For our Project S, here is the time line setup:(^0) IRR 1234
Cash Flows 1,000 500 400 300 100
Sum of PVs for CF1–4 1,000
Net Present Value 0
Thus, we have an equation with one unknown, IRR, and we need to solve for IRR.
Although it is easy to find the NPV without a financial calculator, this is nottrue
of the IRR. If the cash flows are constant from year to year, then we have an annuity,
and we can use annuity formulas as discussed in Chapter 2 to find the IRR. However,
if the cash flows are not constant, as is generally the case in capital budgeting, then it
is difficult to find the IRR without a financial calculator. Without a calculator, you
must solve Equation 7-2 by trial-and-error—try some discount rate and see if the
equation solves to zero, and if it does not, try a different discount rate, and continue
until you find the rate that forces the equation to equal zero. The discount rate that
causes the equation (and the NPV) to equal zero is defined as the IRR. For a realis-
tic project with a fairly long life, the trial-and-error approach is a tedious, time-
consuming task.
Fortunately, it is easy to find IRRs with a financial calculator. You follow proce-
dures almost identical to those used to find the NPV. First, you enter the cash flows as
shown on the preceding time line into the calculator’s cash flow register. In effect, you
have entered the cash flows into the equation shown below the time line. Note that we
have one unknown, IRR, which is the discount rate that forces the equation to equal
zero. The calculator has been programmed to solve for the IRR, and you activate this
program by pressing the button labeled “IRR.” Then the calculator solves for IRR and
displays it on the screen. Here are the IRRs for Projects S and L as found with a fi-
nancial calculator:^6
It is also easy to find the IRR using the same spreadsheet we used for the NPV. With
Excel,we simply enter this formula in Cell B6: IRR(B4:F4).For Project S, the result
is 14.5 percent.^7
IRRL11.8%.
IRRS14.5%.
1,000
500
(1IRR)^1
400
(1IRR)^2
300
(1IRR)^3
100
(1IRR)^4
0.
268 CHAPTER 7 The Basics of Capital Budgeting: Evaluating Cash Flows
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(^6) To find the IRR with an HP-10B or HP-17B, repeat the steps given in Footnote 3. Then, with an HP-10B,
press , and, after a pause, 14.49, Project S’s IRR, will appear. With the HP-17B, simply
press to get the IRR. With both calculators, you would generally want to get both the NPV
and the IRR before clearing the cash flow register. The Technology Supplementexplains how to find IRR with
several other calculators.
(^7) Note that the full range is specified, because Excel’sIRR function assumes that the first cash flow (the neg-
ative $1,000) occurs at t 0. Also you can use the function wizard if you don’t have the formula memorized.
IRR%
IRR/YR