# Given the following revenue flow, what is the internal rate of return.(32,000) 15,000 14,000 11,000 2,000 500

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### 1 Answer

The internal rate of return is the annualized effective compounded return also known as the rate of return for which the net present value or NPV is 0.

Here, there is an initial outflow of 32000 to start with, an inflow of 15000 in year 1, an inflow of 14000 in year 2, an inflow of 11000 in year 3, an inflow of 2000 in year 4 and an inflow of 500 in year 5.

If the internal rate of return is taken to be r, the NPV is:

32000 + 15000/(1 + r) + 14000/(1 + r)^2 + 11000/(1 + r)^3 + 2000/(1 + r)^4 + 500/(1 + r)^5

The value of r for which NPV = 0, can only be determined by using a trial and error method.

As the final inflows are quite small start with a high value of r.

If r = 14%

-32000 + 15000/(1 + r) + 14000/(1 + r)^2 + 11000/(1 + r)^3 + 2000/(1 + r)^4 + 500/(1 + r)^5 = -798.97

If r = 15%

-32000 + 15000/(1 + r) + 14000/(1 + r)^2 + 11000/(1 + r)^3 + 2000/(1 + r)^4 + 500/(1 + r)^5 = -254.26

If r = 16%

-32000 + 15000/(1 + r) + 14000/(1 + r)^2 + 11000/(1 + r)^3 + 2000/(1 + r)^4 + 500/(1 + r)^5 = 274.81

The internal rate of return lies between 15% and 16%. The same process can be continued repeatedly to obtain a more precise value of r for which the value of the NPV is approximately equal to 0. This is easier done using an computer and software like Microsoft Excel.

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