Finance

IRR and NPV Calculator for Investment Projects

Q: What is IRR and how do you calculate it?

The **IRR (Internal Rate of Return)** is the discount rate that makes NPV equal zero — it is the project's effective annual yield. There is no closed-form formula; it is found iteratively. Decision rule: if **IRR > your required return (discount rate)**, accept the project. In Excel: `=IRR(cash_flows)` where the first value is the negative initial investment.

Q: What is NPV and when is it positive?

**NPV (Net Present Value)** is the sum of discounted future cash flows minus the initial investment: `NPV = −Investment + Σ CashFlow/(1+r)^t`. **NPV > 0**: the project creates more wealth than your best alternative — accept. **NPV = 0**: breakeven with your opportunity cost. **NPV < 0**: destroys value — reject. NPV depends heavily on the chosen discount rate.

Q: What discount rate should I use?

Use **your opportunity cost** — the best alternative return available to you. For personal decisions, compare to a savings account or bond yield. For businesses, use the **WACC** (Weighted Average Cost of Capital). For higher-risk projects, add a **risk premium** of 5-15 percentage points. US Treasury 10Y (~4.5%) is the standard risk-free baseline for USD projects.

Q: What is the difference between NPV and IRR?

**NPV** measures **absolute wealth created** (dollars today). **IRR** measures **percentage return**. Example: Project A invests $1M, NPV +$500K (IRR 40%). Project B invests $10M, NPV +$2M (IRR 25%). By NPV you pick B (more dollars). By IRR you pick A (higher percent). Rule: when mutually exclusive (can only do one), maximize **NPV**. When independent, accept any project where IRR exceeds your hurdle rate.

Q: Why is my IRR negative or very high?

**Very high IRR**: either genuinely excellent return, overestimated cash flows, or underestimated investment. **Negative IRR**: cash flows never recover the investment even at 0% discount. Check units, time periods, and signs. **Multiple IRRs** occur when cash flows flip signs more than once — trust NPV only in those cases.

Q: How do I handle uneven cash flows?

This calculator assumes **constant annual cash flow**. For variable flows: (1) use the average for a quick estimate; (2) use Excel `=NPV(rate; flows)` plus `=IRR(flows)` with actual year-by-year values; (3) for flows growing at a constant rate, use the Gordon model: NPV = F / (r − g). Always add salvage value as the final-period cash flow.

Q: Is a small positive NPV enough to justify the investment?

**Depends on risk and effort**. NPV of +$5K on a $1M project (0.5%) is essentially indifferent — any surprise erases it. Best practice: require a **safety margin** of NPV/Investment ≥ 20-30%. Also run a downside scenario (flows down 30%): does NPV stay positive? Projects worth doing have clearly positive NPV that survives shocks.

Q: Can a project have high IRR but low NPV?

**Yes, in small-scale projects**. Example: invest $10K, receive $20K in one year = IRR 100%, NPV +$3.3K (at 50% hurdle). Very high percentage but small absolute dollars. For individuals replicating capital, the high IRR may compound well. For corporations maximizing shareholder wealth, higher NPV wins even at lower IRR.

Q: How do I include taxes in the analysis?

Always use **after-tax cash flows**. Formula: Net Flow = (Revenue − Operating Costs − Depreciation) × (1 − Tax Rate) + Depreciation. Depreciation reduces taxable income but is not a cash outflow — so you add it back. The effective corporate tax rate in the US is roughly 21% federal plus state. For individuals, apply your marginal income tax rate to project profits.

Q: How do I compare projects with different time horizons?

Do not compare raw NPV across projects of different lengths — it is biased toward longer projects. **Solution**: calculate the **Equivalent Annual NPV (EAN)** by dividing each NPV by the annuity factor at the same discount rate. Or replicate the shorter project over the same total horizon and recalculate. The EAN converts different-length projects to a common annualized basis.

