📚 Worksheet Answers – Chapter 22: Costs | 第22章：成本 练习答案解析
This worksheet answer guide covers the core cost concepts, break-even calculations and exam-style applications tested in Chapter 22 of the Cambridge International AS & A Level Business course. Use it to check your definitions, formulae, workings and evaluation points before you attempt timed practice questions.
本练习答案解析覆盖剑桥国际 AS 与 A Level 商务课程第 22 章中常考的成本核心概念、盈亏平衡计算以及考试题型应用。请用本答案核对你的定义、公式、计算步骤和评估要点，然后再进行限时练习。
Every answer below follows the same structure that earns full marks: a precise definition, a business example, the correct formula, a clear working sequence and a short evaluation sentence where the question asks you to judge. If your own answer lacks any of these five elements, rewrite it before moving on.
以下每一道题的答案都遵循同一套拿满分的结构：精准定义、企业实例、正确公式、清晰计算步骤，以及在要求判断时给出的一句评估。若你自己的答案缺少这五个要素中的任何一个，请先重写再继续往下做。
1. Key Cost Concepts & Classification | 成本核心概念与分类
Model answer: A fixed cost (FC) does not change with the level of output in the short run, such as rent, rates and salaried managers. A variable cost (VC) changes directly with output, such as raw materials and piece-rate labour.
参考答案：固定成本（FC）在短期内不随产量变化，例如租金、地方税和管理人员薪金。变动成本（VC）随产量直接变化，例如原材料和计件工资。
Direct costs can be traced to a specific product or department, whereas indirect costs, often called overheads, are shared across the business. Worksheet answers should show clear classification rather than just memorising examples.
直接成本可以追溯到具体产品或部门，而间接成本（通常称为管理费用）由整个企业共同承担。练习答案应体现清晰的分类逻辑，而不只是记住例子。
A high-scoring answer never labels a cost on the basis of what it is called, but on the basis of how it behaves in the specific scenario given. The same item can be fixed for one firm and variable for another, so always quote the case.
高分答案从不根据费用的名称来归类，而是根据它在题目给定情境中的行为来归类。同一项支出对某家企业是固定成本，对另一家企业却可能是变动成本，因此一定要结合案例来作答。
| Cost item | Classification | Reason |
|---|---|---|
| Factory rent | Fixed indirect | Does not vary with output; shared by all products |
| Raw materials | Variable direct | Rises in proportion to units produced; traceable to the product |
| Salaried managers | Fixed indirect | Paid a set annual amount regardless of output |
| Piece-rate wages | Variable direct | Paid per unit assembled, so varies directly with output |
| Electricity for machines | Variable indirect (semi-variable) | Has a standing charge plus a usage element |
| Advertising campaign | Fixed indirect | Budget agreed in advance, not driven by units sold |
2. Fixed, Variable and Semi-Variable Costs | 固定成本、变动成本与半变动成本
Semi-variable costs contain both elements. A telephone bill, a delivery driver on a basic salary plus mileage, or a salesperson on a low basic wage plus commission all behave partly as fixed and partly as variable costs. In calculations, split them before you start.
半变动成本同时包含两种成分。电话账单、采用基本工资加里程补贴的送货司机、领取低底薪加佣金的销售人员，都属于部分固定、部分变动的成本。计算前请先把它拆分。
Total fixed costs are constant in the short run, but average fixed cost falls continuously as output rises because the same amount is spread over more units. This is the arithmetic reason why mass production usually lowers unit cost.
总固定成本在短期内保持不变，但平均固定成本随产量上升而持续下降，因为同样的金额被分摊到更多单位上。这就是大规模生产通常能降低单位成本的算术原因。
Variable cost per unit is normally assumed constant in exam questions, which makes total variable cost a straight line through the origin. If a question gives a bulk-purchase discount, note that the line becomes less steep and state that assumption explicitly.
