Table of Contents
Internal Rate of Return (IRR) Explained: Formula and Examples
- 5 min read
- Authored & Reviewed by: CLFI Team
The Internal Rate of Return, or IRR, measures how fast an investment grows each year once the timing of all cash flows is considered. It connects what you invest today with what you receive in the future. Investors and companies use it to compare projects, analyse deals, and decide whether an opportunity clears their target return.
Definition:
Internal Rate of Return (IRR)
The discount rate that makes the net present value (NPV) of all cash flows equal to zero, representing the annualised return on an investment.
- What it means: The rate that balances today’s investment with future cash inflows.
- Why it matters: It helps compare opportunities using a consistent annual rate.
- Used with: NPV, MIRR, payback, and qualitative judgment.
- Limitations: Results can mislead when project size, timing, or cash flow patterns differ.
Table of Contents
What Is the Internal Rate of Return?
The IRR represents the percentage return that equates the present value of an investment’s future inflows to its initial cost.
When an investment’s IRR is higher than the company’s hurdle rate or Weighted Average Cost of Capital (WACC), it creates value. If it falls below that threshold, it reduces value.
Definition:
Internal Rate of Return (IRR)
The discount rate that makes the net present value (NPV) of an investment’s cash flows equal zero, interpreted as the project’s internal annual growth rate.
How IRR Is Calculated
IRR is the discount rate that makes the net present value (NPV) of cash flows equal zero. In practice, analysts find it through iteration, testing rates until the discounted inflows equal the initial outlay.
Modern tools simplify this process through spreadsheet functions such as =IRR() or =XIRR() in Excel; XIRR() handles irregular cash flow dates and returns an annualised rate based on actual timing.
Conceptually, IRR can be viewed as the investment’s internal growth rate. It answers a simple question: “What annual return does this project deliver, once timing and value are both considered?”
In practice, executives use IRR to compare projects with different scales and durations on a common return basis. It provides a clear percentage benchmark for decision making, yet it should be interpreted together with NPV, payback, and strategic fit to avoid misleading choices where cash flow size or timing differences matter.
IRR Formula
Expanded form and variable definitions
IRR Formula
0 = CF0 + CF1 (1 + IRR) + CF2 (1 + IRR)2 + CF3 (1 + IRR)3 + … + CFN (1 + IRR)N
Definitions
CF0
Initial investment or outlay, usually negative (cash outflow).
CF1 … CFN
Cash flows received or paid at each period.
n
Time period index (typically years).
N
Total number of periods in the project.
NPV
Net Present Value. IRR is the discount rate where NPV = 0.
IRR
Internal Rate of Return — the annualised return balancing inflows and outflow.
What Is IRR Used For?
Teams use the Internal Rate of Return to judge whether an investment clears the required return and how it ranks versus alternatives. In capital planning, IRR helps compare establishing new operations with expanding existing ones.
An energy company, for example, can evaluate a new power plant against a renovation plan and select the option with the higher IRR that also meets its hurdle rate. Benefits include a common percentage benchmark and simple project ranking.
IRR Benchmark Example: New Power Plant vs. Renovation
The following table shows how an energy company could compare two capital projects using the internal rate of return (IRR). Both options require similar levels of investment but differ in duration, cash flow pattern, and expected risk.
| Project | Initial Outlay (£m) | Project Life (Years) | Average Annual Cash Inflow (£m) | IRR | Hurdle Rate | NPV @ 8% (£m) |
|---|---|---|---|---|---|---|
| Project A – New Solar Power Plant | 120 | 12 | 22 | 11.5% | 8% | +38 |
| Project B – Renovation of Existing Gas Plant | 85 | 8 | 16 | 9.4% | 8% | +14 |
Based on the results, Project A (the new solar power plant) delivers a higher IRR of 11.5% and a larger NPV at the company’s 8% hurdle rate. This suggests it generates more value relative to cost. However, its longer duration and higher capital intensity increase exposure to cost overruns and technology shifts. If management seeks stability and faster recovery, Project B may be preferred despite its lower return. In most cases, the higher-IRR, positive-NPV option should proceed, provided risk and funding capacity remain acceptable.
