## Sunday, 17 December 2017

### Investopedia: What is the 'IRR Rule'?

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IRR Rule
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What is the 'IRR Rule'

The IRR rule is a guideline for evaluating whether to proceed with a project or investment. The IRR rule states that if the internal rate of return (IRR) on a project or an investment is greater than the minimum required rate of return, typically the cost of capital, then the project or investment should 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.
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BREAKING DOWN 'IRR Rule'
The higher the IRR on a project and the greater the amount by which it exceeds the cost of capital, the higher the net cash flows to the investor. The IRR rule is used to evaluate projects in capital budgeting, but it may not always be rigidly enforced. For example, a company may prefer a project with a lower IRR over one with a higher IRR because the former provides other intangible benefits, such as being part of a bigger strategic plan or impeding competition. A company may also prefer a larger project with a lower IRR to a much smaller project with a higher IRR because of the higher cash flows generated by the larger project.

Example Internal Rate or Return Rule Decision

Assume there are two projects that a company is reviewing. Management must decide whether to move forward with one, none or both of the projects. The cash flow patterns for each project are as follows:

Project A

Initial Outlay = \$5,000

Year one = \$1,700

Year two = \$1,900

Year three = \$1,600

Year four = \$1,500

Year five = \$700

Project B

Initial Outlay = \$2,000

Year one = \$400

Year two = \$700

Year three = \$500

Year four = \$400

Year five = \$300

The IRR for each project must be calculated. This is through an iterative process, solving for IRR in the following equation:

\$0 = (initial outlay x -1) + CF1 / (1 + IRR) ^ 1 + CF2 / (1 + IRR) ^ 2 + ... + CFX / (1 + IRR) ^ X

Using the above examples, the IRR for each project is calculated 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 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 A = 16.61%

IRR Project B = 5.23%

If the company's cost of capital is 10%, management should proceed with Project A and reject Project B.
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Internal Rate Of Return - IRR
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Internal rate of return (IRR) is a metric used in capital budgeting measuring the profitability of potential investments. Internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does.

The following is the formula for calculating NPV:

where:

Ct = net cash inflow during the period t

Co= total initial investment costs

r = discount rate, and

t = number of time periods

To calculate IRR using the formula, one would set NPV equal to zero and solve for the discount rate r, which is here the IRR. Because of the nature of the formula, however, IRR cannot be calculated analytically, and must instead be calculated either through trial-and-error or using software programmed to calculate IRR.

Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake the project. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective projects a firm is considering on a relatively even basis. Assuming the costs of investment are equal among the various projects, the project with the highest IRR would probably be considered the best and undertaken first.

IRR is sometimes referred to as "economic rate of return” (ERR).
BREAKING DOWN 'Internal Rate Of Return - IRR'

You can think of IRR as the rate of growth a project is expected to generate. While the actual rate of return that a given project ends up generating will often differ from its estimated IRR rate, a project with a substantially higher IRR value than other available options would still provide a much better chance of strong growth. One popular use of IRR is in comparing the profitability of establishing new operations with that of expanding old ones. For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand a previously existing one. While both projects are likely to add value to the company, it is likely that one will be the more logical decision as prescribed by IRR.

In theory, any project with an IRR greater than its cost of capital is a profitable one, and thus it is in a company’s interest to undertake such projects. 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 in order to be worthwhile. Any project with an IRR that exceeds the RRR will likely be deemed a profitable one, 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 chances are these will be the most profitable.

IRRs can also be compared against prevailing rates of return in the securities market. If a firm can't find any projects with IRRs greater than the returns that can be generated in the financial markets, it may simply choose to invest its retained earnings into the market.

Although IRR is an appealing metric to many, it should always be used in conjunction with NPV for a clearer picture of the value represented by a potential project a firm may undertake.
Issues with 'Internal Rate of Return (IRR)'

While IRR is a very popular metric in estimating a project’s profitability, it can be misleading if used alone. Depending on the initial investment costs, a project may have a low IRR but a high NPV, meaning that while the pace at which the company sees returns on that project may be slow, the project may also be adding a great deal of overall value to the company.

