📚 Year 12 OCR Business: Quick Formula & Theorem Handbook | Year 12 OCR 商务：公式定理速查手册
This handbook contains all essential formulas and theorems you need for Year 12 OCR Business. Each formula is presented clearly, followed by a concise explanation of its application, helping you master quantitative skills for your exam.
本手册汇集了 Year 12 OCR 商务课程所有必备公式与定理。每个公式均清晰列出，并附有简明应用解释，助你攻克考试中的定量分析题目。
1. Breakeven Analysis | 盈亏平衡分析
The breakeven point is the output level at which total revenue equals total costs, resulting in neither profit nor loss.
盈亏平衡点是指总收入等于总成本的产出水平，此时企业既不盈利也不亏损。
Breakeven (units) = Fixed Costs ÷ (Selling Price per Unit – Variable Cost per Unit)
盈亏平衡点（单位） = 固定成本 ÷（单位售价 – 单位可变成本）
The term (Selling Price – Variable Cost) is called the contribution per unit. It shows how much each unit sold contributes towards covering fixed costs and then generating profit.
（售价 – 可变成本）这一项称为单位贡献。它表示每售出一单位产品能为弥补固定成本并创造利润所作的贡献。
2. Contribution and Margin of Safety | 贡献与安全边际
Contribution is a key concept for understanding cost-volume-profit relationships. Total contribution is used to calculate profit directly.
贡献是理解成本-产量-利润关系的关键概念。总贡献可直接用于计算利润。
Contribution per unit = Selling Price per Unit – Variable Cost per Unit
单位贡献 = 单位售价 – 单位可变成本
Total Contribution = Contribution per Unit × Quantity Sold
总贡献 = 单位贡献 × 销售数量
Profit = Total Contribution – Fixed Costs
利润 = 总贡献 – 固定成本
The margin of safety shows how far actual output can fall before the business reaches its breakeven point.
安全边际表明在实际产出降至盈亏平衡点之前，企业尚可承受的产量下跌幅度。
Margin of Safety (units) = Actual Output – Breakeven Output
安全边际（单位） = 实际产量 – 盈亏平衡产量
A higher margin of safety implies lower risk. It can also be expressed as a percentage of actual output.
安全边际越高意味着风险越低。它也可以表示为实际产量的百分比。
3. Profitability Ratios | 盈利能力比率
Profitability ratios assess a firm’s ability to generate earnings relative to its revenue, assets or capital employed.
盈利能力比率用于衡量企业相对于其收入、资产或投入资本创造利润的能力。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100
毛利率 =（毛利 ÷ 收入）× 100
This ratio reveals how efficiently a business turns raw materials and direct labour into profit before deducting overheads. A higher percentage indicates better control of production or purchasing costs.
该比率揭示企业在扣除间接费用之前将原材料和直接人工转化为利润的效率。百分比越高，说明对生产或采购成本的控制越好。
Net Profit Margin = (Net Profit Before Tax ÷ Revenue) × 100
净利率 =（税前净利润 ÷ 收入）× 100
Net profit margin takes all expenses into account, giving a complete picture of overall profitability from trading activities.
净利率将所有费用均考虑在内，从经营活动中全面反映企业的整体盈利水平。
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100
已动用资本回报率 =（营业利润 ÷ 已动用资本）× 100
Capital employed is typically calculated as Total Equity + Non-current Liabilities, or Total Assets – Current Liabilities. ROCE measures the return generated from every pound invested in the business, making it a crucial metric for investors.
已动用资本通常计算为总权益 + 非流动负债，或者总资产 – 流动负债。ROCE 衡量从投入企业的每英镑资本中获得的回报，是投资者关注的关键指标。
4. Liquidity Ratios | 流动性比率
Liquidity ratios indicate a firm’s ability to meet its short-term obligations as they fall due.
流动性比率反映企业偿还到期短期债务的能力。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
A current ratio between 1.5:1 and 2:1 is generally considered healthy, but this can vary by industry. A ratio below 1 suggests potential cash flow problems.
