# Internal Rate of Return (IRR)

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## What is the Internal Rate of Return (IRR)?

The internal rate of return (IRR) is a financial metric that allows investors and businesses to evaluate the potential profitability and rate of return of different investment opportunities. At its core, the IRR represents the annualized rate of return that would make the net present value (NPV) of all cash flows from a project equal to zero.

In other words, the IRR calculates the breakeven discount rate where an investment’s expected future cash inflows have a present value precisely equal to the initial capital outlay. It is the rate at which an investment generates just enough compounded returns to recover its upfront costs.

The IRR serves as a key cost-benefit analysis tool in capital budgeting and investment analysis. It allows different projects to be assessed and ranked based on their projected rates of return, facilitating comparisons on an equal basis.

## Techopedia Explains the IRR Meaning

The internal rate of return is the discount rate that sets the present value of an investment opportunity’s future cash flows equal to the initial investment required.

Another plausible definition of the internal rate of return (IRR) is the annualized effective compounded return rate that would cover the cost of capital of said investment. For example, if a project has a 12% IRR, it means that the expected annual return on the initial investment is 12% after accounting for the time value of money of all future cash flows.

The higher the IRR, the more room an investor or business will have to tolerate a higher cost of capital as the project is expected to produce attractive annualized returns.

## How Does the IRR Work?

The IRR is calculated by applying the discounted cash flow (DCF) formula to project future cash inflows and outflows over a series of periods. The discount rate that equates an investment’s NPV to zero by offsetting its costs and future cash streams is the IRR.

### Internal Rate of Return Formula

The formula used to calculate the IRR sets the NPV equation’s result to zero and solves for the discount rate (r), which is the unknown IRR:

0 = -Initial Investment + CF1/(1+r)1 + CF2/(1+r) 2 + … + CFn/(1+r)^n

Where:

• CF1…CFn = future cash flows for each period
• r = the discount rate (which is the IRR)
• n = the total number of periods

This formula is identical to the NPV formula. However, the sum of the discounted future cash flows is forced to be zero to calculate what would be the discount rate (r) that satisfies this equation. That rate is the IRR.

### How to Calculate IRR?

Since there is no algebraic solution to this type of polynomial equation, the IRR must be calculated through an iterative process of trial and error. Various computational techniques are used to approximate the IRR, such as the Newton-Raphson method or simple iterative cycles that apply different discount rates until the NPV equals zero.

The IRR can be calculated in spreadsheet programs like Microsoft Excel using the IRR() function, which applies these iterative techniques to solve for the discount rate that zeroes out the investment’s NPV based on the project’s forecasted cash flows and initial cost.

## Using IRR for Capital Budgeting

Now that we have explored the meaning of the internal rate of return, it is worth asking in which instances this metric is used in the real world.

The primary use of the IRR is for evaluating potential investment opportunities as part of the capital budgeting process. Capital budgeting involves selecting projects and investments that will provide the highest future returns for a given acceptable risk level.

In this context, the IRR acts as a crucial metric to assess each alternative to rank them based on their expected rate of return. The general rule is that companies should invest in opportunities with an IRR that exceeds their minimum required rate of return, known as their hurdle rate.

A company’s hurdle rate for investments is typically benchmarked as its cost of capital or weighted average cost of capital (WACC). This represents the blended cost of financing for a business, accounting for both the cost of its debt and equity financing based on the percentage that they both contribute to the firm’s overall financial structure.

For example, a firm that uses 60% debt and 40% equity to finance its assets will have a WACC that will be closer to the interest rate it pays on its debts.

If an investment’s projected IRR surpasses this minimum hurdle rate, it should generate returns that are high enough to repay funding costs and create positive net value for the business. As long as a project’s IRR exceeds the hurdle rate, it is deemed a financially acceptable investment opportunity.

