IGCSE Edexcel Business: Calculation Practice | IGCSE Edexcel 商务计算题专项训练

📚 IGCSE Edexcel Business: Calculation Practice | IGCSE Edexcel 商务计算题专项训练

This article is designed to sharpen your calculation skills for the IGCSE Edexcel Business exam. Each section presents a key formula, a worked example, and step-by-step explanations to help you tackle quantitative questions with confidence. Practise these methods repeatedly to improve speed and accuracy.

本文旨在为 IGCSE Edexcel 商务考试磨炼计算技能。每个部分都展示关键公式、示例解析和分步说明，帮助你自信地应对量化题目。反复练习这些方法，以提高解题速度和准确性。

1. Revenue, Total Costs and Profit | 收入、总成本与利润

Revenue is the income generated from selling goods or services. It is calculated by multiplying the selling price per unit by the quantity sold. The formula is:

收入是销售商品或服务产生的所得。通过单位售价乘以销售数量来计算。公式为：

Revenue = Selling Price per unit × Quantity sold

Total costs consist of fixed costs (FC) which do not change with output, and variable costs (VC) which change directly with the level of production. Total variable cost is variable cost per unit multiplied by quantity. Thus, the formula for total costs is:

总成本包括固定成本（FC，不随产量变化）和可变成本（VC，直接随产量变化）。总可变成本等于单位可变成本乘以数量。因此，总成本的公式为：

Total Costs = Fixed Costs + (Variable Cost per unit × Quantity)

Profit is the reward for taking risk and is calculated by subtracting total costs from revenue. If the result is negative, the business makes a loss.

利润是承担风险的回报，用收入减去总成本来计算。如果结果为负，企业就产生亏损。

Profit = Revenue − Total Costs

Worked Example: A café sells 2,000 cups of coffee at £3.50 each. Fixed costs are £2,000 per month and the variable cost per cup is £1.20. Calculate the monthly profit.

示例：一家咖啡店以每杯 3.50 英镑的价格出售 2,000 杯咖啡。每月固定成本为 2,000 英镑，每杯可变成本为 1.20 英镑。计算每月利润。

Step 1: Revenue = 2,000 × £3.50 = £7,000
步骤1：收入 = 2,000 × 3.50 英镑 = 7,000 英镑
Step 2: Total Variable Costs = 2,000 × £1.20 = £2,400
步骤2：总可变成本 = 2,000 × 1.20 英镑 = 2,400 英镑
Step 3: Total Costs = £2,000 + £2,400 = £4,400
步骤3：总成本 = 2,000 英镑 + 2,400 英镑 = 4,400 英镑
Step 4: Profit = £7,000 − £4,400 = £2,600
步骤4：利润 = 7,000 英镑 − 4,400 英镑 = 2,600 英镑

2. Break-even Point: Calculation and Interpretation | 盈亏平衡点：计算与解读

The break-even point is the level of output where total revenue equals total costs, so the business makes neither profit nor loss. The formula using contribution is:

盈亏平衡点是总收入等于总成本的产出水平，此时企业既不盈利也不亏损。使用贡献的公式为：

Break-even output = Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)

The denominator (Selling Price − Variable Cost) is known as contribution per unit. Break-even output must always be rounded up to the nearest whole unit if the result contains a decimal, as you cannot sell a fraction of a product.

分母（售价 − 可变成本）称为单位贡献。如果结果含有小数，盈亏平衡产量必须向上取整到最接近的整数，因为你无法销售部分产品。

Worked Example: Stationery Ltd makes notebooks. Selling price is £5 per notebook, variable cost is £2 per notebook, and fixed costs are £9,000 per month. Find the break-even output and break-even revenue.

示例：文具公司生产笔记本。每本售价 5 英镑，每本可变成本 2 英镑，每月固定成本为 9,000 英镑。求盈亏平衡产量和盈亏平衡收入。

Contribution per unit = £5 − £2 = £3
单位贡献 = 5 英镑 − 2 英镑 = 3 英镑
Break-even output = £9,000 ÷ £3 = 3,000 notebooks
盈亏平衡产量 = 9,000 英镑 ÷ 3 英镑 = 3,000 本
Break-even revenue = 3,000 × £5 = £15,000
盈亏平衡收入 = 3,000 × 5 英镑 = 15,000 英镑

Interpreting the break-even point allows managers to set sales targets and assess the risk of not covering costs. If the expected sales are well above 3,000 units, the product is likely profitable.