流动比率通常在 1.5:1 至 2:1 之间被视为健康水平，但这也因行业而异。比率低于 1 可能预示着现金流问题。
Acid Test Ratio (Quick Ratio) = (Current Assets – Inventory) ÷ Current Liabilities
酸性测试比率（速动比率）=（流动资产 – 存货）÷ 流动负债
This ratio excludes inventory because it may not be quickly convertible into cash. A result of 1:1 or higher is often desirable, indicating the business can pay its immediate debts without selling stock.
该比率剔除存货，因为存货未必能迅速变现。结果通常希望达到 1:1 或更高，表明企业无需出售库存即可偿还短期债务。
5. Efficiency Ratios | 效率比率
Efficiency ratios show how well a business uses its assets and manages its liabilities internally.
效率比率体现企业内部运用资产和管理负债的水平。
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
存货周转率（次）= 销售成本 ÷ 平均存货
A higher turnover means goods are sold and replaced more frequently, reducing holding costs. The result can also be converted into number of days.
周转率越高，意味着商品出售和补货越频繁，从而降低持有成本。该结果也可转换为周转天数。
Inventory Turnover (days) = (Average Inventory ÷ Cost of Sales) × 365
存货周转天数 =（平均存货 ÷ 销售成本）× 365
Trade Receivable Days = (Trade Receivables ÷ Credit Sales) × 365
应收账款周转天数 =（应收账款 ÷ 赊销收入）× 365
This indicates the average number of days a business takes to collect payment from its credit customers. Shorter collection periods improve cash flow.
该指标表示企业收回赊销账款的平均天数。较短的收款期有助于改善现金流。
Trade Payable Days = (Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 =（应付账款 ÷ 赊购金额）× 365
A longer payable period suggests the business is using suppliers’ credit effectively, but might risk damaging relationships if stretched too far.
较长的付款期表明企业有效利用了供应商信用，但拖得过久可能有损关系。
6. Investment Appraisal: Payback Period | 投资评估：回收期
The payback period measures how long it takes for the initial investment in a project to be recovered from its net cash inflows.
回收期衡量一个项目的初始投资通过其净现金流入全额收回所需的时间。
When annual net cash flows are constant, the formula is simple.
当年净现金流恒定时，公式很简单。
Payback Period = Initial Investment ÷ Annual Net Cash Flow
回收期 = 初始投资 ÷ 年净现金流
If cash flows vary, calculate the cumulative cash flow year by year until the initial outlay is covered. The exact point is often found by assuming cash flows occur evenly throughout the year.
若现金流不固定，则逐年计算累计现金流，直至初始支出被完全覆盖。通常假设年内现金流均匀发生，来得出精确的时间点。
A shorter payback period is preferred as it reduces risk and frees up capital sooner. However, this method ignores any returns after the payback point and the time value of money.
较短的回收期更为有利，因为它能降低风险并更快释放资金。但该方法忽略了回收期后的所有回报，也未考虑货币的时间价值。
7. Investment Appraisal: ARR | 投资评估：平均回报率
The Accounting Rate of Return (ARR) expresses the average annual profit of a project as a percentage of the initial investment or average investment.
平均回报率（ARR）将项目的年平均利润表示为初始投资或平均投资的百分比。
ARR = (Average Annual Profit ÷ Initial Investment) × 100
ARR =（年平均利润 ÷ 初始投资）× 100
To find average annual profit, deduct total depreciation and other expenses from total net cash inflows over the project’s life, then divide by the number of years. The higher the ARR, the more attractive the project appears.
计算年平均利润时，需从项目生命周期内的总净现金流入中扣除总折旧和其他费用，再除以年数。ARR 越高，项目看起来越有吸引力。
ARR is straightforward and uses familiar profit figures, yet it also ignores the time value of money and the timing of profits.
ARR 简便易用且采用熟悉的利润数据，但它同样忽视了货币的时间价值以及利润产生的时间点。
8. Decision Trees and Expected Value | 决策树与期望值
A decision tree is a visual tool for evaluating different choices when outcomes are uncertain. The expected value (EV) helps quantify the likely financial outcome of each option.
决策树是一种在结果不确定时评估不同选项的可视化工具。期望值（EV）有助于量化每个选项的预期财务结果。
Expected Value = (Probability of Outcome 1 × Payoff 1) + (Probability of Outcome 2 × Payoff 2) + …
期望值 = （结果1的概率 × 收益1） + （结果2的概率 × 收益2） + …
Probabilities must sum to 1 for each set of branches. After calculating the EV for each option, the net gain is found by subtracting the initial cost of the decision.
