Worksheet Answers – Chapter 21: Costs & Break-even Analysis | 第21章 成本与盈亏平衡分析练习题答案

📚 Worksheet Answers – Chapter 21: Costs & Break-even Analysis | 第21章 成本与盈亏平衡分析练习题答案

This worksheet answer guide covers the key learning outcomes for Chapter 21, focusing on cost classification, contribution, break-even calculation, margin of safety, and interpretation of break-even charts. Each answer is written in the style expected by Cambridge International AS & A Level Business examiners, with clear workings and business reasoning.

本工作纸答案指南涵盖第21章的核心学习目标，重点包括成本分类、贡献毛利、盈亏平衡计算、安全边际以及盈亏平衡图的解读。每道题均按照剑桥国际AS与A Level商务考试评分标准编写，提供清晰的计算步骤和商业推理。

1. Key Cost Terminology | 核心成本术语

Fixed costs (FC) are expenses that do not change with output in the short run, such as rent, insurance, and salaried managers. Variable costs (VC) vary directly with production or sales volume, such as raw materials and piece-rate labour. Semi-variable costs contain both fixed and variable elements, for example a telephone bill with a fixed line rental plus call charges.

固定成本（FC）是短期内不随产量变化的支出，例如租金、保险费和管理人员薪金。变动成本（VC）随生产量或销售量直接变化，例如原材料和计件工资。半变动成本同时包含固定和变动两部分，例如含固定月租和通话费的电话账单。

Total costs (TC) are the sum of fixed costs and variable costs: TC = FC + VC. A worksheet answer should always define terms before applying them to a case. Common examples are fixed costs such as rent and depreciation, variable costs such as direct materials, and semi-variable costs such as electricity and telephone charges.

总成本（TC）是固定成本与变动成本之和：TC = FC + VC。工作纸答案应先定义术语，再应用到案例中。常见的例子包括固定成本（如租金和折旧）、变动成本（如直接材料）以及半变动成本（如电费和电话费）。

Cost type | 成本类型	Definition | 定义	Example | 示例
Fixed | 固定	Does not change with output | 不随产量变化	Rent | 租金
Variable | 变动	Changes directly with output | 随产量直接变化	Raw materials | 原材料
Semi-variable | 半变动	Has fixed and variable elements | 含固定和变动两部分	Phone bill | 电话费

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2. Fixed vs Variable Costs in Practice | 固定成本与变动成本的实际区分

In a worksheet question, examiners often expect students to classify costs from a given list. A common error is to assume that all labour is a variable cost. Direct labour paid per unit produced is variable, but permanent supervisors paid a monthly salary are fixed.

在工作纸题目中，考官通常希望学生对给定成本进行分类。一个常见错误是假设所有人工成本都是变动成本。按产量计酬的直接人工属于变动成本，但按月领薪的固定主管属于固定成本。

Rent can become semi-variable if a factory pays a base rent plus extra charges for heavy usage. Similarly, electricity used to power machinery is variable, but lighting the office may be treated as fixed in short-run decisions. Students should justify their classification using the definition of each cost type.

如果工厂支付基本租金外加高使用量附加费，租金也可能成为半变动成本。同样，驱动机器的电费属于变动成本，但办公室照明在短期决策中可视为固定成本。学生应运用各类成本的定义来证明自己的分类。

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3. Calculating Total Costs | 计算总成本

Given fixed costs of $20,000 per month and variable costs of $6 per unit, a worksheet answer should first write the cost equation: TC = FC + (VC per unit × Q), where Q is output. Always define Q clearly before substituting numbers.

若每月固定成本为20,000美元，变动成本为每单位6美元，工作纸答案应首先写出成本方程：TC = FC +（单位变动成本 × Q），其中Q为产量。在代入数字之前，务必先明确Q的含义。

TC = FC + VC × Q

For Q = 5,000 units, total variable cost = $6 × 5,000 = $30,000, so total cost = $20,000 + $30,000 = $50,000. Always show these steps to gain method marks, even if the final answer is slightly wrong.

