What is Internal Rate of Return (IRR)?

IRR is the discount rate that makes the Net Present Value (NPV) of all cash flows from a project equal to zero. It is the 'break-even' rate of return considering the time value of money. If IRR exceeds the required rate of return (hurdle rate), the project adds value; if below, it destroys value.

What is the difference between IRR and NPV?

NPV measures the absolute dollar value created or destroyed by a project at a specified discount rate. IRR is the break-even rate that makes NPV=0. NPV directly answers 'how much value does this create?' while IRR answers 'what rate of return does this generate?' When comparing mutually exclusive projects, NPV is more reliable - projects can have the same IRR but very different NPVs due to scale differences.

What is MIRR (Modified IRR)?

MIRR addresses two key weaknesses of IRR: (1) it assumes reinvestment of cash flows at the IRR itself (often unrealistic); (2) it may produce multiple IRRs for non-conventional cash flows. MIRR uses separate rates for financing (cost of capital) and reinvestment (safe reinvestment rate), producing a single realistic answer.

What is a good IRR for a project?

A good IRR depends on the hurdle rate - the minimum required return based on risk and cost of capital. For corporate projects: typically 10-15%+. For real estate: 12-20%+. For venture capital: 25-35%+. The key is that IRR exceeds the weighted average cost of capital (WACC) by a meaningful margin to justify the project's risk.

Why can a project have multiple IRRs?

Multiple IRRs occur when cash flows change sign more than once (non-conventional cash flows) - for example, an initial outflow, then positive inflows, then a large cleanup/decommissioning cost at the end. Descartes' Rule of Signs states there can be as many positive IRRs as there are sign changes. In these cases, use NPV or MIRR instead.

IRR Calculator

Internal Rate of Return · NPV at any discount rate · MIRR · Payback Period · NPV profile chart

Initial Investment ?

Holding Period

Ending Balance ?

Periodic Cash Flow ?

Frequency

Payment Timing

End of period Beginning

Optional Metrics

Hurdle Rate ?

Reinvestment Rate ?

Initial Investment

Hurdle Rate ?

Reinvestment Rate

Annual Cash Flows (positive = inflow)

Year	Cash Flow ($)

📊 Enter your investment details and click Calculate to see IRR, NPV, MIRR, and full sensitivity analysis.

Internal Rate of Return (IRR)

19.44%

per year · exceeds hurdle rate of 10%

NPV at Hurdle Rate

+$37,908

MIRR

14.62%

✓ ACCEPT

IRR (19.44%) exceeds hurdle rate (10.00%) - project adds value

Total Cash Inflows

$60,000

all positive CF

Total Cash Outflows

$40,000

investment + negatives

Payback Period

3.3 yrs

Disc. payback: 3.9 yrs

NPV at:

NPV = $37,908

💰 Cash Flow Schedule

Period	Cash Flow	PV Factor	Present Value	Cumulative PV

📈 NPV Profile

📊 NPV Sensitivity (Discount Rate vs NPV)

Discount Rate	NPV	Decision

What Is Internal Rate of Return?

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows from a project exactly equal to zero. It is the investment's "break-even" rate of return, fully accounting for the time value of money.

In simpler terms: IRR answers the question "If this project were a bank account, what interest rate would it be earning?" A project with an IRR of 15% is equivalent to a 15% annually compounding investment.

0 = CF₀ + CF₁/(1+IRR) + CF₂/(1+IRR)² + … + CFₙ/(1+IRR)ⁿ CF₀ = initial investment (negative) · CF₁…CFₙ = future cash flows · Solved iteratively

The IRR Decision Rule

IRR > Hurdle Rate: Accept - project generates returns above its cost of capital → creates value
IRR = Hurdle Rate: Indifferent - project exactly covers cost of capital
IRR < Hurdle Rate: Reject - returns insufficient to cover cost of capital → destroys value

ℹ️

IRR cannot be solved algebraically for most real-world cash flows - it requires iterative numerical methods (Newton-Raphson or bisection). This calculator uses binary search with 500 iterations, accurate to 0.001%.

NPV vs. IRR: Which to Use?

