📚 CCEA GCSE Business: Formula & Theorem Quick Reference | CCEA GCSE商务：公式定理速查手册
This quick reference handbook brings together all the essential formulas, ratios and key business theorems required for the CCEA GCSE Business Studies specification. Mastering these calculations will help you analyse financial statements, assess business performance and tackle quantitative questions with confidence. Every formula below is paired with a short explanation, a worked example and the interpretation an examiner expects to see.
本速查手册汇总了CCEA GCSE商务考试所需的所有关键公式、比率和基本商业定理。掌握这些计算方法，将帮助你分析财务报表、评估企业绩效，并自信应对定量计算题。下文每一条公式都配有简要说明、计算示例，以及考官期望看到的解读方式。
1. Revenue, Costs & Profit | 收入、成本与利润
Total Revenue = Selling Price per Unit × Quantity Sold
Total revenue is the income a business generates from selling its goods or services before any costs are deducted. It is the top-line figure on an income statement, and it rises either because the price rises, because the volume sold rises, or because both rise together.
总收入指企业在扣除任何成本之前，通过销售商品或服务所获得的收入。它是损益表上最顶端的数字。总收入上升的原因只有三种：售价上升、销量上升，或两者同时上升。
Total Costs = Fixed Costs + Variable Costs
Fixed costs do not change with output (e.g. rent, salaries, insurance), while variable costs vary directly with output (e.g. raw materials, packaging, piece-rate wages). Total costs are therefore the sum of the two, which means costs can only be controlled by attacking the fixed or the variable element separately.
固定成本不随产量变化（如租金、薪金、保险费），而可变成本随产量同向变动（如原材料、包装、计件工资）。因此总成本等于两者之和，这意味着控制成本必须分别从固定成本和可变成本两部分入手。
Profit = Total Revenue − Total Costs
Profit is what remains once every cost has been paid. If total costs exceed total revenue the business makes a loss. Profit is not the same as cash: a profitable business can still run out of cash if its customers pay late.
利润是支付全部成本之后剩余的部分。若总成本大于总收入，企业即发生亏损。利润并不等于现金：一家盈利的企业如果客户付款迟缓，仍然可能因现金短缺而陷入困境。
Average Unit Cost = Total Costs ÷ Output
A bakery sells 4,000 loaves at £1.50 each, so total revenue = 4,000 × £1.50 = £6,000. Fixed costs are £2,500, variable cost is £0.60 per loaf, so total variable cost = £2,400 and total cost = £4,900. Profit = £6,000 − £4,900 = £1,100, and average unit cost = £4,900 ÷ 4,000 = £ rises because fixed costs are spread over more units - this is called economies of scale.
某面包店以每个1.50英镑售出4,000个面包，总收入 = 4,000 × 1.50 = 6,000英镑。固定成本为2,500英镑，单位可变成本为0.60英镑，则总可变成本 = 2,400英镑，总成本 = 4,900英镑。利润 = 6,000 − 4,900 = 1,100英镑，平均单位成本 = 4,900 ÷ 4,000 = 1.225英镑/个。随着产量提高，平均单位成本会下降，因为固定成本被分摊到更多产品上，这就是规模经济。
2. Break-Even Analysis | 盈亏平衡分析
Break-Even Output = Fixed Costs ÷ (Selling Price − Variable Cost per Unit)
The bottom of the fraction (selling price minus variable cost per unit) is the contribution each sale makes towards paying off fixed costs. Break-even output is the number of units the business must sell for total revenue to equal total costs, at which point profit is exactly zero.
分母部分（单位售价减单位可变成本）是每卖出一件产品为抵补固定成本所做出的贡献。盈亏平衡产量就是企业必须卖出的、使总收入恰好等于总成本的数量，此时利润为零。
Break-Even Revenue = Break-Even Output × Selling Price
different products at different prices. Using the bakery figures: contribution per unit = £1.50 − £0.60 = £0.90, so break-even output = £2,500 ÷ £0.90 = 2,777.8, which must be rounded up to 2,778 loaves. Break-even revenue = 2,778 × £1.50 = £4,167.