当Q = 5,000件时，总变动成本 = 6美元 × 5,000 = 30,000美元，因此总成本 = 20,000美元 + 30,000美元 = 50,000美元。务必展示这些步骤以获得方法分，即使最终答案略有错误。

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4. Contribution per Unit | 单位贡献毛利

Contribution per unit is the amount each unit sold contributes toward covering fixed costs and generating profit. It is calculated as: Selling price per unit − Variable cost per unit. Contribution is not profit unless fixed costs have been fully covered.

单位贡献毛利是每售出一单位产品为覆盖固定成本和创造利润所做的贡献。计算公式为：单位售价 − 单位变动成本。贡献毛利并不等于利润，除非固定成本已被完全覆盖。

Contribution per unit = Selling price − Variable cost per unit

If a product sells for $15 and has a variable cost of $9, contribution per unit is $6. Total contribution is calculated as contribution per unit × number of units sold. For 3,000 units, total contribution = $6 × 3,000 = $18,000. If fixed costs are $12,000, profit = $18,000 − $12,000 = $6,000.

如果产品售价为15美元，变动成本为9美元，单位贡献毛利为6美元。总贡献毛利 = 单位贡献毛利 × 销售数量。若售出3,000件，总贡献毛利 = 6美元 × 3,000 = 18,000美元。如果固定成本为12,000美元，则利润 = 18,000美元 − 12,000美元 = 6,000美元。

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5. Break-even Formula | 盈亏平衡公式

Break-even output is the level of sales at which total revenue equals total costs, so the business makes neither profit nor loss. The formula is: Break-even output = Fixed costs ÷ Contribution per unit. Contribution per unit must be used, not selling price.

盈亏平衡产量是总收入等于总成本的销售水平，此时企业既不盈利也不亏损。公式为：盈亏平衡产量 = 固定成本 ÷ 单位贡献毛利。必须使用单位贡献毛利，而不是售价。

Break-even output = Fixed costs ÷ (Selling price − Variable cost per unit)

A common mistake is dividing fixed costs by the selling price, which ignores variable costs and overstates the break-even point. For instance, if fixed costs are $50,000, selling price is $20, and variable cost is $8, the correct break-even output is $50,000 ÷ ($20 − $8) = $50,000 ÷ $12 = 4,167 units, not $50,000 ÷ $20 = 2,500 units.

一个常见错误是将固定成本除以售价，这忽略了变动成本，会高估盈亏平衡点。例如，固定成本为50,000美元，售价为20美元，变动成本为8美元，正确的盈亏平衡产量为50,000美元 ÷（20美元 − 8美元）= 50,000美元 ÷ 12美元 = 4,167件，而不是50,000美元 ÷ 20美元 = 2,500件。

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6. Worked Break-even Calculation | 盈亏平衡计算示例

Example: A business has fixed costs of $40,000, a selling price of $25 per unit, and variable costs of $15 per unit. Contribution per unit = $25 − $15 = $10. Break-even output = $40,000 ÷ $10 = 4,000 units.

示例：某企业固定成本为40,000美元，单位售价为25美元，单位变动成本为15美元。单位贡献毛利 = 25美元 − 15美元 = 10美元。盈亏平衡产量 = 40,000美元 ÷ 10美元 = 4,000件。

At break-even, total revenue = 4,000 × $25 = $100,000 and total cost = $40,000 + (4,000 × $15) = $100,000. This check proves the answer is correct. If the question asks for break-even revenue, multiply break-even output by selling price: 4,000 × $25 = $100,000.

在盈亏平衡点，总收入 = 4,000 × 25美元 = 100,000美元，总成本 = 40,000美元 +（4,000 × 15美元）= 100,000美元。这个验证可证明答案正确。如果题目要求计算盈亏平衡收入，将盈亏平衡产量乘以售价：4,000 × 25美元 = 100,000美元。

In some worksheets, you may also be asked for the break-even point as a percentage of capacity. If maximum capacity is 8,000 units, break-even output of 4,000 units represents 50% of capacity. This helps assess the risk of not reaching break-even.

在某些工作纸中，还可能要求以产能百分比表示盈亏平衡点。如果最大产能为8,000件，则4

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