Introduction to Finance

F01 = 1.00
Enter cash flows for the fifth year
↓ 
5800
ENTER
C01 = 5,800
↓
F01 = 1.00
Computing NPV
To
Press
Display
Prepare to compute IRR
IRR
IRR = 0.00
Compute internal rate of return
↓ CPT
IRR = 13.82
Using spreadsheets, we can illustrate two ways to determine the internal rate of return. We 
will use project A, with its annuity cash fl ows, in these examples. First, we can successively 
compute values of NPV using diff erent discount rates:
Discount Rate (%)
Project A’s NPV
0
$9,000.00
1
$8,149.90
2
$7,338.07
3
$6,562.30
4
$5,820.57
5
$5,110.96
6
$4,431.71
7
$3,781.15
8
$3,157.72
9
$2,559.98
10
$1,986.56
11
$1,436.20
12
$907.70
13
$399.94
14
–$88.13
The NPV goes from 
positive to negative 
here, so the IRR must 
lie between 13 and 
14 percent.
15
–$557.50
16
–$1,009.10
17
–$1,443.79

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17.4 Capital Budgeting Techniques—Internal Rate of Return
533
This shows the IRR is between 13 and 14 percent. This information can be used as input into 
Excel’s graphing capabilities and the NPV profi le can be graphed, which is how we constructed 
Figure 17.1. The NPV profi le gives us a visual perspective of how sensitive the NPV is to a 
change in the project’s cost of capital, or discount rate.
The second way to use the spreadsheet is to compute the IRR by using Excel’s IRR func-
tion. Let’s assume the time 0 through time 5 cash fl ows for project A are in cells B2 through 
B7, as below. By keying = IRR(B2:B7) into a cell (B9, in this case), the spreadsheet will 
compute an exact value of the internal rate of return for project A:
In our example, the initial (time zero) cash fl ow is found in cell B2. Cell B7 contains the 
fi nal cash infl ow for time period fi ve. Using the IRR function, we obtain an exact value for 
project A’s IRR, 13.82 percent, the same as we found using a fi nancial calculator.
The IRR function has the form = IRR(cell of time zero cash fl ow : cell of last cash fl ow, 
initial estimate for the IRR). The last item, the initial estimate for the IRR, is optional and we 
did not use it in the above example for project A. To input an initial guess, we can use percent-
ages (10%) or decimal equivalents (0.10). Many times, we can omit this initial guess and the 
IRR function will compute the IRR with ease.
For project B, with its unequal cash fl ows, a fi nancial calculator or spreadsheet program 
are the most useful. But a trial-and-error process can also be used to fi nd the IRR for project B. 
Discounting the cash fl ows at a 10 percent rate results in a positive NPV of $988, as calculated 
in Table 17.3. A positive NPV indicates that we need to try a higher discount rate, such as 12 
percent, to fi nd the discount rate that results in a zero net present value. The 12 percent PVIFs 
are taken from Table 2 in the Appendix, “Present Value of $1.”
10
In