)NPV versus IRR. Here are the cash ?ows for two mutually exclusive projects:
Project   C0      C1       C2      C3
A      ?$20,000 +$8,000  +$8,000  +$8,000
B      ?$20,000    0        0     +$25,000
a. At what interest rates would you prefer project A to B? Hint: Try
drawing the NPV pro?le of each project.
b. What is the IRR of each project?

Hi!!

To answer question a) you need to compare the the NPV for a range of
discount rates to see which project has the better NPV at defined
rate.

Remember that:

Present Value (PV) for 3 years is:

         CF1           CF2            CF3        
PV  = ---------  +  ----------  +  ----------  
      (1 + r)^1     (1 + r)^2	  (1 + r)^3    

and Net Present Value (NPV):

NPV = PV - I 


For the question b) you need to remember that IRR is the discount rate
R that makes the NPV equals to zero, that is the rate R that
satisfies:

PV = I

You can use different ways to calculate the IRR, for example:
-Trial & Error
-Calculator
-Computer (Excel spreadsheet)

Using an Excel spreadsheet you get:
Use an Excel spreadsheet for the calculations:

-Project A:
Column A :               Column B
A1: -20,000              B1: =IRR(A1:A4)
A2: 8,000
A3: 8,000
A4: 8,000

IRR_A = 9.70%


-Project B:
Column A :               Column B
A1: -20,000              B1: =IRR(A1:A4)
A2: 0
A3: 0
A4: 25,000

IRR_B = 7.72%



I found this problem solved in an Excel file, I think that you can use
it as reference to learn the use of MS Excel to solve problems like
this one, see the Problem 7-19 sheet:
http://merlin.alleg.edu/employee/d/dgoldste/classes/econ427/CH07-03a.xls


Check the value 4.1112% instead 4% at the answer a) table, you will
see that there is no difference at this rate between the two projects,
at this point both NPV profiles will intersect each other if you draw
them. I found this value by trial and error ("just guessing" method).
According to that that if the rate is greater than 4.11% the NPVs of the project A
are higher than that of project B, and if the rate is less than 4.11%
the NPVs of the project B are higher than that of project A. This
means that you would prefer the project B if the interest rate is
below 4.11% and you would prefer project A if the interest rate is
above 4.11%.


I hope this helps you. Feel free to request for a clarification if you need it.

Regards,
livioflores-ga