The internal rate of return is used to measure the profitability of a project, help people manage a budget and choose between competing projects. One way of calculating IRR is using a graph. It is possible to do this using a spreadsheet or a calculator and a piece of paper. The graphical method uses a range of values for the required rate of return (R), and then calculates the net present value (NPV) of a series of cash flows for each given value of R. The point at which NPV=0 is the place where also IRR=R.

## Calculating the IRR

Identify your cash flows. For example: -5 at t=0 3 at t=1 2 at t=2 1 at t=3

Decide on a range of values for R, for example 0.02, 0.04, 0.06 ... 0.30.

Calculate the present value (PV) of each cash flow for each value of R. This obviously involves a lot of calculations (15 for each cash flow), and is better done on a spreadsheet program. The PV of a cash flow C is:

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

Calculate the NPV for each value of R by adding all of the PVs together.

Start to produce your graph by drawing your axes. Write a range of values for R on the X-axis, from 0.02 to 0.30. Do the same for NPV on the Y-axis. If doing this on a spreadsheet program, insert a chart by clicking "insert" then "chart."

Plot your data points. There should be an NPV for every value of R. Plot these so they produce a curve, and then draw a line through this curve. If doing this on a spreadsheet, you will need to highlight the data for the X-axis and the Y-axis. It will produce your axes automatically. You need only label them "R" and "NPV." Select the option that plots a curve through your data points.

Follow the curve down to the point at which NPV=0. This is the point at which R=IRR. In this case that point occurs where R is between 0.22-0.24, meaning the IRR is between 22 percent and 24 percent.

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