📚 Pre-U WJEC Business: Formula & Theorem Quick Reference Handbook | 商务公式定理速查手册
This handbook brings together all the essential formulas and analytical theorems you need to master for the Pre-U WJEC Business examination. Keep it close as a fast reference when revising profitability, liquidity, investment decisions and cost management.
本手册汇集了Pre-U WJEC商务考试必须掌握的所有核心公式与分析定理。在复习盈利能力、流动性、投资决策与成本管理时，可将其作为快速查阅的随身工具。
1. Profitability Ratios | 盈利能力比率
Gross profit margin reveals how efficiently a business turns raw materials into profit before overheads. It is the foundation of pricing and cost control.
毛利润率反映企业在扣除间接费用之前，将原材料转化为利润的效率，是定价与成本控制的基础。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
Operating profit margin shows the percentage of revenue left after covering both direct and indirect operating expenses. It signals operational health.
营业利润率显示在覆盖所有直接与间接营业费用之后，收入留存的比例，是经营健康状况的信号。
Operating Profit Margin = (Operating Profit ÷ Revenue) × 100%
Net profit margin gives the ultimate bottom-line profitability after all expenses, including tax and interest, have been deducted.
净利润率是扣除所有费用（含税与利息）之后的最终底线盈利能力指标。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
Return on Capital Employed (ROCE) measures how effectively a business generates profit from its long-term capital. A higher ROCE appeals to investors.
已动用资本回报率(ROCE)衡量企业运用长期资本产生利润的有效性。较高的ROCE对投资者具有吸引力。
ROCE = (Operating Profit ÷ Capital Employed) × 100%
Capital Employed = Total Equity + Non‑Current Liabilities, or equivalently Total Assets – Current Liabilities.
已动用资本 = 总权益 + 非流动负债，或等于总资产 – 流动负债。
2. Liquidity Ratios | 流动性比率
The current ratio tests a firm’s ability to cover short‑term obligations with short‑term assets. A ratio of 1.5–2 is often considered healthy.
流动比率检验企业用短期资产覆盖短期债务的能力。1.5到2之间通常被认为是健康水平。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test (or quick) ratio excludes inventories, offering a stricter measure of immediate liquidity.
酸性测试（速动）比率剔除库存，提供了对即时流动性的更严格衡量。
Acid Test Ratio = (Current Assets – Inventories) ÷ Current Liabilities
3. Efficiency Ratios | 效率比率
Inventory turnover tells how many times stock is sold and replaced over a period. A higher figure suggests efficient inventory management.
存货周转率表示库存在一个时期内的售出与补充次数。数字越高，说明存货管理效率越高。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventories
Inventory Turnover (days) = (Average Inventories ÷ Cost of Sales) × 365
Trade receivables days measure the average time credit customers take to pay. Shorter is better for cash flow.
应收账款周转天数衡量赊销客户平均付款时间。越短越有利于现金流。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
Trade payables days indicate how long a business takes to pay its suppliers. Stretching payables conserves cash but must not damage relationships.
应付账款周转天数显示企业向供应商付款所需的时间。延长付款可保留现金，但不能损害供应商关系。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
Asset turnover reveals how many pounds of revenue are generated per pound of total assets. It is a key productivity metric.
资产周转率显示每英镑总资产能产生多少英镑收入，是重要的生产力度量指标。
Asset Turnover = Revenue ÷ Total Assets
4. Shareholder Ratios | 股东比率
Dividend per share quantifies the cash return distributed to ordinary shareholders per share owned.
每股股息量化了每持有一股普通股所能获得的现金回报。
Dividend Per Share = Total Dividends ÷ Number of Ordinary Shares
Dividend yield relates the annual dividend income to the current market price, helping investors compare income streams.
股息收益率将年度股息收入与当前市价联系起来，帮助投资者比较收益流。
Dividend Yield = (Dividend Per Share ÷ Market Price Per Share) × 100%
Earnings per share (EPS) measures the profit attributable to each ordinary share. It drives valuation and market sentiment.
