📚 Worksheet Answers – Chapter 23 | 第23章作业答案详解
This article provides comprehensive answers and explanations for the Chapter 23 worksheet on Costs, Revenues and Profit from the Cambridge A‑Level Business syllabus. Each section tackles a typical exam‑style question or core concept, breaking down the reasoning and calculations step by step. Use these solutions to deepen your understanding of cost behaviour, contribution and break‑even analysis.
本文为剑桥A‑Level商务课程第23章“成本、收入与利润”作业单提供完整的答案与解析。每一个小节都针对一道典型考题或核心概念，逐步拆解推理过程和计算步骤。通过这些解答，你可以加深对成本性态、贡献和盈亏平衡分析的理解。
1. Fixed and Variable Costs | 固定成本与可变成本
Question: Distinguish between fixed costs and variable costs, giving one example of each from a clothing manufacturer.
Answer: Fixed costs do not change with the level of output in the short run. They must be paid even if production is zero. A typical fixed cost for a clothing manufacturer is the monthly rent for its factory. In contrast, variable costs vary directly with the quantity of garments produced. The cost of fabric used to make shirts is a clear variable cost – the more shirts are produced, the greater the total fabric expense.
Question: 区分固定成本与可变成本，并分别举出一个服装制造商的例子。
Answer: 固定成本在短期内不随产量变化而改变，即使产量为零也必须支付。服装制造商的典型固定成本是工厂的月租金。可变成本则与服装产量直接相关，生产衬衫所用的布料成本就是典型的可变成本——产量越多，布料总支出越大。
2. Semi‑Variable Costs | 半变动成本
Question: A warehouse’s electricity bill includes a standing charge of £80 per month plus £0.15 for each unit consumed. Classify this cost and explain your reasoning.
Answer: This is a semi‑variable cost because it contains both a fixed element (the standing charge of £80, which is payable regardless of usage) and a variable element (the £0.15 per unit, which rises with consumption). Semi‑variable costs are common for utilities and maintenance contracts.
Question: 某仓库的电费包括每月固定收费80英镑加上每消耗一度电0.15英镑。请对该成本进行分类并解释理由。
Answer: 这是一项半变动成本，因为它同时包含固定部分（无论是否用电都要支付的80英镑基本费）和变动部分（随用电量变化的度电费）。半变动成本在水电费和维修合同中十分常见。
3. Calculating Total Costs | 总成本计算
Question: A bakery has fixed costs of £2,000 per week and variable costs of £1.20 per loaf. Calculate the total cost if it produces 8,000 loaves.
Answer: Total Cost = Fixed Costs + (Variable cost per unit × Quantity). Plugging in the numbers: £2,000 + (£1.20 × 8,000) = £2,000 + £9,600 = £11,600. The bakery will incur a total cost of £11,600 for that week.
Question: 一家面包店每周固定成本为2,000英镑，每条面包的可变成本为1.20英镑。若生产8,000条面包，总成本是多少？
Answer: 总成本 = 固定成本 + (单位可变成本 × 数量)。代入数字：£2,000 + (£1.20 × 8,000) = £2,000 + £9,600 = £11,600。该周总成本为11,600英镑。
4. Average Cost (Unit Cost) | 平均成本（单位成本）
Question: Using the data from Question 3, calculate the average cost per loaf.
Answer: Average cost = Total cost ÷ Output. So, £11,600 ÷ 8,000 = £1.45 per loaf. Notice that the average cost consists of an average fixed cost of £0.25 (£2,000 ÷ 8,000) plus the variable cost of £1.20. As output rises, average fixed cost falls, pulling down the average cost.
Question: 利用第3题的数据，计算每条面包的平均成本。
Answer: 平均成本 = 总成本 ÷ 产量。£11,600 ÷ 8,000 = 每条 £1.45。注意，平均成本由平均固定成本£0.25（£2,000 ÷ 8,000）加上可变成本£1.20构成。随着产量增加，平均固定成本下降，从而拉低平均成本。
5. Revenue and Profit | 收入与利润
Question: The bakery sells each loaf for £1.95. Calculate the total revenue and the profit when 8,000 loaves are sold.
Answer: Total revenue = Price × Quantity = £1.95 × 8,000 = £15,600. Profit = Total revenue – Total cost = £15,600 – £11,600 = £4,000. The business makes a profit of £4,000. If total costs had exceeded revenue, a loss would be recorded.
Question: 该面包店以每条£1.95的价格出售面包。计算销售8,000条时的总收入和利润。
Answer: 总收入 = 单价 × 销量 = £1.95 × 8,000 = £15,600。利润 = 总收入 – 总成本 = £15,600 – £11,600 = £4,000。企业获得利润£4,000。若总成本超过收入，则会产生亏损。
6. Understanding Contribution | 理解贡献（贡献毛益）
Question: Explain what is meant by ‘contribution per unit’ and why managers find it useful.
Answer: Contribution per unit is the amount each unit sold contributes towards paying off fixed costs and, once those are covered, towards profit. It is calculated as Selling price – Variable cost per unit. Managers use contribution to assess whether adding or dropping a product line will improve overall profitability, because it isolates the items that truly affect the bottom line from those that are unavoidable in the short term.