考试题目通常假定单位变动成本不变，因此总变动成本是一条从原点出发的直线。如果题目给出批量采购折扣，请注意这条线的斜率会变缓，并明确写出这一假设。
TC = FC + VC TVC = VC per unit × Q
AFC = FC ÷ Q AVC = VC ÷ Q
3. Direct and Indirect (Overhead) Costs | 直接成本与间接成本
Direct costs are traceable to a single unit, product line, department or contract: direct materials, direct labour and direct expenses. Indirect costs, or overheads, cannot be traced in this way and must be apportioned using a fair basis such as floor area, machine hours or number of employees.
直接成本可以追溯到单个产品、产品线、部门或合同：直接材料、直接人工和直接费用。间接成本（即管理费用）无法这样追溯，必须按合理基础分摊，例如占地面积、机器工时或员工人数。
The classification matters for decision making because contribution analysis only uses variable direct costs, whereas full-cost pricing adds an absorbed share of overheads to each unit. A worksheet answer that mixes the two will produce the wrong unit price.
这种分类对决策很重要，因为边际贡献分析只使用变动的直接成本，而全部成本定价法则要为每件产品加进一份分摊的管理费用。混淆两者会算出错误的单价。
Indirect costs also drive the difference between short-run and long-run decisions. In the short run a firm may accept an order that covers variable cost only; in the long run every cost must be covered if the business is to survive.
间接成本也是短期与长期决策差异的来源。短期内企业可能接受只覆盖变动成本的订单；但长期来看，只有覆盖全部成本企业才能生存。
4. Cost Formulae You Must Memorise | 必须背熟的成本公式
Examiners award method marks for a correct formula even when the arithmetic slips. Write the formula on the first line of your working, then substitute, then calculate. Never present a bare number.
即使算术出错，只要公式正确，考官仍会给方法分。请把公式写在计算过程的第一行，然后代入数据，最后得出结果。千万不要只写一个孤零零的数字。
Average total cost is also called unit cost. Marginal cost is the addition to total cost from producing one more unit, and in the short run it is driven by variable costs plus any step increase in fixed costs.
平均总成本也称为单位成本。边际成本是多生产一单位所带来的总成本增量，在短期内它由变动成本加上固定成本的阶梯式上升共同决定。
AC = TC ÷ Q = AFC + AVC
MC = ΔTC ÷ ΔQ
Total revenue TR = Price × Quantity
Profit = TR − TC
5. Short-Run and Long-Run Cost Behaviour | 短期与长期成本行为
In the short run at least one factor of production is fixed, usually capital such as premises and machinery. Only labour and materials can be varied, so the firm operates on a fixed capacity and faces diminishing returns when it overloads that capacity.
在短期内至少有一种生产要素是固定的，通常是厂房与机器等资本。只有劳动力和原材料可以变动，因此企业的产能固定，一旦超负荷运转就会出现报酬递减。
In the long run all factors are variable: the firm can build a second plant, lease more warehousing or exit a market entirely. This is the time horizon where economies and diseconomies of scale can be exploited or must be managed.
在长期内所有要素都可变：企业可以新建第二座工厂、租用更多仓库，甚至完全退出某个市场。正是在这个时间维度上，规模经济可以被利用，而规模不经济必须被管理。
A strong worksheet answer distinguishes the two by naming the fixed factor. Saying only 'in the short run things cannot change' is too vague to earn the second mark.
出色的练习答案会通过点明那个固定要素来区分两者。只说"短期内什么都改不了"太笼统，拿不到第二分。
6. Economies and Diseconomies of Scale | 规模经济与规模不经济
Internal economies of scale lower average cost as the firm itself grows. Purchasing economies come from bulk buying, technical economies from larger, more efficient machinery, financial economies from cheaper borrowing, managerial economies from specialists, and marketing economies from spreading a fixed campaign over more units.
内部规模经济随着企业自身扩大而降低平均成本。采购经济来自批量购买，技术经济来自更大更高效的机器，财务经济来自更低的融资成本，管理经济来自专业人才，营销经济来自把固定推广费用分摊到更多单位。
External economies of scale arise from the industry or region rather than the firm: a local pool of skilled labour, specialist suppliers and improved transport links all cut costs for everyone located there.
