📚 Worksheet Answers – Chapter 25: Investment Appraisal | 第25章 投资评估练习题答案
This post provides model worksheet answers for Chapter 25, Investment Appraisal, in the Cambridge International A Level Business course. The focus is on payback period, average rate of return (ARR), and net present value (NPV), using a typical two-project exam scenario. All workings are shown so you can see exactly where each figure comes from.
本文为剑桥国际 A Level 商务课程第25章“投资评估”提供标准练习题答案。内容围绕回收期、平均收益率（ARR）和净现值（NPV）展开，采用典型的双项目考试情景。所有计算步骤均完整展示，便于你理解每个数字的来源。
1. How to Use These Worksheet Answers | 如何使用本练习题答案
This answer set uses a common exam-style scenario: a manufacturing business is comparing two projects, Alpha and Beta. The cost of capital is 10% per year. Always show workings in the exam; final answers alone often lose marks.
本答案采用常见的考试题型情景：一家制造企业正在比较两个项目 Alpha 和 Beta。资本成本为每年 10%。考试中务必展示计算过程，只写最终答案通常会被扣分。
Work through each question before checking the model answer. Then compare your method, not just your final number. If your answer differs, trace back to see whether the error is in the cash flow table, the discount factor, or the final subtraction.
每道题先自己完成，再对照标准答案。不仅要对比最终结果，还要对比解题方法。如果答案不同，请回溯检查是现金流表格、折现系数还是最终减法出现了错误。
2. Worksheet Data and Discount Factors | 练习题数据与折现系数
The table below gives the initial investment and forecast net cash flows for both projects. All figures are in USD; ignore taxation and inflation for simplicity.
下表给出两个项目的初始投资和预计净现金流。所有金额以美元计；为简化，忽略税收和通货膨胀。
| Year (年份) | Project Alpha (项目 Alpha) | Project Beta (项目 Beta) |
|---|---|---|
| 0 (initial cost) | (300,000) | (250,000) |
| 1 | 80,000 | 70,000 |
| 2 | 90,000 | 80,000 |
| 3 | 100,000 | 90,000 |
| 4 | 110,000 | 100,000 |
| 5 | 120,000 | 60,000 |
The 10% discount factors are listed separately because many NPV errors come from using the wrong factor or applying it to the wrong year.
10% 折现系数单独列出，因为很多 NPV 错误都来自用错系数或将系数用到错误的年份。
| Year (年份) | 10% Discount Factor (10% 折现系数) |
|---|---|
| 1 | 0.909 |
| 2 | 0.826 |
| 3 | 0.751 |
| 4 | 0.683 |
| 5 | 0.621 |
3. Formula Reminder for Investment Appraisal | 投资评估公式复习
Revise these three formulas before attempting Chapter 25 questions. The same formulas will be used in the model answers below.
做第25章题目之前，先复习以下三个公式。下面的标准答案会反复使用这些公式。
Payback period = Year before full recovery + (Unrecovered cost at start of year ÷ Net cash flow in that year)
回收期 = 完全回收前一年 +（当年年初未回收成本 ÷ 当年净现金流）
ARR = (Average annual profit ÷ Initial investment) × 100%
平均收益率 =（平均年利润 ÷ 初始投资）× 100%
NPV = Σ (Net cash flow in year t × Discount factor for year t) − Initial investment
净现值 = Σ（第 t 年净现金流 × 第 t 年折现系数）− 初始投资
4. Question 1 – Payback Period for Project Alpha | 第1题 – 项目 Alpha 的回收期
To find the payback period, calculate cumulative net cash flows year by year until the initial cost is recovered.
计算回收期时，需要逐年计算累计净现金流，直到初始投资全部收回。
- Year 1: 80,000 cumulative = 80,000; remaining = 220,000
- Year 2: 90,000 cumulative = 170,000; remaining = 130,000
- Year 3: 100,000 cumulative = 270,000; remaining = 30,000
- Year 4: 110,000 cumulative = 380,000; full recovery during Year 4
第1年：80,000 累计 = 80,000；剩余 = 220,000。第2年：90,000 累计 = 170,000；剩余 = 130,000。第3年：100,000 累计 = 270,000；剩余 = 30,000。第4年：110,000 累计 = 380,000；第4年内完全回收。
The unrecovered cost at the start of Year 4 is 30,000 USD. The net cash flow in Year 4 is 110,000 USD.
第4年初未回收成本为 30,000 美元，第4年净现金流为 110,000 美元。
Payback period = 3 + (30,000 ÷ 110,000) = 3.27 years
回收期 = 3 +（30,000 ÷ 110,000）= 3.27 年
Therefore Project Alpha pays back in about 3 years and 3.3 months. If the firm’s maximum acceptable payback is 4 years, Alpha is acceptable.
因此项目 Alpha 的回收期约为 3 年零 3.3 个月。如果企业可接受的最长回收期为 4 年，则 Alpha 可以接受。
5. Question 2 – Payback Period for Project Beta | 第2题 – 项目 Beta 的回收期
Apply the same cumulative cash flow method to Project Beta.
对项目 Beta 采用同样的累计现金流方法。
- Year 1: 70,000 cumulative = 70,000; remaining = 180,000
- Year 2: 80,000 cumulative = 150,000; remaining = 100,000
- Year 3: 90,000 cumulative = 240,000; remaining =
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