📚 Quick Reference Handbook for Business Formulas & Theorems | 商务公式定理速查手册
This quick reference handbook brings together the essential formulas, ratios and key economic principles that every Year 11 Cambridge Business student needs to memorise. It covers break-even analysis, profitability, liquidity, efficiency, cash flow, budgeting and the core theorems explaining how businesses grow and control costs. Use it to revise systematically and to check your understanding before assessments.
本速查手册汇集了Year 11剑桥商务学生必须掌握的核心公式、比率和关键经济学原理，涵盖盈亏平衡分析、盈利能力、流动性、效率、现金流、预算以及解释企业如何成长与控制成本的基本定理。你可以用它进行系统复习，并在考试前检查自己的理解。
1. Break-even Analysis | 盈亏平衡分析
Break-even analysis calculates the level of output at which total revenue equals total costs, so a business makes neither a profit nor a loss. It helps managers decide on pricing, output levels and the viability of a product.
盈亏平衡分析计算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。它帮助管理者决定价格、产量和产品的可行性。
Break-even output (units) = Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)
Alternatively, this can be written as BEP = FC ÷ (P − VC). The denominator (P − VC) is known as the contribution per unit.
也可以写作BEP = FC ÷（P − VC）。分母（售价减单位变动成本）称为单位贡献毛利。
Contribution per unit = Selling Price per unit − Variable Cost per unit. Total contribution is the sum of all unit contributions and is used to cover fixed costs and then generate profit.
单位贡献毛利 = 单位售价 − 单位变动成本。总贡献是所有单位贡献之和，先用于弥补固定成本，之后就是利润。
Margin of safety is the amount by which actual or planned output exceeds the break-even level. It indicates the risk of making a loss.
安全边际是实际或计划产量超过盈亏平衡产量的部分，它表明发生亏损的风险大小。
Margin of Safety = Actual Output − Break-even Output
2. Profit and Contribution Margin | 利润与贡献毛利
Profit is the financial reward for taking a business risk. The basic profit equation links revenue and costs.
利润是承担商业风险的财务回报。基本的利润公式把收入和成本联系起来。
Profit = Total Revenue − Total Costs
Total revenue = Price × Quantity sold. Total costs = Fixed Costs + Variable Costs. Gross profit is calculated before deducting operating expenses.
总收入 = 售价 × 销售数量。总成本 = 固定成本 + 变动成本。毛利是在扣除营业费用之前计算的。
Gross Profit = Sales Revenue − Cost of Sales
A high contribution per unit means each sale makes a large contribution towards fixed costs. Managers often focus on maximising total contribution when deciding which product to promote.
单位贡献毛利越高，每次销售对固定成本的贡献越大。管理者在决定推广哪个产品时经常关注总贡献的最大化。
3. The Accounting Equation | 会计等式
The accounting equation is the foundation of the statement of financial position (balance sheet). It shows that everything a business owns is funded either by what it owes or by the owners.
会计等式是财务状况表（资产负债表）的基础。它表明企业拥有的一切要么由负债提供资金，要么由所有者提供资金。
Assets = Liabilities + Equity
Assets include non-current assets such as property and equipment, and current assets such as inventory and trade receivables. Liabilities are split into non-current and current. Equity represents the owners’ stake in the business.
资产包括非流动资产（如房产设备）和流动资产（如存货、应收账款）。负债分为非流动和流动。权益代表所有者对企业的投入。
4. 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 employed. The table below summarises the three most important ones for Year 11.
盈利能力比率衡量企业相对于收入、资产或资本运用产生利润的能力。下表汇总了Year 11必须掌握的三个最重要的比率。
| Ratio | Formula |
|---|---|
| Gross Profit Margin | (Gross Profit ÷ Revenue) × 100% |
| Net Profit Margin | (Net Profit ÷ Revenue) × 100% |
| Return on Capital Employed (ROCE) | (Operating Profit ÷ Capital Employed) × 100% |
Net profit is usually profit before tax, and capital employed often equals total assets − current liabilities, or equity + non-current liabilities. A rising ROCE suggests the business is using its funds efficiently.
净利润通常指税前利润，资本运用额通常等于总资产减流动负债，或权益加非流动负债。ROCE上升表明企业正高效地使用资金。
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess whether a business has enough short-term assets to cover its short-term debts. Two key measures are used.
流动性比率评估企业是否有足够的短期资产来偿还短期债务。两个关键指标经常被使用。
Current Ratio = Current Assets ÷ Current Liabilities
A ratio between 1.5:1 and 2:1 is often considered healthy, but this varies by industry.
