Suppose you are offered $5000 today but must make the following payments:

year 0    5000
year 1   -2500
year 2   -2000
year 3   -1000
year 4   -1000

a.  What is the IRR of this offer?
b.  If the appropriate discount rate is 10%, should you accept this offer?
c.  If the appropriate discount rate is 20%, should you accept this offer?
d.  What is the NPV of the offer if the appropriate discount rate is 10%? 20%?
e.  Are the decisions under the NPV rule in part (d) consistent with
those of the IRR rule?

Hello!
I've done the calculations you require in Excel, using the NPV and IRR
functions. You can download this file from the following link:

http://www.filefactory.com/file/b0b2a0/

Based on the information from this spreadsheet, we can now answer your questions.

a. The IRR of this offer is 13.99%

b. This question and the following one are a bit tricky. The usual
decision rule when using IRR is:

Discount Rate < IRR ----> Accept Project
Discount Rate > IRR ----> Reject Project

However, this decision rule only applies for the cases in which there
is an initial cash outflow, and then several cash inflows across the
next years. In this case, however, the stream of payments from the
project in question is just the opposite. There is a cash inflow at
the beginning, and then cash outflows during the next four years.
Given that this is the case, then the decision rule for IRR must be
REVERSED. We thus get that the appropiate decision rule for this case
is:

Discount Rate < IRR ----> Reject Project
Discount Rate > IRR ----> Accept Project

Therefore, since the discount rate (10%) is lower than the IRR, we
conclude that the offer should be rejected.

c. Using the "reversed" decision rule, we conclude that since the
discount rate (20%) is higher than the IRR, the offer should be
accepted.

d. These are shown in the Excel file. The NPV when the discount rate
is 10% is -$359.95. When the discount rate is 20%, the NPV is $466.82.

e. The decision rule when using the NPV (this is irrespective of
whether there is an initial cash outflow or inflow, as with the IRR)
is that projects with positive NPV should be accepted, while projects
with negative NPV should be rejected. Therefore, we conclude that:

When Discount Rate = 10% --> NPV = -$359.95 ---> REJECT OFFER
When Discount Rate = 20% --> NPV = $466.82  ---> ACCEPT OFFER

As you can see, using NPV, we've arrived to the same decision we got
when we used the appropiate decision rule with IRR. So the answer is
yes, they are consistent.


If you want additional information about the IRR, you might want to
check the following links:

Wikipedia - Internal Rate of Return
http://en.wikipedia.org/wiki/Internal_rate_of_return

Internal Rate of Return
http://hspm.sph.sc.edu/COURSES/ECON/irr/irr.html

Google search terms
internal rate return
://www.google.com.ar/search?sourceid=navclient&ie=UTF-8&rls=GGLF,GGLF:2006-25,GGLF:en&q=internal+rate+return


I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.

Best wishes!
elmarto