📚 Year 11 CCEA Business: Formula & Theorem Quick Reference Handbook | CCEA 商务公式定理速查手册
Success in CCEA GCSE Business requires more than just definitions — you need quick and accurate recall of the key formulas, ratios and decision-making tools. This handbook brings together all the essential quantitative tools you will meet in Year 11, organised for rapid revision and classroom use. Each section pairs explanation with worked examples so you can move confidently from the formula sheet to the exam answer.
要在 CCEA GCSE 商务考试中脱颖而出，仅靠背诵概念是不够的——你需要快速、准确地调取关键公式、比率和决策工具。本手册汇聚了 Year 11 阶段所有必备的定量工具，按主题整理，便于课堂查阅和考前速记。每一节都以解释搭配实例，帮助你自信地从公式清单走向考场答案。
1. Revenue and Cost Formulas | 收入与成本公式
Total revenue is the money a business receives from selling its goods or services. It is calculated by multiplying the selling price per unit by the quantity sold.
总收入是企业出售商品或服务所获得的全部款项，由单位售价乘以销售数量计算得出。
Total Revenue = Selling Price per Unit × Quantity Sold
Total costs are the sum of all expenses a business incurs. They are divided into fixed costs, which do not change with output, and variable costs, which vary directly with the level of production.
总成本是企业发生的全部费用之和，分为不随产量变动的固定成本和直接随产量变动的可变成本。
Total Costs = Fixed Costs + Variable Costs
Total variable costs rise as output increases. They are found by multiplying the variable cost per unit by the number of units produced.
总可变成本随产量上升而增加，由单位可变成本乘以生产数量得出。
Total Variable Costs = Variable Cost per Unit × Quantity
Profit (or loss) is the difference between total revenue and total costs over a given period. A positive number indicates a profit; a negative number signals a loss.
利润（或亏损）是在特定时期内总收入与总成本之间的差额。正值表示盈利，负值表示亏损。
Profit = Total Revenue − Total Costs
2. Break-even Analysis | 盈亏平衡分析
Break‑even output is the level of production at which total revenue equals total costs — the business makes neither a profit nor a loss. It is expressed in units.
盈亏平衡产量是总收入等于总成本时的生产水平，此时企业既不盈利也不亏损，通常以单位数表示。
Break‑even Output (units) = Fixed Costs ÷ Contribution per Unit
Contribution per unit is the amount each sale contributes towards covering fixed costs and then generating profit. It is the difference between the selling price and the variable cost per unit.
单位贡献是每销售一单位产品为覆盖固定成本并创造利润所作的贡献，等于售价与单位可变成本之差。
Contribution per Unit = Selling Price − Variable Cost per Unit
To find the break‑even revenue, multiply the break‑even output by the selling price. This is especially useful when a business sells multiple products and only has revenue data.
若要求盈亏平衡收入，可将盈亏平衡产量乘以售价。当企业经营多种产品且仅有收入数据时，这个指标尤为实用。
Break‑even Revenue = Break‑even Units × Selling Price
3. Contribution and Margin of Safety | 贡献与安全边际
Total contribution measures how much money is left after variable costs are deducted from sales revenue. It is first used to cover fixed costs, with any remainder becoming profit.
贡献总额衡量销售收入扣除可变成本后剩余的金额，首先用于弥补固定成本，如有结余则形成利润。
Total Contribution = Contribution per Unit × Quantity Sold
Alternatively, total contribution can be calculated directly from income statements as sales revenue minus total variable costs.
贡献总额也可直接从利润表中计算，即销售收入减去总可变成本。
Total Contribution = Sales Revenue − Total Variable Costs
The margin of safety shows how far sales can fall before the business starts making a loss. It is the difference between actual (or budgeted) sales and the break‑even point, expressed either in units or as a percentage.
安全边际表示销售额可以下降到何种程度而企业仍未亏损，是实际（或预算）销售量与盈亏平衡点之差，可以单位数或百分比表示。
Margin of Safety (units) = Actual Sales Units − Break‑even Units
Margin of Safety (%) = (Actual Sales − Break‑even Sales) ÷ Actual Sales × 100
4. Profit and Profit Margins | 利润与利润率
Gross profit is the surplus after a business deducts the cost of sales from its revenue. Cost of sales includes the direct costs of buying or making the goods sold.
毛利润是销售收入扣除销售成本后的余额，销售成本包括购买或生产已售商品的直接成本。
Gross Profit = Sales Revenue − Cost of Sales
The gross profit margin expresses gross profit as a percentage of revenue. It reveals how efficiently a business turns sales into gross profit before overheads are deducted.
