Cost Benefit Analysis Formula for AI Projects成本效益分析公式完整指南：成本、收益、折现、敏感性、情景比较、决策验证、案例与实操

Calculate discounted NPV, BCR, ROI, and payback在线计算折现 NPV、BCR、ROI 与回收期

Enter incremental cash-equivalent benefits and costs by year. The calculator applies the same discount convention to both sides and keeps the benefit-realization assumption visible.

逐年输入相对于“维持现状”的增量收益和成本。计算器会对两侧采用同一折现口径，并把收益实现率单独显示，避免把预测收益直接当成必然发生。

What is the cost benefit analysis formula?成本效益分析公式是什么？

Present value of benefits (PVB) =
  Σ [Benefit at time t ÷ (1 + discount rate)^t]

Present value of costs (PVC) =
  Σ [Cost at time t ÷ (1 + discount rate)^t]

Net present value (NPV) = PVB − PVC

Benefit-cost ratio (BCR) = PVB ÷ PVC

Return on investment (ROI) =
  (PVB − PVC) ÷ PVC × 100%

The formulas are simple; the difficult work is defining a credible “with-project” change against business as usual, assigning costs and benefits to the correct period, avoiding double counting, selecting consistent units and discount rates, and preserving non-monetized impacts beside the summary metrics.

公式本身很简单，真正困难的是：相对于“照常运营”定义可信的项目增量变化；把成本和收益放入正确时期；避免重复计算；选择一致的计量单位和折现率；并在汇总指标旁保留无法货币化的影响。

Choose the metric that answers the decision选择能够回答决策问题的指标

Use NPV and BCR together. With identical discounted inputs, ROI equals BCR minus one, expressed as a percentage: a BCR of 1.70 corresponds to approximately 70% ROI. Payback adds a liquidity and timing view but should not replace lifetime value. No single metric determines strategic fit, operational feasibility, legal permission, or acceptable risk.

应同时使用 NPV 和 BCR。在折现输入完全相同时，ROI 等于 BCR 减一并表示为百分比：BCR 为 1.70，大致对应 70% 的 ROI。回收期补充了流动性和时间视角，但不能替代全生命周期价值。任何单一指标都无法决定战略匹配、运营可行性、法律许可或风险可接受性。

Calculate incremental value against business as usual相对于照常运营计算增量价值

Cost-benefit analysis compares options, not a project against zero. Define business as usual as the credible future without the proposed investment, including existing contracts, expected demand growth, required maintenance, known hiring, and planned process changes. Then calculate only the difference caused by each option.

成本效益分析比较的是不同方案，而不是拿项目和“零”比较。应把“照常运营”定义为不实施拟议投资时的可信未来，包括现有合同、预期需求增长、必要维护、已知招聘和计划中的流程变化。随后只计算每个方案造成的差异。

Incremental benefit at time t =
  outcome with project at t − outcome under business as usual at t

Incremental cost at time t =
  cost with project at t − cost under business as usual at t

For example, if analysis demand would rise 15% without AI and the team would already add two contractors, avoided contractor cost may be incremental. If a contract was ending regardless of the project, its removal is not an AI benefit. Record the owner and evidence for every business-as-usual assumption.

例如，如果没有 AI，分析需求也会增长 15%，团队原本会增加两名外包人员，那么避免的外包成本可能属于增量收益。如果某项合同无论是否实施项目都会终止，那么其取消就不是 AI 收益。应为每个“照常运营”假设记录负责人和证据。

Include the complete cost and benefit boundary纳入完整的成本与收益边界

Use opportunity cost for internal labor: time spent implementing the project cannot simultaneously deliver another priority. Keep sunk costs—past spending that cannot change—outside the forward decision, while still recording them for governance or lessons learned.

内部劳动应使用机会成本：实施项目所占用的时间无法同时用于其他优先事项。已经发生且无法改变的沉没成本不应进入前瞻决策，但仍可为治理或经验总结保留记录。

Discount future costs and benefits consistently一致地折现未来成本与收益

Discounting converts values occurring in different years to a common present-value basis. A future value is divided by one plus the discount rate raised to the period number. Year 0 is not discounted. Use the organization’s approved rate and valuation policy; do not copy a public-sector social discount rate into a private investment model without confirming that it answers the same question.

