# Internal Rate of Return (IRR) & Formula

The internal rate of return (IRR) is a metric used in financial analysis to estimate the profitability of potential investments. Solving for IRR is an iterative process using the following equation: > $0 = Σ CFt ÷ (1 + IRR)t CF = net cash flow IRR = internal rate of return t = period (from 0 to last period) > $0 = (initial outlay \−1) + CF1 ÷ (1 + IRR)1 + CF2 ÷ (1 + IRR)2 + ... + CFX ÷ (1 + IRR)X Using the above examples, the company can calculate IRR for each project as: $0 = (−$5,000) + $1,700 ÷ (1 + IRR)1 + $1,900 ÷ (1 + IRR)2 + $1,600 ÷ (1 + IRR)3 + $1,500 ÷ (1 + IRR)4 + $700 ÷ (1 + IRR)5 IRR Project A = **16.61 %** $0 = (−$2,000) + $400 ÷ (1 + IRR)1 + $700 ÷ (1 + IRR)2 + $500 ÷ (1 + IRR)3 + $400 ÷ (1 + IRR)4 + $300 ÷ (1 + IRR)5 IRR Project B = **5.23 %** Given that the company’s cost of capital is 10%, management should proceed with Project A and reject Project B. The internal rate of return (IRR) is a financial metric used to assess the attractiveness of a particular investment opportunity. 1:30 The formula and calculation used to determine this figure are as follows: 0 \= NPV \= ∑ t \= 1 T C t ( 1 \+ I R R ) t − C 0 where: C t \= Net cash inflow during the period t C 0 \= Total initial investment costs I R R \= The internal rate of return t \= The number of time periods \\begin{aligned} &\\text{0}=\\text{NPV}=\\sum\_{t=1}^{T}\\frac{C\_t}{\\left(1+IRR\\right)^t}-C\_0\\\\ &\\textbf{where:}\\\\ &C\_t=\\text{Net cash inflow during the period t}\\\\ &C\_0=\\text{Total initial investment costs}\\\\ &IRR=\\text{The internal rate of return}\\\\ &t=\\text{The number of time periods}\\\\ \\end{aligned} 0\=NPV\=t\=1∑T(1+IRR)tCt−C0where:Ct\=Net cash inflow during the period tC0\=Total initial investment costsIRR\=The internal rate of returnt\=The number of time periods 1. Using the formula, one would set NPV equal to zero and solve for the discount rate, which is the IRR. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis. IRR calculations rely on the same formula as NPV does. The IRR rule states that if the IRR on a project or investment is greater than the minimum RRR — typically the cost of capital, then the project or investment can be pursued.

## What Is Internal Rate of Return (IRR)?

The internal rate of return (IRR) is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis.

IRR calculations rely on the same formula as NPV does. Keep in mind that IRR is not the actual dollar value of the project. It is the annual return that makes the NPV equal to zero.

Generally speaking, the higher an internal rate of return, the more desirable an investment is to undertake. IRR is uniform for investments of varying types and, as such, can be used to rank multiple prospective investments or projects on a relatively even basis. In general, when comparing investment options with other similar characteristics, the investment with the highest IRR probably would be considered the best.

## Formula and Calculation for IRR

The formula and calculation used to determine this figure are as follows:

0 = NPV = ∑ t = 1 T C t ( 1 + I R R ) t − C 0 where: C t = Net cash inflow during the period t C 0 = Total initial investment costs I R R = The internal rate of return t = The number of time periods \begin{aligned} &\text{0}=\text{NPV}=\sum_{t=1}^{T}\frac{C_t}{\left(1+IRR\right)^t}-C_0\\ &\textbf{where:}\\ &C_t=\text{Net cash inflow during the period t}\\ &C_0=\text{Total initial investment costs}\\ &IRR=\text{The internal rate of return}\\ &t=\text{The number of time periods}\\ \end{aligned} 0=NPV=t=1∑T(1+IRR)tCt−C0where:Ct=Net cash inflow during the period tC0=Total initial investment costsIRR=The internal rate of returnt=The number of time periods

