📚 Business Formulas & Theorems Quick Reference | 商务公式定理速查手册
This quick reference handbook brings together all the essential formulas and theorems that you need to master for the Year 10 OCR GCSE Business course. Whether you are calculating profit, evaluating investment opportunities using ARR, or checking liquidity with the current ratio, having these key relationships at your fingertips will help you work confidently through data-response questions and multiple-choice tests. Keep this guide beside you while practising past papers, and you will soon find that applying the formulas becomes second nature.
本速查手册汇集了Year 10 OCR GCSE商务课程需要掌握的所有核心公式与定理。不论是计算利润、运用平均报酬率（ARR）评估投资机会，还是用流动比率检查企业流动性，熟记这些关键关系都能让你更有信心地应对数据分析题和选择题。练习历年真题时，把这本指南放在手边，你很快就会发现公式的运用变得得心应手。
1. Revenue and Profit | 收入与利润
Revenue is the total income generated from selling goods or services before any costs are deducted. It is calculated by multiplying the selling price per unit by the quantity sold. Revenue is often called the 'top line' because it sits at the top of an income statement.
收入是指企业在扣除任何成本之前，通过销售产品或服务所获得的总收入。它由单位售价乘以销售数量计算得出。收入通常被称为“顶行”，因为它在利润表中位于最上方。
Revenue = Selling Price per Unit × Quantity Sold
Profit is what remains after all costs have been subtracted from revenue. Two types of profit are commonly used: gross profit, which subtracts only the cost of sales, and net profit, which also accounts for expenses and overheads. Profits can be reinvested in the business or distributed to owners.
利润是收入减去所有成本后的剩余部分。常用的利润有两种：毛利（仅减去销售成本）和净利润（进一步扣除费用和间接成本）。利润可以再投资于企业，也可以分配给所有者。
Profit = Total Revenue – Total Costs
2. Total Costs, Fixed Costs and Variable Costs | 总成本、固定成本与变动成本
Total costs represent the full expense of running a business. They are made up of fixed costs, which do not vary with output, and variable costs, which change directly with the level of production or sales.
总成本代表企业运营的全部支出。它由固定成本（不随产出变化）和变动成本（直接随产量或销量变化）两部分组成。
Total Costs = Fixed Costs + Variable Costs
Fixed costs include items such as rent, salaries, insurance premiums and straight-line depreciation. Even if the business produces zero units, fixed costs must still be paid in the short run. Variable costs include raw materials, packaging and piece-rate wages. As output increases, total variable costs rise proportionally.
固定成本包括租金、薪金、保险费和直线折旧等项目。即使企业产量为零，在短期内也必须支付固定成本。变动成本包括原材料、包装和计件工资。随着产量增加，总变动成本按比例上升。
Variable Costs = Variable Cost per Unit × Quantity Produced
3. Contribution per Unit and Total Contribution | 单位贡献与总贡献
Contribution is the amount of revenue remaining after variable costs have been covered. It 'contributes' towards paying fixed costs and, once they are covered, towards profit. Managers use contribution to make pricing and product-range decisions.
贡献是指收入在覆盖变动成本后的剩余金额。它“贡献”于支付固定成本，并在固定成本得以覆盖后贡献于利润。管理者利用贡献来做定价和产品组合决策。
Contribution per Unit = Selling Price per Unit – Variable Cost per Unit
Total contribution is found by multiplying the unit contribution by the number of units sold. It can also be expressed as total revenue minus total variable costs. If total contribution equals fixed costs, the business reaches its break-even point.
总贡献由单位贡献乘以销售数量得出，也可以表示为总收入减去总变动成本。如果总贡献等于固定成本，企业就达到了盈亏平衡点。
Total Contribution = Contribution per Unit × Quantity Sold = Total Revenue – Total Variable Costs
4. Break-Even Point (Units) | 盈亏平衡点（单位）
The break-even point is the level of output at which total revenue exactly equals total costs, resulting in neither a profit nor a loss. It is one of the most important planning tools for new enterprises and for launching new products. The formula uses contribution per unit to show how many items must be sold to cover all fixed costs.
盈亏平衡点是指总收入恰好等于总成本时的产出水平，企业不盈不亏。它是新企业创业和推出新产品时最重要的规划工具之一。该公式利用单位贡献来表示必须销售多少件产品才能覆盖全部固定成本。
Break-even Point (units) = Fixed Costs ÷ Contribution per Unit
To use the formula correctly, always check that the selling price and variable cost per unit are based on the same time period. The break-even chart can also be used to display the break-even point visually, along with the margin of safety.
使用公式时要确保单位售价和单位变动成本基于相同的时间段。盈亏平衡图也可用于直观展示盈亏平衡点以及安全边际。
5. Margin of Safety | 安全边际
The margin of safety measures how much sales can fall before the business reaches its break-even point. It is a key indicator of risk: the wider the margin, the lower the risk of making a loss. It may be expressed in units or as a monetary value.
安全边际衡量的是在达到盈亏平衡点之前销售额可以下降多少。它是一个关键的风险指标：安全边际越宽，发生亏损的风险越低。安全边际可以用销售数量或金额来表示。
Margin of Safety (units) = Actual Sales (units) – Break-even Sales (units)
For example, if a business sells 1,000 units and the break-even point is 750 units, the margin of safety is 250 units. This means sales could drop by 250 units before the business starts making a loss.