Both NPV and IRR are derived from the same discounted cash flow (DCF) framework, but they answer different questions and have different strengths:

Criterion	NPV	IRR
What it measures	Dollar value created	Rate of return
Decision rule	NPV > 0 → Accept	IRR > hurdle rate → Accept
Scale sensitivity	Yes ✓ (accounts for size)	No ✗ (ignores scale)
Multiple solutions	Always one answer ✓	May have multiple ✗
Reinvestment assumption	Cost of capital ✓ (realistic)	At IRR itself ✗ (often high)
Mutually exclusive projects	Always reliable ✓	Can mislead ✗
Communicability	Less intuitive ✗	Easy to compare ✓

⚠️

When IRR and NPV conflict: When comparing mutually exclusive projects, NPV is always the correct metric. IRR can favor a smaller, higher-rate project over a larger, higher-NPV project. The project that maximizes NPV maximizes shareholder value - always the correct goal.

The Scale Problem: A Classic Example

Project A costs $1,000, returns $1,500 in 1 year → IRR = 50%. Project B costs $1,000,000, returns $1,200,000 in 1 year → IRR = 20%. At a 10% hurdle rate, Project A has higher IRR, but Project B creates far more value: NPV of A = $364 vs NPV of B = $90,909. Choose B.

MIRR: Modified Internal Rate of Return

The Modified Internal Rate of Return (MIRR) corrects two fundamental weaknesses of standard IRR:

Unrealistic reinvestment assumption: Standard IRR assumes all positive cash flows are reinvested at the IRR itself. If IRR is 30%, this means every cash flow is assumed to compound at 30% - often impossible. MIRR uses a separate, realistic reinvestment rate (typically the cost of capital or risk-free rate).
Multiple IRR problem: Non-conventional cash flows (multiple sign changes) can produce multiple IRR solutions. MIRR always produces exactly one answer.

MIRR = [FV(positive CFs at reinvestment rate) / PV(negative CFs at financing rate)]^(1/n) - 1 Positive CFs compounded forward at reinvestment rate · Negative CFs discounted back at financing rate

MIRR Step-by-Step: Example

Investment: -$40,000 at year 0. Cash flows: Year 1: $10,000, Year 2: $20,000, Year 3: $30,000. Reinvestment rate: 5%. Financing rate: 10%.

Step 1 - FV of positive cash flows at 5%:
Year 1: $10,000 × (1.05)² = $11,025 | Year 2: $20,000 × (1.05)¹ = $21,000 | Year 3: $30,000 × (1.05)⁰ = $30,000
FV total = $62,025

Step 2 - PV of negative cash flows at 10%:
Year 0: $40,000 / (1.10)⁰ = $40,000

Step 3 - MIRR: ($62,025 / $40,000)^(1/3) - 1 = 15.74%
Compare to IRR of 19.44% - MIRR is lower and more realistic.

💡

MIRR is always between the reinvestment rate and the standard IRR. The larger the spread between IRR and reinvestment rate, the larger the difference between IRR and MIRR. For projects with modest cash flows and realistic reinvestment opportunities, the two metrics converge.

Capital Budgeting: Real-World IRR Applications

IRR is one of the most widely used metrics in capital budgeting - the process by which companies decide which long-term investments to pursue.

1. Equipment Purchase Decisions

A company considering a $500,000 machine that generates $120,000/year in cost savings for 6 years and has a salvage value of $50,000. IRR = approximately 15.8%. If the company's cost of capital is 9%, the project clears the hurdle by 6.8 percentage points.

2. Real Estate Investment

Real estate investors model property purchase price (outflow), annual rental income net of expenses (inflows), and eventual sale price (final large inflow). The IRR of this stream is called the property's "unlevered IRR" - typically targeted at 12-20% for institutional investors, higher for value-add deals.

3. Private Equity and Venture Capital

PE funds measure performance in IRR terms because investments occur at different times and exits occur after varying hold periods. A fund targeting a 20%+ IRR with a 3× cash-on-cash multiple over a 5-year hold is a standard institutional PE benchmark.

4. Bond Yield to Maturity (YTM)

Bond YTM is mathematically identical to IRR: it's the discount rate that makes the present value of all coupon payments and par value equal to the current market price. Our Finance Calculator (TVM) solves for this in the I/Y tab.

5. Lease vs. Buy Analysis

IRR can compare the cash flow streams of leasing vs. purchasing equipment. The lease creates a series of periodic outflows; buying creates a large upfront cost with potentially different depreciation tax benefits.

