📚 Year 10 CCEA Business: Formulae & Theorems Quick Reference Handbook | Year 10 CCEA 商务公式定理速查手册
This quick reference handbook compiles the essential formulas and theorems for Year 10 CCEA GCSE Business Studies. Whether you are calculating break-even, analysing profitability, or interpreting cash flow, these key equations will support your revision and exam preparation. Each formula is presented with a brief explanation and direct Chinese translation to help bilingual learners master the content efficiently.
本速查手册汇集了Year 10 CCEA GCSE商务课程的核心公式和定理。无论你是计算盈亏平衡、分析盈利能力还是解读现金流，这些关键公式都将助力你的复习与备考。每个公式都附有简要说明和中英文对照，帮助双语学习者高效掌握内容。
1. Revenue, Costs and Profit | 收入、成本与利润
Total Revenue = Price × Quantity
Total Revenue (TR) is the income a business receives from selling its goods or services. It is calculated by multiplying the selling price per unit by the number of units sold.
总收入（TR）是企业销售商品或服务获得的收入，由单位售价乘以销售数量计算得出。
Total Cost = Fixed Costs + Variable Costs
Total Cost (TC) is the sum of all expenses needed to produce a given level of output. Fixed costs remain unchanged regardless of output, while variable costs change directly with the level of production.
总成本（TC）是生产一定产量所需的全部费用之和。固定成本不论产量高低均保持不变，可变成本则随产量增减而直接变动。
Profit = Total Revenue − Total Cost
Profit is the financial gain a business makes when revenue exceeds costs. If total costs are greater than total revenue, the business makes a loss.
利润是企业收入超过成本时获得的财务收益。若总成本大于总收入，企业就发生亏损。
Contribution per unit = Selling Price per unit − Variable Cost per unit
Contribution is the amount left from each unit sold after covering variable costs. It contributes towards paying fixed costs and generating profit.
单位贡献毛益是每销售一个单位产品在扣除可变成本后剩余的金额，用于弥补固定成本并创造利润。
Total Contribution = Contribution per unit × Quantity Sold
Total contribution represents the overall amount available to cover fixed costs and earn profit. Profit can also be expressed as Total Contribution − Fixed Costs.
总贡献表示可用于覆盖固定成本和获取利润的总金额。利润也可表示为总贡献 − 固定成本。
2. Break-even Analysis | 盈亏平衡分析
Break-even Point (units) = Fixed Costs ÷ Contribution per unit
The break-even point is the level of output at which total revenue equals total costs, meaning the business makes neither a profit nor a loss. This formula tells you how many units must be sold just to cover all costs.
盈亏平衡点是总收入等于总成本的产量水平，即企业既不盈利也不亏损。此公式可算出需要销售多少单位才能刚好覆盖所有成本。
Break-even Point (£) = Fixed Costs ÷ Contribution Margin Ratio
argin ratio. The contribution margin ratio = (Contribution per unit ÷ Selling Price) × 100%.
以销售额表示的盈亏平衡点，可用固定成本除以贡献毛益率求得。贡献毛益率 = （单位贡献毛益 ÷ 售价） × 100%。
Contribution Margin Ratio = (Contribution per unit ÷ Selling Price) × 100%
This ratio shows the proportion of each pound of sales that contributes towards fixed costs and profit. It is useful for calculating break-even revenue quickly.
该比率显示每一英镑销售收入中用于弥补固定成本和创造利润的比例，有助于快速计算盈亏平衡收入额。
3. Margin of Safety | 安全边际
Margin of Safety (units) = Actual Output − Break-even Output
Margin of safety shows how much sales can fall before the business reaches its break-even point and starts making a loss. It is a measure of risk.
安全边际表明销售量下降多少后企业会达到盈亏平衡点并开始亏损，是衡量风险的指标。
Margin of Safety (£) = Margin of Safety (units) × Selling Price
This converts the safety margin into monetary terms. A higher margin of safety in pounds means greater protection against a downturn in sales.
这将安全边际转换为货币形式。以货币计量的安全边际越大，抵御销售下滑的保护程度就越高。
Margin of Safety (%) = (Margin of Safety (units) ÷ Actual Output) × 100%
Expressed as a percentage, the margin of safety makes it easy to compare risk across different products or time periods.
以百分比表示的安全边际便于比较不同产品或不同时期的风险高低。
4. Profit Margins | 利润率
Gross Profit = Sales Revenue − Cost of Sales
Gross profit is the profit a business makes after deducting the direct costs of producing its goods or services. It does not yet account for overheads or other operating expenses.
毛利是企业扣除生产商品或服务的直接成本后获得的利润，尚未考虑间接费用或其他经营开支。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100%
This ratio indicates how efficiently a business turns its sales into gross profit. A higher margin suggests better control over production costs.
该比率反映企业将销售收入转化为毛利的效率。毛利率越高，说明对生产成本的管控越好。
Net Profit = Gross Profit − Operating Expenses and Interest
Net profit is the actual profit after all expenses have been deducted. It is the 'bottom line' that shows the overall financial performance.
净利润是扣除所有费用后的实际利润，即显示整体财务表现的'底线'利润。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100%
This measures what percentage of each pound of sales ends up as profit after all costs. It is a key indicator of overall profitability.
