How to Calculate Internal Rates of Return

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The internal rate of return on a project is a measure of the profitability of an investment, used to decide which projects or companies to invest in -- a process known as capital budgeting. The method explained here is the graphical method, which calculates an approximate value. The example uses a spreadsheet program. Such programs usually have an IRR function, so learning to calculate it yourself is only useful if you do not always have access to a computer. Alternatively, it is possible to use a financial calculator that is programmed to make the calculation.

The internal rate of return on a project is a measure of the profitability of an investment, used to decide which projects or companies to invest in -- a process known as capital budgeting. The method explained here is the graphical method, which calculates an approximate value. The example uses a spreadsheet program. Such programs usually have an IRR function, so learning to calculate it yourself is only useful if you do not always have access to a computer. Alternatively, it is possible to use a financial calculator that is programmed to make the calculation.

Open a spreadsheet and add a column for required rate of return (R) by putting a header in the top left cell. Add values for R ranging from 0.02, 0.04, 0.06 ... 0.20. Next to this, add a column for NPVs using the title "NPV."

Add columns for each of your cash flows to these first two columns. The simplest and most common types of cash flow are a single negative outflow followed by inflows in the following periods (T). For example:

C0=-$5 C1=$3 C2=$2 C3=$1

C0 represents the initial investment, C1, C2 and C3 are the returns.

Calculate PVs for the full range of R values. Cash flows are discounted using required rates of return, giving the present value of a cash flow that may occur in the future. The general form of the present value formula is:

PV(C)=C/(1+R)^T

For period T=3 the formula would be:

PV(C3)=1/(1+R)^3

Calculate these for each C and for each value of R.

Calculate the NPV for each value of R. Do this by using a SUM function in the NPV column.

Plot a graph with NPV on the Y-axis and R on the X-axis. Where NPV=0, IRR=R. In this case, the IRR falls between R=0.22 and 0.24. The IRR of the project is between 22 percent and 24 percent.

References

About the Author

Jan Gerards has won several awards for his writing, including a creative writing scholarship from the Deutscher Akademischer Austausch Dienst. He holds a Bachelor of Arts in land economy from the University of Cambridge.

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