📚 Year 11 CAIE Business Studies: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This article compiles the essential formulas and key theoretical relationships required for the Year 11 CAIE Business Studies syllabus. You can use it as a revision checklist to ensure you remember how to calculate profitability, liquidity, break-even, and more, while also understanding the 'why' behind each figure.
本文汇总了 Year 11 CAIE 商务课程必备的核心公式与重要理论关系。你可以把它当作一份复习清单，确保自己既会计算盈利能力、流动性、盈亏平衡等关键指标，也理解每个数字背后的商业含义。
1. Revenue and Profit Formulas | 收入与利润公式
Revenue (sales revenue or turnover) is the income earned from selling goods or services. It is calculated by multiplying the selling price per unit by the quantity sold.
收入（销售收入或营业额）是企业通过销售商品或服务获得的所得，计算方式为销售单价乘以销售数量。
Revenue = Selling price per unit × Quantity sold
Gross profit is the profit a business makes after deducting the direct costs of producing or purchasing the goods sold. It shows how efficiently a business manages its production or purchasing.
毛利是扣除所售商品的直接生产或采购成本后的利润，反映企业生产或采购环节的效率。
Gross profit = Revenue - Cost of sales
Net profit (profit for the year) takes away all other expenses, including overheads, interest and tax. It represents the final amount of profit available to the owners.
净利润（年度利润）扣除了所有其他费用，包括间接费用、利息和税金，代表最终归属于所有者的利润额。
Net profit = Gross profit - Operating expenses - Interest - Tax
Cost of sales is the direct cost of the goods that have been sold. It is calculated by adding opening inventory to purchases and subtracting closing inventory.
销售成本是已售商品的直接成本，等于期初存货加采购额减去期末存货。
Cost of sales = Opening inventory + Purchases - Closing inventory
2. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm's ability to generate profit relative to its revenue, assets, or capital. They help stakeholders compare performance across periods or with competitors.
盈利能力比率衡量企业相对于收入、资产或资本创造利润的能力，帮助利益相关者跨时期或与竞争对手对比业绩。
Gross profit margin (also called gross margin) expresses gross profit as a percentage of revenue. A higher margin suggests good control over production or purchasing costs.
毛利率指毛利占收入的百分比，毛利率越高通常说明生产或采购成本控制越好。
Gross profit margin = (Gross profit ÷ Revenue) × 100%
Net profit margin shows what percentage of revenue remains as net profit after all expenses. It is a key indicator of overall cost management.
净利率反映扣除所有费用后，收入中有多大比例转化为净利润，是衡量整体成本管理的关键指标。
Net profit margin = (Net profit ÷ Revenue) × 100%
Return on capital employed (ROCE) measures the profitability of the long-term capital invested in the business. Capital employed is usually defined as shareholders' equity plus non-current liabilities, or total assets less current liabilities.
资本报酬率衡量企业投入的长期资本所创造的利润水平。资本占用通常指股东权益加非流动负债，或总资产减流动负债。
ROCE = (Net profit before interest and tax ÷ Capital employed) × 100%
3. Liquidity Ratios | 流动性比率
Liquidity ratios assess a business's ability to meet its short-term debts as they fall due. Two main ratios are used: the current ratio and the acid test (quick) ratio.
流动性比率评估企业偿还短期到期债务的能力。主要使用流动比率和速动比率两个指标。
The current ratio compares all current assets (cash, receivables, inventory) with current liabilities. A ratio between 1.5 and 2 is often considered healthy, though acceptable levels vary by industry.
流动比率将所有流动资产（现金、应收账款、存货）与流动负债进行比较。一般认为1.5至2之间是健康水平，但行业不同可接受水平也有差异。
Current ratio = Current assets ÷ Current liabilities
The acid test ratio (quick ratio) excludes inventory from current assets because inventory can be harder to turn into cash quickly. A ratio of 1:1 or above is often seen as satisfactory.
速动比率从流动资产中剔除存货，因为存货变现速度较慢。通常认为1:1或以上比较理想。
Acid test ratio = (Current assets - Inventory) ÷ Current liabilities
4. Break-even Analysis | 盈亏平衡分析
Break-even is the level of output at which total revenue equals total costs – the business makes neither a profit nor a loss. Understanding break-even helps managers set sales targets and evaluate risk.
