The internal rate of return (IRR) is used to evaluate how profitable a proposed project is when investigating options during capital budgeting decisions. When considering several projects for investment, the project with the higher IRRs are almost always selected over those with lower IRRs. IRR is the value at which a project returns a net present value (NPV) of zero. While calculating IRR is easier with a financial calculator or spreadsheet software, you can do it by hand using a trial and error process.

Make a table with "Period" and "Cash Flow" as column headers. Cash flow (CF) periods are typically done on a monthly or yearly basis.

List period numbers in ascending order, starting with 0, until the number of periods for the project has been reached.

List the cash flows for each period. Cash flows are typically done on a monthly or yearly basis. Be sure to include a negative value for cash flow at period 0, to represent initial cash outlay.

Write out the equation: NPV = CF(0) + CF(1)/(1+r) + CF(2)/(1+r)^2 + CF(3)/(1+r)^3 + CF(4)/(1+r)^4.... Keep going until the cash flow number matches the number of cash flows you have in the table. Note that the "^" indicates an exponential power.

Substitute the cash flow value of period 0 for CF(0).

Substitute the cash flow value of period 1 for CF (1). Repeat this for each period until all cash flow values are substituted.

Pick an arbitrary value for r. For example, 10 per cent.

Calculate the total for NPV as dictated by the operational signs in the formula. If NPV is positive, the value of r is too low and needs to be increased. If NPV is positive, the value of r is too high and must be decreased.

Repeat until an NPV value of 0 is reached. When NPV equals 0, r represents the IRR of the project. Once the gap between two r-values is narrowed to one (e.g., 12 and 13 per cent), decimal places are added to the r-value to give a more precise measure of NPV.