Typical IRR Benchmarks by Sector

Sector / Investment Type	Typical Target IRR	Hurdle Rate
S&P 500 Large-Cap Corporate Projects	12-15%	8-10% (WACC)
Real Estate - Core	7-10%	5-7%
Real Estate - Value-Add	12-18%	8-12%
Real Estate - Opportunistic	18-25%+	12-15%
Private Equity (buyout)	20-25%+	15-18%
Venture Capital (early stage)	35-50%+	25-30%
Infrastructure Projects	8-12%	5-8%

IRR Limitations and Pitfalls

1. The Multiple IRR Problem

When cash flows change sign more than once (non-conventional), multiple IRRs can exist. Descartes' Rule of Signs: the maximum number of positive IRRs equals the number of sign changes in the cash flow series.

Classic example: invest $1,000 (year 0), receive $3,000 (year 1), pay $2,500 cleanup cost (year 2). Signs: -, +, -. This produces two possible IRRs (approximately 3% and 290%). Neither is meaningful without additional analysis. Use NPV or MIRR instead.

2. No IRR for Certain Cash Flows

If all cash flows are negative (or all positive), no positive IRR exists. Similarly, very unusual cash flow patterns may have no real-number IRR solution.

3. Reinvestment Rate Assumption

Standard IRR implicitly assumes all intermediate cash flows are reinvested at the IRR itself. For a 30% IRR project, this means assuming you can reinvest $10,000 received in year 1 at 30% annually - often unrealistic. MIRR corrects this by using an explicit, realistic reinvestment rate.

4. Mutually Exclusive Projects

IRR can rank mutually exclusive projects incorrectly when they differ in scale or timing of cash flows. Always use NPV to choose between mutually exclusive alternatives.

5. Non-Normal Cash Flows

Projects with large terminal costs (environmental cleanup, nuclear decommissioning, mine reclamation) have non-normal cash flow patterns. The large negative terminal value can produce an IRR that misleadingly looks high early in the project's life.

The Payback Period: A Simpler Supplement

The payback period is the simplest capital budgeting metric: how many years until you recover your initial investment from cash inflows. It doesn't account for the time value of money (unlike discounted payback period) and ignores all cash flows after payback.

Payback Period = Year before full recovery + (Remaining Cost / Cash Flow in year) Discounted Payback: same but discounts each CF to PV first

Despite its limitations, payback period is widely used as a risk metric - shorter payback means faster capital recovery and less exposure to long-run uncertainty.

Frequently Asked Questions

How do I calculate IRR in Excel?

In Excel: =IRR(values, [guess]) where values is a range of cash flows starting with the initial investment (negative). Example: if CF0=-40000, CF1=10000, CF2=20000, CF3=30000 are in cells A1:A4, then =IRR(A1:A4) returns ~19.44%. Use =MIRR(values, finance_rate, reinvest_rate) for the modified IRR. Use =XIRR(values, dates) for irregular timing. This calculator produces the same results as Excel's IRR function.

What if my IRR calculation returns an error or no solution?

This usually means: (1) all cash flows are the same sign - at least one must be positive and one negative; (2) the cash flows have an unusual pattern with no real-number solution; (3) you have multiple IRRs due to non-conventional flows (multiple sign changes). In cases 2 and 3, use NPV at your hurdle rate as the primary decision metric instead of IRR.

What is the hurdle rate / cost of capital?

The hurdle rate (minimum acceptable rate of return) equals the project's cost of capital - the rate of return required to compensate investors for the project's risk. For a company, this is typically the WACC (Weighted Average Cost of Capital): a blend of the cost of equity (from CAPM) and the after-tax cost of debt, weighted by the capital structure. Projects must clear this rate to create shareholder value.

Is a higher IRR always better?

Not always. A higher IRR can reflect higher risk (VC investments need 35%+ IRR because most fail). For mutually exclusive projects, a higher IRR doesn't mean higher value - a small $1,000 investment at 50% IRR creates less value than a $1,000,000 investment at 15% IRR (given a 10% hurdle rate). NPV is the true measure of value creation; IRR tells you the rate, not the magnitude.

How is IRR used in real estate?

Real estate IRR models the full investment lifecycle: initial purchase (large negative CF), annual net operating income after expenses (positive CFs), and eventual sale proceeds (large positive CF at end). The IRR of this series is compared to the cost of capital or target return. Leveraged IRR (with mortgage financing) is typically higher than unlevered IRR because debt amplifies returns - but also amplifies losses.