### How to Calculate IRR

- Using the formula, one would set NPV equal to zero and solve for the discount rate, which is the IRR.
- The initial investment is always negative because it represents an outflow.
- Each subsequent cash flow could be positive or negative, depending on the estimates of what the project delivers or requires as a capital injection in the future.
- However, because of the nature of the formula, IRR cannot be easily calculated analytically and instead must be calculated iteratively through trial and error or by using software programmed to calculate IRR (e.g., using Excel).

### How to Calculate IRR in Excel

Using the IRR function in Excel makes calculating the IRR easy. Excel does all the necessary work for you, arriving at the discount rate you are seeking to find. All you need to do is combine your cash flows, including the initial outlay as well as subsequent inflows, with the IRR function. The IRR function can be found by clicking on the Formulas Insert (*fx*) icon.

Here is a simple example of an IRR analysis with cash flows that are known and annually periodic (one year apart). Assume a company is assessing the profitability of Project X. Project X requires $250,000 in funding and is expected to generate $100,000 in after-tax cash flows the first year and grow by $50,000 for each of the next four years.

Image by Sabrina Jiang © Investopedia 2020

In this case, the IRR is 56.72%, which is quite high.

Excel also offers two other functions that can be used in IRR calculations: the XIRR, and the MIRR. XIRR is used when the cash flow model does not exactly have annual periodic cash flows. The MIRR is a rate-of-return measure that includes the integration of cost of capital and the risk-free rate.

## Understanding IRR

The ultimate goal of IRR is to identify the rate of discount, which makes the present value of the sum of annual nominal cash inflows equal to the initial net cash outlay for the investment. Several methods can be used when seeking to identify an expected return, but IRR is often ideal for analyzing the potential return of a new project that a company is considering undertaking.

Think of IRR as the rate of growth that an investment is expected to generate annually. Thus, it can be most similar to a compound annual growth rate (CAGR). In reality, an investment will usually not have the same rate of return each year. Usually, the actual rate of return that a given investment ends up generating will differ from its estimated IRR.

## What Is IRR Used For?

IRR is also useful for corporations in evaluating stock buyback programs. Clearly, if a company allocates substantial funding to repurchasing its shares, then the analysis must show that the company’s own stock is a better investment — that is, has a higher IRR — than any other use of the funds, such as creating new outlets or acquiring other companies.

Individuals can also use IRR when making financial decisions — for instance, when evaluating different insurance policies using their premiums and death benefits. The general consensus is that policies that have the same premiums and a high IRR are much more desirable. Note that life insurance has a very high IRR in the early years of policy — often more than 1,000%. It then decreases over time. This IRR is very high during the early days of the policy because if you made only one monthly premium payment and then suddenly died, your beneficiaries would still get a lump sum benefit.

Another common use of IRR is in analyzing investment returns. In most cases, the advertised return will assume that any interest payments or cash dividends are reinvested back into the investment. What if you don’t want to reinvest dividends but need them as income when paid? And if dividends are not assumed to be reinvested, are they paid out, or are they left in cash? What is the assumed return on the cash? IRR and other assumptions are particularly important on instruments like annuities, where the cash flows can become complex.

Finally, IRR is a calculation used for an investment’s money-weighted rate of return (MWRR). The MWRR helps determine the rate of return needed to start with the initial investment amount factoring in all of the changes to cash flows during the investment period, including sales proceeds.

## Using IRR with WACC

Most IRR analyses will be done in conjunction with a view of a company’s weighted average cost of capital (WACC) and NPV calculations. IRR is typically a relatively high value, which allows it to arrive at an NPV of zero. Most companies will require an IRR calculation to be above the WACC. WACC is a measure of a firm’s cost of capital in which each category of capital is proportionately weighted. All sources of capital, including common stock, preferred stock, bonds, and any other long-term debt, are included in a WACC calculation.

