Internal Rate of Return

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					Internal Rate of Return RUMLO                                   Barry Marshall-Kalina

Internal Rate of Return
This is an alternative accounting appraisal method within the Discounted Cash Flow
family of methods. It aims to show a maximum value for the interest rate of a project.

Consider the previous example that used 10%: the Net Present Value of this project
was minus £214. If a different discount rate were chosen then the Net Present Value
would become another figure. Reworking this example, but this time using a
discount rate of 8%, it is found that the Net Present Value is now a positive one:

                         Cash Flows          Discount Factor        Present Values
                             £                     8%                     £
    End of Year
         0                  -10,000            1.000                    -10,000
         1                  + 3,000            0.926                    + 2,778
         2                  + 4,000            0.857                    + 3,428
         3                  + 5,000            0.794                    + 3,970
                                      NET PRESENT VALUE =                +176

Using a discount rate of 10% gives a negative NPV; using 8% gives a positive one.
So, somewhere between 8% and 10% there is a discount rate that will produce an
NPV equal to zero. And it is that discount rate that is called the INTERNAL RATE
OF RETURN (IRR) of the project. The Internal Rate of Return is the discount rate of
the project that will generate a Net Present Value equal to zero.

Before spreadsheets became readily available the only way of calculating a project’s
Internal Rate of Return was by trial and error. However, with spreadsheets they may
be readily calculated. If no computer is handy then for a rough and ready answer
interpolation may be used.

In example 4, an 8% discount factor gives an NPV of = +£176 and a 10% discount
factor gives an NPV of = -£214

So, a 2% discount swing produces a swing from positive to negative in the NPV of
176 + 214 = £390. The IRR must therefore be at 8% + (     /390)*2% = 8.9%.
We’ll call this 9%.

What does this 9% mean? It presents the maximum rate of interest that could be
paid on funds borrowed to finance the investment for it to be worthwhile. So, if
money can only be borrowed to fund the project at, say, 12% interest rates then the
project is not economically viable. It’s like borrowing money at 12% and investing it
at 9% - a good way of going bust. On the other hand if money can be borrowed at
4% then it is economic to use such money to fund a project that will be generating

It is a sort of break-even figure. If money can be borrowed more cheaply than that,
then go ahead; if it cannot, abandon the project. Of course, it should always be
remembered that factors other than the purely economic and financial may quite
legitimately affect the decision as to whether to go ahead with an investment or not.

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