例如，如果某企业销售1 000件产品，盈亏平衡点为750件，那么安全边际就是250件。这意味着在开始亏损之前，销量可以下降250件。
6. Gross Profit Margin | 毛利率
The gross profit margin shows the percentage of revenue that remains after subtracting the cost of sales. It is a measure of how efficiently a business turns raw materials and direct labour into revenue. A high or improving gross profit margin suggests strong pricing power or effective cost control in production.
毛利率显示扣除销售成本后剩余收入占收入的百分比。它衡量的是企业将原材料和直接人工转化为收入的效率。毛利率高或者不断改善，表明企业在生产环节具有强大的定价能力或有效的成本控制。
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
Gross profit is calculated as revenue minus cost of sales. Cost of sales includes direct materials, direct labour and manufacturing overheads. Comparing the gross profit margin with industry averages helps businesses benchmark their performance.
毛利等于收入减去销售成本。销售成本包括直接材料、直接人工和制造费用。将毛利率与行业平均水平进行比较，有助于企业衡量自身表现。
7. Net Profit Margin | 净利率
Net profit margin reveals what percentage of every pound of revenue turns into net profit after all expenses – including overheads, finance costs and possibly tax – have been deducted. It is a comprehensive performance indicator that reflects the overall efficiency of the business.
净利率揭示了在扣除所有费用（包括间接成本、融资成本，有时还包括税款）之后，每一英镑收入中有多大比例转化为了净利润。它是一个反映企业整体效率的综合性绩效指标。
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
A falling net profit margin might result from rising energy bills, increased marketing spend or higher interest payments. Because net profit is the 'bottom line', this margin is watched closely by shareholders and lenders.
净利率下降可能源于能源账单上涨、营销支出增加或利息支付上升。由于净利润是“底行”，这一比率受到股东和贷款人的密切关注。
8. Average Rate of Return (ARR) | 平均报酬率
The average rate of return is a capital budgeting technique used to evaluate the profitability of an investment project. It expresses the average annual profit as a percentage of the initial investment. ARR is popular because it is easy to calculate, but it ignores the time value of money.
平均报酬率是一种资本预算技术，用于评估投资项目的盈利能力。它将平均年利润表示为初始投资的百分比。ARR之所以流行，是因为它容易计算，但它忽略了货币的时间价值。
ARR = (Average Annual Profit ÷ Initial Investment) × 100%
To find the average annual profit, add up all the net cash inflows over the project's life, subtract the initial investment to get total profit, then divide by the number of years. A project with a higher ARR is generally preferred, provided it meets the company's target rate.
要计算平均年利润，首先将项目寿命期内所有净现金流入相加，减去初始投资得到总利润，再除以年数。一般来说，只要满足公司的目标回报率，ARR较高的项目更受青睐。
9. Return on Capital Employed (ROCE) | 已用资本回报率
ROCE measures how efficiently a business uses its long-term capital to generate profit. Capital employed typically includes shareholders' equity and non-current liabilities. A high and stable ROCE indicates that the business is good at turning invested money into profit.
ROCE衡量企业使用长期资本创造利润的效率。已用资本通常包括股东权益和非流动负债。ROCE高且稳定，表明企业善于将投入的资金转化为利润。
ROCE = (Net Profit ÷ Capital Employed) × 100%
At Year 10 level, capital employed is often simplified to total equity plus long-term loans, or even just total assets minus current liabilities, depending on the information provided. ROCE is a key profitability ratio that external investors examine before committing funds.
在Year 10阶段，已用资本通常简化为总权益加长期借款，或者甚至只是总资产减去流动负债，这取决于所提供的信息。ROCE是外部投资者投入资金前会审视的关键盈利比率。
10. Liquidity Ratios: Current Ratio and Acid Test Ratio | 流动比率与速动比率
Liquidity ratios assess a firm's ability to meet its short-term debts as they fall due. The current ratio compares total current assets with current liabilities, while the acid test ratio (quick ratio) adopts a stricter approach by excluding inventory, which may take longer to convert into cash.
流动性比率评估企业偿付到期短期债务的能力。流动比率将流动资产总额与流动负债进行比较，而速动比率（酸性测试比率）则采用更严格的方法，排除了变现速度可能较慢的存货。
Current Ratio = Current Assets ÷ Current Liabilities
Acid Test Ratio = (Current Assets – Inventory) ÷ Current Liabilities
A current ratio of between 1.5:1 and 2:1 is often regarded as healthy, while an acid test ratio of 1:1 or above suggests the business can pay its immediate liabilities without relying on inventory sales. Ratios that are too high may mean the company is holding too much idle cash.
流动比率在1.5:1至2:1之间通常被视为健康，而速动比率为1:1或以上表明企业无需依赖存货销售就能支付即时负债。比率太高可能意味着公司持有过多闲置现金。
11. Net Cash Flow and Closing Balance | 净现金流量与期末余额
Cash flow is the movement of money into and out of a business over a period. Net cash flow is simply the difference between total cash inflows (receipts) and total cash outflows (payments). A positive net cash flow adds to the business's cash balance, while a negative net cash flow reduces it.
现金流是在一段时期内企业资金的流入与流出。净现金流量就是现金流入总额（收入）与现金流出总额（支出）之间的差额。正的净现金流量会使企业现金余额增加，而负的净现金流量会使之减少。
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
The closing balance at the end of a month is found by adding the net cash flow for that month to the opening balance. The closing balance then becomes the opening balance for the following month. Cash flow forecasts are vital for identifying potential overdrafts well in advance.
月末期末余额由当月净现金流量加上期初余额得出。期末余额随即成为下个月的期初余额。现金流量预测对于提前发现潜在透支至关重要。
Closing Balance = Opening Balance + Net Cash Flow
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