毛利率以百分比形式表示毛利润占收入的比例，揭示企业在扣除间接费用前将销售转化为毛利润的效率。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100
Net profit is the ‘bottom line’ that remains after all expenses — including overheads, interest and tax — have been subtracted from gross profit.
净利润是毛利润扣除所有费用（包括间接费用、利息和税金）后的最终收益，常被称为“底线”。
Net Profit = Gross Profit − Expenses
The net profit margin compares net profit to sales revenue. A higher percentage means a business retains more from each pound of sales after paying all costs.
净利润率将净利润与销售收入进行比较。该百分比越高，表明企业支付全部成本后从每英镑销售中保留的收益越多。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100
5. Liquidity Ratios | 流动性比率
The current ratio measures a firm’s ability to pay its short‑term debts using current assets. A figure between 1.5 and 2.0 is often considered healthy, though this varies by industry.
流动比率衡量企业用流动资产偿还短期债务的能力，一般认为 1.5 至 2.0 之间较为理想，但会因行业而异。
Current Ratio = Current Assets ÷ Current Liabilities
The acid test ratio (quick ratio) excludes inventory from current assets because stock is not always easily converted into cash. It provides a stricter test of liquidity.
速动比率（酸性测试比率）从流动资产中剔除存货，因为库存未必能迅速变现，从而提供了更为严格的流动性检验。
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
While the current ratio can paint an overly optimistic picture if a business holds large amounts of slow‑moving stock, the acid test ratio focuses on cash, receivables and short‑term investments only.
若企业持有大量滞销库存，流动比率可能会过于乐观；速动比率则仅关注现金、应收账款和短期投资，排除了库存的干扰。
6. Efficiency Ratios | 效率比率
Inventory turnover shows how many times a company sells and replaces its stock during a period. A higher figure often indicates efficient stock management, though excessively high turnover might risk stock‑outs.
存货周转率显示企业在一定时期内销售并更新存货的次数。周转率较高通常意味着库存管理效率高，但过高也可能引发缺货风险。
Inventory Turnover = Cost of Sales ÷ Average Inventory
Average inventory is calculated by adding opening and closing inventory values and dividing by two. This smooths out seasonal fluctuations.
平均存货通过期初与期末存货相加后除以二求出，这样可平滑季节性波动。
Average Inventory = (Opening Inventory + Closing Inventory) ÷ 2
The trade receivables days ratio tells how long, on average, customers take to pay. Fewer days mean quicker cash inflow and lower risk of bad debts.
应收账款周转天数反映客户平均需要多少天付款。天数越少意味着现金流入越快，坏账风险越低。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
The trade payables days ratio measures how long a business takes to settle its own bills. Managing this balance is important: paying too early can strain cash flow, while delaying too long may harm supplier relationships.
应付账款周转天数衡量企业自身付清账单所需的平均时间。把握这一平衡很关键：付款过早会挤压现金流，拖欠过久则可能损害供应商关系。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
7. Return on Capital Employed (ROCE) | 资本回报率
Return on Capital Employed (ROCE) evaluates how efficiently a business uses its long‑term funds to generate profit. It is expressed as a percentage, and a higher ROCE indicates a more profitable use of capital.
资本回报率衡量企业利用长期资金创造利润的效率，以百分比表示。ROCE 越高，说明资本运用的盈利能力越强。
ROCE = (Net Profit before Interest and Tax ÷ Capital Employed) × 100
Capital employed usually represents the total long‑term finance invested in the business. It can be calculated as total assets minus current liabilities, or as shareholders’ equity plus non‑current liabilities.
资本运用额通常代表投入企业的长期资金总额，可以按总资产减去流动负债计算，也可按股东权益加上非流动负债计算。
Investors and lenders watch ROCE closely because it reveals whether the business is generating a sufficient return on the money entrusted to it. A falling ROCE trend can signal weakening competitiveness or rising inefficiency.
投资者和贷款人密切关注 ROCE，因为它揭示了企业是否在受托资金上获得足够回报。ROCE 呈下降趋势可能意味着竞争力减弱或效率下降。
8. Cash Flow Forecasting | 现金流预测
A cash flow forecast predicts the inflows and outflows of cash over a future period. It helps managers anticipate shortages and arrange overdraft facilities in advance.
现金流预测是对未来时期现金流入与流出的预估，有助于管理者预判资金缺口并提前安排透支额度。
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
The closing balance at the end of a period is the amount of cash remaining in the business. It becomes the opening balance for the next period.
期末现金余额是企业在期末持有的现金额，并将成为下一期的期初余额。
Closing Balance = Opening Balance + Net Cash Flow
Consistently positive net cash flows build a healthy cash buffer, while persistent negative flows can quickly lead to insolvency, even if the business is profitable on paper.