In theory, any project with an IRR greater than its cost of capital should be profitable. In planning investment projects, firms will often establish a required rate of return (RRR) to determine the minimum acceptable return percentage that the investment in question must earn to be worthwhile. The RRR will be higher than the WACC.

Any project with an IRR that exceeds the RRR will likely be deemed profitable, although companies will not necessarily pursue a project on this basis alone. Rather, they will likely pursue projects with the highest difference between IRR and RRR, as these likely will be the most profitable.

IRR may also be compared against prevailing rates of return in the securities market. If a firm can’t find any projects with IRR greater than the returns that can be generated in the financial markets, then it may simply choose to invest money in the market. Market returns can also be a factor in setting an RRR.

Analyses will also typically involve NPV calculations at different assumed discount rates.

## IRR vs. Compound Annual Growth Rate

The CAGR measures the annual return on an investment over a period of time. The IRR is also an annual rate of return. However, the CAGR typically uses only a beginning and ending value to provide an estimated annual rate of return.

IRR differs in that it involves multiple periodic cash flows — reflecting that cash inflows and outflows often constantly occur when it comes to investments. Another distinction is that CAGR is simple enough that it can be calculated easily.

## IRR vs. Return on Investment (ROI)

Companies and analysts may also look at the return on investment (ROI) when making capital budgeting decisions. ROI tells an investor about the total growth, start to finish, of the investment. It is not an annual rate of return. IRR tells the investor what the annual growth rate is. The two numbers normally would be the same over the course of one year but won’t be the same for longer periods of time.

ROI is the percentage increase or decrease of an investment from beginning to end. It is calculated by taking the difference between the current or expected future value and the original beginning value, divided by the original value and multiplied by 100.

ROI figures can be calculated for nearly any activity into which an investment has been made and an outcome can be measured. However, ROI is not necessarily the most helpful for lengthy time frames. It also has limitations in capital budgeting, where the focus is often on periodic cash flows and returns.

## Limitations of the IRR

IRR is generally most ideal for use in analyzing capital budgeting projects. It can be misconstrued or misinterpreted if used outside of appropriate scenarios. In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values. Moreover, if all cash flows have the same sign (i.e., the project never turns a profit), then no discount rate will produce a zero NPV.

Within its realm of uses, IRR is a very popular metric for estimating a project’s annual return. However, it is not necessarily intended to be used alone. IRR is typically a relatively high value, which allows it to arrive at an NPV of zero. The IRR itself is only a single estimated figure that provides an annual return value based on estimates. Since estimates in IRR and NPV can differ drastically from actual results, most analysts will choose to combine IRR analysis with scenario analysis. Scenarios can show different possible NPVs based on varying assumptions.

As mentioned, most companies do not rely on IRR and NPV analyses alone. These calculations are usually also studied in conjunction with a company’s WACC and an RRR, which provides for further consideration.

Companies usually compare IRR analysis to other tradeoffs. If another project has a similar IRR with less up-front capital or simpler extraneous considerations, then a simpler investment may be chosen despite IRRs.

In some cases, issues can also arise when using IRR to compare projects of different lengths. For example, a project of short duration may have a high IRR, making it appear to be an excellent investment. Conversely, a longer project may have a low IRR, earning returns slowly and steadily. The ROI metric can provide some more clarity in these cases, although some managers may not want to wait out the longer time frame.

## Investing Based on IRR

The internal rate of return rule is a guideline for evaluating whether to proceed with a project or investment. The IRR rule states that if the IRR on a project or investment is greater than the minimum RRR — typically the cost of capital, then the project or investment can be pursued.

Conversely, if the IRR on a project or investment is lower than the cost of capital, then the best course of action may be to reject it. Overall, while there are some limitations to IRR, it is an industry-standard for analyzing capital budgeting projects.