盈亏平衡点是总收入等于总成本的产量水平，此时企业不盈不亏。掌握盈亏平衡有助于管理者设定销售目标并评估风险。
Contribution per unit is the amount each unit sold contributes towards covering fixed costs and then generating profit. It is found by subtracting variable cost per unit from the selling price per unit.
单位贡献毛益是指每销售一单位产品在补偿固定成本后，对利润的贡献额，计算公式为销售单价减去单位变动成本。
Contribution per unit = Selling price per unit - Variable cost per unit
The break-even point in units is calculated by dividing total fixed costs by contribution per unit. The result tells you the minimum number of units that must be sold to avoid a loss.
以数量表示的盈亏平衡点等于总固定成本除以单位贡献毛益，结果即为为了避免亏损必须销售的最低产品数量。
Break-even output (units) = Total fixed costs ÷ Contribution per unit
You can also calculate break-even in revenue terms by multiplying break-even units by selling price per unit, or by using the contribution margin ratio.
也可通过盈亏平衡销量乘以单价，或利用贡献毛益率来计算以金额表示的盈亏平衡点。
Break-even revenue = Break-even units × Selling price per unit
The margin of safety shows how much sales can fall before the business starts making a loss. It is the difference between actual (or budgeted) sales and break-even sales, often expressed as a percentage.
安全边际反映的是销售额可以下降多少而不至于亏损。它是实际（或预算）销售额与盈亏平衡销售额之间的差额，通常以百分比表示。
Margin of safety = Actual sales - Break-even sales
5. Average Rate of Return (ARR) | 平均回报率
ARR is a method of investment appraisal that measures the average annual profit from a project as a percentage of the initial investment. It is easy to understand but ignores the timing of cash flows.
平均回报率是一种投资评估方法，衡量项目平均年利润占初始投资的百分比。它简单易懂，但忽略了现金流的时间价值。
ARR = (Average annual profit from investment ÷ Initial cost of investment) × 100%
When calculating ARR, average annual profit is the total expected profit over the life of the project (after depreciation) divided by the number of years. Always show the answer as a percentage and compare with the business's target rate.
计算平均回报率时，平均年利润是项目寿命期内的预期总利润（扣除折旧后）除以年数。结果应以百分比表示，并与企业的目标回报率进行比较。
6. Depreciation – Straight-line Method | 折旧 – 直线法
Depreciation spreads the cost of a non-current asset over its useful life. The straight-line method charges the same amount of depreciation each year.
折旧将非流动资产的成本在其使用年限内分摊。直线法每年计提的折旧额相同。
Annual depreciation = (Original cost - Residual value) ÷ Useful life (years)
The residual (scrap) value is the estimated amount the asset can be sold for at the end of its useful life. Straight-line depreciation is widely used because it is simple and consistent.
残值是资产在使用寿命结束时预计可以出售的金额。直线折旧法因其简单且一致而广泛使用。
7. Working Capital and Cash Flow | 营运资金与现金流
Working capital (net current assets) measures the short-term financial health of a business. It is the capital available to fund day-to-day operations.
营运资金（净流动资产）衡量企业短期财务健康状况，是可用于日常经营活动的资金。
Working capital = Current assets - Current liabilities
A positive working capital figure suggests the business can meet its short-term obligations; a negative figure could signal liquidity problems. However, too much working capital might mean resources are tied up unproductively.
营运资金为正说明企业有能力偿还短期债务，为负则可能面临流动性问题。但过多的营运资金也可能意味着资源被低效占用。
The net cash flow for a period is simply cash inflows minus cash outflows. This figure is used when constructing cash flow forecasts.
某一期间的净现金流就是现金流入量减去现金流出量，这一数字用于编制现金流量预测。
Net cash flow = Total cash inflows - Total cash outflows
8. Inventory Management – EOQ Model | 存货管理 – 经济订货量模型
While the full Economic Order Quantity (EOQ) calculation is sometimes explored in Year 12, Year 11 students should understand the principle: EOQ finds the ideal order size that minimises the combined costs of holding inventory and ordering inventory.