每股收益(EPS)衡量归属于每一普通股的利润，是估值和市场情绪的关键驱动力。
EPS = (Net Profit – Preference Dividends) ÷ Number of Ordinary Shares
The price/earnings (P/E) ratio shows how many years it would take to recover the share price through earnings. A high P/E may indicate growth expectations.
市盈率(P/E)显示通过盈利收回股价所需的年数。高市盈率可能意味着市场对增长的期望。
P/E Ratio = Market Price Per Share ÷ Earnings Per Share
5. Gearing and Interest Cover | 杠杆与利息覆盖
The gearing ratio assesses the proportion of long‑term debt in the capital structure. High gearing amplifies risk and return.
杠杆比率评估长期债务在资本结构中的比例。高杠杆会放大风险与回报。
Gearing Ratio = (Long‑Term Debt ÷ Capital Employed) × 100%
Alternatively, the debt‑to‑equity ratio is often used: Long‑Term Debt ÷ Total Equity. Both indicate financial leverage.
此外，常用债务权益比率：长期债务 ÷ 总权益。两者均表明财务杠杆水平。
Debt‑to‑Equity = Long‑Term Debt ÷ Total Equity
Interest cover shows how easily operating profit can pay interest charges. A value below 2 signals potential stress.
利息覆盖倍数显示营业利润支付利息费用的容易程度。低于2可能预示着资金压力。
Interest Cover = Operating Profit ÷ Interest Payable
6. Break‑even Analysis | 盈亏平衡分析
Contribution per unit is the surplus after variable costs are deducted from the selling price. It is used to cover fixed costs and generate profit.
单位贡献毛利是售价减去变动成本后的盈余，用于弥补固定成本并产生利润。
Contribution Per Unit = Selling Price Per Unit – Variable Cost Per Unit
The break‑even point in units tells how many items must be sold to cover all fixed and variable costs exactly.
以数量计算的盈亏平衡点说明需要卖出多少件产品才能恰好覆盖所有固定与变动成本。
Break‑Even Units = Total Fixed Costs ÷ Contribution Per Unit
Break‑even revenue converts the unit figure into sales value, often used for service‑based businesses.
盈亏平衡收入将数量转化为销售额，常用于服务型企业。
Break‑Even Revenue = Break‑Even Units × Selling Price Per Unit
The margin of safety shows the cushion between actual sales and the break‑even point. A large margin reduces risk.
安全边际显示实际销售与盈亏平衡点之间的缓冲。较大的安全边际可降低风险。
Margin of Safety (units) = Actual Sales Units – Break‑Even Units
To achieve a target profit, add the desired profit to fixed costs before dividing by contribution.
要实现目标利润，需在固定成本之上加上期望利润，再除以单位贡献毛利。
Target Profit Units = (Total Fixed Costs + Target Profit) ÷ Contribution Per Unit
7. Budgeting and Variance Analysis | 预算与差异分析
Variance analysis measures the difference between actual and budgeted figures, helping managers control the business.
差异分析衡量实际与预算数字之间的差异，帮助管理者控制业务。
Total Sales Variance = Actual Sales Revenue – Budgeted Sales Revenue
A favourable variance occurs when actual revenue exceeds budget or actual costs are lower than budgeted.
当实际收入超过预算或实际成本低于预算时，产生有利差异。
Sales price variance isolates the effect of charging a different price from the one planned.
销售价格差异分离出收取价格与计划价格不同所带来的影响。
Sales Price Variance = (Actual Price – Budgeted Price) × Actual Quantity Sold
Sales volume variance measures the impact of selling a different quantity than budgeted, multiplied by the budgeted price.
销售数量差异衡量实际销量与预算不同所造成的影响，乘以预算单价。
Sales Volume Variance = (Actual Quantity – Budgeted Quantity) × Budgeted Price
Direct material cost variance can be split into price and usage components. The price variance captures the difference in purchase cost.