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Reviewed by: Martín Rodríguez (política editorial ) · Last reviewed: 5 jun 2026

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You have $10 million and someone offers a project that returns $3M per year for 5 years. Should you take it or leave the money earning 40% in a savings account? Two classic financial metrics answer this: NPV (Net Present Value) and IRR (Internal Rate of Return). The NPV tells you how much wealth in today's dollars the project creates after accounting for your opportunity cost. The IRR tells you the project's effective return, which you can directly compare to your best alternative (savings account, bonds, another business). This calculator takes your initial investment, expected annual cash flow, project duration, and discount rate (opportunity cost), then returns NPV, IRR, payback period, total cash received, and an automatic verdict. Used in business decisions (CapEx, expansions, new products), real estate investing (does rental income beat a bond?), equipment evaluation, personal projects (franchise, online course, crypto staking). 2026 data — customize to your situation.

Last reviewed: June 4, 2026 Verified by Martín Rodríguez Source: Ross, Westerfield, Jaffe — Corporate Finance (Chapter NPV/IRR), Damodaran Online — Valuation Data, CFA Institute — Investment Analysis 100% private

IRR (Internal Rate of Return) is the discount rate that makes NPV equal zero — it is the project's effective yield. NPV (Net Present Value) is the wealth created in today's dollars after subtracting your opportunity cost. Rule: if IRR > discount rate and NPV > 0, the project is worth it. Formula: NPV = −Investment + Σ CashFlow/(1+r)^t.

When to use this calculator

Decide whether rental income from an apartment beats a sovereign bond.
Your company analyzes expansion to a new city with CapEx of $50M.
You're deciding between buying a franchise or investing in a diversified portfolio.
Compare two industrial machines with different costs and useful lives.
Evaluate crypto staking or liquidity pools against a fixed-income alternative.

Example: $100K investment, $25K annual cash flow for 6 years, 10% discount rate

Initial investment: $100,000 (year 0).
Cash flows: $25,000 per year for 6 years.
Discount rate: 10% annually (your opportunity cost).
NPV formula: −Investment + Σ Cash Flow / (1+r)^t.
Calculation: −100,000 + 25,000/(1.10)¹ + 25,000/(1.10)² + ... + 25,000/(1.10)⁶.
Present values: $22,727 + $20,661 + $18,783 + $17,075 + $15,523 + $14,112 = $108,882.
NPV: −100,000 + 108,882 = +$8,882 (positive).
IRR: ≈ 12.98% (the rate that zeroes out NPV).
Payback: 100,000 / 25,000 = 4.0 years.

Result: NPV positive (+$8,882) and IRR 12.98% > discount rate 10%: the project beats your opportunity cost. Both signals agree — accept. Sensitivity check: if discount rate rises to 13%, NPV turns slightly negative.

How it works

4 min read

What are NPV and IRR

They are the two classic indicators for project evaluation, found in every corporate finance textbook (Brealey-Myers, Ross, Damodaran).

Net Present Value (NPV)

The sum of discounted future cash flows in today's dollars, minus the initial investment:

NPV = −Investment + Σ (Cash Flow_t / (1+r)^t)   for t = 1 to n

NPV > 0: project generates more value than your required return → ACCEPT.

NPV = 0: indifferent (project returns exactly your required rate).

NPV < 0: project destroys value → REJECT.

Internal Rate of Return (IRR)

The discount rate r* that makes NPV = 0. Represents the project's effective return rate.

0 = −Investment + Σ (Cash Flow_t / (1+r*)^t)

No closed-form solution — calculated iteratively (bisection or Newton-Raphson).

IRR > discount rate → project returns more than your opportunity cost → ACCEPT.

IRR < discount rate → returns less → REJECT.

Payback Period

Years needed to recover the investment without discounting. Useful but secondary — ignores time value of money.