When evaluating multiple competing projects, companies will generally prioritize those with the highest IRR above their hurdle rate as those that have the most potential to produce profitable growth. Projects below the hurdle rate get rejected in both scenarios.

## IRR vs. Other Investment Analysis Metrics

While the internal rate of return is a widely utilized metric, it is not the only tool for analyzing investments. Two other common metrics used by investors and businesses include the net present value (NPV) and return on investment (ROI).

### IRR vs. Net Present Value (NPV)

The net present value (NPV) calculates the present dollar value of an investment’s future cash flows minus its upfront costs. The NPV provides the expected profit amount in today’s dollars at the required rate of return.

An NPV of zero indicates that the project covers its financing costs. Meanwhile, a positive NPV indicates that the project exceeds its cost of capital.

The formula to calculate the NPV is the following:

NPV = Sum of Present Value of Future Cash Flows – Initial Investment

Unlike the IRR, which is an implied rate, the NPV results in a dollar value that gauges the project’s expected profitability. While useful for evaluating single projects, the NPV does not facilitate quick comparisons and ranking like IRR percentages do.

### IRR vs. Return on Investment (ROI)

The return on investment (ROI) metric is simply the ratio of net income or profit generated by an investment relative to its initial cost. It is often expressed as a percentage return.

ROI = (Gain from Investment – Cost of Investment) / Cost of Investment

The ROI metric does not account for the time value of money or the timing of the project’s cash flows as the IRR does. It simply indicates how much the total investment increases or decreases in value by the end.

While the IRR, NPV, and ROI metrics all provide details on the performance of a given investment, the IRR is usually prioritized for ranking projects in capital budgeting due to its efficiency when it comes to comparing various options and the fact that it accounts for the time value of money.

## IRR Use Cases

The IRR analysis has applications across many investment scenarios and industries for both businesses and individuals.

Corporate Capital BudgetingPrivate Equity InvestingReal Estate InvestingVenture CapitalPersonal Finance

The IRR is core to capital budgeting processes where companies evaluate potential investments in new projects, equipment, facilities, expansion plans, and more. Initiatives are ranked by IRR versus the hurdle rate.

Private equity firms use IRR projections to evaluate potential acquisitions, leveraged buyouts, and investments in companies. They target minimum IRR thresholds, often starting at 20% or so.

Both commercial and residential real estate investors utilize IRR analysis to evaluate opportunities in the marketplace versus their required rates of return based on cap rates and financing costs.

High IRRs are targeted by VCs evaluating startup investments. However, the IRR can be distorted by early exit events like acquisitions.

Individuals can also calculate IRRs when evaluating major financial decisions involving mortgages, annuities, insurance policies, investment portfolios, and more.

## IRR Examples

To further illustrate how to calculate IRR, let’s look at some possible scenarios for investments:

### Example 1: Basic IRR Calculation

A company is evaluating a \$10 million investment in new machinery. The project is projected to generate \$3 million in additional annual cash flows for 6 years.

The IRR would be calculated as follows:

0 = -10,000,000 + 3,000,000/(1+r)1 + 3,000,000/(1+r)2 + 3,000,000/(1+r)3 + 3,000,000/(1+r)4 + 3,000,000/(1+r)5 + 3,000,000/(1+r)6

Solving for r using software, spreadsheets, or iterations results in an IRR of approximately 17.5%. If the company’s hurdle rate is 12%, this investment would be financially acceptable since the IRR of 17.5% exceeds that minimum threshold.

### Example 2: Unconventional Cash Flows

Now let’s look at an example with more complex and unconventional cash flows.

A company must invest \$5 million upfront in a given expansion project. It will generate \$2 million in year 1, have a \$1 million outflow in year 2 due to additional costs, and then it will generate \$3 million in years 3 and 4.

The formula to calculate IRR in this case would be as follows:

0 = -5,000,000 + 2,000,000/(1+r)1 – 1,000,000/(1+r)2 + 3,000,000/(1+r)3 + 3,000,000/(1+r)4

Solving for r reveals that there are two IRR values that satisfy this equation: 13.6% and 37%.