Programme Content Overview
The Executive Certificate in Corporate Finance, Valuation & Governance delivers a full business-school-standard curriculum through flexible, self-paced modules. It covers five integrated courses — Corporate Finance, Business Valuation, Corporate Governance, Private Equity, and Mergers & Acquisitions — each contributing a defined share of the overall learning experience, combining academic depth with practical application.
Chart: Percentage weighting of each core course within the CLFI Executive Certificate curriculum.
Grow expertise. Lead strategy.
Build a better future with the Executive Certificate in Corporate Finance, Valuation & Governance.
Corporations also use IRR when considering share buybacks.
If the expected IRR from repurchasing stock exceeds that of other opportunities such as new projects or acquisitions, the buyback may be a more efficient use of funds.
In private markets, IRR is essential for benchmarking fund performance. General Partners (GPs) report gross IRR to measure deal performance before fees, while Limited Partners (LPs) assess net IRR after management fees and carried interest.
Strong, consistent IRRs signal efficient deployment and exit discipline, helping firms raise new capital.
In practice, IRR is usually calculated in spreadsheets using =IRR() or =XIRR(). However, when cash flows are irregular or when reinvestment rates differ from the project return, MIRR provides a truer picture of profitability.
Definition:
Modified Internal Rate of Return (MIRR)
The Modified Internal Rate of Return (MIRR) refines the traditional IRR by assuming that positive cash flows are reinvested at a more realistic rate—usually the firm’s cost of capital—instead of at the project’s own return. MIRR also discounts negative cash flows at the financing rate, creating a single, more accurate measure of performance that removes the multiple-IRR problem and better reflects real reinvestment conditions.
It aligns assumptions with how companies actually deploy excess cash and finance ongoing investments.
For this reason, analysts often compare MIRR with NPV to assess both the rate and the total value created, ensuring that results remain economically consistent rather than purely mathematical.
The Two IRR Formulas: Definition and Estimation
When studying IRR, two formulas often appear. They are closely connected, yet serve different purposes. One defines what IRR means in financial theory, while the other helps estimate it in practice when solving manually. Understanding the link between the two prevents confusion about how IRR is actually derived.
1) The Definition Formula — The Core Equation of IRR
The internal rate of return is the discount rate that makes the Net Present Value (NPV) of all cash flows equal zero. This equation expresses the fundamental relationship between an investment’s outflows and inflows over time:
0 = CF0 + CF1 / (1 + IRR) + CF2 / (1 + IRR)2 + … + CFN / (1 + IRR)N
This is the core definition of IRR. It states that at the internal rate of return, the present value of inflows equals the investment’s cost. In practice, solving this equation requires trial and error — adjusting the rate until the NPV equals zero. Spreadsheet functions such as =IRR() or =XIRR() follow this same iterative logic automatically.
2) The Interpolation Formula — A Manual Estimation Shortcut
Before spreadsheets became common, analysts estimated IRR manually by testing two discount rates — one producing a positive NPV and another producing a negative NPV — and then interpolating between them. The closer these two rates are, the more accurate the estimate:
IRR Linear Interpolation (Manual Approximation)
Use two discount rates with opposite-sign NPVs to estimate IRR without a solver.
Interpolation Formula
IRR = ra + NPVa NPVa − NPVb ( rb − ra )
Definitions
ra
Lower discount rate tested (ideally gives a positive NPV).
rb
Higher discount rate tested (ideally gives a negative NPV).
NPVa, NPVb
NPVs computed at ra and rb respectively.
Purpose
Linear approximation of the true IRR between two tested rates.
=IRR()/=XIRR() to verify.
Here, ra and rb are the two trial discount rates, while NPVa and NPVb are the NPVs computed at those rates. The formula assumes that between these two points, the relationship between NPV and the discount rate is approximately linear, allowing for a simple estimation of the rate where NPV equals zero.