Simple payback = Investment / Annual cash flow

Decision Table

NPV	IRR vs Discount Rate	Decision
> 0	IRR > r	ACCEPT (aligned signals)
= 0	IRR = r	Indifferent
< 0	IRR < r	REJECT (aligned signals)
> 0	IRR < r	Rare — complex flows, trust NPV
< 0	IRR > r	Rare — complex flows, trust NPV

NPV Reference Table

Example: $100 invested, $20/year constant cash flow (IRR of this project = 15%):

Project years	Rate 5%	Rate 10%	Rate 15%	Rate 20%	Rate 30%
5 years	−$13.2	−$24.2	−$32.9	−$40.2	−$52.9
10 years	+$54.4	+$22.9	−$0.4	−$16.1	−$39.5
15 years	+$107.1	+$52.1	+$17.3	−$4.9	−$32.1
20 years	+$149.3	+$70.1	+$25.6	−$0.6	−$28.5

When rate = IRR (15%), NPV hovers near zero at long horizons.

Typical Discount Rates

Source	Rate (approx 2026)	When to use
US savings account	4-5%	Low-risk personal decisions
US Treasury 10Y	4-5% USD	Risk-free baseline
S&P 500 historical avg	~10% nominal	Equity opportunity cost
VC / startup hurdle	25-40%	High-risk ventures
Real estate	6-10%	Rental property analysis
WACC (US large cap)	8-12%	Corporate projects
WACC (SME)	12-20%	Smaller companies

For high-risk projects (new venture, innovation), add a risk premium of 5-15 percentage points above your baseline.

Example 1: Apartment Rental

Scenario: Buy apartment for USD 100,000. Rents for USD 500/month = USD 6,000/year. Hold 10 years, sell for USD 110,000.

Initial investment: −USD 100,000
Cash flows (years 1-9): USD 6,000
Cash flow (year 10): USD 6,000 + USD 110,000 = USD 116,000
Discount rate: 7% USD

NPV ≈ −$1,966 USD (slightly negative)
IRR ≈ 6.7% USD

Verdict: returns less than a 7% bond (not financially compelling, though property has emotional value, inflation hedge, etc.).

Example 2: Franchise

Scenario: Cafe franchise. Initial investment $50,000. Net cash flow $15,000/year for 5 years. Discount rate 20%.

NPV = −50,000 + 15,000 × [1 − 1.20^(−5)] / 0.20
    = −50,000 + 15,000 × 2.991
    = −50,000 + 44,860
    = −$5,140 (negative NPV)
IRR ≈ 15.2% (below 20%)

Verdict: Not worth it at 20% hurdle rate. Becomes worthwhile only if your discount rate falls below ~15.2%.

NPV and IRR with Variable Cash Flows

This calculator assumes constant annual cash flow. For variable flows, use Excel or Google Sheets:

=NPV(rate; cash_flows) — note this is a present-value-of-future-flows function; subtract the initial investment separately

=IRR(cash_flows) — first row must be the negative initial investment

Why IRR Can Mislead

1. Different project scales: High IRR on a small project does not beat lower IRR on a large one. NPV wins.
2. Multiple IRRs: If cash flows flip signs multiple times, multiple IRRs exist. Trust NPV only.
3. Reinvestment assumption: IRR assumes reinvesting intermediate cash flows at the same rate — often unrealistic at high IRRs. Modified IRR (MIRR) corrects this.
4. Mutually exclusive projects: If choosing between A and B, pick highest NPV, not highest IRR.

Discounted Payback

Year	Cash Flow	Present Value (10%)	Cumulative
0	−100,000	−100,000	−100,000
1	25,000	22,727	−77,273
2	25,000	20,661	−56,611
3	25,000	18,783	−37,828
4	25,000	17,075	−20,753
5	25,000	15,523	−5,230
6	25,000	14,112	+8,882

Discounted payback: just over 5 years (at 10% rate).
Simple payback: 4.0 years.

WACC — Corporate Discount Rate

WACC = (E/V × Re) + (D/V × Rd × (1 − T))

Where:

E = market value of equity, D = market value of debt, V = E + D

Re = cost of equity (from CAPM), Rd = cost of debt

T = corporate tax rate

CAPM: Re = Rf + β × (Rm − Rf)

Rf = risk-free rate (US Treasury 10Y ~4.5%)

β = sector beta, Rm − Rf = market risk premium (~6-8%)

Common Mistakes in NPV/IRR Analysis

1. Wrong currency: USD cash flows → USD rate. Inflation-adjusted flows → real rate.
2. Ignoring taxes: Always use after-tax cash flows.
3. Missing salvage value: Add terminal asset sale to final year cash flow.
4. Ignoring working capital: Upfront investment in inventory/receivables is a real cash outflow.
5. Overestimating cash flows: Run pessimistic/base/optimistic scenarios.
6. Comparing different time horizons: Use equivalent annual NPV for fair comparison.

