📚 IB WJEC Business: Formula Summary Handbook | IB WJEC 商务：公式汇总手册
This concise handbook brings together all the essential quantitative formulas required for IB Business Management and WJEC Business examinations. Whether you are calculating profitability, assessing liquidity or evaluating investment projects, having these formulas at your fingertips will save time and improve accuracy in both structured questions and case studies.
这本简洁的手册汇集了 IB 商务管理和 WJEC 商务考试所需的所有核心量化公式。无论你在计算盈利能力、评估流动性还是评价投资项目，随时查阅这些公式都能帮你节省时间、提高作答准确性，从容应对结构题与案例分析。
1. Profitability Ratios | 盈利能力比率
Profitability ratios measure a firm’s ability to generate earnings relative to its sales, assets and capital. They are crucial for assessing whether a business is making acceptable returns.
盈利能力比率衡量企业相对于销售额、资产和资本创造盈利的能力，是判断企业回报是否令人满意的关键指标。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
This ratio shows the percentage of revenue left after subtracting the cost of sales. A rising gross margin may indicate better cost control or increasing selling prices.
该比率反映扣除销售成本后收入剩余的百分比。毛利率上升通常意味着成本控制改善或售价提高。
Net Profit Margin = (Net Profit before interest and tax ÷ Revenue) × 100%
Net profit margin takes account of all operating expenses. It reveals the overall cost efficiency of the business.
净利率考虑了所有运营费用，揭示企业的整体成本效率。
Return on Capital Employed (ROCE) = (Net Profit before interest and tax ÷ Capital Employed) × 100%
ROCE indicates how effectively a company uses its long-term capital. Capital employed is often calculated as total equity plus non-current liabilities, or total assets minus current liabilities.
资本回报率表明企业利用长期资本的效率。资本使用额通常用股东权益加非流动负债，或用总资产减流动负债计算。
2. Liquidity Ratios | 流动性比率
Liquidity ratios assess a firm’s ability to meet short-term obligations as they fall due. They are a vital sign of financial health.
流动性比率评估企业到期偿付短期债务的能力，是财务健康状况的重要信号。
Current Ratio = Current Assets ÷ Current Liabilities
A current ratio above 1 suggests the business has enough current assets to cover its current liabilities, though the ideal level varies by industry.
流动比率高于 1 表明企业有足够的流动资产覆盖流动负债，但理想水平因行业而异。
Acid Test (Quick) Ratio = (Current Assets − Inventories) ÷ Current Liabilities
The acid test ratio excludes inventories, which may not be readily converted into cash. A result of 1 or above is generally considered safe.
速动比率排除了不易快速变现的存货。一般认为结果在 1 或以上较为安全。
3. Efficiency Ratios | 效率比率
Efficiency ratios highlight how well a business manages its resources, particularly inventory, receivables and payables.
效率比率侧重于企业如何管理资源，尤其是存货、应收账款和应付账款。
Inventory Turnover (Days) = (Average Inventory ÷ Cost of Sales) × 365
A lower number of days suggests inventory is selling quickly, reducing holding costs and the risk of obsolescence.
天数越低表明存货销售越快，从而降低持有成本和过时风险。
Receivables Days = (Trade Receivables ÷ Credit Sales Revenue) × 365
This measures the average time taken to collect debts from credit customers. Shorter collection periods improve cash flow.
该指标衡量从赊销客户收回欠款的平均时间。收账期越短，现金流越好。
Payables Days = (Trade Payables ÷ Credit Purchases) × 365
Payables days show how long a business takes to pay its suppliers. A longer period can help cash flow but may harm supplier relationships.
应付账款天数表示企业向供应商付款的用时。期限较长有助于现金流，但可能损害供应商关系。
Asset Turnover = Revenue ÷ Net Assets
Asset turnover measures how efficiently a business uses its assets to generate sales revenue. A higher ratio indicates better utilisation.
资产周转率衡量企业利用资产创造销售收入的效率，比率越高表明资产利用率越好。
4. Shareholder Ratios | 股东比率
Shareholder ratios help investors evaluate the return and value of their shares. They are widely used in WJEC and IB finance topics.
股东比率帮助投资者评估股票回报与价值，在 WJEC 和 IB 财务专题中广泛应用。
Earnings per Share (EPS) = (Net Profit − Preference Dividends) ÷ Number of Ordinary Shares Issued
EPS shows the amount of profit attributable to each ordinary share. A rising EPS is often seen as a positive signal by the market.
每股盈利显示每一普通股应占的利润额。EPS 上升通常被市场视为积极信号。
Dividend per Share = Total Ordinary Dividends ÷ Number of Ordinary Shares Issued
This tells shareholders exactly how much income they receive per share held. It can be compared with EPS to assess dividend cover.
该比率告诉股东每股实际分得的股息，可与 EPS 对比以评估股息保障倍数。
Dividend Yield = (Dividend per Share ÷ Market Price per Share) × 100%
Dividend yield expresses the annual dividend as a percentage of the current share price, enabling comparison with other investments.
股息率将年度股息表示为当前股价的百分比，便于与其他投资品比较。
Price/Earnings (P/E) Ratio = Market Price per Share ÷ Earnings per Share
The P/E ratio indicates how much investors are willing to pay for each unit of earnings. A high P/E may reflect strong growth expectations.
市盈率显示投资者为每单位盈利愿意支付的价格。较高的市盈率可能反映强劲的增长预期。
5. Gearing Ratio | 杠杆比率
The gearing ratio examines the proportion of a company’s capital that comes from debt. It is a key measure of financial risk.
