IRR & NPV Guide · 内部收益率与净现值指南

IRR & NPV Calculator Guide: How to Value Cash FlowsIRR 与 NPV 计算器指南：如何评估投资现金流的价值

By CalcSpace• Updated August 2026• 8 min read · 8 分钟阅读

Whether you're evaluating a stock, a rental property, or a business acquisition, the question is the same: is this investment actually worth what it costs? Two numbers answer it — Net Present Value (NPV) and Internal Rate of Return (IRR). They sound academic, but the math is the same one your savings account uses to decide what future dollars are worth today. This guide makes the formulas concrete, walks through a real example, and warns about the pitfalls that trip up most first-time users.

What Is NPV?

Net Present Value is the sum of all cash flows from an investment — inflows and outflows — each discounted back to today's dollars. If you invest $100,000 today and receive $30,000 a year for 5 years, the NPV tells you whether the total received is more, less, or exactly equal to the $100,000 you put up, after accounting for the time value of money.

NPV = Σ [ CF_t / (1 + r)^t ]

CF_t — cash flow at time t (positive = inflow, negative = outflow)
r — discount rate (your required return)
t — time period (typically years)

NPV > 0 → accept. NPV < 0 → reject. NPV = 0 → indifferent.

The discount rate r is your opportunity cost — what you'd earn on an equivalent-risk investment. For a stock you might use 8% (the long-run S&P 500 return). For a real estate investment, perhaps 5%. The higher r, the less future cash flows matter today.

Worked Example: A Rental Property

You buy a rental property for $200,000, putting 25% down and borrowing the rest. Over the next 5 years you collect net rental income (after mortgage, taxes, maintenance) of $12,000/year, then sell for $240,000 after paying off the mortgage. What discount rate makes this worthwhile?

Cash flows from your pocket (assuming you paid $50,000 down):

Year 0: −$50,000 (down payment + closing)
Year 1: +$12,000
Year 2: +$12,000
Year 3: +$12,000
Year 4: +$12,000
Year 5: +$12,000 + ($240,000 − mortgage balance) ≈ +$170,000

Discount at 8%:

NPV = −50,000 + 12,000/1.08 + 12,000/1.08² + 12,000/1.08³ + 12,000/1.08⁴ + 170,000/1.08⁵
= −50,000 + 11,111 + 10,288 + 9,526 + 8,820 + 117,892
≈ $107,637

That's positive — meaning at an 8% required return, this deal is worth about $107K more than it costs. Run the same numbers at a 15% discount rate and you'll see NPV drop sharply. Higher required return → fewer deals look attractive.

What Is IRR?

IRR is the discount rate that makes NPV exactly zero. In plain terms: what rate of return is this investment actually delivering? If your NPV is positive at 8% and negative at 15%, the IRR is somewhere in between — the rate at which the deal "breaks even."

There's no closed-form formula; IRR is solved iteratively (Newton-Raphson or trial-and-error in a spreadsheet). The decision rule:

IRR > your required return → accept.
IRR < your required return → reject.

In the rental example above, IRR works out to about 22% — meaning the deal earns 22% per year on your money, far above an 8% hurdle. That tracks with the NPV we computed.

When IRR Lies — Five Pitfalls

IRR is popular but treacherous. Five situations where it can mislead you:

Multiple IRRs. If cash flows change sign more than once (e.g., a project that requires reinvestment in year 5), the math has multiple mathematical solutions — and Excel will pick the wrong one. Use NPV instead.
Ignores project size. A $1,000 investment returning 100% IRR is a $1,000 gain. A $1,000,000 investment returning 20% IRR is a $200,000 gain. IRR alone doesn't tell you which deal is better — NPV does.
Reinvestment assumption. IRR assumes interim cash flows are reinvested at the IRR. NPV assumes reinvestment at the discount rate. The NPV assumption is more realistic for most projects.
No risk adjustment. A 20% IRR on a guaranteed Treasury is fantastic; a 20% IRR on a startup is mediocre once you weight the probability of failure.
Doesn't handle timing well. Two investments can have the same IRR but vastly different cash-flow profiles. Always look at the year-by-year numbers.

💡 Use NPV as your primary screen

For business and real-estate decisions, NPV is the more reliable metric. Use IRR for quick ranking and to communicate with non-technical stakeholders ("this deal returns 18%") — but never let IRR be the final word.

How to Pick the Discount Rate

The hardest part of NPV isn't the formula — it's choosing r. Three common approaches:

Method	Discount rate	Best for
WACC (weighted average cost of capital)	Mix of debt and equity cost	Business projects
Opportunity cost	Return you'd earn elsewhere at similar risk	Personal investments
Hurdle rate	A fixed number your firm requires (e.g., 15%)	Corporate budgeting

For personal decisions, the rule of thumb: pick the return you could earn in a low-cost index fund (historically 7–10% real), and add a risk premium for anything less liquid or more uncertain (real estate: +2%, startup: +10%+).

Try It

Use the IRR & NPV Calculator to:

Model a real-estate deal — enter your down payment, expected rental income, and projected sale price.
Sweep the discount rate from 5% to 20% and watch NPV cross zero — that's the IRR.
Compare two competing investments at the same discount rate to see which has higher absolute NPV (often not the one with higher IRR!).

