📚 Year 8 Cambridge Business: Formula & Theorem Quick-Reference Handbook | 八年級劍橋商務：公式定理速查手冊
Mastering key formulas and theorems is essential for success in Year 8 Cambridge Business. This quick‑reference handbook brings together the most important equations you will encounter when analysing business performance, calculating profits, and making financial decisions. Each entry explains what the formula measures, how to use it, and a worked example to reinforce your understanding.
掌握关键公式和定理对于在八年級劍橋商務课程中取得成功至关重要。这本速查手册汇集了你在分析企业绩效、计算利润和做出财务决策时会遇到的最重要的公式。每个条目都解释了该公式衡量什么、如何使用，并附有实例以巩固你的理解。
1. Revenue Formula | 收入公式
Revenue is the total income earned by a business from selling its products or services before any costs are deducted. It is also called turnover or sales revenue. The formula is straightforward:
收入是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。它也被称为营业额或销售收入。公式非常简单：
Revenue = Selling Price per unit × Quantity Sold
mber of units the business manages to sell. For example, if a bakery sells 200 cupcakes at $3 each, then Revenue = $3 × 200 = $600.
单位售价是顾客为购买单件商品支付的金额，销售数量是企业实际售出的商品件数。例如，如果一家面包店以每个3美元的价格出售了200个纸杯蛋糕，那么收入 = 3美元 × 200 = 600美元。
2. Total Costs Formula | 总成本公式
Total costs represent the full expenditure that a business incurs while producing and selling its goods or services. Costs are split into two broad categories: fixed costs and variable costs.
总成本代表企业在生产和销售商品或服务过程中发生的全部支出。成本分为两大类：固定成本和变动成本。
Total Costs = Fixed Costs + Variable Costs
like raw materials and packaging, change directly with the level of output. If a firm pays $1,000 in fixed costs each month and its variable costs total $2 per unit for 500 units, then Total Costs = $1,000 + ($2 × 500) = $2,000.
固定成本，如租金和保险，不随产量变化而变化。变动成本，如原材料和包装，直接随着产出水平变化。如果一家公司每月的固定成本为1,000美元，变动成本为每件2美元，共生产500件，那么总成本 = 1,000美元 + (2美元 × 500) = 2,000美元。
3. Profit Formula | 利润公式
Profit is the financial reward a business receives after deducting all costs from its revenue. Profit is a fundamental indicator of business success. The profit formula is:
利润是企业在从收入中扣除所有成本后获得的财务回报。利润是衡量企业成功与否的基本指标。利润公式为：
Profit = Total Revenue – Total Costs
the business makes a loss. For instance, a mobile phone case seller has monthly revenue of $4,500 and total costs of $3,200. Profit = $4,500 – $3,200 = $1,300.
如果总收入超过总成本，企业就盈利。如果总成本大于总收入，企业就亏损。例如，一家手机壳卖家的月收入为4,500美元，总成本为3,200美元。利润 = 4,500美元 – 3,200美元 = 1,300美元。
4. Contribution per Unit | 单位贡献
Contribution is not the same as profit. It is the amount left over from the selling price after variable costs have been subtracted. This money contributes towards paying off fixed costs and, once they are covered, towards profit.
贡献与利润不同。它是售价减去变动成本后剩下的金额。这笔钱用于抵消固定成本，固定成本被覆盖后则成为利润。
Contribution per Unit = Selling Price per Unit – Variable Cost per Unit
Imagine a company sells sunglasses for $25 a pair. The variable cost to make one pair is $15. Contribution per unit = $25 – $15 = $10. This $10 from each sale is used to cover fixed costs such as shop rent and staff salaries.
假设一家公司以每副25美元的价格出售太阳镜。生产一副太阳镜的变动成本为15美元。单位贡献 = 25美元 – 15美元 = 10美元。每卖出一副所获得的10美元用于支付店铺租金和员工工资等固定成本。
5. Break-even Point (Units) | 盈亏平衡点（单位）
The break‑even point is the level of output at which total revenue equals total costs. At this point the business makes neither a profit nor a loss. The break‑even formula is:
盈亏平衡点是指总收入等于总成本时的产出水平。在这一点上，企业既不盈利也不亏损。盈亏平衡公式为：
Break‑even (units) = Fixed Costs ÷ Contribution per Unit
Alternatively, you can write it as Fixed Costs ÷ (Selling Price per unit – Variable Cost per unit). If a business has fixed costs of $2,000, a selling price of $20 per unit, and a variable cost of $12 per unit, contribution per unit is $8. Break‑even = $2,000 ÷ $8 = 250 units. The business must sell 250 units to cover all its costs.