折现把不同年份发生的价值转换到共同的现值基础。未来价值要除以“一加折现率”的期数次方。第 0 年不折现。应使用组织获批的折现率和估值政策；不要未经确认就把公共部门社会折现率复制到私人投资模型，因为两者可能回答不同问题。

Present value at time t =
  future amount at t ÷ (1 + discount rate)^t

Discount factor at time t =
  1 ÷ (1 + discount rate)^t

Do not add inflation to a real discount rate and then apply it to nominal cash flows without a consistent conversion. State the currency, price year, nominal or real basis, tax treatment, discount rate, timing convention, and horizon at the top of the model.

不要在实际折现率上简单加通胀，再把结果应用于名义现金流。模型顶部必须说明币种、价格基年、名义或实际口径、税务处理、折现率、时间约定和分析期限。

Apply six rules before calculating BCR or NPV计算 BCR 或 NPV 前应用六条规则

1. Use incremental flows.使用增量现金流。Subtract the business-as-usual outcome from every option.从每个方案中减去照常运营的结果。
2. Use one price basis.使用同一价格口径。Keep all values real or all values nominal with a matching rate.所有价值均使用实际口径，或均使用名义口径并匹配折现率。
3. Assign the correct period.分配到正确时期。Record when resources are consumed and benefits are realized, not when a slide predicts them.记录资源实际消耗和收益实际实现的时间，而不是演示文稿预测的时间。
4. Use mutually exclusive value routes.使用互斥价值路径。Do not count the same recovered hour as avoided cost, added output, and strategic capacity.不要把同一个回收工时同时算作避免成本、新增产出和战略产能。
5. Include negative effects.纳入负面影响。Model correction, downtime, incidents, transition loss, and residual risk.建模修正、停机、事故、过渡损失和剩余风险。
6. Keep an evidence register.保留证据登记表。Attach source, owner, method, date, confidence, and refresh rule to each input.为每项输入附上来源、负责人、方法、日期、置信度和刷新规则。

Calculate a three-year AI project example计算一个三年期 AI 项目示例

This hypothetical example evaluates an AI-assisted data-analysis workflow over three years using an 8% discount rate. Year 0 includes implementation, integration, and training. Annual benefits combine mutually exclusive, verified routes: avoided external analysis, realized value from reused capacity, and lower rework. All figures are illustrative and rounded.

这个假设示例使用 8% 折现率评估一个三年期 AI 辅助数据分析工作流。第 0 年包括实施、集成和培训。年度收益由互斥且可验证的价值路径组成：避免的外部分析支出、回收产能实际再利用的价值，以及返工减少。所有数字仅用于演示并做了四舍五入。

The base case has positive NPV, BCR above 1, and discounted payback during year 2. That is not an automatic approval. Review whether the benefit evidence is attributable, whether the option meets nonfinancial constraints, whether a lower-cost option creates better value, and whether downside scenarios remain acceptable.

基准情景的 NPV 为正、BCR 大于 1，并在第 2 年内实现折现回收。但这并不意味着自动批准。还应审查收益证据能否归因、方案是否满足非财务约束、是否存在价值更高的低成本方案，以及下行情景是否仍可接受。

Calculate discounted payback with uneven cash flows计算不均匀现金流的折现回收期

Do not divide initial cost by an average annual benefit when cash flows vary. Accumulate discounted net benefits period by period. In the example, the unrecovered balance after year 1 is $54,815. Year 2 contributes $114,883 of discounted net benefit, so interpolation gives approximately 1 + 54,815 ÷ 114,883 = 1.48 years.

当现金流不均匀时，不要用初始成本除以平均年度收益。应逐期累计折现净收益。在示例中，第 1 年末尚未回收 $54,815；第 2 年提供 $114,883 的折现净收益，因此插值得到约 1 + 54,815 ÷ 114,883 = 1.48 年。

Discounted net flow at time t =
  (benefit at t − cost at t) ÷ (1 + rate)^t

Payback =
  full periods before crossing
  + unrecovered balance before crossing
    ÷ discounted net flow in crossing period

Interpolation assumes the crossing-period flow arrives evenly. If benefits arrive at a known date—such as annual contract avoidance—use monthly or quarterly periods instead. State whether the reported payback is simple or discounted because they answer different questions.

