sales revenue.
以单位计的盈亏平衡点是用总固定成本除以单位贡献求出的。知道了这个数字，就可以将其转化为销售收入。
Break‑even point (units) = Fixed Costs ÷ Contribution per unit
Break‑even point (revenue) = Break‑even units × Selling Price per unit
Margin of safety is the difference between actual or budgeted sales and the break‑even level. It tells a business how much sales can fall before it starts making a loss.
安全边际是实际或预算销售量与盈亏平衡水平之间的差额，它告诉企业销售下降多少才会开始亏损。
Margin of Safety (units) = Actual Sales units – Break‑even units
On a break‑even chart, the total revenue line and total cost line cross at the break‑even point. The area above shows profit, below shows loss.
在盈亏平衡图上，总收入线与总成本线相交于盈亏平衡点。交点上方区域表示盈利，下方表示亏损。
3. Cash Flow Management | 现金流管理
Cash flow is the movement of money into and out of a business. Net cash flow measures the monthly health of cash, and closing balances help predict future shortfalls.
现金流是资金流入和流出企业的运动。净现金流衡量每月的现金状况，期末余额有助于预测未来的现金短缺。
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
The closing balance for each period becomes the opening balance for the next. It is calculated by adding net cash flow to the opening balance.
每个期间期末余额将成为下一期间的期初余额。其计算方法是将净现金流加上期初余额。
Closing Balance = Opening Balance + Net Cash Flow
Positive net cash flow means more money is coming in than going out, whereas negative cash flow signals a potential liquidity problem even if the business is profitable on paper.
净现金流为正表示流入资金多于流出，而净现金流为负则预示了潜在的流动性问题，即使企业在账面上是盈利的。
4. Profitability Ratios | 盈利能力比率
Profitability ratios evaluate how efficiently a business converts sales into profit and how well it uses its capital. They are essential for comparing performance across periods or with competitors.
盈利能力比率评估企业将销售转化为利润的效率以及它运用资本的成效。这些比率对于跨时期或与竞争对手比较业绩至关重要。
The gross profit margin shows the percentage of sales revenue remaining after paying for the cost of sales. A higher margin suggests strong pricing or cost control.
毛利率显示在支付销售成本后剩余的销售收入百分比。较高的毛利率意味着较强的定价或成本控制能力。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100
Net profit margin reveals how much profit is generated from each dollar of sales after all expenses are paid. It is a key indicator of overall efficiency.
净利率揭示在支付所有费用后，每一美元销售收入产生多少利润，是衡量整体效率的关键指标。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100
Return on Capital Employed (ROCE) measures how effectively a business uses its long‑term capital to generate profit. Capital employed typically equals total assets minus current liabilities or shareholders’ equity plus non‑current liabilities.
资本回报率 (ROCE) 衡量企业运用长期资本创造利润的有效性。资本运用通常等于总资产减去流动负债，或股东权益加上非流动负债。
ROCE = (Profit before Tax ÷ Capital Employed) × 100
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm’s ability to meet its short‑term debts as they fall due. They are vital for survival even when profits look healthy.
流动性比率评估企业偿还短期债务的能力。即使利润看起来不错，流动性对生存也至关重要。
The current ratio compares total current assets with total current liabilities. A ratio of around 1.5:1 to 2:1 is often considered safe, though it varies by industry.
流动比率将流动资产总额与流动负债总额进行比较。通常 1.5:1 至 2:1 的比率被认为是安全的，但因行业而异。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test (quick) ratio is a stricter measure because it removes inventory – the least liquid current asset. A result close to 1:1 is desirable.
酸性测试（速动）比率是一种更严格的指标，因为它剔除了存货——流动性最差的流动资产。结果接近 1:1 是理想的。
Acid Test Ratio = (Current Assets – Inventory) ÷ Current Liabilities
6. Working Capital | 营运资金
Working capital represents the day‑to‑day finance available to run the business. It is the difference between current assets and current liabilities.
