📚 Year 12 Cambridge Business: Formula & Theorem Quick Reference Handbook | 剑桥Year 12商务：公式定理速查手册
Mastering the key formulas and theorems is essential for success in Year 12 Cambridge Business. This quick reference handbook compiles all the critical equations you need—from break-even analysis and ratio calculations to investment appraisal techniques—presented in a clear, bilingual format to support your revision and exam preparation.
掌握关键公式和定理是学好剑桥Year 12商务的基础。这本速查手册汇总了所有核心方程式——从盈亏平衡分析、比率计算到投资评估技术——以清晰的双语形式呈现，为你的复习和备考提供有力支持。
1. Break-even Analysis | 盈亏平衡分析
The break-even point shows the level of output at which total revenue equals total costs, so the business makes neither profit nor loss. The margin of safety indicates how far sales can drop before reaching the break-even point.
盈亏平衡点表示总收入等于总成本的产出水平，此时企业不盈不亏。安全边际则表明了在达到盈亏平衡点之前，销售额可以下降的幅度。
Break-even Point (units) = Total Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)
Margin of Safety (units) = Actual Output − Break-even Output
Margin of Safety (%) = (Margin of Safety in units ÷ Actual Output) × 100
Contribution per unit is the amount each unit sold contributes to covering fixed costs and then to profit. Total contribution is thus a key figure in break-even calculations.
单位贡献是每售出一单位产品可用于补偿固定成本并创造利润的金额。因此，总贡献在盈亏平衡计算中十分关键。
Contribution per unit = Selling Price per unit − Variable Cost per unit
Total Contribution = Contribution per unit × Quantity Sold
For example, if fixed costs are $10,000, selling price is $50 and variable cost $30, then contribution per unit is $20 and the break-even point is 10,000 ÷ 20 = 500 units.
例如，如果固定成本为10,000元，售价50元，变动成本30元，则单位贡献为20元，盈亏平衡点为500件。
2. Profit and Contribution Targets | 利润与贡献目标
To achieve a target profit, the required output can be calculated by treating the profit like a fixed cost that must be covered. This extends the break-even formula.
要实现目标利润，可将利润视作必须覆盖的固定成本，从而计算所需的产量。这延伸了盈亏平衡公式。
Output for Target Profit = (Total Fixed Costs + Target Profit) ÷ Contribution per unit
Alternatively, profit can be expressed in terms of contribution: total contribution minus fixed costs equals profit (or loss). This relationship underpins cost–volume–profit analysis.
或者，利润可以用贡献表示：总贡献减去固定成本等于利润（或亏损）。这一关系是成本-数量-利润分析的基础。
Profit = Total Contribution − Total Fixed Costs
Understanding these links helps managers set sales targets and evaluate the financial impact of changes in costs or pricing.
理解这些联系有助于管理者设定销售目标，并评估成本或定价变动对财务的影响。
3. Profit Margins | 利润率
Gross profit margin measures the percentage of revenue remaining after direct costs (cost of sales). It reflects the efficiency of production or purchasing.
毛利率衡量扣除直接成本（销售成本）后剩余的销售收入百分比，反映了生产或采购的效率。
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
Net profit margin takes into account all expenses and shows the overall profitability of the business after all costs are deducted.
净利率则考虑了所有费用，显示扣除所有成本后企业整体的盈利能力。
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
Operating profit margin focuses on the core trading activities before interest and tax. A declining net margin may signal rising expenses or falling sales efficiency.
营运利润率关注核心经营活动，不含利息和税收。净利率下降可能表明费用上升或销售效率降低。
Operating Profit Margin (%) = (Operating Profit ÷ Revenue) × 100
4. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm’s ability to meet short-term obligations. The current ratio compares all current assets to current liabilities.
流动性比率评估企业偿还短期债务的能力。流动比率将所有流动资产与流动负债进行比较。
Current Ratio = Current Assets ÷ Current Liabilities
Because inventory may not be quickly convertible to cash, the acid test ratio (quick ratio) excludes inventory for a more stringent measure. A ratio below 1:1 can indicate possible liquidity problems.
由于存货可能不易迅速变现，酸性测试比率（速动比率）剔除了存货，衡量更严格。该比率低于1:1可能意味着流动性问题。
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
5. Efficiency Ratios | 效率比率
Stock turnover ratio indicates how many times a business sells and replaces its inventory over a period. A higher figure suggests efficient stock management.
存货周转率反映企业在一定时期内存货的售出和补充次数。较高的数值意味着存货管理更高效。
Stock Turnover Ratio (times) = Cost of Sales ÷ Average Stock
Trade receivable days show how long on average customers take to pay. Shorter periods improve cash flow and reduce the risk of bad debts.
应收账款周转天数显示客户平均付款所需的时长。较短的天数有利于现金流，并降低坏账风险。
Trade Receivable Days = (Trade Receivables ÷ Credit Sales) × 365
Similarly, trade payable days measure how long a business takes to pay its suppliers. A longer period can help cash flow but may strain supplier relationships.
类似地，应付账款周转天数衡量企业支付供应商的平均时间。较长的天数有助于现金流，但可能影响与供应商的关系。
Trade Payable Days = (Trade Payables ÷ Credit Purchases) × 365
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