插值假定回收期内的现金流均匀发生。如果收益在已知日期发生，例如年度合同支出避免，应改用月度或季度周期。必须说明报告的是简单回收期还是折现回收期，因为两者回答的问题不同。

Prevent double counting in AI benefit formulas防止 AI 收益公式重复计算

Create a value ledger with one row per outcome, a unique identifier, causal mechanism, baseline, formula, owner, and overlap group. If two rows share the same overlap group, explain why both remain or remove one.

建立价值台账，每个结果一行，并记录唯一标识、因果机制、基线、公式、负责人和重叠组。如果两行属于同一重叠组，应解释为何都保留，否则删除其中一项。

Test sensitivity, scenarios, and switching values检验敏感性、情景与转换值

A point estimate hides decision risk. Use one-way sensitivity to identify influential inputs, coherent scenarios to show combinations of conditions, and switching values to show how far an assumption can move before the decision rule changes.

点估计会隐藏决策风险。使用单因素敏感性识别影响最大的输入；使用一致情景展示多种条件的组合；使用转换值说明某项假设变化多少会导致决策规则改变。

With costs unchanged, the example reaches BCR 1 when realized benefits fall to about 58.8% of the base forecast. In other words, benefits can fall by roughly 41.2% before NPV reaches zero. This is a switching value, not a probability. Pair it with evidence about how plausible such a shortfall is.

在成本不变时，该示例在实际收益降至基准预测约 58.8% 时达到 BCR 1。换言之，收益可下降约 41.2%，NPV 才会降至零。这是转换值，不是发生概率；还必须结合证据判断如此大的缺口是否可能出现。

Do not create a “downside” scenario by changing only one convenient variable. Link adoption, productivity, quality, demand, capacity reuse, and support cost in ways that can occur together. Preserve the formula and source behind every scenario value.

不要只改变一个方便的变量就称为“下行情景”。应以现实中可能同时发生的方式联动采用率、生产力、质量、需求、产能再利用和支持成本，并为每个情景数值保留公式和来源。

Value AI benefits from observed operational evidence从已观察的运营证据估值 AI 收益

Eligible annual tasks =
  total annual tasks × eligible share

AI-exposed tasks =
  eligible tasks × observed adoption

Net hours recovered =
  exposed tasks ×
  (baseline labor − assisted labor − review − rework) ÷ 60

Realized capacity value =
  net hours recovered × approved reuse rate × value per reused hour

Use accepted output, not generated output. Include all roles that prepare, review, correct, document, or operate the workflow. Apply adoption only to eligible tasks. Value recovered capacity only to the extent that it is reused for approved work; keep unused capacity visible instead of assigning it a fictional cash value.

应使用合格产出，而不是生成产出。纳入准备、审核、修正、记录或运营工作流的所有角色。采用率只应用于合格任务。只有回收产能被实际用于获批工作时才进行估值；未使用产能应保持可见，而不是赋予虚构的现金价值。

For risk reduction, model expected loss carefully: change in event probability multiplied by the attributable impact, less control and residual-risk costs. Use ranges when events are rare, and never present the full worst-case loss as an annual benefit.

对于风险降低，应谨慎建模期望损失：事件概率变化乘以可归因影响，再扣除控制成本和剩余风险成本。稀有事件应使用区间，绝不能把完整的最坏情况损失当作年度收益。

Keep material non-monetized impacts beside the formula在公式旁保留重大非货币影响

Not every consequence should be forced into dollars. Data privacy, explainability, employee impact, accessibility, supplier lock-in, resilience, strategic learning, and decision quality may be material even when credible valuation is unavailable. Describe direction, affected stakeholders, scale, timing, evidence strength, and whether the impact is a constraint.

并非每种后果都应强行换算成货币。数据隐私、可解释性、员工影响、无障碍、供应商锁定、韧性、战略学习和决策质量，即使无法可信估值，也可能非常重要。应说明影响方向、受影响利益相关者、规模、时间、证据强度，以及它是否构成约束。

Structure the calculation so another reviewer can reproduce it构建可供他人复现的计算表

Separate inputs, calculations, outputs, and evidence registers into visible areas. Lock formula cells, version assumption changes, and add automated checks: totals reconcile, discount factors decline correctly, all flows have units, no blank owners remain, and low/base/high ordering is logical.

