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A project‟s internal rate of return (IRR) is the interest rate that the project essentially pays out. It is the
interest rate that a bank would have to pay so that the project‟s cash outflows would exactly finance its
cash inflows. Instead of investing money in the project, one could invest money in a bank paying a
rate of interest equal to the project‟s IRR and receive the same cash flows. One can think of the IRR as
an interest rate that a project pays to its investors. For example, a project that costs $100,000 to set up
but then returns $10,000 every year forever has an IRR of 10%. If a project costs $100,000 to set up
and then ends the following year when it pays back $105,000, that project would have an IRR of 5%.
The IRR is the rate of return generated by the project.
Most financial calculators and spreadsheet programs have functions that find IRR using cash flows
supplied by the user. For example, consider a project that requires a cash outflow of $100 in year 0
and produces cash inflows of $40 for each of four years. To find the IRR using a financial calculator,
one must specify that the present value equals -$100, annual payments equal +$40, and n, the number
of years, equals 4. The present value and the annuity payments must have opposite signs in order to
indicate to the calculator that the direction of cash flows has changed. The last step is to issue the
instruction for the calculator to find the interest rate that makes these cash flows make sense. The
answer is the IRR, which in this example is 21.9%. For the beer brewery cash flows specified in
Exhibit 6.4, the IRR is 21.7%.
Most TVOM problems involve specifying an interest rate and some of the cash flows and then
instructing the calculator to find the missing cash flow variable—either present value, future value, or
annual payment. IRR calculations involve specifying all of the cash flows and instructing the
calculator to find the missing interest rate.
The IRR also happens to be the discount rate at which the project‟s cash flows have an NPV of
zero. This relationship can be used to verify that an IRR is correct. First, calculate NPV at a guessed
IRR. If the resulting NPV is zero, the guessed IRR is in fact correct. If not, guess again. The IRR
eventually can be found by trial and error.
For example, consider again the case in which the initial cash outflow is $100, followed by four
annual cash inflows of $40. To use the trial and error method, one should calculate the NPV at a
guessed discount rate. When we find the discount rate at which the NPV is zero, we will have
identified the IRR. If we guess 10%, the NPV is $26.79. Apparently, the guessed discount rate is too
low. A higher discount rate will give a lower NPV. So guess again, maybe 30% this time. At 30%, the
NPV is -$13.35. Apparently, 30% is too high. The next guess should be lower. Following this
algorithm, the IRR of 21.9% will eventually be located.
The IRR rule stipulates that a project should be accepted if its IRR is greater than some agreed-on
threshold, and rejected otherwise. That is, to be accepted, a project must produce percentage returns
higher than some company-mandated minimum. Often the minimum threshold is set equal to the
firm‟s cost of capital. If the IRR beats the WACC, then the project is accepted. If the IRR is less than
the WACC, the project is rejected.
For example, suppose a project costs $1,000 to set up, and then is expected to produce a one-time
cash inflow of $1,100 one year later. The IRR of this project is 10%. If the company imposes a
minimum threshold of 20%, this project will be rejected. If the company‟s threshold is 8%, this project
will be accepted. We saw earlier that the brewery project IRR is 21.7%. If the agreed threshold is the
brewery‟s 20% WACC, then the IRR rule would indicate that the project should be accepted.