盈亏平衡收入用金额表达同一概念，当企业以不同价格销售多种产品时尤为实用。仍用面包店的数字：单位贡献 = 1.50 − 0.60 = 0.90英镑，因此盈亏平衡产量 = 2,500 ÷ 0.90 = 2,777.8，必须向上取整为2,778个。盈亏平衡收入 = 2,778 × 1.50 = 4,167英镑。
| Accuracy rule | 精确规则 | Always round break-even output UP to the next whole unit, because you cannot sell part of a product and 2,777 units would still leave a small loss. | 盈亏平衡产量一律向上取整，因为无法卖出半个产品，2,777个仍会带来小额亏损。 |
| Chart reading | 图表解读 | On a break-even chart the total revenue line starts at the origin, the total cost line starts at the level of fixed costs, and the crossing point is break-even. | 在盈亏平衡图上，总收入线从原点出发，总成本线从固定成本的高度出发，两线交点即盈亏平衡点。 |
| Limitation | 局限性 | Break-even assumes costs and prices stay constant, which is rarely true in practice. | 盈亏平衡分析假设成本与价格保持不变，现实中很少成立。 |
3. Contribution & Margin of Safety | 边际贡献与安全边际
Contribution per Unit = Selling Price − Variable Cost per Unit
Contribution is the money left from each sale after variable costs have been paid, and it is the amount available to cover fixed costs and then generate profit. It is not the same as profit, because fixed costs have not yet been deducted.
边际贡献是每笔销售在支付可变成本之后剩余的部分，用于抵补固定成本，抵补完之后才形成利润。它不等于利润，因为固定成本尚未扣除。
Total Contribution = Contribution per Unit × Output
Profit = Total Contribution − Fixed Costs
al variable costs, which gives the same answer. In the bakery example total contribution = £0.90 × 4,000 = £3,600, and profit = £3,600 − £2,500 = £1,100, matching the earlier figure.
总贡献也可用总收入减总可变成本计算，结果相同。在面包店的例子中，总贡献 = 0.90 × 4,000 = 3,600英镑，利润 = 3,600 − 2,500 = 1,100英镑，与前面的结果一致。
Margin of Safety = Actual Output − Break-Even Output
Margin of Safety % = Margin of Safety ÷ Actual Output × 100
iness makes a loss. Here it is 4,000 − 2,778 = 1,222 loaves, or 1,222 ÷ 4,000 × 100 = 30.6% is resilient; a margin close to zero means a small fall in demand would push it into loss.
安全边际显示销售量在开始亏损之前还能下降多少。此处为4,000 − 2,778 = 1,222个，即1,222 ÷ 4,000 × 100 = 30.6%。安全边际高说明企业抗风险能力强；若接近零，则需求稍有下滑便会转为亏损。
4. Cash Flow Forecasting | 现金流量预测
Net Cash Flow = Cash Inflows − Cash Outflows
Closing Balance = Opening Balance + Net Cash Flow
A cash flow forecast records money actually moving in and out of the business in a given month, usually on a cash basis rather than an accruals basis. The closing balance of one month automatically becomes the opening balance of the next, so the forecast builds cumulatively.
现金流量预测记录某一月份企业实际流入与流出的现金，通常以收付实现制而非权责发生制编制。上月的期末余额自动成为下月的期初余额，因此预测是逐月累积的。
| Month | 月份 | Inflows £ | 流入 | Outflows £ | 流出 | Net £ | 净额 | Closing Balance £ | 期末余额 |
| January | 5,000 | 4,200 | +800 | 2,800 |
| February | 4,000 | 4,600 | −600 | 2,200 |
| March | 6,500 | 4,300 | +2,200 | 4,400 |
In this example the opening balance in January was £2,000. The business survives a negative month in February only because it built up a buffer in January, which is exactly why cash flow forecasting matters. Cash flow problems are usually caused by late payment from customers, too much credit offered, overstocking, or unexpected costs.
本示例中1月的期初余额为2,000英镑。企业能够挺过2月的净流出，全靠1月积累的缓冲资金，这正是现金流量预测的意义所在。现金流问题通常由客户延迟付款、赊销过多、库存积压或意外支出造成。
5. Profitability Ratios | 盈利能力比率
Gross Profit = Revenue − Cost of Sales
Gross Profit Margin = Gross Profit ÷ Revenue × 100
ue so that businesses of different sizes can be compared. Using the bakery: gross profit = £6,000 − £2,400 = £3,600, so gross profit margin = £3,600 ÷ £6,000 × 100 = 60%.