营运资金代表用来经营企业日常业务的可用资金，即流动资产与流动负债之间的差额。
Working Capital = Current Assets – Current Liabilities
Too little working capital can lead to cash shortages and an inability to pay suppliers, while too much might suggest inefficient use of resources.
营运资金过少可能导致现金短缺和无法支付供应商，而过多则可能意味着资源使用效率低下。
7. Market & Sales Performance Metrics | 市场与销售表现指标
Market share measures a company’s sales as a percentage of the total market sales. It shows how competitive the business is within its industry.
市场份额衡量一家公司销售额占市场总销售额的百分比，表明企业在其行业中的竞争地位。
Market Share = (Company’s Sales ÷ Total Market Sales) × 100
Sales growth compares the change in sales revenue from one period to the next, expressed as a percentage. It helps track whether the business is expanding.
销售增长率将本期的销售收入与上一期相比的变化以百分比表示，有助于追踪企业是否在扩张。
Sales Growth = ((Current Sales – Previous Sales) ÷ Previous Sales) × 100
8. Human Resource Metrics | 人力资源指标
Businesses measure workforce performance to improve efficiency and morale. Labour productivity connects output with employee input, while turnover and absenteeism reveal engagement levels.
企业衡量劳动力绩效以提高效率和士气。劳动生产率将产出与员工投入联系起来，而员工流失率和缺勤率则反映了敬业度水平。
Labour Productivity = Total Output ÷ Number of Employees
Labour turnover is the rate at which staff leave a business and are replaced. High turnover can increase recruitment costs and lower morale.
劳动力流失率是指员工离职和被替换的比率。高流失率会增加招聘成本并降低士气。
Labour Turnover = (Number of Staff Leaving ÷ Average Number of Staff) × 100
Absenteeism calculates the proportion of scheduled work time lost through absence. Even brief spikes can signal dissatisfaction.
缺勤率计算的是因缺勤而损失的计划工作时间比例。即使短暂上升也可能表明员工不满。
Absenteeism Rate = (Number of Days Absent ÷ Total Working Days) × 100
9. Key Financial Statement Equations | 关键财务报表等式
The balance sheet follows the accounting equation, showing that everything a business owns is funded either by borrowing (liabilities) or by the owners’ investment (equity).
资产负债表遵循会计等式，即企业拥有的一切要么来自借款（负债），要么来自所有者投资（权益）。
Assets = Liabilities + Equity
On the income statement, the layout moves from revenue down to profit. Remembering the structure helps when calculating missing figures.
在损益表中，结构是从销售收入向下计算到利润。记住这个结构有助于计算缺失数字。
Sales Revenue – Cost of Sales = Gross Profit
Gross Profit – Operating Expenses = Net Profit
10. Quick Tips for Formula Recall | 公式记忆速记诀窍
Break formulas into ‘families’ – profit, break‑even, liquidity, workforce. Use flashcards with a question on one side and the calculation on the other. Write solutions out by hand to strengthen memory.
把公式分成“族”——利润类、盈亏平衡类、流动性类、劳动力类。使用闪卡，一面写问题，另一面写计算过程。亲手写出解题过程能强化记忆。
Turn each ratio into a simple sentence: for example, ‘Current Ratio is Current Assets divided by Current Liabilities’. Say it aloud while solving a past paper question.
把每个比率变成一句简单的话，例如：“流动比率等于流动资产除以流动负债”。在做真题时大声说出来。
Remember that all percentage margins follow the same pattern: (part ÷ whole) × 100. If you are looking for margin, the ‘whole’ is usually sales revenue; for ROCE it is capital employed.
记住所有百分比利润率都遵循相同模式：(部分÷整体)×100。如果你要求利润率，“整体”通常是销售收入；而 ROCE 的整体则是资本运用。
Draw a break‑even chart from memory and label the lines (TR, TC, FC). Writing down the intersection point formula while visualising the chart helps lock in the equation.
凭记忆画一张盈亏平衡图，并标出各线条（总收入、总成本、固定成本）。一边在脑中想象图表，一边写下交点公式，这有助于牢记等式。
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