Internal Rate of Return (IRR)Defined with Formula and Examples

Written By:
Lisa Borga

Reviewed By:
FundsNet Staff

The internal rate of return is a way to measure your return on investment for projects or investments that do not take into account external factors.

This metric can be used to help determine whether or not potential investments will be profitable.

Typically an investor is going to want a high IRR rather than a low IRR because an investment with a high IRR is likely to add value to a portfolio.

Investors can even use the IRR to rank investments.

Generally, the investment with the highest IRR would be the best choice assuming the investments have similar characteristics.

The IRR is a discount rate which when used in a discounted cash flow analysis, sets the net present value of all of the cash flows being considered to zero.

The IRR does not give the actual dollar amount of an investment but instead gives the annual return that would make the net present value equal zero.

Important Features

• The internal rate of return is the annual growth rate of an investment over time.
• The IRR is equal to the discount rate at which the net present value is equal to zero.
• The IRR is useful for companies that are analyzing potential capital budget projects and want to compare the annual rates of return that may occur over time.

How to Calculate the IRR

The formula for IRR, as well as how to calculate it, are listed below.

0 = NPV = t∑t=1 Ct/​(1+IRR)t​​ − C0​

Where:

IRR = Internal rate of return

Ct = Net cash inflow during period t

t = Number of time periods

C0 = Initial investment cost

Calculating IRR

To use the IRR formula, the NPV is set to zero, and then the discount rate, which is the IRR, can be solved for.

The initial investment will be negative since it represents an outflow.

After this, the cash flows may be negative or positive.

This depends on what estimates are being used for what the investment is expected to deliver or possibly requires, such as a capital injection sometime in the future.

However, because of the way the formula for IRR works, it is difficult to calculate the IRR.

Calculating IRR requires a lot of trial and error or using software that is designed to calculate this rate.

Using Excel to Calculate IRR

The IRR function in Excel makes it easy to calculate IRR.

You just put in the numbers, and it does the work.

You’ll need to combine the cash flows; this includes the initial outlay and subsequent inflows using the IRR function.

You can find the IRR function by clicking Formulas Insert (fx) icon.2.

For an example of this with known cash flows that are a year apart, consider a company that is assessing how profitable investment Z is.

This investment will require funding of $100,000 and is predicted to generate after-tax cash flows of 50,000 in the first year and increase by 50,000 for each of the next four years:

The IRR in this situation is 41.05%.

As you can see in the above example, we used =IRR(B3:B8) to calculate the IRR of 41%.

Excel does have two other functions that can be used for calculating IRR.

These are the XIRR and the MIRR.

If a cash flow model does not have annual periodic cashflows, then XIRR should be used.

The MIRR measures a rate of return that takes into account the risk-free rate and the cost of capital.

Understanding Internal Rate of Return

The purpose of calculating the IRR is to find the discount rate.

Doing this takes the present value of the sum of annual nominal cash inflows and makes it equal to the investment’s initial net cash outlay.

Although there are a number of methods that can be used to calculate expected returns, the IRR is often thought to be the best for identifying possible returns for new projects that are under consideration.

IRR is the annual rate of growth for an investment.

It is similar to the compound annual growth rate.

Although investments generally do not have the same rate of return every year, so an investment’s actual rate of return is likely to be different from the investment’s estimated IRR.

How to use Internal Rate of Return (IRR)

The IRR is used in planning for a number of financial or investment decisions.

One common use for the IRR is for capital planning, such as when a company is trying to decide whether it would be more profitable to set up new operations or expand the current operations.

Although either of these choices might increase the value of the company, using IRR would show which of these choices would likely be more profitable.

It is important to remember that IRR does not take into account changing discount rates.

Therefore, IRR may not work well for long-term projects if the discount rate is predicted to fluctuate.

The IRR can be a good tool for corporations that want to evaluate stock buyback programs as well.

If a company designates a considerable amount of funds to repurchase its own shares, then it is important that the stock is a better use of the funds than other available options, meaning this use would have a higher IRR than the other options.

The IRR can be used by individuals as well as companies for help in making financial decisions.

This tool is useful for analyzing investment returns or choosing the best insurance policy.

Often, the return investors will see when trying to choose an investment will assume that any cash dividends or interest payments will be left in the investment, which can make it harder to analyze returns if the dividends are not going to be reinvested.