When there are multiple IRRs calculated, it indicates an unconventional or abnormal cash flow pattern. In these cases, the IRR may be distorted and may fail to provide a realistic outlook of the investment’s performance. More context would be needed on the investment details and assumptions to analyze it.

## Limitations of Internal Rate of Return

While powerful, the IRR is not a perfect analysis tool and has some key limitations to understand:

Reinvestment Rate Assumptions

The calculation assumes that any positive cash flows are reinvested at the computed IRR rate itself. In reality, companies may reinvest these cash flows at a lower or higher rate depending on available opportunities.

Multiple IRRs for Unusual Cash Flows

As shown in the second example above, the IRR can have multiple mathematically valid values when cash flow patterns are unconventional with mixtures of negative and positive flows. This ambiguity distorts the insights that the metric can provide.

No Absolute Dollar Returns

The percentage output does not reveal the expected dollar value of the project’s returns. A high IRR could be produced by a small investment versus a lower IRR on a much larger investment that could be more advantageous to companies with ample cash reserves to deploy.

Project Timing Discrepancies

The IRR tends to favor shorter-term projects over longer-lived assets or initiatives. The time value of money typically affects cash flows in the latest years of the investment the most. If most of the money that the project will produce will be made in later stages, the IRR may not be the best gauge to evaluate the investment’s performance.

Project Timing Discrepancies

The IRR tends to favor shorter-term projects over longer-lived assets or initiatives. The time value of money typically affects cash flows in the latest years of the investment the most. If most of the money that the project will produce will be made in later stages, the IRR may not be the best gauge to evaluate the investment’s performance.

External Factor Exclusions

The IRR does not account for externalities like inflation, opportunity costs, merits of underlying investments, risk factors, tax implications, and other similar factors.

Due to these limitations, IRR analysis is usually coupled with other capital budgeting metrics, sensitivity analysis, benchmarking to hurdle rates, payback periods, accounting ratios, scenario modeling, and qualitative assessments of risk and strategic value. The combination of these studies can help leaders and managers make more informed assessments of all available opportunities.

## The Pros and Cons of IRR Analysis

Like any financial tool, the IRR has its strengths and weaknesses that should be carefully weighed. These are some of the most prominent ones:

Pros

• Accounts for the time value of money
• Provides a standardized, percentage-based metric to compare investment opportunities
• Utilizes cash flows, offering a clearer picture than accounting profits
• Prioritizes higher rates of compounded returns.
• Facilitates easy determination of project attractiveness compared to capital benchmarks
• Aligns investment selection with maximizing shareholder value creation

Cons

• Relies heavily on accurate projections, subject to forecasting uncertainties
• Vulnerable to distortion from abnormal cash flow patterns
• Fails to indicate expected dollar profit or scale of investment
• Favors shorter projects over longer-term investment opportunities with potentially higher terminal values
• Ignores tax implications, external factors, opportunity costs, project risks, and qualitative implications

## The Bottom Line

The internal rate of return (IRR) is one of the most widely used techniques in corporate finance and capital budgeting to evaluate if an investment has enough merits to be executed.

By providing an expected rate of compounded annual returns, it allows organizations to methodically evaluate and rank investment opportunities against their cost of capital.

However, the IRR is not a perfect metric and has some shortcomings that must be weighed. It should be utilized as one component of a comprehensive investment evaluation framework that includes other studies like the net present value (NPV), accounting ratios, payback periods, opportunity costs, qualitative factors, risk profiles, and strategic implications.

When calculated and interpreted correctly as part of a multi-faceted analysis, the IRR serves as an invaluable decision-making tool for assessing an investment’s potential profitability and facilitating capital allocation to maximize shareholder value creation over the long term.

## References

1. Newton Raphson Method (Geeksforgeeks)