外部规模经济来自行业或地区而非企业本身：当地熟练劳动力储备、专业供应商以及改善的交通网络，都会降低该地区所有企业的成本。
Diseconomies of scale push average cost back up once the firm becomes too large. Communication breaks down, layers of management slow decisions, coordination between departments becomes bureaucratic and worker motivation falls because individuals feel anonymous.
当企业规模过大时，规模不经济会把平均成本重新推高。沟通失灵、管理层级拖慢决策、部门间协调变得官僚化，员工因感到自己无足轻重而积极性下降。
7. Break-Even Analysis: Formula and Worked Example | 盈亏平衡分析：公式与例题
Model answer: Break-even output is the level of sales at which total revenue equals total cost, so the business makes neither a profit nor a loss. It is calculated as fixed costs divided by contribution per unit.
参考答案：盈亏平衡产量是总收入等于总成本的销售量，此时企业既不盈利也不亏损。其计算方式为固定成本除以单位边际贡献。
Break-even output (units) = FC ÷ (Price − VC per unit)
Break-even revenue = Break-even output × Price
Worked example from the worksheet: fixed costs are $40,000, the selling price is $20 and variable cost per unit is $12. Contribution per unit is therefore $8, and break-even output is 40,000 ÷ 8 = 5,000 units.
练习中的例题：固定成本为 40,000 美元，售价 20 美元，单位变动成本 12 美元。因此单位边际贡献为 8 美元，盈亏平衡产量为 40,000 ÷ 8 = 5,000 件。
Break-even revenue is 5,000 × $20 = $100,000. At 7,000 units the margin of safety is 2,000 units and profit is 2,000 × $8 = $16,000. Always label units, currency and the word 'units' itself.
盈亏平衡收入为 5,000 × 20 = 100,000 美元。若实际销量为 7,000 件，安全边际为 2,000 件，利润为 2,000 × 8 = 16,000 美元。请务必标注单位、货币以及"件"这个量词。
8. Contribution, Margin of Safety and Target Profit | 边际贡献、安全边际与目标利润
Contribution is what each unit sold contributes towards fixed costs and then profit. It is the single most useful number in this chapter because it links cost, price and volume in one figure.
边际贡献是每售出一件产品对固定成本和利润所作的贡献。它是本章最有用的一个数字，因为它把成本、价格和销量联系在一个数值中。
Contribution per unit = Price − VC per unit
Total contribution = Contribution per unit × Q = TR − TVC
Margin of safety = Actual output − Break-even output
Output for target profit = (FC + Target profit) ÷ Contribution per unit
Using the same data, a target profit of $ 8,000 units. A margin of safety expressed as a percentage is (2,000 ÷ 7,000) × 100 = 28.6 %, which is a useful way to show how much sales can fall before a loss appears.
沿用同一组数据，若目标利润为 24,000 美元，则需要 (40,000 + 24,000) ÷ 8 = 8,000 件。若把安全边际表示为百分比，则为 (2,000 ÷ 7,000) × 100 = 28.6 %，这能直观说明销量下滑多少才会转为亏损。
9. Interpreting and Criticising a Break-Even Chart | 盈亏平衡图的解读与批评
On a break-even chart the horizontal axis is output or sales volume and the vertical axis is revenue and cost in currency. The fixed cost line is horizontal, the total cost line starts at the fixed cost level, and total revenue starts at the origin. The two lines cross at the break-even point.
盈亏平衡图的横轴是产量或销量，纵轴是以货币表示的收入与成本。固定成本线为水平线，总成本线从固定成本的水平起步，总收入线从原点出发，两条线相交处即为盈亏平衡点。
The area between the total revenue and total cost lines below the break-even point is the loss zone; above it is the profit zone. Shading them in and labelling each region is a quick way to secure the interpretation marks.
盈亏平衡点之下，总收入线与总成本线之间的区域是亏损区；之上是盈利区。把两个区域涂色并标注，是拿到解读分的快捷方法。
Every chart rests on simplifying assumptions: selling price is constant, variable cost per unit is constant, all output is sold, fixed costs do not change and only one product is made. In evaluation, argue that in real markets competitors force price cuts and unsold stock builds up, so the chart understates risk.