虽然完整的经济订货量计算有时在 Year 12 中探讨，但 Year 11 学生应理解其原则：EOQ 旨在找出使存货持有成本和订货成本总和最小的理想订货量。
The formula involves ordering costs, holding costs, and annual demand. Recognising the trade-off is more important than the formula at this stage.
公式涉及订货成本、持有成本和年需求量。现阶段认识到其中的权衡关系比记住公式更重要。
EOQ = √(2 × Annual demand × Ordering cost per order ÷ Holding cost per unit per year)
9. Productivity and Labour Turnover | 生产率与员工流失率
Labour productivity measures output per worker and is a key determinant of efficiency. Higher productivity can lead to lower unit costs.
劳动生产率衡量每个工人的产出，是效率的关键决定因素。生产率提高可带来更低的单位成本。
Labour productivity = Total output ÷ Number of workers
Alternatively, you may calculate output per labour hour. In both cases, the goal is to see whether more output is being generated from the same resources.
也可以计算每工时产出。无论哪种方式，目标都是判断是否用同样的资源生产出更多产品。
Labour turnover measures the rate at which employees leave a business. High turnover can be disruptive and costly.
员工流失率衡量员工离开企业的速度。流失率过高可能造成混乱且代价高昂。
Labour turnover = (Number of staff leaving in a period ÷ Average number of staff) × 100%
10. Market Share and Market Growth | 市场份额与市场增长率
Market share indicates the portion of total market sales that a business captures. It is an important measure of competitive strength.
市场份额表明企业在整个市场总销售中所占的比重，是衡量竞争实力的重要指标。
Market share = (Company's sales revenue ÷ Total market sales revenue) × 100%
Market growth shows the rate at which the size of the market is expanding (or shrinking). It is often used to decide the attractiveness of a market.
市场增长率反映市场规模扩张或萎缩的速度，常用于判断市场的吸引力。
arket growth = ((Current market size - Previous market size) ÷ Previous market size) × 100%
11. Price and Income Elasticity of Demand | 需求的价格弹性和收入弹性
Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price. Firms use PED to predict the effect of price changes on revenue.
需求的价格弹性衡量需求量对价格变化的反应程度。企业利用 PED 来预测价格变动对收入的影响。
PED = (% Change in quantity demanded) ÷ (% Change in price)
If PED is greater than 1 (ignoring the sign), demand is elastic – a price cut increases total revenue. If PED is less than 1, demand is inelastic – a price rise increases total revenue.
若 PED 数值（忽略符号）大于 1，需求富有弹性，降价会增加总收入；若小于 1，需求缺乏弹性，提价会增加总收入。
Income elasticity of demand (YED) measures how demand responds to changes in consumer income. It helps classify goods as normal or inferior.
需求的收入弹性衡量需求对消费者收入变化的反应程度，有助于区分正常品和劣等品。
YED = (% Change in quantity demanded) ÷ (% Change in income)
12. Key Theoretical Relationships (No Calculation Required) | 核心理论关系（无需计算）
Besides formulas, several concepts describe predictable links. When interest rates fall, borrowing becomes cheaper, which often boosts investment and consumer spending.
除公式外，还有一些概念描述了可预测的关联。当利率下降时，借贷成本降低，通常会刺激投资和消费支出。
A strong currency makes exports more expensive and imports cheaper, whereas a weak currency makes exports cheaper and imports more expensive. This affects the competitiveness of internationally trading businesses.
本币强势使出口更贵、进口更便宜；本币弱势则使出口更便宜、进口更贵，这会影响从事国际贸易的企业的竞争力。
Economies of scale refer to the cost advantages that a business can achieve as it increases its scale of production. The average cost per unit falls as output rises, up to a certain point.
规模经济指企业扩大生产规模时获得的成本优势。在产量提升到一定程度之前，单位平均成本会下降。
Diseconomies of scale may occur if a business becomes too large, causing average costs to rise due to communication problems, bureaucracy, or poor motivation.
如果企业规模过大，可能会出现规模不经济，由于沟通问题、官僚作风或士气低落导致平均成本上升。
Published by TutorHao | CAIE IGCSE Business Studies Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图