📚 Worksheet – Chapter 30: Investment Appraisal | 工作表 – 第30章：投资评估
This worksheet consolidates Cambridge A-Level Business Chapter 30 on investment appraisal. It reviews payback period, average rate of return (ARR), net present value (NPV), discount factors, and the qualitative issues that influence final investment decisions.
本工作表单巩固剑桥 A-Level 商务第30章"投资评估"的内容，复习投资回收期、平均回报率、净现值、折现因子，以及影响最终投资决策的定性因素。
Capital expenditure decisions are among the most important choices a business ever makes, because the money is committed for years, it is difficult to reverse, and it shapes the future capacity, cost base and competitiveness of the firm. This worksheet therefore combines calculation practice with the evaluative writing that examiners reward.
资本支出决策是企业所做的最重要决策之一，因为资金会被长期占用、难以逆转，并且会决定企业未来的产能、成本结构与竞争力。因此，本工作表把计算训练与考官所看重的评价性写作结合起来。
1. Overview and Learning Objectives | 概述与学习目标
By completing this worksheet, you will be able to define investment appraisal, explain the three main quantitative techniques, calculate payback, ARR and NPV, compare their strengths and weaknesses, and discuss the qualitative factors that shape final capital expenditure decisions.
完成本工作表单后，你将能够定义投资评估，解释三种主要定量方法，计算投资回收期、平均回报率和净现值，比较它们的优缺点，并讨论影响最终资本支出决策的定性因素。
The learning objectives are closely aligned with the Cambridge International AS and A Level Business syllabus, which requires both accurate calculations and balanced evaluation of quantitative and qualitative evidence.
这些学习目标与剑桥国际 AS 和 A Level 商务大纲紧密衔接，该大纲要求既能准确计算，也能平衡评价定量与定性证据。
Before you begin, note the two skills that carry the most marks: showing every stage of your working with correct units (years, months, £, %), and using the phrase "it depends on..." when you weigh up the results.
开始之前，请注意两项占分最多的技能：完整展示每一步计算并写出正确单位（年、月、£、%），以及在权衡结果时使用"这取决于……"这类表述。
2. Key Terminology | 关键术语
The table below summarises the core terms used in Chapter 30. You should be able to define and apply each term in context.
下表总结了第30章中使用的核心术语。你应当能够在具体情境中定义并运用每个术语。
| Term | 中文术语 | Definition | 中文释义 |
|---|---|---|---|
| Investment appraisal | 投资评估 | The quantitative and qualitative techniques used to judge whether a capital project is worth undertaking. | 用于判断某项资本项目是否值得实施的定量与定性方法。 |
| Capital expenditure | 资本支出 | Spending on long-term assets such as machinery, buildings, vehicles or IT systems. | 用于机器、厂房、车辆或 IT 系统等长期资产的支出。 |
| Payback period | 投资回收期 | The time taken for cumulative net cash inflows to equal the initial outlay. | 累计净现金流入等于初始投资额所需的时间。 |
| Average rate of return (ARR) | 平均回报率 | Average annual profit expressed as a percentage of the capital invested. | 年均利润占投资资本的百分比。 |
| Net present value (NPV) | 净现值 | The sum of discounted future net cash flows minus the initial investment. | 折现后未来净现金流量之和减去初始投资额。 |
| Discount factor | 折现因子 | The multiplier used to convert a future cash flow into its present value. | 把未来现金流换算为现值的乘数。 |
| Cost of capital | 资本成本 | The rate of return the business must earn to satisfy lenders and shareholders; used as the discount rate. | 企业为满足债权人与股东要求而必须赚取的回报率，即折现率。 |
| Net cash flow | 净现金流量 | Cash inflows minus cash outflows in a period; it is not the same as profit. | 某期间现金流入减现金流出，不等同于利润。 |
| Residual value | 残值 | The estimated scrap or resale value of an asset at the end of its useful life. | 资产使用寿命结束时估计的报废或转售价值。 |
3. Why Investment Appraisal Matters | 为何投资评估重要
Capital projects are expensive, long lasting and usually irreversible. Once a factory is built or a machine is installed, the money cannot easily be recovered, so a poor decision can damage cash flow, profitability and even survival for many years.
资本项目成本高、周期长，且通常不可逆。一旦厂房建成或机器安装完成，资金就难以收回，因此一次糟糕的决策可能在未来多年损害现金流、盈利能力，甚至威胁企业生存。
Investment appraisal also forces managers to justify their proposals with evidence. This improves the quality of decision making and makes it easier to raise finance, because banks and shareholders want to see projected returns before they commit funds.
投资评估还迫使管理者用证据来证明其提案的合理性。这提高了决策质量，也更容易融资，因为银行和股东在投入资金前希望看到预期回报。
- It allows several competing projects to be ranked and compared objectively.
- 它使多个相互竞争的项目能够被客观地排序和比较。
- It highlights the timing of cash inflows, which matters for liquidity planning.
- 它突出现金流入的时间分布，这对流动性规划至关重要。
- It reduces the risk of over-optimistic or emotional investment decisions.
- 它降低了过度乐观或情绪化投资决策的风险。
- It provides a benchmark that can be reviewed after the project is completed.
- 它提供了一个可在项目完成后进行复查的基准。
4. Payback Period | 投资回收期
The payback period answers a simple question: how long does it take before the business has got its money back? It is the most widely used technique in practice because it is quick, easy and focuses on risk and liquidity.
