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

Step 1.

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

Step 2.

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

Step 3.

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

Step 4.

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

Step 5.

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."

Step 6.

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.

Step 7.

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.