Jessica Wachter Notes for Finance 604
Topic 5: Capital Budgeting: NPV vs. Internal rate of return (IRR)
A well-known survey of CFOs finds that 75% of CFOs use the NPV technique. RWJ
chapter 5 discusses alternatives to NPV and says thy they are wrong.
Here we are going to focus on the alternative to NPV which is a little bit right – the IRR.
NPV rule =⇒Accept if NPV >0. Otherwise, reject.
IRR rule =⇒Accept if IRR > r (discount rate). Otherwise, reject.
(a) Definition of IRR
Definition The Internal Rate of Return is the rate of return rsuch that the NPV = 0:
0 = C0+C1
1 + r+C2
(1 + r)2+C3
(1 + r)3+· · ·
Sometimes, the IRR rule works very well.
Example Assume C0=−$100 and C1= $110:
NPV = −100 + 110
1 + r.
So:
−100 + 110
1 + r= 0 implies
IRR = 110
100 −1 = 10%.
If r= 8%:
•IRR rule says accept.
•NPV rule also says accept because r= 8% ⇒NPV = 1.85 >0.
Remarks:
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Jessica Wachter Notes for Finance 604
•We’ve already come across an IRR in this course: The YTM is the IRR for buying a
coupon bond!
Remember that the YTM was somewhat of a problematic notion. We wanted to use
it as a yardstick for comparing bonds as investments. However, it was a flawed
yardstick, as you only receive the YTM if you reinvest at the YTM – which may not
happen!
•Similarly, people like to think of IRR as the rate of return on their investment.
However, this holds true only if you can invest the intermediate cash flows at the IRR.
However, this assumption is even less realistic when dealing with a project than when
dealing with a bond. A bond is an instrument traded on the market. If rates stay
approximately fixed, you might be able to reinvest your cash flows at the same rate.