投资回收期回答一个简单的问题：企业需要多久才能收回投入的资金？它是最广泛使用的实务方法，因为快速、简便，并聚焦于风险和流动性。
s before full recovery + (unrecovered amount ÷ cash flow in the recovery year) × 12 months
Work through the cumulative cash flow column year by year until the total first exceeds the initial outlay. The exact month is found by dividing the amount still outstanding by the cash flow of that year and multiplying by twelve.
逐年计算累计现金流量，直到总额首次超过初始投资额。精确到月的方法是用仍未收回的金额除以当年的现金流量，再乘以12。
Worked example: A machine costs £200,000 and is expected to generate net cash flows of £60,000, £70,000, £80,000 and £90,000 over four years.
例题：一台机器成本 £200,000，预计四年净现金流量分别为 £60,000、£70,000、£80,000 和 £90,000。
| Year | Net cash flow (£) | Cumulative (£) |
|---|---|---|
| 0 | −200,000 | −200,000 |
| 1 | 60,000 | −140,000 |
| 2 | 70,000 | −70,000 |
| 3 | 80,000 | +10,000 |
| 4 | 90,000 | +100,000 |
Recovery happens during year 3, when £70,000 is still outstanding out of an £ . The payback period is therefore 2 years 10.5 months, often rounded to 2 years 11 months.
回收发生在第3年，当年尚有 £70,000 未收回，而当年流入为 £80,000。70,000 ÷ 80,000 = 0.875，0.875 × 12 = 10.5 个月。因此投资回收期为 2 年 10.5 个月，通常约等于 2 年 11 个月。
- Advantages: simple, quick, emphasises liquidity and risk, and useful when technology dates quickly.
- 优点：简单、快速，强调流动性与风险，在技术更新迅速的行业尤其有用。
- Disadvantages: ignores all cash flows after payback, ignores total profitability, and ignores the time value of money within the payback window.
- 缺点：忽略回收期之后的所有现金流，忽略总体盈利能力，也忽略回收期内资金的时间价值。
5. Average Rate of Return (ARR) | 平均回报率
ARR, also called the accounting rate of return, compares the average annual profit of a project with the capital invested. It is expressed as a percentage, which makes it easy to compare with interest rates or with the returns on other projects.
平均回报率（ARR）也称会计回报率，把项目的年均利润与投入资本进行比较。它以百分比表示，因此易于与利率或其他项目回报进行比较。
ARR = (average annual profit ÷ initial investment) × 100%
Average annual profit = (total net cash flow − initial investment) ÷ number of years
Using the same machine: total net cash flow over four years is £300,000, so total profit is £300,000 − £200,000 = £100,000. Average annual profit is £100,000 ÷ 4 = £25,000, and ARR is £25,000 ÷ £200,000 × 100 = 12.5%.
仍以上述机器为例：四年净现金流量合计 £300,000，因此总利润为 £300,000 − £200,000 = £100,000。年均利润为 £100,000 ÷ 4 = £25,000，ARR 为 £25,000 ÷ £200,000 × 100 = 12.5%。
If the case states depreciation or a residual value, deduct depreciation to convert cash flow into profit, or use average investment of (initial cost + residual value) ÷ 2 as the denominator. Always follow the formula given in the question.
如果题目给出折旧或残值，应扣除折旧把现金流量换算为利润，或用平均投资额（初始成本 + 残值）÷ 2 作为分母。务必按照题目给出的公式作答。
- Advantages: uses the whole life of the project, produces a percentage that is easy to compare with the cost of borrowing, and uses familiar profit data.
- 优点：考虑项目全生命周期，结果以百分比呈现，便于与借款成本比较，且使用企业熟悉的利润数据。
- Disadvantages: ignores the timing of cash flows, ignores the size of the project, and profit can be manipulated by accounting policies.
- 缺点：忽略现金流的时间分布，忽略项目规模，且利润可被会计政策影响。
6. Net Present Value and Discount Factors | 净现值与折现因子
Money received today is worth more than the same money received in five years, because it could be invested or used to reduce borrowing. NPV recognises this by discounting every future cash flow back to its present value.
今天收到的钱比五年后收到的同样金额更有价值，因为它可以被投资或用于偿还借款。净现值通过对每一笔未来现金流进行折现来体现这一点。
Discount factor = 1 ÷ (1 + r)ⁿ
NPV = Σ (net cash flow × discount factor) − initial investment
Here r is the discount rate, normally the cost of capital, and n is the number of years into the future. Discount factors are usually supplied in the exam, but you should be able to calculate them for a single year.
其中 r 为折现率，通常即资本成本，n 为未来年数。考试中通常会提供折现因子表，但你应能计算单一年份的折现因子。
| Year | Factor at 10% | Factor at 15% |
|---|---|---|
| 1 | 0.909 | 0.870 |
| 2 | 0.826 | 0.756 |
| 3 | 0.751 | 0.658 |
| 4 | 0.683 | 0.572 |
| 5 | 0.621 | 0.497 |
Discounting the machine's cash flows at 10% gives present values of £54,540, £57,820, £60,080 and £61,470, a total of £233,910. NPV = £233,910 − £200,000 = £33,910, so the project adds value and should be accepted.
以10%折现该机器的现金流量，得到现值 £54,540、£57,
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