解读盈亏平衡点有助于管理者设定销售目标，并评估无法覆盖成本的风险。如果预期销量远高于 3,000 件，该产品很可能盈利。

3. Margin of Safety | 安全边际

Margin of safety shows how much sales can fall before the business reaches its break-even point. It is a measure of risk. The formula is:

安全边际显示在达到盈亏平衡点之前，销售额可以下降多少。这是一个风险度量指标。公式为：

Margin of Safety = Actual Sales (units) − Break-even Output (units)

A large margin of safety indicates lower risk, while a small margin suggests the business could easily slip into a loss. It can also be expressed as a percentage or in revenue terms.

较大的安全边际表明风险较低，而较小的边际则意味着企业很容易陷入亏损。它也可以用百分比或以收入形式表示。

Worked Example: If Stationery Ltd expects to sell 4,500 notebooks, and the break-even output is 3,000 units, calculate the margin of safety in units and as a percentage.

示例：如果文具公司预计销售 4,500 本，盈亏平衡产量为 3,000 本，计算以数量和百分比表示的安全边际。

Margin of safety (units) = 4,500 − 3,000 = 1,500 units
安全边际（数量） = 4,500 − 3,000 = 1,500 本
Margin of safety (%) = (1,500 ÷ 4,500) × 100 = 33.3%
安全边际（%） = (1,500 ÷ 4,500) × 100 = 33.3%

A 33.3% margin of safety means sales can drop by a third before the business stops making a profit, giving management confidence.

33.3% 的安全边际意味着在停止盈利之前，销售额可以下降三分之一，这给管理层带来信心。

4. Contribution and Total Contribution | 贡献与总贡献

Contribution is the amount of money left after variable costs have been deducted from sales, which contributes towards covering fixed costs and generating profit. The per-unit formula is:

贡献是从销售额中扣除可变成本后剩余的金额，用于覆盖固定成本并产生利润。单位公式为：

Contribution per unit = Selling Price − Variable Cost per unit

Total contribution is the contribution per unit multiplied by the number of units sold. Once total contribution equals fixed costs, the break-even point is reached.

总贡献是单位贡献乘以销售数量。一旦总贡献等于固定成本，就达到了盈亏平衡点。

Worked Example: A gym sells memberships at £40 per month, with variable costs of £10 per member. Fixed costs are £15,000. If 800 members join, calculate total contribution and profit.

示例：一家健身房以每月 40 英镑出售会员资格，每位会员的可变成本为 10 英镑。固定成本为 15,000 英镑。如果有 800 名会员加入，计算总贡献和利润。

Contribution per member = £40 − £10 = £30
每位会员贡献 = 40 英镑 − 10 英镑 = 30 英镑
Total contribution = 800 × £30 = £24,000
总贡献 = 800 × 30 英镑 = 24,000 英镑
Profit = Total contribution − Fixed Costs = £24,000 − £15,000 = £9,000
利润 = 总贡献 − 固定成本 = 24,000 英镑 − 15,000 英镑 = 9,000 英镑

Contribution analysis is particularly useful in short-term decision-making, such as accepting a special order or deciding whether to discontinue a product.

贡献分析在短期决策中特别有用，例如是否接受特殊订单或决定停产某种产品。

5. Cash Flow Forecasts: Net Cash Flow and Closing Balance | 现金流预测：净现金流与期末余额

A cash flow forecast predicts the future inflows and outflows of cash over a period. Two crucial calculations are net cash flow and closing balance. The formulas are:

现金流预测预估未来一段时期内的现金流入与流出。两项关键计算是净现金流和期末余额。公式为：

Net Cash Flow = Total Cash Inflows − Total Cash Outflows

Closing Balance = Opening Balance + Net Cash Flow

The closing balance of one month becomes the opening balance of the next month. A negative closing balance signals a potential liquidity problem.