Related Calculators

Compound Interest — the foundation of discounting.

Loan Payment — the flip side of investment.

Simple Interest — baseline for short-term analysis.

Frequently asked questions

What is IRR and how do you calculate it?

The IRR (Internal Rate of Return) is the discount rate that makes NPV equal zero — it is the project's effective annual yield. There is no closed-form formula; it is found iteratively. Decision rule: if IRR > your required return (discount rate), accept the project. In Excel: =IRR(cash_flows) where the first value is the negative initial investment.

What is NPV and when is it positive?

NPV (Net Present Value) is the sum of discounted future cash flows minus the initial investment: NPV = −Investment + Σ CashFlow/(1+r)^t. NPV > 0: the project creates more wealth than your best alternative — accept. NPV = 0: breakeven with your opportunity cost. NPV < 0: destroys value — reject. NPV depends heavily on the chosen discount rate.

What discount rate should I use?

Use your opportunity cost — the best alternative return available to you. For personal decisions, compare to a savings account or bond yield. For businesses, use the WACC (Weighted Average Cost of Capital). For higher-risk projects, add a risk premium of 5-15 percentage points. US Treasury 10Y (~4.5%) is the standard risk-free baseline for USD projects.

What is the difference between NPV and IRR?

NPV measures absolute wealth created (dollars today). IRR measures percentage return. Example: Project A invests $1M, NPV +$500K (IRR 40%). Project B invests $10M, NPV +$2M (IRR 25%). By NPV you pick B (more dollars). By IRR you pick A (higher percent). Rule: when mutually exclusive (can only do one), maximize NPV. When independent, accept any project where IRR exceeds your hurdle rate.

Why is my IRR negative or very high?

Very high IRR: either genuinely excellent return, overestimated cash flows, or underestimated investment. Negative IRR: cash flows never recover the investment even at 0% discount. Check units, time periods, and signs. Multiple IRRs occur when cash flows flip signs more than once — trust NPV only in those cases.

How do I handle uneven cash flows?

This calculator assumes constant annual cash flow. For variable flows: (1) use the average for a quick estimate; (2) use Excel =NPV(rate; flows) plus =IRR(flows) with actual year-by-year values; (3) for flows growing at a constant rate, use the Gordon model: NPV = F / (r − g). Always add salvage value as the final-period cash flow.

Is a small positive NPV enough to justify the investment?

Depends on risk and effort. NPV of +$5K on a $1M project (0.5%) is essentially indifferent — any surprise erases it. Best practice: require a safety margin of NPV/Investment ≥ 20-30%. Also run a downside scenario (flows down 30%): does NPV stay positive? Projects worth doing have clearly positive NPV that survives shocks.

Can a project have high IRR but low NPV?

Yes, in small-scale projects. Example: invest $10K, receive $20K in one year = IRR 100%, NPV +$3.3K (at 50% hurdle). Very high percentage but small absolute dollars. For individuals replicating capital, the high IRR may compound well. For corporations maximizing shareholder wealth, higher NPV wins even at lower IRR.

How do I include taxes in the analysis?

Always use after-tax cash flows. Formula: Net Flow = (Revenue − Operating Costs − Depreciation) × (1 − Tax Rate) + Depreciation. Depreciation reduces taxable income but is not a cash outflow — so you add it back. The effective corporate tax rate in the US is roughly 21% federal plus state. For individuals, apply your marginal income tax rate to project profits.

How do I compare projects with different time horizons?

Do not compare raw NPV across projects of different lengths — it is biased toward longer projects. Solution: calculate the Equivalent Annual NPV (EAN) by dividing each NPV by the annuity factor at the same discount rate. Or replicate the shorter project over the same total horizon and recalculate. The EAN converts different-length projects to a common annualized basis.