IRR Calculator (2026) — Internal Rate of Return, Free

About the IRR Calculator

Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of an investment equal to zero. It shows the average annual percentage return an investment generates, accounting for the timing and size of cash flows.

Our IRR calculator supports two scenarios:

• Fixed Cash Flow: Same annual cash flow every year (stable projects)
• Irregular Cash Flow: Different cash flows each year (realistic projects)

Our calculator helps you:

• Calculate IRR percentage: See the effective annual return
• Compare investments: Evaluate which opportunity is most profitable
• Evaluate projects: Determine if expected returns meet requirements
• Analyze cash flows: View NPV at different discount rates
• Make decisions: Accept projects with IRR > cost of capital

How IRR Is Calculated

IRR is the discount rate that makes NPV = 0:

NPV Formula (What IRR Solves For)

NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ

Where:

• CF = Cash flow in each period
• r = Discount rate (the IRR we're solving for)
• NPV = 0 (at IRR, by definition)

IRR is found using iterative methods (Newton-Raphson method) because there's no direct algebraic formula.

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Fixed Cash Flow IRR

How It Works

When cash flows are constant at regular intervals, IRR calculation becomes more predictable:

NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ

Where all CF₁ through CFₙ are equal (fixed amounts at fixed intervals).

Fixed Cash Flow Parameters

Parameter	Options	Meaning
Initial Investment	Negative amount	Starting amount invested (outflow)
Duration	Years + Months	Total investment period (e.g., 2 years 6 months)
Payment Amount	Any dollar amount	Consistent payment per period
Payment Type	Deposit / Withdraw	Direction of cash flow (in or out)
Frequency	Monthly / Quarterly / Annually	How often payments occur
Timing	Beginning / End of Period	When payment is made (affects discount timing)
Ending Balance	Any dollar amount	Terminal value returned at end of period (salvage/residual)

Payment Type Explanation

Option	Meaning	When to Use
Deposit	Cash flowing into the investment	Annuity investments, savings plans, insurance funds
Withdraw	Cash flowing out of the investment	Loan repayments, withdrawal from fund

Payment Frequency Impact

Different frequencies create different numbers of periods:

Frequency	Example: 2 Years 6 Months
Monthly	30 monthly payments
Quarterly	10 quarterly payments
Annually	2-3 annual payments

More frequent payments → More periods → Potentially different IRR

Payment Timing Impact

Beginning of Period: Payment made at start (immediate discount benefit) End of Period: Payment made at end (standard accounting)

This affects the discount factor calculation and final IRR:

• Beginning payments have slightly lower present values (earlier discount)
• End payments are discounted one more period

Ending Balance (Terminal Value)

The Ending Balance is an amount you receive back at the end of the investment period. This represents:

• Salvage value of equipment
• Residual value of a lease
• Maturity value of a bond or investment
• Final payout or return of principal

How it affects IRR:

• Adds a final positive cash flow in the last period
• Increases total returns, typically raising IRR
• Essential for realistic project evaluations (without it, some projects have no IRR)

Example: Equipment purchase for $5,000 with monthly rental income of $200 for 2 years, then sold for $2,000 at end:

• Initial: -$5,000
• Monthly deposits: $200 × 24 = 24 payments of $200
• Ending Balance: +$2,000 (equipment sale)

Example 1: Fixed Cash Flow (Investment Account)

Scenario: Open an investment account with -$10,000, deposit $100 monthly for 2 years 6 months, receive $15,000 back

Parameters:

• Initial Investment: -$10,000 (money you invest)
• Duration: 2 years 6 months
• Payment Amount: $100
• Payment Type: Deposit (additional contributions)
• Frequency: Monthly (12 × 2.5 = 30 monthly payments)
• Timing: Beginning of month
• Ending Balance: $15,000 (final value returned)

This creates a cash flow stream:

• Period 0: -$10,000 (initial investment)
• Periods 1-30: +$100 (monthly deposits)
• Final period: $100 + $15,000 (last deposit + account liquidation)

The calculator finds the discount rate where NPV = 0, giving you the investment's IRR.

