Internal rate of return

The IRR method ( also: Internal interest rate method, method of internal rate of return method or the internal rate of return, in short: IRR method or IZM or IZS method, in English: IRR - Internal Rate of Return ) is a method the dynamic investment calculation. It enables to apply for an investment or capital investment, in the irregular and fluctuating yields, a ( theoretical) average to calculate annual return.

The discount factor, when used the discounted future payments based on the present price or the initial investment, ie internal rate of return. If this rate of return greater than the discount (read: the yield is greater than the interest on capital plus risk premium ), the investment is more than the total run time calculated economically.

The IRR method was originally developed to increase the efficiency of investment decisions in companies. The aim of the calculations was to determine that investment decision, which affects the overall system operation is most advantageous.

Procedure

It searches the interest rate i, at which the net present value

Of the given project is equal to zero. The investment I the sum of all discounted cash flows ( payments) is at times t compared with Ct.

To solve the equation, that is, to determine the rate of interest i, usually one uses an interpolation method:

• .

Regarding the experimental rates (,), the closer together are the experimental rates, the smaller the interpolation error.

In practice, the Newton method is used in addition to the above presented mathematical solution method on the basis of geometric series regulators falsi. Modern spreadsheet programs such as Microsoft Excel include add-ons, which the zeros calculation support ( Solver - to German: " Goal Seek "). The Regula - falsi - formula can be used in OpenOffice.org Calc and MS Excel very easy with the IRR function (internal rate of return capital function) represent.

The problem, however, is that geometric series with more than one sign change lead to mathematically there may be multiple zeros. Such rows have to be adjusted. Can also be specified for the interest rate, a starting value.

Critical assessment

Lending or borrowing

If the following two projects are compared, the IRR method does not help:

Both projects have the same internal rate of return on (and) by this method are therefore equally attractive. (: The exact look or in this case ) shows that will be presented at Project A money initially to 50% and is borrowed from Project B However, when looking at the KW is. When money is borrowed, a low interest rate is desired, that is, the IRR should be lower than the opportunity cost and not higher.

Multiple IRRs

In most countries, the taxes are paid in the following year, which means that the income and the tax burden does not occur in the same period. The following example is a project that requires an investment in the amount of 2,000,000 €, while during his ( five years here ) Running time an additional profit of € 600,000 p. a brings. The tax rate is 50 % and is paid in the following period:

(Note: The investment in the amount of € 2 million in reducing the tax burden for this period to € 1,000,000, which is added in. )

The calculations of the IRR and KW revealed the following:

With both interest rates the condition is met. The reason for this lies in the fact that it is not a normal investment (up to a sign change in the payment row) is: After the sign rule of Descartes, a polynomial equation as many positive zeros have such sign change. In the example, this two-time change of sign causes the ( mathematically correct ) result is not unique ( Which IRR is correct? ).

In practice such series come about not only by the delay of tax payments, but can also maintenance costs during the life of the project or the scrapping of a plant at the end of the term arise.

One way to circumvent a final (second) sign change is to calculate a modified IRR: The cash flow for the 6th year is calculated in the fifth and added to this and the IRR calculated again. This result, however, that the results will be incorrect - the capital value of the original series of payments is positive and above the interest rate so determined yet.

Mutually exclusive projects

In order to fulfill a specific job, companies often have the choice between mutually exclusive projects. Again, the IRR method are misleading:

Both projects are lucrative and after the IRR decision rule would have to be carried out the project C, but as the KW shows D is preferred over C because it has the higher monetary value. However, the IRR method can also be used here: In consideration of the incremental cash flows ( the difference between the two projects) leads the internal rate of return the same result as the net present value method ( the incremental IRR is 50 %, that is, when the incremental IRR is greater than the discount rate, should the "larger" project - in this case - are carried out ) Example D.

Neglect of the term structure of interest

The IRR method is based on the assumption that the short-and long -term interest rates are the same ( see formula, only an interest rate ). This applies to rare in reality. The interest rates vary considerably in terms of maturity. Short of money, ie loans with a relatively short duration, has a lower interest rate on, so it is cheaper than long money, ie loans with a longer maturity. Inverted yield structures have been observed, for example in the early 1990s. The net present value method, that's not a problem as simply the cash flows can be discounted at different rates:

An alternative is to calculate the weighted average of the interest over the term, but critics call this variant to the complexity of the bill increased unnecessarily when there is a simple solution.

In practice, the term structure problem, and thus the question of what interest rate the IRR should be compared (, or), usually neglected. The amount recognized in the statement of investments calculation interest is also never only financing, the interest, but rather a required minimum rate. This can be adjusted based on the term of the interest rate structure. Expected changes in interest rates may also be covered through a modification of the interest rates:

Conclusion

• The method of internal rate of return is not suitable to compare several investment projects of different height, length and investment timing with each other. It is quite possible that an investment with a higher internal rate of return lower capital value than another investment with a lower IRR.
• The validity of the calculated value is limited depending on the investment object. In financial investment internal rate of return equal to the effective interest rate. For property investment, however, the internal Zinfuß is merely a theoretical limit interest rate to which an investment would be economically.
• Furthermore, this method assumes that all capital flows are reinvested at the internal rate of return ( reinvestment assumption ) and not to the market interest rate ( net present value ). The reinvestment assumption is classified in practice mainly as unrealistic.
• The above examples show that it is possible to modify the IRR method so that it returns useful results. However, the question arises whether this is necessary in view of the reliability and mathematical simplicity of the net present value method.
• The method of the internal rate is well in practice for the evaluation of individual investments in incompletely defined scenarios. Measure size is a desired minimum rate of return. Rate exceeds this minimum return, the investment is in itself useful.
• The above options to make the IRR method practically usable, run as a result of an application of the net present value addition: The actual investment is in a roundabout way ( IRR method) or directly ( net present value ) compared to a reference rate.

Variants of the internal interest rate methods

For internal interest rate methods arise in practice, different variants, depending on whether it is operated with a linear or exponential rate of interest. Which is shown below.

• ISMA - International Securities Market Association (now ICMA - International Capital Market Association )
• SIA - Securities Industries Association
• Treasury