## IRR Example

Assume a company is reviewing two projects. Management must decide whether to move forward with one, both, or neither. Its cost of capital is 10%. The cash flow patterns for each are as follows:

**Project A**

**Project B**

The company must calculate the IRR for each project. Initial outlay (period = 0) will be negative. Solving for IRR is an iterative process using the following equation:

$0 = Σ CFt ÷ (1 + IRR)t

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

Using the above examples, the company can calculate IRR for each project as:

### IRR Project A:

$0 = (−$5,000) + $1,700 ÷ (1 + IRR)1 + $1,900 ÷ (1 + IRR)2 + $1,600 ÷ (1 + IRR)3 + $1,500 ÷ (1 + IRR)4 + $700 ÷ (1 + IRR)5

IRR Project A = **16.61 %**

### IRR Project B:

$0 = (−$2,000) + $400 ÷ (1 + IRR)1 + $700 ÷ (1 + IRR)2 + $500 ÷ (1 + IRR)3 + $400 ÷ (1 + IRR)4 + $300 ÷ (1 + IRR)5

IRR Project B = **5.23 %**

Given that the company’s cost of capital is 10%, management should proceed with Project A and reject Project B.

## What does internal rate of return mean?

The internal rate of return (IRR) is a financial metric used to assess the attractiveness of a particular investment opportunity. When you calculate the IRR for an investment, you are effectively estimating the rate of return of that investment after accounting for all of its projected cash flows together with the time value of money. When selecting among several alternative investments, the investor would then select the investment with the highest IRR, provided it is above the investor’s minimum threshold. The main drawback of IRR is that it is heavily reliant on projections of future cash flows, which are notoriously difficult to predict.

## Is IRR the same as ROI?

Although IRR is sometimes referred to informally as a project’s “return on investment,” it is different from the way most people use that phrase. Often, when people refer to ROI, they are simply referring to the percentage return generated from an investment in a given year or across a stretch of time. But that type of ROI does not capture the same nuances as IRR, and for that reason, IRR is generally preferred by investment professionals.

Another advantage of IRR is that its definition is mathematically precise, whereas the term ROI can mean different things depending on the context or the speaker.

## What is a good internal rate of return?

Whether an IRR is good or bad will depend on the cost of capital and the opportunity cost of the investor. For instance, a real estate investor might pursue a project with a 25% IRR if comparable alternative real estate investments offer a return of, say, 20% or lower. However, this comparison assumes that the riskiness and effort involved in making these difficult investments are roughly the same. If the investor can obtain a slightly lower IRR from a project that is considerably less risky or time-consuming, then they might happily accept that lower-IRR project. In general, though, a higher IRR is better than a lower one, all else being equal.

## Related terms:

### Annuities: Insurance for Retirement

An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees. read more

### Buyback

A buyback is a repurchase of outstanding shares by a company to reduce the number of shares on the market and increase the value of remaining shares. read more

### Compound Annual Growth Rate (CAGR)

The compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its ending one. read more

### Capital Budgeting

Capital budgeting is a process a business uses to evaluate potential major projects or investments. It allows a comparison of estimated costs versus rewards. read more

### Cash Dividend

A cash dividend is a distribution paid to stockholders as part of the corporation's current earnings or accumulated profits and guides the investment strategy for many investors. read more

### Conventional Cash Flow

Conventional cash flow is a series of inward and outward cash flows over time in which there is only one change in the cash flow direction. read more

### Cost of Capital : Formula & Calculation

Cost of capital is the required return a company needs in order to make a capital budgeting project, such as building a new factory, worthwhile. read more

### Discount Rate

"Discount rate" has two distinct definitions. I can refer to the interest rate that the Federal Reserve charges banks for short-term loans, but it's also used in future cash flow analysis. read more

### Dividend

A dividend is the distribution of some of a company's earnings to a class of its shareholders, as determined by the company's board of directors. read more

### Hurdle Rate

A hurdle rate is the minimum rate of return on a project or investment required by a manager or investor. read more