Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

IV. Capital Budgeting 9. Net Present Value and

Other Investment Criteria

(^318) © The McGraw−Hill
Companies, 2002
To illustrate the idea behind the IRR, consider a project that costs $100 today and
pays $110 in one year. Suppose you were asked, “What is the return on this invest-
ment?” What would you say? It seems both natural and obvious to say that the return is
10 percent because, for every dollar we put in, we get $1.10 back. In fact, as we will see
in a moment, 10 percent is the internal rate of return, or IRR, on this investment.
Is this project with its 10 percent IRR a good investment? Once again, it would seem
apparent that this is a good investment only if our required return is less than 10 percent.
This intuition is also correct and illustrates the IRR rule:
Based on the IRR rule, an investment is acceptable if the IRR exceeds the required
return. It should be rejected otherwise.
Imagine that we want to calculate the NPV for our simple investment. At a discount
rate of R,the NPV is:
NPV
$100 [110/(1 R)]
Now, suppose we don’t know the discount rate. This presents a problem, but we can still
ask how high the discount rate would have to be before this project was deemed unac-
ceptable. We know that we are indifferent between taking and not taking this investment
when its NPV is just equal to zero. In other words, this investment is economicallya
break-even proposition when the NPV is zero because value is neither created nor de-
stroyed. To find the break-even discount rate, we set NPV equal to zero and solve for R:
NPV 0 
$100 [110/(1 R)]
$100 $110/(1 R)
1 R$110/100 1.1
R10%
This 10 percent is what we already have called the return on this investment. What we
have now illustrated is that the internal rate of return on an investment (or just “return”
for short) is the discount rate that makes the NPV equal to zero. This is an important ob-
servation, so it bears repeating:
The IRR on an investment is the required return that results in a zero NPV when it is
used as the discount rate.
The fact that the IRR is simply the discount rate that makes the NPV equal to zero is
important because it tells us how to calculate the returns on more complicated invest-
ments. As we have seen, finding the IRR turns out to be relatively easy for a single-
period investment. However, suppose you were now looking at an investment with the
cash flows shown in Figure 9.4. As illustrated, this investment costs $100 and has a cash
288 PART FOUR Capital Budgeting

FIGURE 9.4

Project Cash Flows

Year 0

–$100 +$60 +$60

12