📚 Investment Appraisal: Payback, ARR and NPV | 投资评估：回收期法、平均收益率法与净现值法
Investment appraisal is a systematic decision-making process used by businesses to evaluate major capital spending projects. In A-Level Business, the focus is on three quantitative methods—payback period, average rate of return (ARR), and net present value (NPV)—supported by qualitative judgement.
投资评估是企业用于评价重大资本支出项目的系统化决策方法。在 A-Level 商务中，重点是三种定量方法——回收期法、平均收益率法（ARR）和净现值法（NPV）——并结合定性判断。
1. The purpose of investment appraisal | 投资评估的目的
Capital investment is a strategic decision because it commits a business to a long-term course of action. Investment appraisal provides financial tools to evaluate whether the expected returns justify the initial spending and the risk involved.
资本投资是一项战略决策，因为它使企业承诺长期的行动方向。投资评估提供财务工具，以评价预期回报是否证明初始支出和所涉风险是合理的。
In the Cambridge A-Level Business syllabus, the core methods are payback period, average rate of return (ARR) and net present value (NPV). Examiners expect both calculations and evaluative comment.
在剑桥 A-Level 商务课程大纲中，核心方法包括回收期法、平均收益率法（ARR）和净现值法（NPV）。考官既要求计算，也要求评价性评论。
2. Key cash flow concepts | 关键现金流概念
Investment appraisal focuses on cash flow rather than accounting profit. Cash flow is the actual movement of money into and out of the business, which affects liquidity and the ability to repay lenders.
投资评估关注现金流而非会计利润。现金流是资金实际流入和流出企业的运动，影响流动性和偿还贷款的能力。
The three relevant cash flow categories are: initial investment, annual net cash inflows, and residual or scrap value. Depreciation is added back or excluded because it is a non-cash expense.
三类相关现金流是：初始投资、年度净现金流入以及残值或余值。折旧被加回或排除，因为它是非现金费用。
3. Payback period: calculation | 回收期计算
Payback period is the length of time required for the cumulative net cash inflows to equal the initial investment. For constant annual cash inflows, the formula is simple:
回收期是指累计净现金流入等于初始投资所需的时间。对于每年固定的现金流入，计算公式很简单：
Payback period = Initial investment ÷ Annual net cash inflow
For uneven cash flows, add the annual inflows until the cumulative total reaches the initial cost. If the cost is $80,000 and inflows are $30,000, $30,000 and $40,000, payback is 2 years + ($20,000 ÷ $40,000) = 2.5 years.
对于不均衡现金流，逐年累加现金流入直至累计总额达到初始成本。如果成本为 80,000 美元，现金流入为 30,000 美元、30,000 美元和 40,000 美元，则回收期 = 2 年 +（20,000 ÷ 40,000）= 2.5 年。
4. Payback period: advantages and disadvantages | 回收期的优缺点
The payback method is simple to calculate and explain. It is particularly useful for firms facing cash-flow problems because it identifies how quickly cash will be recovered.
回收期法计算简单、易于解释。它特别适合面临现金流问题的企业，因为它能确定现金多快能够收回。
It also helps to assess risk: a shorter payback period usually means lower exposure to uncertainty. Small businesses often use it as a screening tool.
它还有助于评估风险：回收期越短，通常意味着面临的不确定性越低。小企业常将其用作筛选工具。
However, payback ignores all cash flows after the payback date, so it cannot measure total profitability. It also ignores the time value of money, treating cash received in year 1 and year 3 as equal.
然而，回收期法忽略回收日期之后的所有现金流，因此无法衡量总盈利性。它还忽略货币时间价值，将第 1 年和第 3 年收到的现金视为同等价值。
5. Average rate of return (ARR): calculation | 平均收益率计算
ARR measures the average annual accounting profit generated by a project as a percentage of the initial investment. It uses profit rather than cash flow, so depreciation is deducted.
ARR 衡量项目产生的平均年度会计利润占初始投资的百分比。它使用利润而非现金流，因此要扣除折旧。
ARR = (Average annual profit ÷ Initial investment) × 100%
Average annual profit = (Total net cash inflows − Total depreciation) ÷ Number of years. Suppose a machine costs $120,000, lasts 6 years, and total cash inflows are $192,000. Total profit = $192,000 − $120,000 = $72,000. Average annual profit = $72,000 ÷ 6 = $12,000. ARR = ($12,000 ÷ $120,000) × 100% = 10%.
平均年度利润 =（总净现金流入 − 总折旧）÷ 年数。假设一台机器成本为 120,000 美元，使用年限为 6 年，总现金流入为 192,000 美元。总利润 = 192,000 − 120,000 = 72,000 美元。平均年度利润 = 72,000 ÷ 6 = 12,000 美元。ARR =（12,000 ÷ 120,000）× 100% = 10%。
6. ARR: interpretation, advantages and disadvantages | 平均收益率的判断与优缺点
Managers compare ARR with a target rate, such as the firm’s cost of capital or a minimum required return. If ARR exceeds the target, the project is acceptable; when comparing projects, the highest ARR is preferred.
管理者将 ARR 与目标收益率（如企业资本成本或最低要求回报率）进行比较。如果 ARR 超过目标，则项目可接受；在比较项目时，优先选择 ARR 最高的项目。
ARR uses all project cash flows, not just those up to payback. It is expressed as a percentage, making it easy to compare with other investments and with accounting ratios such as return on capital employed.
ARR 使用项目的所有现金流，而不仅仅是回收期之前的现金流。它以百分比表示，便于与其他投资以及资本回报率等会计比率进行比较。
ARR is based on average profit rather than actual cash, so liquidity is ignored. Because it does not discount future profits, it fails to account for the timing of returns.
ARR 基于平均利润而非实际现金，因此忽略了流动性。由于它不对未来利润折现，因此无法考虑回报的时间性。
7. Net present value (NPV): time value of money | 净现值与货币时间价值
Net present value recognises the time value of money: cash received earlier is more valuable because it can be reinvested. Each future net cash inflow is multiplied by a discount factor to convert it to a present value.
净现值认识到货币的时间价值：较早收到的现金更有价值，因为它可以再投资。每个未来净现金流入乘以折现因子，将其转换为现值。
NPV = [CF₁ ÷ (1 + r)¹] + [CF₂ ÷ (1 + r)²] + … + [CFₙ ÷ (1 + r)ⁿ] − Initial investment
The discount rate r is the business’s cost of finance or required rate of return. A project is accepted if NPV is positive because it is expected to add value.
折现率 r 是企业的融资成本或要求回报率。如果 NPV 为正，则项目被接受，因为预期会增加价值。
8. NPV calculation and interpretation | 净现值计算与判断
Example: a project requires $100,000 and is expected to generate net cash inflows of $30,
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