A similar issue arises when using IRR to compare projects of different lengths. For example, a project of a short duration may have a high IRR, making it appear to be an excellent investment, but may also have a low NPV. Conversely, a longer project may have a low IRR, earning returns slowly and steadily, but may add a large amount of value to the company over time.

Another issue with IRR is not one strictly inherent to the metric itself, but rather to a common misuse of IRR. People may assume that, when positive cash flows are generated during the course of a project (not at the end), the money will be reinvested at the project’s rate of return. This can rarely be the case. Rather, when positive cash flows are reinvested, it will be at a rate that more resembles the cost of capital. Miscalculating using IRR in this way may lead to the belief that a project is more profitable than it actually is in reality. This, along with the fact that long projects with fluctuating cash flows may have multiple distinct IRR values, has prompted the use of another metric called modified internal rate of return (MIRR). MIRR adjusts the IRR to correct these issues, incorporating cost of capital as the rate at which cash flows are reinvested, and existing as a single value. Because of MIRR’s correction of the former issue of IRR, a project’s MIRR will often be significantly lower than the same project’s IRR. (For more, see: Internal Rate Of Return: An Inside Look.)
IRR
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The internal rate of return (IRR) represents the interest rate in which the net present value (NPV) of a project's expected total cash flows, both positive and negative, sum to zero. The IRR of a project is used as a benchmark; if the IRR of a specific project is higher than a company's required rate of return. the firm accepts the project. If, however, the IRR of a project is calculated to be below a company's required rate of return, the company does not move forward with the project.
BREAKING DOWN 'IRR'

IRR is a metric used across many financial concentrations as a measurement for cash flow analysis. The most common way it's used is as a project-based tool, but it can also be used by investors when evaluating investments and capital acquisitions. The formula for IRR is labor-intensive and takes the initial cash outflow (P0) and sums it with all future cash flows (P1...PN), divided by the IRR and square rooted to the power of the period. The equation for IRR is as follows: 0 = P0 + P1 / (1+IRR) + P2 / (1+IRR)^2 + ... + PN / (1+IRR)^N, where N represents the last period in the sequence of cash flows.
The Importance of the IRR Benchmark

All companies seek to initiate projects with high IRRs; higher IRRs result in higher-percentage returns on investments. Therefore, IRR is used as a decision-making tool for situations that include a single project or multiple projects. If a company is evaluating a single project, it looks at the IRR and rejects or accepts the project based on the relationship between its IRR and the company's minimum required return. If a company is evaluating a group of projects, it looks at each one's IRR and chooses a combination of projects that results in the highest collective IRR. If two or more projects are mutually exclusive, meaning that choosing one bars the other from being chosen, the company accepts the project with the highest IRR.

IRR does not take into account the overall size of a project's investment or return. While IRR is an accurate benchmark for managerial decision making, company leaders should also look at the size of the dollar return when making decisions. For example, a small project might have a high IRR percentage-wise but a low dollar return. Conversely, a large project may have a smaller IRR yet have a much larger dollar return, making it an attractive investment.
The Net Internal Rate Of Return - Net IRR
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The net internal rate of return (Net IRR) is a measure of a portfolio or fund's performance that is equal to the internal rate of return (IRR) after management fees and carried interest have been accounted for. It is a capital budgeting and portfolio management term.
BREAKING DOWN 'The Net Internal Rate Of Return - Net IRR '

The IRR is a discount rate where the present value of future cash flows of an investment is equal to the cost of the investment. The net IRR is a modified IRR value that has taken into consideration management fees and any carried interest.
Pooled Internal Rate Of Return - PIRR
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A method of calculating the overall internal rate of return (IRR) of a portfolio of several projects by combining their individual cashflows. The overall IRR of the portfolio is then calculated from this pooled cash flow.
BREAKING DOWN 'Pooled Internal Rate Of Return - PIRR'

The pooled IRR concept can be applied, for example, in the case of a private equity group that has several funds. The pooled IRR can establish the overall IRR for the private equity group, and is better suited for this purpose than say average IRR of the funds, which may not give an accurate picture of overall performance.

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