净利率衡量每一英镑销售收入在扣除所有成本后最终转化为利润的比例，是总体盈利能力的关键指标。
5. Return on Investment | 投资回报率
Return on Investment (ROI) = (Net Profit ÷ Cost of Investment) × 100%
ROI evaluates the efficiency of an investment. It shows the percentage return relative to the money put in.
投资回报率（ROI）用以评估投资效率，显示相对于投入资金的百分比回报。
Return on Capital Employed (ROCE) = (Operating Profit ÷ Capital Employed) × 100%
ROCE measures how well a business uses its long-term capital to generate profits. Capital employed is often calculated as Total Assets − Current Liabilities.
资本回报率（ROCE）衡量企业运用长期资本创造利润的能力。资本使用额通常按总资产 − 流动负债计算。
6. Liquidity Ratios | 流动性比率
Current Ratio = Current Assets ÷ Current Liabilities
The current ratio shows whether a business has enough short-term assets to cover its short-term debts. A ratio above 1 is generally considered healthy.
流动比率显示企业是否有足够的短期资产偿还短期债务。比率高于1通常被视为健康。
Acid Test Ratio (Quick Ratio) = (Current Assets − Inventory) ÷ Current Liabilities
The acid test ratio is a stricter measure of liquidity as it excludes inventory, which may take longer to convert into cash. It focuses on the most liquid assets.
酸性测试比率（速动比率）是更严格的流动性指标，因为它剔除了存货，后者变现速度可能较慢。它重点关注流动性最强的资产。
7. Efficiency Ratios | 效率比率
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
This ratio measures how many times a business sells and replaces its inventory over a period. A higher turnover usually indicates efficient inventory management.
该比率衡量企业在一个时期内销售并补充存货的次数。周转率越高，通常说明存货管理越高效。
Inventory Turnover (days) = (Average Inventory ÷ Cost of Sales) × 365
Expressed in days, this shows how long it takes on average to sell the inventory. Shorter holding periods often improve cash flow.
以天数表示，反映平均需要多少天才能售出存货。持有期越短，往往对现金流越有利。
Trade Receivables Days = (Trade Receivables ÷ Credit Sales) × 365
This calculates the average number of days it takes for a business to collect money from customers who bought on credit. Shorter collection periods are generally better.
该公式计算企业平均需要多少天才能从赊销客户那里收回款项。回收期越短通常越好。
Trade Payables Days = (Trade Payables ÷ Credit Purchases) × 365
This shows the average time a business takes to pay its suppliers. Longer payment periods can help cash flow but must not damage supplier relationships.
该指标显示企业平均需要多少天向供应商付款。付款期较长有助于现金流，但不可损害与供应商的关系。
8. Productivity and Unit Cost | 生产力与单位成本
Labour Productivity = Total Output ÷ Number of Workers
Labour productivity measures the efficiency of the workforce. A higher output per worker means more is being produced with the same number of employees.
劳动生产率衡量员工的效率。人均产出越高，意味着用相同人数生产的产品更多。
Unit Labour Cost = Total Labour Cost ÷ Total Output
This formula shows the labour cost embedded in each unit of output. Firms aim to keep unit labour costs low to remain competitive.
该公式显示每一单位产出中所包含的人工成本。企业力求保持较低的单位人工成本以维持竞争力。
9. Market Position Ratios | 市场地位比率
Market Share = (Company Sales ÷ Total Market Sales) × 100%
Market share indicates the portion of a market controlled by a particular business. It is a key measure of competitiveness and brand strength.
市场份额表明某个企业所控制的市场部分。它是衡量竞争力和品牌实力的关键指标。
Market Size = Total Sales Revenue of All Firms in the Market
Market size is the total value or volume of sales in a given market. It is needed to calculate market share.
市场规模是某一市场中所有企业的销售总额或总量，用于计算市场份额。
Market Growth (%) = ((New Market Size − Old Market Size) ÷ Old Market Size) × 100%
Market growth shows how much the overall market has expanded or contracted over a period. Positive growth signals increasing demand.
市场增长率显示整个市场在一段时期内扩大或缩小的幅度。正增长表示需求在上升。
10. Price Elasticity of Demand | 需求价格弹性
Price Elasticity of Demand (PED) = % Change in Quantity Demanded ÷ % Change in Price
PED measures how responsive the demand for a product is to a change in its price. It helps businesses predict how price changes affect total revenue.
需求价格弹性（PED）衡量产品需求量对价格变动的反应程度，有助于企业预测价格变动如何影响总收入。
% Change = ((New Value − Original Value) ÷ Original Value) × 100%
To calculate PED, first compute the percentage changes in quantity demanded and in price using this formula. If PED > 1, demand is elastic; if PED < 1, demand is inelastic.
计算PED时，先用此公式分别计算需求量和价格的变动百分比。若PED大于1，需求富有弹性；若PED小于1，需求缺乏弹性。
11. Cash Flow | 现金流
Net Cash Flow = Total Cash Inflows − Total Cash Outflows
Net cash flow is the difference between cash coming into and going out of a business during a specific period. A positive net cash flow means more cash was received than spent.
净现金流量是指某一时期内流入企业的现金与流出企业的现金之间的差额。净现金流量为正，表示收到的现金多于支出的现金。
Closing Balance = Opening Balance + Net Cash Flow
The closing balance at the end of a month becomes the opening balance for the next month. This formula helps forecast how cash reserves will change over time.
期末余额就是下一个月的期初余额。该公式有助于预测现金储备随着时间推移会如何变化。
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