Example 2: Fixed Cash Flow (Loan Repayment)

Scenario: -$100,000 initial investment, $30,000 annual cash flow for 5 years

Find the rate where NPV = 0:

At 5%:

• NPV = -$100,000 + $30,000/1.05 + $30,000/1.05² + $30,000/1.05³ + $30,000/1.05⁴ + $30,000/1.05⁵
• NPV = -$100,000 + $28,571 + $27,211 + $25,915 + $24,681 + $23,526 = $29,904

At 10%:

• NPV = -$100,000 + $30,000/1.10 + $30,000/1.10² + $30,000/1.10³ + $30,000/1.10⁴ + $30,000/1.10⁵
• NPV = -$100,000 + $27,273 + $24,793 + $22,539 + $20,490 + $18,628 = $13,723

At 15%:

• NPV = -$100,000 + $30,000/1.15 + ... (continuing similar calculation)
• NPV ≈ $1,568

IRR ≈ 15.2% (where NPV = 0)

Fixed Cash Flow Advantages

Advantage	Explanation
Simple calculation	All future flows are identical
Predictable pattern	Easy to understand and verify
Stable projects	Represents consistent revenue streams
Quick comparison	Compare multiple similar projects easily

When Fixed Cash Flow Applies

• Equipment with guaranteed lease payments
• Annuity investments with equal payments
• Rental properties with stable rents
• Long-term service contracts
• Stable business projects with predictable returns

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Irregular Cash Flow IRR

How It Works

When cash flows vary by year, the NPV calculation becomes more complex:

NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ

Where CF₁, CF₂, CF₃, etc. are all different values.

Example: Irregular Cash Flow

Scenario: -$50,000 initial investment with varying cash flows

Year	Cash Flow
0	-$50,000
1	-$10,000
2	$30,000
3	$50,000

Find the rate where NPV = 0:

At 10%:

• NPV = -$50,000 + (-$10,000)/1.10 + $30,000/1.10² + $50,000/1.10³
• NPV = -$50,000 - $9,091 + $24,793 + $37,565 = $3,267

At 15%:

• NPV = -$50,000 + (-$10,000)/1.15 + $30,000/1.15² + $50,000/1.15³
• NPV = -$50,000 - $8,696 + $22,675 + $32,873 = -$3,148

IRR ≈ 12.9% (between 10-15%, where NPV = 0)

Irregular Cash Flow Advantages

Advantage	Explanation
Realistic	Matches actual project cash flows
Flexibility	Handles variable revenue streams
Detailed analysis	Shows impact of timing of cash flows
Project-specific	Captures unique cash flow patterns

When Irregular Cash Flow Applies

• Most real business projects
• Product launches (low early, ramping up)
• Equipment purchase with declining usage
• Real estate development (slow start, ramp-up, decline)
• Software products (high R&D, then recurring revenue)
• Manufacturing expansion (variable utilization)

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Fixed vs. Irregular: Comparison

Aspect	Fixed Cash Flow	Irregular Cash Flow
Annual Amount	Constant	Varies each year
Calculation	More straightforward	Requires iteration
Real-world Use	Leases, annuities, bonds	Most business projects
Predictability	Highly predictable	May be uncertain
Time Value Impact	Uniform discount effect	Timing matters greatly

Key Difference Example

Two projects, same total cash inflows ($120,000), same initial investment (-$100,000)

Project A (Fixed): -$100,000 → $40,000 → $40,000 → $40,000

• Steady returns, lower early IRR

Project B (Irregular): -$100,000 → $20,000 → $40,000 → $60,000

• Backloaded returns (delayed), lower IRR than Project A because money comes in later

Project C (Irregular): -$100,000 → $60,000 → $40,000 → $20,000

• Front-loaded returns (faster), higher IRR than Project A because money comes in earlier

Same total return, different timing, different IRR!

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IRR Advantages & Disadvantages

Advantages

Advantage	Why It Matters
Simple percentage	Easy to understand and compare
Single number	Summarizes entire project return
Time-aware	Accounts for when cash flows occur
Decision rule	Compare against cost of capital

Disadvantages & Limitations

Limitation	Impact	Solution
May not exist	Some cash flows have no IRR	Check for sign changes
Multiple IRRs possible	Non-conventional patterns	Use NPV instead
Ignores scale	$100k and $1M same treatment	Adjust targets by project size
Reinvestment assumption	Assumes reinvest at IRR rate	Use Modified IRR (MIRR)
Biased toward short projects	May favor quick returns	Use NPV or MIRR

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IRR vs. Other Metrics

Metric	Formula	Measures	Best For
IRR	Rate where NPV = 0	Percentage return	Comparing investment returns
NPV	Sum of discounted cash flows	Dollar value created	Final yes/no decisions
Payback Period	Time to recover investment	Liquidity, risk	Quick cash flow assessment
Profitability Index	PV of inflows / Initial investment	Return per dollar	Capital rationing
MIRR	IRR with realistic reinvestment rate	Adjusted return	More realistic comparison

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IRR Decision Rules

Single Project

• Accept if: IRR > Cost of Capital (your required return)
• Reject if: IRR < Cost of Capital

Example: If your cost of capital is 12% and project IRR is 15%, accept the project.

