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Internal Rate of Return

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The internal rate of return (IRR) is a capital budgeting metric used by firms to

decide whether they should make investments. It is an indicator of the efficiency

of an investment, as opposed to net present value (NPV), which indicates value

or magnitude.

The IRR is the annualized effective compounded return rate which can be

earned on the invested capital, i.e., the yield on the investment.

A project is a good investment proposition if its IRR is greater than the rate of

return that could be earned by alternate investments (investing in other projects,

buying bonds, even putting the money in a bank account). Thus, the IRR should

be compared to any alternate costs of capital including an appropriate risk

premium.

Mathematically the IRR is defined as any discount rate that results in a net

present value of zero of a series of cash flows.

In general, if the IRR is greater than the project's cost of capital, orhurdle rate,

the project will add value for the company.

Contents

1 Methodo 1.1 Example

2 Graph of NPV as a function of i for the example

3 Problems with using internal rate of return (IRR)

4 See also

5 External links

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Method

To find the internal rate of return, find the value(s) ofr that satisfies the

following equation:

(SeeNet Present Value for details on this formula.)

Example

Internal Rate of Return (IRR)

IRR = r, IRR = 17.09%

Net Present Value (NPV)

Thus using r = IRR = 17.09%,

Graph of NPV as a function of i for the example

Year Cash Flow

0 -100

1 +30

2 +35

3 +40

4 +45

2

http://en.wikipedia.org/wiki/Net_present_valuehttp://en.wikipedia.org/wiki/Net_present_value

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This graph shows the changing of NPV in relation to i

Problems with using internal rate of return (IRR)

As an investment decision tool, the calculated IRR should not be used to rate

mutually exclusive projects, but only to decide whether a single project is worth

investing in.

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Two mutually exclusive projects

In cases where one project has a higher initial investment than a second

mutually exclusive project, the first project may have a lower IRR (expected

return), but a higher NPV (increase in shareholders' wealth) and should thus be

accepted over the second project (assuming no capital constraints).

IRR makes no assumptions about the reinvestment of the positive cash flow

from a project. As a result, IRR should not be used to compare projects of

different duration and with a different overall pattern of cash flows. ModifiedInternal Rate of Return (MIRR) provides a better indication of a project's

efficiency in contributing to the firm's discounted cash flow.

The IRR method should not be used in the usual manner for projects that start

with an initial positive cash inflow (or in some projects with large negative cash

flows at the end), for example where a customer makes a deposit before a

specific machine is built, resulting in a single positive cash flow followed by a

series of negative cash flows (+ - - - -). In this case the usual IRR decision rule

needs to be reversed.

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If there are multiple sign changes in the series of cash flows, e.g. (- + - + -),

there may be multiple IRRs for a single project, so that the IRR decision rule

may be impossible to implement. Examples of this type of project are strip

mines and nuclear powerplants, where there is usually a large cash outflow at

the end of the project.

In general, the IRR can be calculated by solving a polynomial equation. Sturm's

Theorem can be used to determine if that equation has a unique real solution.

Importantly, the IRR equation cannot be solved analytically (i.e. in its general

form) but only via iterations.

A critical shortcoming of the IRR method is that it is commonly misunderstood

to convey the actual annual profitability of an investment. However, this is not

the case because intermediate cash flows are almost never reinvested at the

project's IRR; and, therefore, the actual rate of return (akin to the one that wouldhave been yielded by stocks or bank deposits) is almost certainly going to be

lower. Accordingly, a measure called Modified Internal Rate of Return (MIRR)

is used, which has an assumed reinvestment rate, usually equal to the project's

cost of capital.

Despite a strong academic preference for NPV, surveys indicate that executives

prefer IRR over NPV. Apparently, managers find it easier to compare

investments of different sizes in terms of percentage rates of return than by

dollars of NPV. However, NPV remains the "more accurate" reflection of valueto the business. IRR, as a measure of investment efficiency may give better

insights in capital constrained situations. However, when comparing mutually

exclusive projects, NPV is the appropriate measure.

In addition if the NPV of one project is higher than another and the other project

has a higher IRR, then the cross over point method can be used to solve this

dispute.

Cross Over Point > IRR = Accept project with higher NPV and if the Cross

Over Point < IRR = Accept project with higher IRR

See also

Accounting

Capital budgeting

Cost of capital

Finance

Net present value

Discounted cash flow

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External links

Capital Budgeting, audio lecture with slide show

Misleading IRR values , tied-up and free capital

Calculate IRR Calculating IRR using Excel

An example of IRR using a savings account

IRR web calculator

Retrieved from "http://en.wikipedia.org/wiki/Internal_rate_of_return"

Categories: Mathematical finance

This page was last modified on 25 March 2008, at 04:53.

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