某个月的期末余额成为下个月的期初余额。负的期末余额预示着潜在的流动性问题。

Worked Example: In January, a small retailer has an opening balance of £500. Cash inflows from sales are £3,200, and outflows (wages, rent, stock) total £3,600. Calculate the closing balance for January.

示例：一月，一家小零售商的期初余额为 500 英镑。销售现金流入为 3,200 英镑，流出（工资、租金、存货）总计 3,600 英镑。计算一月的期末余额。

Net cash flow = £3,200 − £3,600 = −£400
净现金流 = 3,200 英镑 − 3,600 英镑 = −400 英镑
Closing balance = £500 + (−£400) = £100
期末余额 = 500 英镑 + (−400 英镑) = 100 英镑

Although the business made a loss of cash in January, it still has a positive closing balance. The manager should investigate ways to reduce outflows or increase inflows for the following months to avoid an overdraft.

尽管一月份现金亏损，但期末余额仍然为正。经理应研究减少流出或增加流入的方法，以避免接下来几个月的透支。

6. Gross Profit and Net Profit Margins | 毛利润率与净利润率

Profit margins measure how much profit a business makes for every £1 of sales. They are essential for comparing performance over time or between competitors. The formulas are:

利润率衡量企业每英镑销售额能产生多少利润。这对于跨越时间或竞争对手之间的比较至关重要。公式为：

Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100

Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100

Gross profit is revenue minus cost of sales (the direct costs of producing goods). Net profit is gross profit minus all other expenses (overheads).

毛利润是收入减去销售成本（生产商品的直接成本）。净利润是毛利润减去所有其他费用（间接费用）。

Worked Example: A clothing brand has revenue of £120,000, cost of sales of £50,000, and operating expenses of £30,000. Calculate gross and net profit margins.

示例：一个服装品牌收入为 120,000 英镑，销售成本为 50,000 英镑，运营费用为 30,000 英镑。计算毛利率和净利率。

Gross Profit = £120,000 − £50,000 = £70,000
毛利润 = 120,000 英镑 − 50,000 英镑 = 70,000 英镑
Gross Profit Margin = (£70,000 ÷ £120,000) × 100 = 58.33%
毛利率 = (70,000 英镑 ÷ 120,000 英镑) × 100 = 58.33%
Net Profit = £70,000 − £30,000 = £40,000
净利润 = 70,000 英镑 − 30,000 英镑 = 40,000 英镑
Net Profit Margin = (£40,000 ÷ £120,000) × 100 = 33.33%
净利率 = (40,000 英镑 ÷ 120,000 英镑) × 100 = 33.33%

A higher net profit margin indicates better control of overall expenses. If the margin falls over time, the business may need to cut costs or raise prices.

较高的净利率表明对总费用的控制更好。若该比率随时间下降，企业可能需要削减成本或提高价格。

7. Average Rate of Return (ARR) | 平均收益率

ARR is used in investment appraisal to measure the average annual profit as a percentage of the initial investment. It helps compare the profitability of different projects. The formula is:

ARR 用于投资评估，衡量平均年利润占初始投资的百分比。它有助于比较不同项目的盈利能力。公式为：

ARR (%) = (Average Annual Profit ÷ Initial Investment) × 100

Average annual profit is calculated by dividing the total profit over the project’s life by the number of years. Remember that total profit is total cash inflows minus total costs (including the initial investment). Alternatively, the exam may provide net cash flows; you subtract the initial cost to find total profit.

平均年利润是用项目寿命期内的总利润除以年数计算的。请记住，总利润是总现金流入减去总成本（包括初始投资）。或者，考试可能提供净现金流；你需要减去初始成本得出总利润。

Worked Example: A company invests £50,000 in a project that is expected to last 5 years. Over five years, the total net cash inflows (after operating costs) are £80,000. Calculate ARR.