毛利润衡量的是在支付间接费用之前通过交易所获得的利润，毛利率则将其表示为收入的百分比，便于不同规模企业之间的比较。以面包店为例：毛利润 = 6,000 − 2,400 = 3,600英镑，毛利率 = 3,600 ÷ 6,000 × 100 = 60%。
Net Profit = Gross Profit − Expenses
Net Profit Margin = Net Profit ÷ Revenue × 100
rketing and interest, so it is the truer measure of overall performance. Here net profit = £3,600 − £2,500 = £1,100 and net profit margin = £1,100 ÷ £6,000 × 100 = 18.3%. A large gap between gross and net margin suggests overheads are too high.
净利润扣除租金、工资、营销费用和利息等全部剩余支出，因此更能真实反映整体经营绩效。此处净利润 = 3,600 − 2,500 = 1,100英镑，净利率 = 1,100 ÷ 6,000 × 100 = 18.3%。若毛利率与净利率差距很大，通常说明间接费用过高。
Return on Capital Employed = Operating Profit ÷ Capital Employed × 100
liabilities, or equivalently total assets − current liabilities. With operating profit of £1,100 and capital employed of £5,000, ROCE = 22%, meaning every £1 invested generates 22 pence of operating profit.
资本回报率（ROCE）反映投入企业的资金使用效率。运用资本 = 所有者权益总额 + 非流动负债，也等于总资产 − 流动负债。若营业利润为1,100英镑、运用资本为5,000英镑，则ROCE = 22%，意味着每投入1英镑可产生22便士的营业利润。
6. Liquidity & Efficiency Ratios | 流动性与效率比率
Current Ratio = Current Assets ÷ Current Liabilities
Acid Test Ratio = (Current Assets − Inventory) ÷ Current Liabilities
The current ratio tests whether a business can pay its short-term debts from short-term assets; a figure between 1.5:1 and 2:1 is usually considered healthy. The acid test removes inventory because stock may be hard to sell quickly, and a result close to 1:1 is acceptable. A current ratio of 3:1 may look strong but could indicate idle cash or unsold stock.
流动比率检验企业能否用短期资产偿还短期债务，一般认为1.5:1至2:1较为健康。速动比率剔除存货，因为库存可能不易迅速变现，接近1:1即可接受。流动比率达到3:1看似稳健，却可能意味着现金闲置或存货滞销。
Inventory Turnover = Cost of Sales ÷ Average Inventory
Receivables Days = Trade Receivables ÷ Revenue × 365
Payables Days = Trade Payables ÷ Cost of Sales × 365
age inventory = (opening inventory + closing inventory) ÷ 2. A rising receivables figure signals poor credit control, while a very long payables period may damage supplier relationships.
这些效率比率衡量存货周转速度、客户付款速度以及企业支付供应商所需时间。平均存货 =（期初存货 + 期末存货）÷ 2。应收账款天数上升说明信用管理不佳，而应付账款天数过长则可能损害与供应商的关系。
7. Market Share, Sales Growth & Market Size | 市场份额、销售增长与市场规模
Market Share % = Business Sales ÷ Total Market Sales × 100
Market share measures the proportion of total market sales captured by one business, and it can be calculated on the basis of value (money) or volume (units). If a firm sells £2 million in a market worth £20 million, its market share is 10%. Market share can rise even when total sales fall, provided rivals shrink faster.
市场份额衡量某企业占整个市场销售额的比例，可按金额（价值）或数量（销量）计算。若某企业在价值2,000万英镑的市场中销售200万英镑，其市场份额即为10%。只要竞争对手萎缩得更快，即使企业自身销售额下降，市场份额也可能上升。
Sales Growth % = (Current Year Sales − Previous Year Sales) ÷ Previous Year Sales × 100
Market Size Growth % = (Current Market Size − Previous Market Size) ÷ Previous Market Size × 100
If sales rise from £1.8 million to £2 million, growth = (£2m − £1.8m) ÷ £1.8m × 100 = 11.1%. Comparing a firm' ter than the market means market share is rising; growing more slowly means it is falling.
若销售额从180万英镑增至200万英镑，则增长率 =（200万 − 180万）÷ 180万 × 100 = 11.1%。将企业增长率与市场增长率对比是常见考点：增长快于市场意味着市场份额上升；增长慢于市场则意味着份额下降。