直接材料成本差异可拆分为价格与用量两部分。材料价格差异反映了采购成本的差异。
Material Price Variance = (Actual Price – Standard Price) × Actual Quantity Purchased
The usage variance highlights how efficiently materials were used in production relative to the standard allowance.
用量差异突出材料在生产中的使用效率相对于标准用量的表现。
Material Usage Variance = (Actual Quantity Used – Standard Quantity Allowed) × Standard Price
8. Investment Appraisal | 投资评估
Payback period is the time required to recover the initial investment. Shorter payback reduces risk.
回收期是收回初始投资所需的时间。回收期越短，风险越小。
Payback Period = Time until cumulative net cash flows equal the initial outlay
Accounting Rate of Return (ARR) compares average annual accounting profit to the investment. It is straightforward but ignores time value of money.
会计回报率(ARR)将平均年度会计利润与投资额比较。计算简单但忽略了货币时间价值。
ARR = (Average Annual Profit ÷ Initial Investment) × 100%
Net Present Value (NPV) discounts future cash flows to their present value. A positive NPV means the project adds value.
净现值(NPV)将未来现金流折现为现值。正的NPV表示项目创造价值。
NPV = Σₜ₌₁ⁿ (Cash Flowₜ ÷ (1 + r)ᵗ) – Initial Investment
Where r is the discount rate and t is the year. Use the sum of discounted inflows minus the initial outlay.
其中r为折现率，t为年份。将折现后的流入总和减去初始投资额。
9. Costing Methods and Contribution | 成本计算方法与贡献毛利
Total cost is the sum of all fixed and variable costs incurred. It underpins pricing and profit planning.
总成本是所有固定与变动成本的总和，是定价与利润规划的基础。
Total Cost = Total Fixed Costs + Total Variable Costs
Unit cost is total cost divided by the number of units produced. It is used in absorption costing.
单位成本是总成本除以生产数量，用于吸收成本法。
Unit Cost = Total Cost ÷ Number of Units Produced
Under marginal costing, only variable costs are charged to units. Contribution is the key figure, and profit is calculated as total contribution minus fixed costs.
在边际成本法下，只有变动成本计入单位产品。贡献毛利是关键数据，利润等于总贡献毛利减去固定成本。
Profit = Total Contribution – Total Fixed Costs
10. Price Elasticity of Demand | 需求价格弹性
Price elasticity of demand (PED) measures how responsive quantity demanded is to a price change. It guides pricing strategy.
需求价格弹性(PED)衡量需求量对价格变化的反应程度，可指导定价策略。
PED = % Change in Quantity Demanded ÷ % Change in Price
When PED is greater than 1, demand is elastic and a price cut raises total revenue. When less than 1, demand is inelastic and a price increase raises total revenue.
当PED大于1时，需求富有弹性，降价可提高总收入；当PED小于1时，需求缺乏弹性，提价可增加总收入。
Use the arc elasticity formula if data covers a large jump: %ΔQd = (Q₂ – Q₁) ÷ Q₁ × 100, similarly for price.
如果数据跳跃较大，使用弧弹性公式：需求变动百分比 = (Q₂ – Q₁) ÷ Q₁ × 100，价格变动类似。
11. Decision Trees and Expected Value | 决策树与期望值
Expected value (EV) combines payoffs and probabilities to give an average monetary outcome. It helps choose between uncertain alternatives.
期望值(EV)结合收益与概率得出平均货币结果，有助于在不确定选项之间作出选择。
Expected Value = Σ (Payoff × Probability of that payoff)
The net gain subtracts the cost of a decision from its expected value. Only positive net gains are worth pursuing.
净收益是从期望值中扣除决策成本。只有正净收益才值得实施。
Net Gain = Expected Value – Initial Decision Cost
Decision trees map sequential choices and chance events. Always choose the option with the highest expected value or net gain after rolling back the tree.
决策树用于描绘连续选择与概率事件。应始终选择回推决策树后，期望值或净收益最高的方案。
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