你也可以将其写为：固定成本 ÷ (单位售价 – 单位变动成本)。如果一家企业的固定成本为2,000美元，单位售价为20美元，单位变动成本为12美元，则单位贡献为8美元。盈亏平衡点 = 2,000美元 ÷ 8美元 = 250件。该企业必须销售250件才能覆盖所有成本。
6. Gross Profit and Gross Profit Margin | 毛利与毛利率
Gross profit shows how much money a business makes after paying the direct costs of producing its goods (cost of sales). It does not include overheads like administrative expenses. The gross profit margin expresses this as a percentage of revenue, helping compare profitability across different periods or companies.
毛利润显示企业在支付了直接生产成本（销售成本）后赚了多少钱。它不包括管理费用等间接费用。毛利率将毛利润表示为收入的百分比，有助于比较不同时期或不同公司的盈利能力。
Gross Profit = Revenue – Cost of Sales
Gross Profit Margin = (Gross Profit ÷ Revenue) × 100%
If a clothing store has revenue of $50,000 and the cost of the clothes sold is $30,000, gross profit = $20,000. Gross profit margin = ($20,000 ÷ $50,000) × 100% = 40% is means for every dollar of sales, the store keeps 40 cents after paying for the clothes.
如果一家服装店的收入为50,000美元，所售服装成本为30,000美元，则毛利润 = 20,000美元。毛利率 = (20,000美元 ÷ 50,000美元) × 100% = 40%。这意味着每赚取1美元销售额，商店在支付服装成本后可保留40美分。
7. Net Profit and Net Profit Margin | 净利与净利率
Net profit is the final profit figure after deducting all business expenses, including operating costs, interest and taxes. Net profit margin shows what percentage of revenue remains as true profit.
净利是扣除所有经营费用（包括运营成本、利息和税费）后的最终利润数字。净利率表明收入中有多大比例作为真正的利润保留下来。
Net Profit = Gross Profit – Expenses
Net Profit Margin = (Net Profit ÷ Revenue) × 100%
ontinuing the clothing store example, if total expenses (rent, wages, utilities) amount to $8,000, then net profit = $20,000 – $8,000 = $12,000. Net profit margin = ($12,000 ÷ $50,000) × 100% = 24%. The store keeps 24 cents as final profit from each dollar of sales.
继续以服装店为例，如果总费用（租金、工资、水电）为8,000美元，那么净利 = 20,000美元 – 8,000美元 = 12,000美元。净利率 = (12,000美元 ÷ 50,000美元) × 100% = 24%。该商店从每1美元销售额中获得24美分的最终利润。
8. Working Capital | 营运资金
Working capital measures the short‑term financial health of a business – its ability to pay day‑to‑day expenses and meet immediate debts. A positive working capital figure means the business can cover its short‑term liabilities with its short‑term assets.
营运资金衡量企业的短期财务健康状况——即其支付日常开支和偿还即时债务的能力。正的营运资金意味着企业可以用流动资产偿还流动负债。
Working Capital = Current Assets – Current Liabilities
ey Current assets include cash, inventory and money owed by customers (receivables). Current liabilities include bank overdrafts, suppliers' bills (payables) and short‑term loans. For example, if a firm has current assets of $15,000 and current liabilities of $9,000, working capital = $15,000 – $9,000 = $6,000. The firm has a $6,000 safety cushion.
流动资产包括现金、库存和客户欠款（应收账款）。流动负债包括银行透支、供应商欠款（应付账款）和短期贷款。例如，如果一家公司的流动资产为15,000美元，流动负债为9,000美元，则营运资金 = 15,000美元 – 9,000美元 = 6,000美元。该公司拥有6,000美元的安全缓冲。
9. Current Ratio | 流动比率
The current ratio is another way to assess liquidity. It compares a business’s current assets to its current liabilities as a ratio rather than a monetary amount. A ratio between 1.5 : 1 and 2 : 1 is often considered healthy.