Multiple Projects, Limited Budget

1. Rank by IRR (highest first)
2. Accept projects in order until budget exhausted
3. All must exceed cost of capital

Example: With $500,000 budget and 12% hurdle rate:

• Project A: 18% IRR, $200,000 cost ✓
• Project B: 16% IRR, $300,000 cost ✓
• Project C: 14% IRR, $250,000 cost (Can't fit, not enough budget)
• Select A + B = $500,000

Choosing Between Two Projects

• If IRR is similar, use NPV to decide
• Project with higher NPV adds more value

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IRR Calculation Method: Newton-Raphson

The calculator uses the Newton-Raphson iterative method:

1. Start with initial guess: Assume IRR = 10%
2. Calculate NPV: See if it's positive or negative
3. Adjust rate: Move toward zero NPV
4. Repeat: Until NPV converges to approximately zero
5. Result: IRR is found when NPV ≈ 0

This method converges quickly for most real-world cash flows.

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Common Issues & Solutions

Issue: IRR Doesn't Exist

Cause: Cash flows don't have both positive and negative values

Solution: Ensure you have an initial investment (negative) and at least one positive inflow

Example of invalid cash flow: $100,000 → $150,000 → $200,000 (all positive, no investment)

Issue: Multiple IRRs

Cause: Cash flows change signs multiple times (unusual)

Solution: Use NPV method instead for reliable decision-making

Example: -$100,000 → $200,000 → -$150,000 (sign changes twice)

Issue: Very High or Negative IRR

Cause: Unusual cash flow patterns or project characteristics

Solution: Review cash flow assumptions; use NPV and profitability index for complete picture

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IRR vs. MIRR: When to Use MIRR

Modified IRR (MIRR) is more realistic because it assumes:

• Cash outflows are financed at the cost of capital
• Cash inflows are reinvested at the cost of capital

Use MIRR when:

• IRR is unrealistically high (suggests unrealistic reinvestment rate)
• Comparing projects with very different risk profiles
• You want a more conservative estimate

Example:

• Project IRR: 45% (unrealistic—can you reinvest at 45%?)
• Project MIRR: 18% (realistic—assumes 10% reinvestment)

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Disclaimer: This IRR calculator provides estimates for educational and planning purposes. Actual results depend on cash flow accuracy, market conditions, and assumptions. Consult financial advisors for major investment decisions. Past performance does not guarantee future results.

Frequently Asked Questions

What's a good IRR?

Depends on industry and risk level:

• Treasury bonds: 4-5% (very safe)
• Stock market average: 10% annually (moderate risk)
• Real estate: 8-12% (moderate-high risk)
• Business ventures: 20-50% (high risk)
• Startups: 50%+ expected (very high risk)

How do I compare projects with different time horizons?

IRR automatically accounts for timing, making it excellent for comparing different-length projects. Project with higher IRR is better return per year.

Should I use IRR or NPV?

Use both for complete analysis:

• IRR: Shows percentage return (good for comparison)
• NPV: Shows dollar value created (good for final decision)
• When conflicting: NPV is theoretically correct choice

Can IRR be negative?

Yes. Negative IRR means the project loses value (returns below 0%).

What does profitability index mean?

Profitability Index = PV of Inflows / Initial Investment

• > 1.0: Project is profitable (accept)
• < 1.0: Project destroys value (reject)
• Exactly 1.0: Break-even

How do I handle salvage value or terminal value?

Add it to the final year's cash flow:

• Last Year Cash Flow = Operating CF + Salvage/Terminal Value
• Then calculate IRR normally

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Disclaimer

This calculator is provided for informational and educational purposes only. Results are calculated based on standard formulas and your inputs. While we strive for accuracy, we do not guarantee that results are error-free or suitable for all applications. Always verify important calculations independently before making decisions based on the results. Users are responsible for the accuracy of their inputs and should consult appropriate professionals for critical applications. We are not liable for any decisions made based on these calculations.

Sources & References

The figures, formulas, and guidance behind this IRR Calculator: Fixed & Irregular Cash Flow Analysis draw on authoritative primary sources. For verification and further reading:

• U.S. Small Business Administration
• IRS — Businesses
• U.S. SEC — Investor.gov

Frequently Asked Questions