把输入、计算、输出和证据登记划分到可见区域。锁定公式单元格，为假设变化建立版本，并添加自动检查：总额能够对账、折现因子正确递减、所有现金流都有单位、负责人不为空，且低/基准/高值顺序合理。

Interpret the formulas as evidence, not a verdict把公式视为证据，而不是判决

Compare all feasible options on the same scope and horizon, including a minimum viable change and business as usual. A higher BCR does not always dominate a larger positive NPV when budgets, capacity, strategic objectives, and indivisible investments differ. Document the trade-off and the decision owner’s rationale.

应在相同范围和期限内比较所有可行方案，包括最小可行变更和照常运营。当预算、产能、战略目标和不可分割投资存在差异时，更高的 BCR 不一定优于更大的正 NPV。应记录权衡以及决策负责人的理由。

Use a ten-step cost benefit analysis workflow使用十步成本效益分析流程

1. Define the decision.定义决策。Name the owner, options, deadline, objectives, constraints, and success criteria.明确负责人、方案、截止时间、目标、约束和成功标准。
2. Describe business as usual.描述照常运营。Forecast the credible future without the investment.预测不实施投资时的可信未来。
3. Map the causal mechanism.映射因果机制。Connect the intervention to operational changes and final outcomes.把干预与运营变化和最终结果连接起来。
4. Set scope and horizon.设定范围和期限。Include material setup, operation, transition, and end-of-life effects.纳入重大初始、运营、过渡和生命周期结束影响。
5. Quantify incremental flows.量化增量现金流。Use attributable quantities and mutually exclusive value routes.使用可归因数量和互斥价值路径。
6. Choose the valuation basis.选择估值口径。State currency, price year, real or nominal treatment, and discount rate.说明币种、价格基年、实际或名义处理以及折现率。
7. Calculate present values.计算现值。Apply timing consistently and reconcile undiscounted totals.一致应用时间处理，并核对未折现总额。
8. Calculate NPV, BCR, ROI, and payback.计算 NPV、BCR、ROI 和回收期。Use the same input boundary and label each definition.使用相同输入边界，并标注每个定义。
9. Test risk and uncertainty.检验风险与不确定性。Run sensitivity, coherent scenarios, and switching values.运行敏感性、一致情景和转换值分析。
10. Plan evaluation.规划评估。Assign owners, leading indicators, review dates, and stop or scale rules.分配负责人、领先指标、复核日期以及停止或扩展规则。

Avoid ten cost benefit formula mistakes避免十种成本效益公式错误

Move from formula to evidence and implementation从公式走向证据与实施

Use the cost benefit analysis example for a narrative worked case, the cost benefit analysis template for a reusable decision structure, and the business case template to connect economic evidence with strategy, delivery, risk, and governance.

使用成本效益分析示例查看叙事化完整案例，使用成本效益分析模板建立可复用的决策结构，并使用商业案例模板把经济证据与战略、交付、风险和治理连接起来。

Check the model before presenting the result展示结果前检查模型

• The decision, options, business-as-usual case, owner, deadline, and constraints are explicit.
• All costs and benefits are incremental, attributable, in scope, and placed in the correct period.
• The currency, price year, real or nominal basis, discount rate, horizon, and timing convention are stated.
• AI eligibility, adoption, acceptance, review, rework, and realized capacity reuse are evidenced.
• Every recovered workload unit has one mutually exclusive value route.
• NPV, BCR, ROI, and payback use clearly labeled, consistent input boundaries.
• Low, base, and high scenarios are coherent rather than arbitrary percentage changes.
• Sensitivity identifies influential assumptions and switching values.
• Material non-monetized impacts and mandatory constraints remain visible.
• Every material input has a source, method, date, owner, confidence, and refresh rule.

• 决策、方案、照常运营情景、负责人、截止时间和约束均已明确。
• 所有成本和收益均为增量、可归因、在范围内，并放入正确时期。
• 币种、价格基年、实际或名义口径、折现率、期限和时间约定均已说明。
• AI 合格性、采用、验收、审核、返工和产能实际再利用均有证据。
• 每个回收工作量单位只对应一条互斥价值路径。
• NPV、BCR、ROI 和回收期使用清晰标注且一致的输入边界。
• 低、基准和高情景具有一致逻辑，而不是任意调整百分比。
• 敏感性分析识别了关键假设和转换值。
• 重大非货币影响和强制约束保持可见。
• 每项重大输入都有来源、方法、日期、负责人、置信度和刷新规则。

Cost benefit analysis formula frequently asked questions成本效益分析公式常见问题