每组分支的概率之和必须为1。计算出每个选项的期望值后，再减去该决策的初始成本即可得到净收益。
The manager then chooses the option yielding the highest net expected value. This technique provides a logical basis for choices under risk, though it relies on accurate probability estimates.
管理者通常选择能带来最高净期望值的方案。这种方法为风险决策提供了逻辑基础，但它依赖准确概率估计。
9. Capacity Utilisation and Productivity | 产能利用率与劳动生产率
These measures indicate how intensively a business is using its resources and how efficient its workforce is.
这些指标反映企业使用资源的密集程度以及员工效率的高低。
Capacity Utilisation = (Actual Output ÷ Maximum Possible Output) × 100
产能利用率 =（实际产出 ÷ 最大可能产出）× 100
Operating near full capacity often reduces unit fixed costs, but consistently at or above 100% can strain resources and staff. Most firms target around 90% utilisation.
接近满负荷运营通常能降低单位固定成本，但持续达到或超过 100% 会使资源和员工不堪重负。多数企业将 90% 的利用率作为目标。
Labour Productivity = Output per Period ÷ Number of Employees
劳动生产率 = 当期产出 ÷ 员工人数
Improving labour productivity – through training, automation or motivation – helps to lower unit labour costs and boost competitiveness.
通过培训、自动化或激励等方式提高劳动生产率，有助于降低单位劳动力成本并增强竞争力。
Absenteeism Rate = (Number of Staff Absent ÷ Total Staff) × 100
缺勤率 =（缺勤员工人数 ÷ 总员工人数）× 100
A rising absenteeism rate can indicate low morale and higher costs for cover staff, requiring action from management.
缺勤率上升可能表明员工士气低落以及顶班成本增加，管理层需要就此采取行动。
10. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price.
需求价格弹性衡量需求量对价格变动的反应程度。
PED = % Change in Quantity Demanded ÷ % Change in Price
PED = 需求量变动百分比 ÷ 价格变动百分比
If PED > 1, demand is price elastic: a price cut raises total revenue, while a price rise lowers total revenue. If PED < 1, demand is price inelastic, so revenue moves in the same direction as price changes.
若 PED > 1，需求富有弹性：降价会增加总收入，提价则会减少总收入。若 PED < 1，需求缺乏弹性，因此收入会随价格同向变动。
Firms can use PED estimates to forecast the impact of pricing strategies on sales volume and total revenue, informing decisions on discounts or premium pricing.
企业可利用 PED 估算值来预测定价策略对销量和总收入的影响，从而为折扣或高端定价决策提供依据。
11. Working Capital and Cash Flow | 营运资金与现金流
Working capital, or net current assets, is a measure of day-to-day financial health.
营运资金，也称净流动资产，是衡量日常财务健康状况的指标。
Working Capital = Current Assets – Current Liabilities
营运资金 = 流动资产 – 流动负债
A positive working capital ensures the business can meet short-term debts and fund daily operations without facing a liquidity crisis.
营运资金为正，可确保企业能偿还短期债务并支持日常运转，不会遭遇流动性危机。
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
净现金流 = 总现金流入 – 总现金流出
A cash flow forecast uses this principle period by period to predict the firm’s cash position, highlighting potential deficits that need early action.
现金流量预测就是按时间段运用此原理，以预测企业的现金状况，从而提前发现可能需要提早应对的潜在赤字。
12. Variance Analysis | 差异分析
Variance analysis compares budgeted figures with actual outcomes to identify and explain differences.
差异分析将预算数字与实际结果进行比较，以识别和解释其中的差异。
Variance = Actual – Budget
差异 = 实际值 – 预算值
A positive result for revenue or profit is favourable (F); for costs, a positive variance means overspending and is adverse (A). The reverse signs apply when actual is less than budget.
对于收入或利润，正差异为有利差异 (F)；对于成本，正差异意味着超支，属于不利差异 (A)。当实际值低于预算时，符号则相反。
Managers examine significant variances to control budgets, improve future planning and take corrective action where necessary.
管理者通过审查重大差异来控制预算、改善未来规划，并在必要时采取纠正措施。
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