通常认为1.5:1到2:1的比率是健康的，但视行业而定。
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
The acid test (or quick) ratio excludes inventory because inventory may not be converted into cash quickly. A result of 1:1 or above is typically desirable.
酸性测试（速动）比率剔除了存货，因为存货可能无法快速变现。结果在1:1或以上通常是理想的。
6. Efficiency Ratios | 效率比率
Efficiency ratios indicate how well a business manages its assets and liabilities. They are especially useful for controlling working capital.
效率比率表明企业管理资产和负债的能力，对营运资金控制尤其有用。
| Ratio | Formula |
|---|---|
| Inventory Turnover | Cost of Sales ÷ Average Inventory (times) |
| Trade Receivables Days | (Trade Receivables ÷ Credit Sales Revenue) × 365 |
| Trade Payables Days | (Trade Payables ÷ Credit Purchases) × 365 |
Average inventory = (Opening Inventory + Closing Inventory) ÷ 2. A higher inventory turnover means goods are selling quickly, while a lower receivables days period implies that customers are paying faster.
平均存货 =（期初存货 + 期末存货）÷ 2。存货周转率越高，商品卖得越快；应收账款周转天数越低，客户付款越快。
7. Cash Flow Forecasting | 现金流预测
A cash flow forecast projects future cash inflows and outflows to show whether the business will have enough cash to meet its obligations. The core relationships are straightforward.
现金流预测预估未来的现金流入和流出，以显示企业是否有足够现金来履行其义务。核心关系很简单。
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
The closing cash balance for a period becomes the opening balance for the next period.
一个期间的期末现金余额成为下一期间的期初余额。
Closing Balance = Opening Balance + Net Cash Flow
When forecasting, remember that sales made on credit do not generate immediate cash. Depreciation is a non-cash expense and is not included in cash flow forecasts.
预测时需注意，赊销不会立即产生现金。折旧是非现金支出，不计入现金流预测。
8. Budgeting and Variance Analysis | 预算与差异分析
A budget is a financial plan for the future, and variance analysis compares actual results with the budget to identify areas needing attention.
预算是未来的财务计划，差异分析是将实际结果与预算进行比较，以确定需要关注的领域。
Variance = Actual Figure − Budgeted Figure
For revenue, a positive variance is favourable (earned more than planned). For costs, a negative variance is favourable (spent less than planned). Managers investigate significant variances to improve control.
对收入而言，正差异为有利（收入高于计划）；对成本而言，负差异为有利（支出低于计划）。管理者会调查重大差异以加强控制。
9. Cost Structure and Break-even Chart | 成本结构与盈亏平衡图
Understanding cost behaviour is essential for break-even and decision-making. Total cost is the sum of fixed and variable elements.
理解成本性态对于盈亏平衡和决策至关重要。总成本是固定成本和变动成本之和。
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average cost can be used to assess how costs change with output.
平均成本可用于评估成本如何随产量变化。
Average Cost = Total Cost ÷ Quantity of Output
On a break-even chart, the fixed cost line is horizontal, the total cost line starts at the fixed cost level and slopes upward, and the total revenue line starts at the origin. The point where total revenue and total cost intersect is the break-even point. The distance to the right of BEP up to actual output represents the margin of safety.
在盈亏平衡图中，固定成本线是水平的，总成本线从固定成本处开始并斜向上，总收入线从原点出发。总收入与总成本线的交点为盈亏平衡点。盈亏平衡点右侧到实际产量的距离就是安全边际。
10. Economies of Scale and Diminishing Returns | 规模经济与边际收益递减
Economies of scale are the cost advantages a business gains as it expands output. As the scale of production increases, average costs often fall.
规模经济是企业在扩大产量时获得的成本优势。随着生产规模扩大，平均成本往往会下降。
Average Cost ↓ as Output ↑ (due to economies of scale)
Internal economies of scale arise from factors within the business, such as bulk-buying discounts, technological improvements and specialisation of labour. External economies can come from a skilled local workforce or improved infrastructure.
内部规模经济源于企业内部因素，如批量购买折扣、技术改善和劳动专业化。外部规模经济可能来自熟练的本地劳动力或改善的基础设施。
The law of diminishing returns states that in the short run, when only one factor of production is varied, there will come a point where each additional unit of the variable factor adds less to total output. This helps explain why marginal cost eventually rises.
边际收益递减定律指出，在短期内，当只有一种生产要素可变时，终将达到一个点，此后每增加一单位可变要素所增加的总产出会递减。这有助于解释为什么边际成本最终会上升。
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