杠杆比率考察企业资本中来自债务的比例，是衡量财务风险的关键指标。
Gearing Ratio = (Non-current Liabilities ÷ Capital Employed) × 100%
Capital employed is the sum of non-current liabilities and shareholders’ equity. A gearing ratio above 50% is often regarded as highly geared, meaning greater risk from interest obligations.
资本使用额等于非流动负债加股东权益。杠杆率超过 50% 通常被视为高杠杆，意味着利息义务带来的风险更大。
6. Investment Appraisal – Payback & ARR | 投资评估 – 回收期与平均回报率
Investment appraisal techniques help businesses decide which projects to undertake. Payback period and ARR are straightforward, non-discounted methods.
投资评估技术帮助企业决定采纳哪些项目。回收期和平均回报率是简单直观的非折现方法。
Payback Period = Time taken for cumulative net cash flows to equal the initial investment
Where annual cash flows are constant: Payback Period = Initial Investment ÷ Annual Net Cash Flow. The project with the shorter payback is usually preferred.
当年现金流恒定时：回收期 = 初始投资额 ÷ 年净现金流。回收期较短的项目通常更受青睐。
Average Rate of Return (ARR) = (Average Annual Profit ÷ Initial Investment) × 100%
Average annual profit is calculated as total profits over the project life divided by the number of years. ARR is compared with the firm’s target rate.
平均年度利润由项目期内的总利润除以年数得出。将 ARR 与企业目标回报率比较以做决策。
7. Investment Appraisal – Net Present Value (NPV) | 投资评估 – 净现值
NPV uses discounting to account for the time value of money, making it a more sophisticated and widely recommended technique for both IB and WJEC syllabuses.
净现值运用折现方法考虑货币时间价值，是更为精密的技术，被 IB 和 WJEC 教学大纲广泛推荐。
NPV = Σ [NCFₜ ÷ (1 + r)ᵗ] − I₀
NCFₜ is the net cash flow in period t, r is the discount rate and I₀ is the initial investment. A positive NPV suggests the project will add value to the business.
NCFₜ 为第 t 期的净现金流，r 为折现率，I₀ 为初始投资额。NPV 为正表示项目将为公司增加价值。
8. Break-even Analysis | 盈亏平衡分析
Break-even analysis identifies the level of output at which total revenue equals total costs. It helps managers plan production and set targets.
盈亏平衡分析确定总收入等于总成本时的产出水平，帮助管理者规划生产和设定目标。
Break-even Point (units) = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
The denominator is the contribution per unit. Output above this point generates profit; below it results in a loss.
分母为单位贡献毛利。产出高于此点即产生盈利，低于此点则出现亏损。
Break-even Revenue = Break-even Units × Selling Price per Unit
This gives the sales revenue needed to cover all costs. It is useful for revenue-focused planning.
该公式给出覆盖全部成本所需的销售收入，有助于以收入为导向的规划。
Margin of Safety = (Actual Sales − Break-even Sales) ÷ Actual Sales × 100%
The margin of safety shows how far sales can fall before the business reaches its break-even point. A higher margin means lower risk.
安全边际显示销售下滑多少才会触及盈亏平衡点。边际越高，风险越低。
9. Productivity and Cost Measures | 生产率与成本衡量
Productivity and unit cost measures are fundamental in operations management. They link directly to efficiency and competitiveness.
生产率与单位成本衡量是运营管理的基础，直接关系到效率和竞争力。
Labour Productivity = Total Output per Period ÷ Number of Employees
Higher labour productivity means more output per worker, which can reduce unit labour costs and improve profit margins.
劳动生产率越高，意味着每名员工的产出越多，可降低单位人工成本并改善利润率。
Unit Cost = Total Costs ÷ Total Output
Unit cost (or average cost) is vital for pricing decisions. Economies of scale lead to a fall in unit cost as output rises.
单位成本（即平均成本）对定价决策至关重要。规模经济效应下，随着产量增加单位成本会下降。
Capacity Utilisation = (Actual Output ÷ Maximum Capacity) × 100%
This percentage shows how much of a firm’s production capacity is being used. Low utilisation suggests spare capacity and higher fixed cost per unit.
该百分比表示企业生产能力的利用程度。利用率低下意味着产能闲置，单位固定成本较高。
10. Decision Trees & Expected Value | 决策树与预期价值
Decision trees help businesses evaluate choices under uncertainty. Expected value quantifies the average outcome of a decision, weighted by probabilities.
决策树帮助企业评估不确定条件下的选择。预期价值以概率加权的方式量化决策的平均结果。
Expected Value (EV) = Probability × Payoff
For each branch, multiply the probability (as a decimal) by the financial outcome. Summing the EVs of all branches gives the expected monetary value of an option.
每个分支用概率（小数形式）乘以财务结果。将所有分支的预期价值相加，即得到该选项的预期货币价值。
Net Gain = Total Expected Value − Initial Cost of Decision
Net gain subtracts any upfront investment from the total expected value. A positive net gain indicates the decision is financially worthwhile.
净收益从总预期价值中扣除任何前期投资。净收益为正表明该决策在财务上可行。
When drawing a decision tree, remember to use squares for decision nodes and circles for chance nodes. Always label probabilities clearly and work from right to left when calculating expected values.
绘制决策树时，用方框表示决策节点，圆圈表示机会节点。务必清晰标注概率，计算预期价值时从右向左逐步回推。
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