Question: 解释何为“单位贡献”并说明管理者为何觉得这一概念很有用。
Answer: 单位贡献是每售出一件产品为弥补固定成本及创造利润所贡献的金额，计算公式为售价 – 单位可变成本。管理者利用贡献来评估增加或裁减某一产品线是否会改善整体盈利，因为它将真正影响利润的项目与短期内不可避免的支出区分开来。
7. Total Contribution and Profit | 总贡献与利润
Question: A furniture workshop produces 500 chairs. Each chair sells for £85 and incurs variable costs of £50. Fixed costs are £12,000. Calculate total contribution and profit.
Answer: Contribution per chair = £85 – £50 = £35. Total contribution = 500 × £35 = £17,500. Profit = Total contribution – Fixed costs = £17,500 – £12,000 = £5,500. Alternatively, profit = Total revenue (500 × £85 = £42,500) – Total variable costs (500 × £50 = £25,000) – Fixed costs (£12,000) = £5,500.
Question: 一家家具作坊生产500把椅子。每把售价£85，可变成本£50，固定成本为£12,000。计算总贡献和利润。
Answer: 每把椅子的贡献 = £85 – £50 = £35。总贡献 = 500 × £35 = £17,500。利润 = 总贡献 – 固定成本 = £17,500 – £12,000 = £5,500。或者，利润 = 总收入 (500 × £85 = £42,500) – 总可变成本 (500 × £50 = £25,000) – 固定成本 (£12,000) = £5,500。
8. Break‑Even Point Calculation | 盈亏平衡点计算
Question: Using the chair data from Question 7, determine the break‑even output.
Answer: Break‑even output (units) = Fixed costs ÷ Contribution per unit. Break‑even = £12,000 ÷ £ 42.86 chairs. Since the workshop cannot produce a fraction of a chair, the realistic break‑ this output, total revenue equals total costs and the business makes zero profit or loss.
Break‑even = Fixed Costs ÷ (Selling price – Variable cost per unit)
Question: 使用第7题的椅子数据，计算盈亏平衡产量。
Answer: 盈亏平衡产量 = 固定成本 ÷ 单位贡献。盈亏平衡点 = £12,000 ÷ £35 ≈ 342.86 把椅子。由于无法生产零数，实际盈亏平衡产量为343把。在该产量下，总收入等于总成本，企业既不盈利也不亏损。
9. Interpreting Break‑Even Charts | 盈亏平衡图的解读
Question: Sketch a simple break‑even chart and label the break‑even point, the loss zone and the profit zone.
Answer: A break‑even chart plots total fixed costs, total costs and total revenue against output. The total cost line starts at the level of fixed costs and slopes upward at the rate of variable cost per unit. The total revenue line starts at the origin and slopes upward at the selling price per unit. The break‑even point is where the total revenue and total cost lines intersect. The area to the left of the intersection, where total costs exceed total revenue, is the loss zone. The area to the right is the profit zone.
Question: 绘制一张简化的盈亏平衡图并标出盈亏平衡点、亏损区和盈利区。
Answer: 盈亏平衡图将总固定成本线、总成本线和总收入线按产量绘制。总成本线从固定成本水平开始，以单位可变成本的斜率向上倾斜。总收入线从原点开始，以单位售价的斜率向上倾斜。盈亏平衡点是总收入线与总成本线的交点。交点左侧，总成本高于总收入，为亏损区；交点右侧为盈利区。
10. Margin of Safety | 安全边际
Question: If the furniture workshop expects to sell 500 chairs, calculate the margin of safety in units and explain its meaning.
Answer: Margin of safety = Current output – Break‑even output. Using 343 chairs as the break‑even point, margin of safety = 500 – 43 = 157 chairs. This means sales can fall by 157 chairs before the business reaches break‑even and starts making a loss. It is a cushion against a downturn in demand.
Question: 若该家具作坊预计销售500把椅子，计算以数量表示的安全边际并解释其含义。
Answer: 安全边际 = 当前产量 – 盈亏平衡产量。以343把为盈亏平衡点，安全边际 = 500 – 343 = 157把。这意味着销售量可以下降157把才会到达盈亏平衡并开始亏损。安全边际是抵御需求下滑的缓冲垫。
11. Limitations of Break‑Even Analysis | 盈亏平衡分析的局限性
Question: State two limitations of break‑even analysis and suggest how a business might overcome them.
Answer: First, break‑even analysis assumes that costs can be neatly divided into fixed and variable categories, but in reality many costs are semi‑variable, making the break‑even point less precise. Second, it assumes that the selling price remains constant and that all output is sold, which may not hold true if discounts are given or if demand is lower than expected. A business can overcome these limitations by using sensitivity analysis, testing different price and cost scenarios, and by preparing more flexible budgets that account for stepped fixed costs.
Question: 列举盈亏平衡分析的两个局限性，并建议企业如何克服。
Answer: 首先，盈亏平衡分析假定成本能被清晰划分为固定和可变两类，但实际上许多成本是半变动的，使盈亏平衡点不够精确。其次，它假设售价恒定且所有产品都能售出，如果给予折扣或实际需求低于预期，这一假设便不成立。企业可以通过敏感性分析来克服这些局限，测试不同的价格和成本情境，并编制能反映阶梯式固定成本的更为灵活的预算。
Published by TutorHao | Business Revision Series | aleveler.com
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