Worksheet Answers – Chapter 39: Investment Appraisal | 第39章作业答案：投资评估

📚 Worksheet Answers – Chapter 39: Investment Appraisal | 第39章作业答案：投资评估

This worksheet provides model answers to the exercises in Chapter 39 on Investment Appraisal. The answers cover key financial techniques such as payback period, average rate of return (ARR) and net present value (NPV), as well as the evaluation of qualitative factors and strategic fit. Use these answers to check your understanding and to practise structuring your responses for Paper 1 and Paper 2 case studies.

本作业答案对应第39章投资评估的练习题，提供标准答案范例。内容涵盖回收期、平均收益率(ARR)和净现值(NPV)等核心财务方法，以及定性因素与战略匹配的评估。请对照这些答案检查你的理解，并练习如何组织书面作答，以应对Paper 1和Paper 2的案例分析题。

1. Financial Methods of Investment Appraisal | 投资评估的财务方法

Investment appraisal involves using quantitative techniques to assess whether the expected returns from a capital project justify the initial outlay. The three main methods are payback period, which measures time to recover cost; average rate of return (ARR), which calculates profitability relative to investment; and net present value (NPV), which discounts future cash flows to today's value. Each method has distinct strengths and limitations, and managers often use more than one to support a decision.

投资评估运用定量方法判断资本项目的预期回报是否足以支持初始投入。三种主要的财务方法包括：回收期法，计算收回成本所需时间；平均收益率法(ARR)，计算相对于投资额的盈利水平；净现值法(NPV)，将未来现金流折现为当前价值。每种方法都有独特的优势与局限，管理者通常会结合多种方法辅助决策。

2. Question 1: Payback Period with Constant Cash Flows | 问题1：固定现金流的回收期

Question: Project Alpha requires an initial investment of GBP 80,000 and is expected to produce net cash inflows of GBP 20,000 per year for 6 years. Calculate the payback period.

问题：项目Alpha需要初始投资80,000英镑，预计连续6年每年净现金流入为20,000英镑。计算该项目的回收期。

usiness recovers its entire initial outlay by the end of Year 4. As the project then generates additional cash for a further two years, the short payback suggests low risk in terms of liquidity.

答案：回收期 = 初始投资额 / 年净现金流入 = 80,000 / 20,000 = 4年。这意味着企业在第4年末可收回全部初始投入。由于项目在之后的两年还能继续产生现金流，较短的回收期表明项目的流动性风险较低。

3. Question 2: Payback Period with Uneven Cash Flows | 问题2：不均匀现金流的回收期

Question: Project Beta costs GBP 120,000. Forecast net cash inflows are: Year 1 GBP 10,000; Year 2 GBP 30,000; Year 3 GBP 50,000; Year 4 GBP 40,000; Year 5 GBP 20,000. Find the payback period in years and months.

问题：项目Beta成本为120,000英镑，预计净现金流入如下：第1年10,000英镑，第2年30,000英镑，第3年50,000英镑，第4年40,000英镑，第5年20,000英镑。计算以年和月表示的回收期。

g Year 4. After Year 3, an additional 30,000 is needed (120,000 − 90,000). In Year 4, the project generates 40,000. Payback in Year 4 = 30,000 / 40,000 = 0.75 of a year, or 9 months. Therefore the payback period is 3 years and 9 months.

答案：累计现金流入：第1年末10,000；第2年末40,000；第3年末90,000；第4年末130,000。成本120,000在第4年收回。第3年末尚需30,000（120,000 − 90,000），而第4年产生40,000现金流入。第4年内的回收比例 = 30,000 / 40,000 = 0.75年，即9个月。因此回收期为3年零9个月。

4. Question 3: Average Rate of Return (ARR) | 问题3：平均收益率（ARR）

Question: For Project Beta above, calculate the average rate of return. Assume straight-line depreciation and no residual value.

问题：针对上述项目Beta，计算平均收益率。假设采用直线折旧法且无残值。

00 − 120,000 = 30,000. Average annual profit = 30,000 / 5 = 6,000. ARR = (Average annual profit / Initial investment) × 100 = (6,000 / 120,000) × 100 = 5%. Although the project yields a positive ARR, 5% may be compared against the company's target rate or bank interest to judge acceptability.

答案：5年总净现金流入 = 10,000 + 30,000 + 50,000 + 40,000 + 20,000 = 150,000英镑。总利润 = 总现金流入 − 初始成本 = 150,000 − 120,000 = 30,000英镑。年均利润 = 30,000 / 5 = 6,000英镑。ARR = (年均利润 / 初始投资) × 100 = (6,000 / 120,000) × 100 = 5%。尽管ARR为正，5%需与公司设定的目标收益率或银行利率对比，才能判断项目是否可接受。

5. Question 4: Net Present Value (NPV) Calculation | 问题4：净现值（NPV）计算

Question: Using Project Beta's cash flows and a discount rate of 8%, calculate the net present value. Advise the business on whether to proceed.