How the Two Formulas Connect
Both formulas describe the same concept from different angles. The first is theoretical — it defines what IRR is. The second is practical — it gives a straightforward method to approximate it when solving by hand. Modern software simply automates what the interpolation method achieves manually.
The cash-flow equation defines the problem.
The interpolation formula provides the shortcut to solve it.
Understanding this distinction clarifies why IRR can be found by either solving for NPV = 0 through iteration, or estimating it between two trial rates using interpolation. Both lead to the same result — identifying the rate at which an investment just breaks even in present-value terms.
Comparisons, Advantages and Limits
The Internal Rate of Return is a strong indicator of investment efficiency, but it should never be interpreted on its own.
It works best when assessed alongside complementary metrics such as the
Net Present Value (NPV),
Return on Investment (ROI), or the
Modified Internal Rate of Return (MIRR).
Each measure offers a different perspective on profitability, timing, and scale.
| Metric | Focus | Best For | Limitation |
|---|---|---|---|
| IRR | Annualised percentage return | Ranking similar investments | Insensitive to scale differences |
| NPV | Value created in currency terms | Measuring shareholder value | Requires a discount rate assumption |
| MIRR | Adjusted IRR using realistic reinvestment rate | Refining IRR results for accuracy | Needs reinvestment rate inputs |
| ROI | Total growth from start to finish | Quick, high-level comparison | Ignores time value of money |
Advantages
- Incorporates the time value of money by discounting actual cash flows.
- Produces a clear percentage that is easy to interpret and communicate.
- Applies across industries, from corporate finance to private equity and real estate.
Limitations
- May generate multiple results when cash flows alternate between positive and negative.
- Assumes reinvestment at the same rate, which is rarely realistic in practice.
- Can favour small, quick projects with high rates over larger, longer-term ones that create greater total value.
Example of IRR Calculation
Two projects with different cash-flow patterns, compared on IRR and NPV at a 9% opportunity cost of capital.
Cash Flows (in $ thousands)
| Project | Year 0 | Year 1 | Year 2 |
|---|---|---|---|
| A | -400 | +250 | +300 |
| B | -200 | +140 | +179 |
Results
| Project | IRR (annualised) | NPV @ 9% | Passes 9% hurdle? |
|---|---|---|---|
| A | ≈ 23.3% | ≈ +81.9 | Yes |
| B | ≈ 35.9% | ≈ +79.1 | Yes |
=IRR(values) or =XIRR(values, dates). Because the equation is polynomial, an iterative solver is used rather than algebra.Interpretation
Both projects exceed the 9% hurdle, so both are acceptable in principle. Project B has the higher IRR (≈ 35.9%), indicating a faster annualised return, while Project A shows a slightly higher NPV at 9% in this setup.
Decision rule: if you are ranking by efficiency of return and projects are otherwise comparable, pick Project B for its higher IRR. If scale of value creation at your hurdle rate is the priority, use NPV and consider Project A. Best practice is to review both IRR and NPV before committing.
Conclusion
The Internal Rate of Return (IRR) is a valuable metric for assessing the financial attractiveness of investment opportunities.
It summarises the efficiency of capital use by showing the annualised rate of return that equates an investment’s cost with its future cash inflows.
When applied correctly, IRR helps managers compare and rank projects, decide between competing capital allocations, and communicate expected performance in a simple percentage format.
Yet the value of IRR depends on context.
The calculation assumes that intermediate cash inflows can be reinvested at the same rate, which may not hold in practice.
It can also produce misleading signals when projects differ in size, duration, or risk profile.
To avoid these pitfalls, analysts should review IRR together with complementary measures such as
Net Present Value (NPV)
and Modified IRR (MIRR),
and test outcomes under different discount rate scenarios.
Used alongside sound judgment and sensitivity analysis, IRR remains one of the most practical and enduring tools in corporate finance.
It allows decision-makers to link investment choices with value creation and to evaluate diverse opportunities on a consistent, time-adjusted basis.