Planning Capital Expenditure 309cleanup cost that would have to be paid after the payback horizon. Although the
rule incorporates the time value of money, it is still shortsighted. One might
conjecture that the payback and discounted payback rules are popular since
they are easy to apply. Yet, this ease is paid for in lost opportunities for creating
wealth and occasional misallocation of resources into wasteful projects.
Internal Rate of Return
A project’s internal rate of return (IRR) is the interest rate that the project es-
sentially pays out. It is the interest rate that a bank would have to pay so that
the project’s cash outf lows would exactly finance its cash inf lows. 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 f lows. One can
think of the IRR as an interest rate that a project pays to its investors. For ex-
ample, 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 f lows supplied by the user. For example, consider a project
that requires a cash outf low of $100 in year 0 and produces cash inf lows 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 direc-
tion of cash f lows has changed. The last step is to issue the instruction for the
calculator to find the interest rate that allows these cash f lows to make sense.
The answer is the IRR, which in this example is 21.9%. For the beer brewery
cash f lows specified in Exhibit 10.4, the IRR is 21.7%.
Most TOVM problems involve specifying an interest rate and some of the
cash f lows and then instructing the calculator to find the missing cash f low
variable—either present value, future value, or annual payment. IRR calcula-
tions involve specifying all of the cash f lows 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
f lows 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 outf low is
$100, followed by four annual cash inf lows 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,