问题：沿用项目Beta的现金流，以8%为折现率计算净现值，并给出投资建议。

0 × 0.9259 = 9,259; Y2 30,000 × 0.8573 = 25,719; Y3 50,000 × 0.7938 = 39,690; Y4 40,000 × 0.7350 = 29,400; Y5 20,000 × 0.6806 = 13,612. Sum of PVs = 117,680. NPV = 117,680 − 120,000 = −2,320 (negative). Since NPV is negative, the project fails to earn the required 8% return and should be rejected on financial grounds.

答案：折现因子：(1.08)⁻¹ = 0.9259，(1.08)⁻² = 0.8573，(1.08)⁻³ = 0.7938，(1.08)⁻⁴ = 0.7350，(1.08)⁻⁵ = 0.6806。现值：第1年 10,000 × 0.9259 = 9,259；第2年 30,000 × 0.8573 = 25,719；第3年 50,000 × 0.7938 = 39,690；第4年 40,000 × 0.7350 = 29,400；第5年 20,000 × 0.6806 = 13,612。现值总和 = 117,680。NPV = 117,680 − 120,000 = −2,320（负值）。由于NPV为负，项目的回报未能达到要求的8%折现率，从财务角度应拒绝此项目。

6. Question 5: Mutually Exclusive Projects and NPV | 问题5：互斥项目的NPV比较

Question: A firm must choose between Project X and Project Y, each costing GBP 150,000. Project X forecasts: Y1 GBP 60,000, Y2 GBP 60,000, Y3 GBP 50,000, Y4 GBP 40,000. Project Y forecasts: Y1 GBP 50,000, Y2 GBP 50,000, Y3 GBP 50,000, Y4 GBP 80,000. Using a 10% discount rate, recommend which project to accept based on NPV.

问题：一家企业必须在项目X和项目Y中二选一，两项目成本均为150,000英镑。项目X的预计现金流：第1年60,000，第2年60,000，第3年50,000，第4年40,000。项目Y：第1年50,000，第2年50,000，第3年50,000，第4年80,000。以10%为折现率，依据NPV建议选择哪个项目。

50,000 = 19,015. NPV for Y: 50,000×0.9091 + 50,000×0.8264 + 50,000×0.7513 + 80,000×0.6830 = 45,455 + 41,320 + 37,565 + 54,640 = 178,980. NPV = 178,980 − 150,000 = 28,980. Project Y has the higher NPV and would therefore be recommended, as it adds more shareholder value.

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答案：项目X的净现值：各年现值 0,000×0.8264 + 50,000×0.7513 + 40,000×0.6830 = 54,546 + 49,584 + 37,565 + 27,320 = 169,015。NPV = 169,015 − 150,000 = 19,015。项目Y： 0,000×0.8264 + 50,000×0.7513 + 80,000×0.6830 = 45,455 + 41,320 + 37,565 + 54,640 = 178,980。NPV = 178,980 − 150,000 = 28,980。项目Y的NPV更高，因此建议选择项目Y，因为它能带来更多的股东价值。

7. Question 6: Evaluating Payback and ARR | 问题6：评估回收期法和ARR法

Question: Explain one advantage and one significant disadvantage of the payback method. Then identify an important limitation of ARR that a manager should consider.

问题：解释回收期法的一个优点和一个主要缺点。然后指出管理者在使用ARR法时应注意的一项重要局限。

Answer: A key advantage of payback is its simplicity and focus on liquidity — it helps businesses see how quickly cash is recovered, which is critical when cash flow is tight. However, a serious disadvantage is that it ignores the time value of money and all cash flows beyond the payback point, potentially rejecting profitable long-term projects. For ARR, a major limitation is its reliance on accounting profit rather than cash flow, and it does not consider the timing of returns. Two projects with the same ARR could have very different cash flow profiles and risk levels, yet ARR treats them equally.

答案：回收期法的一大优点是简单易用，且关注流动性——它使企业明白在多长时间内收回现金，这对现金流紧张的情况至关重要。但一个严重缺点是忽略了货币的时间价值以及回收期之后的全部现金流，可能导致拒绝那些长远盈利的项目。对于ARR法，其重要局限在于依赖会计利润而非现金流，且不考虑回报发生的时间。两个ARR相同的项目可能具有截然不同的现金流模式和风险水平，但ARR法会同等对待它们。

8. Question 7: Qualitative Factors in Investment Decisions | 问题7：投资决策中的定性因素

Question: State two qualitative factors that might cause a business to accept a project with a negative NPV.