The IRR can be used in this case to determine the investment return they will likely receive if they use the dividends or interest payments as income instead of reinvesting them.

Individuals can also use IRR to compare insurance policies.

Generally, with insurance policies that have the same premium, a policy with a higher IRR is considered the better choice.

Although the IRR of an insurance policy will typically decrease over time since you will be making more payments yet your beneficiaries will still receive the same lump sum.

Another way individuals can use IRR is to determine the money-weighted rate of return (MWRR) of an investment.

This can be used to see what rate of return will be necessary for an initial investment, and it includes any changes in cash flows during the period of the investment as well as sales proceeds.

Using Weighted Average Cost of Capital (WACC) with the Internal Rate of Return

The weighted average cost of capital or WACC is a value that will generally be taken into account when making decisions using IRR.

WACC is a measurement of a given organization’s cost of capital or the amount that it must earn on an investment in order to pay its investors.

This measurement is weighted for all the sources of capital which an organization uses, such as common and preferred stock, bonds, and any other source of financing, in order to calculate WACC.

This then creates a minimum dimple threshold that many organizations use in order to determine a required rate of return (RRR).

If a given activity does not produce a percentage of return that is greater than the organization’s RRR, then it will generally be rejected.

On the other hand, though an activity that exceeds this threshold may be profitable, it may not be the best use of capital.

Instead, an organization will generally compare different projects’ IRRs and choose the one that has the largest difference between its IRR and its RRR, which represents the greatest potential profit.

Another common consideration outside of WACC in determining RRR is the amount an organization could earn by simply investing in the financial market.

If the market return for investment is greater than a given project, then an organization will likely choose to invest their money in the market; thus, these rates will often be taken into account when setting RRR.

Internal Rate of Return and Compound Annual Growth Rate (CAGR)

Both CAGR and IRR measure the annual returns of a given investment over a specified timeframe.

The difference comes down to the data these formulas account for.

CAGR uses only an initial investment and a final payout in order to provide an estimate for the annual rate of return.

On the other hand, IRR can account for multiple inflows and outflows over several periods reflecting the reality of many more complex investments.

One benefit of CAGR is that it is an easy calculation to make.

Internal Rate of Return and Return on Investment (ROI)

Investors will often choose to use return on investment (ROI) as another metric when making decisions on capital allocation.

Whereas IRR provides a measure of the annual growth rate of an investment, ROI simply tells an investor the total growth of an investment over its entire course.

If the length of time is only for a single year, the measurements will typically be the same, however over a longer period, they will not.

ROI is a simple ratio providing the percentage of increase or if a loss decrease over the life of an investment.

This is calculated simply by taking the expected final value of an investment minus the present value or cost of the investment and dividing it by the present value.

This is then multiplied by 100 to reach the ROI percentage.

Here is the formula for reference:

ROI = (Final Value – Cost of Investment / Cost of Investment) x 100

ROI is an easy-to-use reference for virtually any activity with a measurable outcome and initial investment.

However, ROI does not account for the time to achieve returns or the period, which results in serious limitations, some of which can be solved through use in conjunction with IRR.

The Limitations of Internal Rate of Return

IRR has many strengths when used for capital budgeting; however, when used for other applications, it can easily be misinterpreted.

One example of this is that when positive and negative cash flows interchange over multiple periods, calculations of IRR may result in multiple values.

Additionally, if cash flows are negative, there will never be a discount rate that results in a zero net present value (NPV).

IRR is a widely used metric for providing estimates of the annual returns for activities.

However, this has its limits and typically should not be used as a sole measure.

IRR typically has a high value that will let it arrive at a zero NPV and is only one estimated figure that will provide considerably different results depending on the assumptions used in reaching those estimates.

As a result, IRR, as well as NPV, may provide estimated results that are very different than the eventual outcomes.

Due to this, most users will not utilize IRR and NPV calculations on their own.

Instead, it is best used in conjunction with scenario analysis which can provide several NPVs based on unique assumptions as well as with other measures such as a specific organization’s WACC and RRR to allow for more detailed considerations.

IRR is often used as a measurement to compare with other factors such as the risk and capital requirements of an activity.

This is because even if a project possesses a worse IRR, other considerations may justify choosing another activity.

