Introduction to Finance

Table 17.4
, we calculate 
that when the cash fl ows are discounted at a 12 percent rate, the NPV becomes minus $514.
This indicates that the IRR falls between 10 and 12 percent. Since minus $514 is closer 
to zero than $988 is, you might guess that the IRR is a little above 11 percent. But to obtain 
an exact answer, we need to use a fi nancial calculator or electronic spreadsheet. Doing so, we 
learn that project B’s IRR is 11.3 percent.
10
Similar to the “seesaw eff ect” in bond pricing, a higher discount rate results in a lower NPV, as seen in Figure 17.1. 
TA B L E 1 7 . 4
Net Present Value Calculation for Project B Using a 12 Percent Discount Rate
Year
Cash Flow
×
12% PVIF
=
Present Value
0 –$25,000
1.000
–$25,000
1 
4,000
0.893
3,572
2 
4,000
0.797
3,188
3 
8,000
0.712
5,696
4 
10,000
0.636
6,360
5 
10,000
0.567
5,670
Net present value = –$514

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534
C H A PT E R 1 7 Capital Budgeting Analysis
Projects A and B are acceptable because they provide returns higher than the 10 percent 
cost of capital. However, if the projects are mutually exclusive, we would select project A over 
project B because A’s NPV is higher.
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NPV and IRR
The NPV and IRR methods will always agree as to whether a project enhances or harms share-
holder wealth. If a project returns more than its cost of capital, the NPV is positive. If a project 
returns less than its cost of capital, the NPV is negative. An issue with the use of IRR is that 
it may rank projects diff erently than the NPV. If that occurs, what decision should be made?
If the projects are independent, there is no real issue; the fi rm should do all projects with 
positive NPVs. To state this similarly but in another way, the fi rm should do all projects with 
IRRs greater than their required returns. 
If the projects are mutually exclusive, however, the decision should be made to follow the 
rankings created by the NPV method. The NPV measures the change in shareholder wealth 
that is expected to be generated by the project. As managers should maximize shareholder 
wealth, they should prefer the project with the higher NPV, 
not
the higher IRR.
A second issue that can occur with IRR is that the cash fl ows of a project may alternate in 
sign; meaning, some cash fl ows are positive and some negative. In such a case, it is mathemat-
ically possible to have two or more IRRs. For example, consider the case of a project with an 
initial outlay of $100, a positive cash fl ow of $300 in year one, and a cash outfl ow of –$200 in 
year two because of shut-down costs. Such a project has two IRRs: 0 percent and 100 percent:
NPV at 0%: –100 + 300∕(1 + 0)
1
+ –200∕(1 + 0)
2
= –100 + 300 –200 = 0
NPV at 100%: –100 + 300∕(1 + 1.00)
1
+ –200∕(1 + 100.0)
2
= –100 + 150 –50 = 0
It is easy to think of a real-world project that may require substantial renovations or mainten-
ance over time, or one that may have large end-of-life decommissioning or shut-down costs. 
Thus, for this reason NPV is the preferred approach rather than internal rate of return.
A common misconception is that the IRR represents the compounded return on the funds 
originally invested in the project. What IRR measures is the return earned on the funds that 
remain internally invested in the project (hence the name, 
internal 
rate of return). Some cash 
fl ows from a project are a return of the principal (original investment), while some pay a return 
on the remaining balance of funds invested in the project.
To show that the IRR measures the return earned on the funds that remain internally 
invested in a project, we present the following example. Martin and Barbara have decided to 
upgrade their business computer system to improve the quality and effi
ciency of their work. 
The initial investment is $5,000 and the project will save them $2,010.57 each year for three 
years. They have determined the IRR on the project to be 10 percent. We show how the IRR 
represents the return on the year-by-year unrecovered costs of the project.
Below is the cash fl ow schedule constructed for Martin and Barbara’s computer upgrade 
project.