问题：列举两个可能导致企业接受一个NPV为负的项目的定性因素。

Answer: First, strategic necessity — a project may be essential to meet legal or environmental regulations, such as installing pollution-control equipment, even if its financial return is poor. Second, building brand image or corporate reputation — a firm might invest in sustainable packaging that raises costs in the short run but enhances customer loyalty and long-term market position. Other qualitative considerations include maintaining employee morale, entering a new market for future growth, or responding to competitors' actions that could threaten market share.

答案：首先是战略必要性——项目可能是为满足法律或环境法规所必需的，例如安装污染控制设备，即使财务回报不佳也必须进行。其次是树立品牌形象或企业声誉——企业可能投资可持续包装，短期内成本上升，但能提升客户忠诚度与长期市场地位。其他定性因素还包括：维持员工士气、为未来增长进入新市场，或应对可能威胁市场份额的竞争对手行动。

9. Question 8: Sensitivity Analysis and Risk | 问题8：敏感性分析与风险

Question: If the annual net cash inflows of Project Alpha (GBP 20,000 per year) were actually 10% lower than forecast, how would this affect the payback period and the investment decision?

问题：如果项目Alpha原本每年20,000英镑的净现金流入实际上比预测低10%，这对回收期和投资决策有何影响？

Answer: A 10% 4 years and 5.3 months. This lengthening of the payback period increases liquidity risk. Sensitivity analysis reveals how vulnerable the project is to small changes in key variables. Managers may still accept the project if they believe the downturn is unlikely, or they may set a lower threshold for payback as a result of such 'what-if' questions.

答案：年流入减少10%后为20,000 × 0.9 = 18,000英镑。新回收期 = 80,000 / 18,000 = 4.44年，即4年零5.3个月。回收期延长加大了流动性风险。敏感性分析揭示了项目对关键变量小幅变动的脆弱程度。管理者若认为此类下降概率较低，仍可能接受项目；或者，他们会借助此类“如果-那么”提问来调低回收期接受门槛。

10. Question 9: Investment Appraisal in a Strategic Context | 问题9：战略情境中的投资评估

Question: Discuss why a firm pursuing a differentiation strategy might choose a project with a lower NPV than an alternative project that would deliver cost savings.

问题：讨论为什么实施差异化战略的企业可能会选择一个NPV较低的项目，而放弃另一个能够节省成本的备选项目。

Answer: A differentiation strategy focuses on creating unique features, superior quality, or a strong brand to command premium prices. A lower-NPV project might involve investing in design, R&D, or customer service that aligns with this strategic vision. Although the cost-saving project offers higher immediate NPV, it may not contribute to the distinctive competencies that sustain competitive advantage. Strategic fit is therefore prioritised over pure financial return. For example, a premium car manufacturer may invest heavily in exclusive in-car technology that yields modest short-term returns but reinforces its upmarket reputation.

答案：差异化战略专注于打造独特功能、卓越品质或强大的品牌形象，以获取溢价。一个NPV较低的项目可能涉及设计、研发或客服方面的投资，这些非常符合差异化战略愿景。虽然能够节省成本的备选项目可带来更高的即期NPV，但它未必有助于维持竞争优势的独特能力。因此，战略匹配远比单纯的财务回报更优先。例如，高端汽车制造商可能重金投资独有的车载科技，短期回报不高，却能强化其高端品牌形象。

11. Question 10: Synoptic Links to Stakeholders and Objectives | 问题10：与利益相关者和企业目标的综合联系

Question: How might the objectives of different stakeholders influence the choice of investment appraisal method?

问题：不同利益相关者的目标会如何影响对投资评估方法的选择？

Answer: Shareholders who prioritise profit maximisation typically favour NPV or ARR because these methods indicate the wealth or return generated. Managers concerned with liquidity and short-term survival might prefer payback, as it shows how soon cash is recovered, reducing exposure to uncertainty. Lenders and banks may look for a short payback and stable cash flows to ensure debt can be serviced. Additionally, employees and the local community may value qualitative factors such as job security or environmental impact, prompting management to combine financial methods with a broader stakeholder audit rather than relying on a single figure.

答案：追求利润最大化的股东通常倾向于NPV或ARR法，因为这些方法能显示创造的财富或回报。关注流动性和短期生存的管理者可能偏好回收期法，因为它表明收回现金的速度，从而降低不确定性风险。贷款机构和银行会看重较短的回收期及稳定的现金流，以确保偿债能力。此外，员工和当地社区会重视就业保障或环境影响等定性因素，这会促使管理层在财务方法之外，结合更广泛的利益相关者审核，而不是仅依赖单一财务指标。

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