持续正净现金流能够建立起健康的现金储备，而持续负现金流则可能迅速导致偿债困难，即便企业账面盈利也是如此。
9. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand (PED) measures how responsive the quantity demanded is to a change in price. It helps businesses predict the impact of pricing decisions on sales volumes and revenue.
需求价格弹性衡量需求量对价格变动的反应程度，有助于企业预测定价决策对销售量和收入的影响。
PED = % Change in Quantity Demanded ÷ % Change in Price
If PED is greater than 1, demand is price elastic — a price cut leads to a proportionally larger rise in quantity demanded and can increase total revenue. If PED is less than 1, demand is price inelastic — a price rise causes a smaller percentage drop in sales, so revenue tends to rise.
若 PED 大于 1，需求富有弹性，降价会引来需求量更大幅度的上升，可能提高总收入；若 PED 小于 1，需求缺乏弹性，提价只会引起销售量较小百分比的下降，因此收入往往会增加。
When PED equals exactly 1 (unitary elasticity), the percentage change in quantity demanded is identical to the percentage change in price, leaving total revenue unchanged. Extremes include perfectly elastic demand (PED = ∞) and perfectly inelastic demand (PED = 0).
当 PED 恰好等于 1（单位弹性）时，需求量变化的百分比与价格变化的百分比相同，总收入不变。极端情况包括完全弹性需求（PED = ∞）和完全非弹性需求（PED = 0）。
10. Quick Reference Table of Core Formulas | 核心公式速查表
The table below consolidates the most frequently tested formulas. Use it as a last‑minute checklist before your exam — but always ensure you can explain the meaning behind each number, not merely reproduce it.
下表汇总了最常考查的公式，可作为考前最后一刻的自查清单——但请务必确保你能解释每个数字背后的含义，而不是简单地默写公式。
| Formula (English) | 公式（中文） |
|---|---|
| Total Revenue = Selling Price × Quantity | 总收入 = 售价 × 数量 |
| Total Costs = Fixed Costs + Variable Costs | 总成本 = 固定成本 + 可变成本 |
| Profit = Total Revenue − Total Costs | 利润 = 总收入 − 总成本 |
| Contribution per Unit = Selling Price − Variable Cost per Unit | 单位贡献 = 售价 − 单位可变成本 |
| Break‑even Output = Fixed Costs ÷ Contribution per Unit | 盈亏平衡产量 = 固定成本 ÷ 单位贡献 |
| Margin of Safety (units) = Actual Sales − Break‑even Sales | 安全边际（单位）= 实际销量 − 盈亏平衡销量 |
| Gross Profit Margin = (Gross Profit ÷ Revenue) × 100 | 毛利率 =（毛利润 ÷ 收入）× 100 |
| Net Profit Margin = (Net Profit ÷ Revenue) × 100 | 净利润率 =（净利润 ÷ 收入）× 100 |
| Current Ratio = Current Assets ÷ Current Liabilities | 流动比率 = 流动资产 ÷ 流动负债 |
| Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities | 速动比率 =（流动资产 − 存货）÷ 流动负债 |
| Inventory Turnover = Cost of Sales ÷ Average Inventory | 存货周转率 = 销售成本 ÷ 平均存货 |
| Trade Receivables Days = (Receivables ÷ Credit Sales) × 365 | 应收账款天数 =（应收账款 ÷ 赊销收入）× 365 |
| Trade Payables Days = (Payables ÷ Credit Purchases) × 365 | 应付账款天数 =（应付账款 ÷ 赊购额）× 365 |
| ROCE = (Net Profit before Interest & Tax ÷ Capital Employed) × 100 | 资本回报率 =（息税前净利润 ÷ 资本运用额）× 100 |
| Net Cash Flow = Cash Inflows − Cash Outflows | 净现金流 = 现金流入 − 现金流出 |
| Closing Balance = Opening Balance + Net Cash Flow | 期末余额 = 期初余额 + 净现金流 |
| PED = % Change in Quantity Demanded ÷ % Change in Price | 需求价格弹性 = 需求量变化百分比 ÷ 价格变化百分比 |
Keep this reference with your revision notes and test yourself regularly by covering one column and writing out the formulas from memory. Understanding how each formula connects to real‑world business decisions will give you a genuine edge in the exam.
将这份速查表与复习笔记放在一起，并定期进行自我检测：遮盖一栏，凭记忆写出公式。理解每一个公式与现实商业决策之间的关联，将让你在考试中真正脱颖而出。
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