This post provides an example
where the IRR cannot select the better project but the NPV does provide the
answer.
Question One: Project A involves an initial investment of
$1,000 and a return of $1,000 in one year.
Project B involves an initial investment of $1,000 and a return of
$1,000 in two years. Show that both
projects have an IRR of 0 percent and the IRR value cannot be used for project
selection.
Assume the person has a cost
of capital equal to 10 percent. What
are the NPVs of the two projects?
Confirm based on the NPV that project B is preferable to project A.
Answer to Question One: The problem
was solved with the XIRR and the XNPV functions in Excel. The inputs to the XIRR function are the
dates and the cash flow ranges. The
input to the XNPV function are the date range, the cash flow range and the assumption
on the cost of capital, which in this case is 0.10.
The IRR and NPV for project A
where $1,000 is returned after one year is presented below.
Project A


Date

Cash Flow

1/1/00

1000

1/1/01

1000

XIRR

0%

XNPV

$91.15

The IRR and NPV for project B
where $1,000 is returned after two years is presented below.
Project B


Date


1/1/00

1000

1/1/02

1000

XIRR

0%

XNPV

$173.77

Note that for both projects the
IRR is 0. In both cases, the investor
ties up funds and gets 0 percent. The
difference is that that for project A the funds are tied up for one year while
for project B the funds are tied up for two years. Clearly project A is better to the investor
than project B.
The NPV is larger (less
negative) for project A than project B.
Losses are smaller for project A than project B.
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