所有图表都建立在简化假设之上：售价不变、单位变动成本不变、产量全部售出、固定成本不变、且只生产一种产品。评估时应指出，现实中竞争对手会迫使企业降价、存货会积压，因此该图低估了风险。
10. Using Cost Data in Business Decisions | 用成本数据支持经营决策
Contribution analysis supports short-run decisions such as accepting a special order below the normal price, making or buying a component, or dropping an unprofitable product line. The rule is to accept any order that makes a positive contribution, provided spare capacity exists.
边际贡献分析可支持短期决策，例如接受低于常规价格的特殊订单、决定自制还是外购某个部件，或砍掉亏损产品线。规则是：只要有闲置产能，就应接受任何能带来正边际贡献的订单。
Full-cost analysis is more appropriate for long-run pricing, because in the long run every product must cover its share of overheads. A business that prices below full cost for years will eventually run out of cash.
全部成本分析更适合长期定价，因为长期来看每件产品都必须覆盖其应分摊的管理费用。长期以低于全部成本的价格销售，企业最终会耗尽现金。
In evaluation, refer to qualitative factors: the special order may damage the brand if existing customers learn the lower price, staff may resist outsourcing, and suppliers may raise prices once they know the firm depends on them.
评估时要提及定性因素：若老客户得知更低的价格，特殊订单可能损害品牌；员工可能抵制外包；供应商一旦知道企业依赖自己，可能抬高价格。
11. Common Worksheet Errors and Mark Scheme Tips | 常见错误与评分要点
The most frequent error is confusing profit with contribution. Profit is total contribution minus fixed costs; a product with a positive contribution can still be loss-making once overheads are absorbed.
最常见的错误是把利润与边际贡献混淆。利润等于总边际贡献减去固定成本；一个边际贡献为正的产品，在分摊管理费用后仍可能亏损。
Other repeated mistakes include forgetting to convert percentage figures into decimals, mixing units with currency, rounding too early in a multi-step calculation, and leaving out the evaluation paragraph when the command word is 'discuss' or 'evaluate'.
其他反复出现的错误包括：忘记把百分比转换为小数、把件数与货币单位混用、在多步计算中过早四舍五入，以及当指令词是"讨论"或"评估"时漏写评估段落。
Always show the formula, the substitution and the final answer with units, then write one sentence that answers the actual question. Two accurate lines with a clear conclusion score better than five lines of unstructured arithmetic.
务必写出公式、代入过程和带单位的最终答案，然后用一句话直接回答题目所问。两行准确的计算加一句清晰结论，胜过五行杂乱无章的算式。
12. Quick Revision Checklist | 快速复习清单
Before you close this worksheet, check that you can define fixed, variable, semi-variable, direct and indirect costs and give a business example of each without looking at your notes.
合上这份练习之前，请确认你能在不看笔记的情况下定义固定成本、变动成本、半变动成本、直接成本和间接成本，并为每一项举出企业实例。
You should also be able to calculate break-even output and revenue, contribution per unit, total contribution, margin of safety and the output needed for a target profit, and to explain the limitations of break-even analysis in two or three evaluative sentences.
你还应能计算盈亏平衡产量与收入、单位边际贡献、总边际贡献、安全边际以及实现目标利润所需产量，并能用两三句评估性语言说明盈亏平衡分析的局限。
- Can you classify a cost from a case study, not from memory? | 你能依据案例而不是死记硬背来给成本分类吗？
- Can you write the correct formula before substituting numbers? | 你能在代入数字之前写出正确公式吗？
- Can you always attach units and currency to your answer? | 你能始终在答案中标注单位和货币吗？
- Can you add one sentence of judgement to every calculation question? | 你能为每道计算题补上一句判断性结论吗？
- Can you link cost data to a real decision such as make or buy? | 你能把成本数据与自制或外购等真实决策联系起来吗？
Work through the numerical questions again under timed conditions, then compare your workings with the model answers above. Repetition with feedback is what converts a good worksheet mark into a good exam mark.
请在限时条件下再做一遍计算题，然后把自己的过程与上文参考答案对照。带着反馈的重复练习，才是把练习分数转化为考试分数的关键。
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