示例：一家公司投资 50,000 英镑于一个预计持续 5 年的项目。五年期间，总净现金流入（扣除运营成本后）为 80,000 英镑。计算 ARR。

Total profit = Total net cash inflows − Initial investment = £80,000 − £50,000 = £30,000
总利润 = 总净现金流入 − 初始投资 = 80,000 英镑 − 50,000 英镑 = 30,000 英镑
Average annual profit = £30,000 ÷ 5 = £6,000
平均年利润 = 30,000 英镑 ÷ 5 = 6,000 英镑
ARR = (£6,000 ÷ £50,000) × 100 = 12%
ARR = (6,000 英镑 ÷ 50,000 英镑) × 100 = 12%

An ARR of 12% means the project returns 12% of the initial cost each year on average. When comparing projects, the one with the higher ARR is preferable, but you must also consider other factors like risk.

12% 的 ARR 意味着该项目平均每年回报初始成本的 12%。比较项目时，ARR 较高的更可取，但你也必须考虑风险等其他因素。

8. Liquidity Ratios: Current Ratio and Acid Test Ratio | 流动性比率：流动比率与酸性测试比率

Liquidity ratios assess a firm’s ability to meet its short-term debts. The two key ratios are:

流动性比率评估企业偿付短期债务的能力。两个关键比率是：

Current Ratio = Current Assets ÷ Current Liabilities

Acid Test Ratio = (Current Assets − Inventories) ÷ Current Liabilities

A current ratio of between 1.5:1 and 2:1 is generally considered healthy. A low ratio may signal cash flow problems, while a very high ratio suggests inefficient use of assets. The acid test ratio excludes inventories because they are the least liquid current asset.

流动比率通常在 1.5:1 至 2:1 之间被认为是健康的。较低的比率可能预示着现金流问题，而过高的比率则表明资产使用效率低下。酸性测试比率不包括存货，因为存货是流动性最差的流动资产。

Worked Example: A business has current assets of £45,000 (including £12,000 inventory) and current liabilities of £25,000. Calculate both ratios.

示例：一家企业的流动资产为 45,000 英镑（其中存货 12,000 英镑），流动负债为 25,000 英镑。计算两个比率。

Current Ratio = £45,000 ÷ £25,000 = 1.8 : 1
流动比率 = 45,000 英镑 ÷ 25,000 英镑 = 1.8 : 1
Acid Test Ratio = (£45,000 − £12,000) ÷ £25,000 = £33,000 ÷ £25,000 = 1.32 : 1
酸性测试比率 = (45,000 英镑 − 12,000 英镑) ÷ 25,000 英镑 = 33,000 英镑 ÷ 25,000 英镑 = 1.32 : 1

Both ratios are above 1, indicating the business can cover its short-term debts. The acid test ratio of 1.32 : 1 suggests good liquidity even without selling inventory.

两个比率都高于 1，表明企业能够偿还短期债务。1.32 : 1 的酸性测试比率表明，即使不出售存货，流动性也良好。

9. Combining Calculations: Break-even and Profit Targeting | 综合计算：盈亏平衡与利润目标

Exam questions often require linking multiple concepts. For example, you might need to calculate the break-even point and then determine the number of units needed to achieve a target profit. The formula for target output is:

考试题目经常要求关联多个概念。例如，你可能需要计算盈亏平衡点，然后确定实现目标利润所需的销售量。目标产量的公式是：

Units to achieve target profit = (Fixed Costs + Target Profit) ÷ Contribution per unit

This builds on break-even by adding the desired profit to the numerator.

这是基于盈亏平衡，将期望利润加入分子中。

Worked Example: A bakery has fixed costs of £4,000, selling price of £2.50 per cake, variable cost of £1.00 per cake. Calculate the break-even output and the output needed to achieve a profit of £2,000.

示例：一家面包店的固定成本为 4,000 英镑，每个蛋糕售价为 2.50 英镑，可变成本为每个 1.00 英镑。计算盈亏平衡产量以及实现 2,000 英镑利润所需的产量。

Contribution per cake = £2.50 − £1.00 = £1.50
每个蛋糕的贡献 = 2.50 英镑 − 1.00 英镑 = 1.50 英镑
Break-even output = £4,000 ÷ £1.50 = 2,666.67 → 2,667 cakes (rounded up)
盈亏平衡产量 = 4,000 英镑 ÷ 1.50 英镑 = 2,666.67 → 2,667 个（向上取整）
Target output = (£4,000 + £2,000) ÷ £1.50 = £6,000 ÷ £1.50 = 4,000 cakes
目标产量 = (4,000 英镑 + 2,000 英镑) ÷ 1.50 英镑 = 6,000 英镑 ÷ 1.50 英镑 = 4,000 个

Always round up when dealing with units. The business must sell 4,000 cakes to earn a £2,000 profit. This analysis helps in planning production and promotional efforts.