The calculator accepts any cash-flow pattern, solves IRR with Newton-Raphson, and shows the full NPV curve across a range of discount rates.

无论你是评估股票、租房还是收购企业，问题都一样：这笔投资真的值它要价吗？两个数字能回答——净现值(NPV)与内部收益率(IRR)。它们听起来学术，但用的就是你的储蓄账户用来决定未来美元今天值多少钱的同一套数学。本文把公式讲具体、走一遍真实例子、并提醒最常见的坑。

什么是 NPV？

净现值是一笔投资所有现金流(流入和流出)的总和，每笔都贴现到今天的美元。如果你今天投 $100,000，未来 5 年每年收 $30,000，NPV 告诉你总共收到的钱相比当初投的 $100,000 是多、还是少、还是相等(考虑货币时间价值)。

NPV = Σ [ CF_t / (1 + r)^t ]

NPV > 0 → 接受；NPV < 0 → 拒绝；NPV = 0 → 无所谓。

贴现率 r 是机会成本——同风险下你能在别处赚到的回报。股票可以用 8%(标普 500 长期收益)；房地产可能用 5%。r 越高，未来现金流今天越不值钱。

举例：一套出租房

你花 $200,000 买一套出租房，25% 首付、其余贷款。未来 5 年每年净租金收入(扣除房贷、税费、维修)$12,000，然后 $240,000 出售(扣除剩余贷款)。什么贴现率让这笔交易划算？

从你口袋出的现金流(假设首付 $50,000)：

第 0 年：−$50,000(首付 + 成交费)
第 1 年：+$12,000
第 2 年：+$12,000
第 3 年：+$12,000
第 4 年：+$12,000
第 5 年：+$12,000 + ($240,000 − 房贷余额) ≈ +$170,000

按 8% 贴现：

NPV = −50,000 + 12,000/1.08 + 12,000/1.08² + 12,000/1.08³ + 12,000/1.08⁴ + 170,000/1.08⁵
= −50,000 + 11,111 + 10,288 + 9,526 + 8,820 + 117,892
≈ $107,637

这是正的——意思是在 8% 期望回报下，这笔交易比你付出的成本多值约 $107K。同样现金流按 15% 贴现，NPV 会大幅缩水。期望回报越高 → 看着划算的交易越少。

什么是 IRR？

IRR 是让 NPV 等于零的贴现率。说人话：这笔投资实际给你多少回报率？如果 8% 下 NPV 为正、15% 下为负，IRR 在两者之间——这笔交易"打平"的利率。

没有解析解；IRR 用迭代(牛顿法或电子表格试错)求解。决策规则：

IRR > 期望回报 → 接受。
IRR < 期望回报 → 拒绝。

上面出租房例子，IRR 约 22%——意思是这笔交易每年给你 22% 回报，远超 8% 门槛。这跟我们算的 NPV 一致。

IRR 何时骗你——五个陷阱

IRR 流行但危险。五种会误导你的场景：

多重 IRR。如果现金流多次变换方向(比如项目第 5 年需要追加投资)，数学有多个解——Excel 会选错那个。用 NPV。
忽略项目规模。$1,000 投资 100% IRR 是 $1,000 收益。$1,000,000 投资 20% IRR 是 $200,000 收益。IRR 单独不告诉你哪个更好——NPV 才会。
再投资假设。IRR 假设中间现金流按 IRR 再投资。NPV 假设按贴现率再投资。NPV 的假设对大多数项目更现实。
无风险调整。国债 20% IRR 是好得离谱；初创公司 20% IRR 一旦考虑失败概率就平平。
时间分布不敏感。两笔投资 IRR 相同，但现金流分布可能天差地别。一定要看逐年数字。

💡 NPV 才是主要筛选

商业和房产决策里，NPV 是更可靠的指标。用 IRR 做快速排序和跟非技术人员沟通("这笔交易 18% 回报")——但永远别让 IRR 一锤定音。

如何选贴现率

NPV 最难的不是公式——是选 r。三个常用方法：

方法	贴现率	适合
WACC(加权平均资本成本)	债务 + 权益成本混合	商业项目
机会成本	同风险下别处能赚的回报	个人投资
门槛回报率	公司硬性要求(如 15%)	企业预算

个人决策经验法则：选你在低成本指数基金能赚到的回报(历史上 7–10% 实际收益)，对流动性差或不确定性高的资产加风险溢价(房产：+2%；初创：+10%+)。

动手试试

用 IRR & NPV 计算器：

建模一笔房产交易——输入你的首付、预期租金、预测售价。
把贴现率从 5% 扫到 20%，看 NPV 在哪过零——那就是 IRR。
同样贴现率下比较两笔竞争投资，看谁的绝对 NPV 更高(常常不是 IRR 高的那个!)。

计算器接受任意现金流模式，用牛顿法解 IRR，并显示全贴现率区间的 NPV 曲线。

Open IRR & NPV Calculator → 打开 IRR & NPV 计算器