Similarly, investments with different lengths may also result in difficulty when comparing IRR.

Short-term investments may appear to possess a high IRR that provides the appearance of an excellent investment opportunity.

However, a long-term project may earn significantly more over a longer period of returns but possess a low IRR.

In these cases, ROI may be able to shed some more light.

However, IRR is still a valid metric because investors may still choose the activity that offers short-term returns.

How to Use IRR for Investing

Businesses and investors use IRR as a way to determine whether to continue with an activity or investment.

This uses the internal rate of return rule, which is to only pursue a given activity or investment if the IRR exceeds the user’s required minimum rate of return, often known as the hurdle rate.

At a minimum, this will generally be the cost of capital.

If the IRR is lower for a given activity or investment than the minimum threshold, then it should generally be rejected.

There are many limitations to IRR, but it is standard practice for evaluating activities before committing capital.

Examples of Internal Rate of Return

One of the most common uses of IRR is in choosing between capital investments.

If a business is trying to decide which of two projects to proceed with, it can use IRR to see which project provides a better return on investment.

To show how this works, there is an example below.

A business is considering Project 1 and Project 2, and management wants to choose whichever project is the best investment.

The business’s cost of capital is 9%.

The cash flow patterns are given and can be used to determine each project’s IRR.

Project 1

Initial Outlay = $3,000

Year one = $1,200

Year two = $900

Year three = 700

Year four = $1,500

Project 2

Initial Outlay = $7,000

Year one = $2,900

Year two = $2,300

Year three = $1,800

Year four = $2,200

The formula for solving IRR is:

$0 = Σ CFt ÷ (1 + IRR)t

where:

CF = net cash flow

IRR = internal rate of return

t = period (from 0 to last period)

or when solving

$0 = (initial outlay * −1) + CF1 ÷ (1 + IRR)1 + CF2 ÷ (1 + IRR)2 + … + CFX ÷ (1 + IRR)X

IRR Project 1:

$0 = (−$3,000) + $1,200 ÷ (1 + IRR)1 + $900 ÷ (1 + IRR)2 + $700 ÷ (1 + IRR)3 + $1,500 ÷ (1 + IRR)4

IRR Project A = 16 %

IRR Project 2:

$0 = (−$7,000) + $2,900 ÷ (1 + IRR)1 + $2,300 ÷ (1 + IRR)2 + $1,800 ÷ (1 + IRR)3 + $2,200 ÷ (1 + IRR) 4

IRR Project B = 13 %

With a cost of capital of 9%, Project #1 is the better choice.

Lets see how this can be done using excel, which is so much easier:

What Is the Meaning of Internal Rate of Return?

Internal Rate of Return, or IRR for short, is a specific financial metric that investors use to compare investment opportunities.

By calculating the IRR of an investment, an investor is essentially estimating the rate at which an investment will pay itself back using all of its cash flows and accounting on the time value of money.

Once this is accounted for, an investor can then use the IRR to judge between multiple different investment opportunities and select the one with the highest IRR that exceeds the investor’s own minimum threshold for investment.

IRR does have the significant limitation that it is dependent upon estimations of an investment’s future cash flow, which can be difficult to predict and often highly inaccurate.

What Is the Difference Between Internal Rate of Return and Return on Investment?

Oftentimes IRR is simply referred to casually as “return on investment.”

However, this metric is highly different from ROI.

Generally, what people mean when they use ROI is a percentage measurement of the amount an investment will net over a particular amount of time.

This does not carry the same use as IRR and generally holds less use for professional investors.

Plus, when referring to IRR, the meaning is always clear, but with ROI, it can be extremely vague and depend highly on context leaving IRR the better choice for clear and precise communication.

What Internal Rate of Return is Good?

Whether or not an internal rate of return is good will depend on the specific investor’s cost of capital and opportunity cost.

However, even if it outweighs these factors, investors must consider other factors, including the risk and effort of an investment.

For example, consider an investor contemplating two different stock investments.

Investment A offers a 30% IRR, whereas Investment B offers only 15%.

Assuming these investments both outweigh the cost of capital and opportunity cost, the IRR may make this look like a prime investment, but the risk and effort involved in investment should also be considered.

If the risk or effort involved in Investment A is too great, then it may still be the worse investment option.

When all other factors are equal, though, a higher IRR will always be better.