处理单位时始终向上取整。企业必须销售 4,000 个蛋糕才能赚取 2,000 英镑利润。这种分析有助于规划生产和促销活动。

10. Practice Scenarios: Step-by-Step Solutions | 练习情景：分步解答

This final section offers a mixed scenario to test your ability to switch between formulas. Read the data carefully and identify which calculation is required.

最后一个部分提供一个混合情景，测试你在各个公式之间切换的能力。仔细阅读数据，确定需要进行哪种计算。

Scenario: Trendy Tech Ltd produces smartwatches. Data for one month: Fixed costs £24,000; variable cost £35 per unit; selling price £95 per unit; actual sales 1,200 units. Opening cash balance £8,000; cash inflows from customers £114,000; cash outflows (all costs) £66,000.

情景： 时尚科技公司生产智能手表。一个月的数据：固定成本 24,000 英镑；单位可变成本 35 英镑；单价 95 英镑；实际销量 1,200 件。期初现金余额 8,000 英镑；客户现金流入 114,000 英镑；现金流出（全部成本）66,000 英镑。

Tasks: (a) Calculate break-even output. (b) Calculate margin of safety in units. (c) Calculate net profit for the month. (d) Calculate net cash flow and closing balance. (e) Calculate gross profit margin (assume cost of sales equals variable cost of units sold).

任务： (a) 计算盈亏平衡产量。 (b) 计算以数量表示的安全边际。 (c) 计算当月净利润。 (d) 计算净现金流和期末余额。 (e) 计算毛利率（假设销售成本等于已售单位的可变成本）。

Solutions:

解答：

(a) Contribution per unit = £95 − £35 = £60. Break-even = £24,000 ÷ £60 = 400 units.

(a) 单位贡献 = 95 英镑 − 35 英镑 = 60 英镑。盈亏平衡 = 24,000 英镑 ÷ 60 英镑 = 400 件。

(b) Margin of safety = 1,200 − 400 = 800 units.

(b) 安全边际 = 1,200 − 400 = 800 件。

(c) Revenue = 1,200 × £95 = £114,000. Total variable cost = 1,200 × £35 = £42,000. Total costs = £24,000 + £42,000 = £66,000. Net profit = £114,000 − £66,000 = £48,000.

(c) 收入 = 1,200 × 95 英镑 = 114,000 英镑。总可变成本 = 1,200 × 35 英镑 = 42,000 英镑。总成本 = 24,000 英镑 + 42,000 英镑 = 66,000 英镑。净利润 = 114,000 英镑 − 66,000 英镑 = 48,000 英镑。

(d) Net cash flow = £114,000 − £66,000 = £48,000. Closing balance = £8,000 + £48,000 = £56,000.

(d) 净现金流 = 114,000 英镑 − 66,000 英镑 = 48,000 英镑。期末余额 = 8,000 英镑 + 48,000 英镑 = 56,000 英镑。

(e) Gross profit = Revenue − Cost of sales = £114,000 − £42,000 = £72,000. Gross profit margin = (£72,000 ÷ £114,000) × 100 = 63.16%.

(e) 毛利润 = 收入 − 销售成本 = 114,000 英镑 − 42,000 英镑 = 72,000 英镑。毛利率 = (72,000 英镑 ÷ 114,000 英镑) × 100 = 63.16%.

Such multi-step questions are common in the exam. Always show your workings clearly and double-check whether you need a percentage or a monetary value.

这类多步骤题目在考试中很常见。始终清晰展示步骤，并反复确认答案是百分比还是货币值。

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IGCSE Edexcel Business: Calculation Practice | IGCSE Edexcel 商务计算题专项训练