流动比率是评估流动性的另一种方式。它将企业的流动资产与流动负债进行比较，以比率而非金额的形式表示。通常认为1.5 : 1到2 : 1之间的比率是健康的。
Current Ratio = Current Assets ÷ Current Liabilities
Using the same figures, current assets = $15,000 and current liabilities = $9,000, the current ratio = $15,000 ÷ $9,000 = 1.67 : 1. This means the business has $1.67 in current assets for every $1 of current liabilities, indicating good short‑term financial stability.
使用相同的数字，流动资产 = 15,000美元，流动负债 = 9,000美元，流动比率 = 15,000美元 ÷ 9,000美元 = 1.67 : 1。这意味着企业每1美元的流动负债有1.67美元的流动资产支持，表明短期财务状况良好。
10. Acid Test (Quick) Ratio | 速动比率
The acid test ratio is a stricter measure of liquidity because it removes inventory from current assets. Inventory can be difficult to turn into cash quickly, so this ratio tells you whether a business can pay its immediate debts without relying on selling stock.
速动比率是一种更严格的流动性衡量标准，因为它从流动资产中剔除了库存。库存有时难以迅速变现，因此该比率告诉你企业是否无需依赖出售存货就能偿还即时债务。
Acid Test Ratio = (Current Assets – Inventory) ÷ Current Liabilities
If the previous firm has $3,000 of inventory, then quick assets = $15,000 – $3,000 = $12,000. Acid test ratio = $12,000 ÷ $9,000 = 1.33 : 1. Since the ratio is above 1, the firm can meet its short‑term obligations even if it cannot sell its inventory right away.
如果前述公司的库存为3,000美元，那么速动资产 = 15,000美元 – 3,000美元 = 12,000美元。速动比率 = 12,000美元 ÷ 9,000美元 = 1.33 : 1。由于比率高于1，即使无法立即出售库存，该公司也能偿还短期债务。
11. Mark-up and Margin | 加成率与利润率
Mark‑up and margin are both used to set prices and measure profitability, but they are calculated differently. Mark‑up is based on cost, whereas margin is based on the selling price. Understanding the difference is important for pricing decisions.
加成率和利润率都用于定价和衡量盈利能力，但它们的计算方式不同。加成率基于成本，而利润率基于售价。理解两者的区别对于定价决策很重要。
Mark‑up (%) = (Gross Profit ÷ Cost of Sales) × 100%
Margin (%) = (Gross Profit ÷ Revenue) × 100%
Suppose a shop buys a lamp for $40 and sells it for $60. Gross profit = $20. Mark‑up = ($20 ÷ $40) × 100% = 50%. The seller has added 50% to the cost. Margin = ($20 ÷ $60) × 100% = 33.3%. The profit represents 33.3% of the selling price. The two percentages differ because they use different base figures.
假设一家商店以40美元购入一盏台灯，以60美元售出。毛利润 = 20美元。加成率 = (20美元 ÷ 40美元) × 100% = 50%。卖家在成本基础上加成了50%。利润率 = (20美元 ÷ 60美元) × 100% = 33.3%。利润占售价的33.3%。由于使用的基数不同，两个百分比也不同。
12. Budget Variance | 预算差异
A budget is a financial plan, and a variance measures the difference between the planned (budgeted) figure and the actual outcome. Variances can be favourable (better than planned) or adverse (worse than planned). This helps managers control finances.
预算是财务计划，而差异衡量计划（预算）数字与实际结果之间的差额。差异可以是顺差（好于计划）或逆差（差于计划）。这有助于管理者控制财务。
Variance = Actual Figure – Budgeted Figure
use actual spending is more than planned. For instance, if a marketing department budgeted $5,000 but actually spent $4,200, the variance = $4,200 – $5,000 = –$800. A negative $800 variance on costs is favourable – the department underspent and saved money.
对于收入，正的差异是顺差，因为实际销售高于预期。对于成本，正的差异是逆差，因为实际支出高于计划。例如，如果营销部门预算为5,000美元，但实际只花了4,200美元，差异 = 4,200美元 – 5,000美元 = –800美元。成本上负的800美元差异是顺差——该部门支出低于预算，节省了资金。
Published by TutorHao | Business Revision Series | aleveler.com
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