20. NPV versus IRR. Here are the cash flows 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 profile of each project.
b. What is the IRR of each project?

Hi!!


a. At what interest rates would you prefer project A to B?

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        


You must use the NPV and PV formulas to build the following table:

Rate	  NPVA	          NPVB
0%	 $4,000.00 	 $5,000.00 
2%	 $3,071.07 	 $3,558.06 
4%	 $2,200.73 	 $2,224.91 
4.11%	 $2,153.62 	 $2,153.26 
6%	 $1,384.10 	 $990.48 
8%	 $616.78  	-$154.19
10%	-$105.18 	-$1,217.13
12%	-$785.35	        -$2,205.49
14%	-$1,426.94	-$3,125.71
16%	-$2,032.88	-$3,983.56
18%	-$2,605.82	-$4,784.23
20%	-$3,148.15	-$5,532.41


Note 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%.

(Note: I used an spreadsheet to do the calculations and find the value
4.11% by guessing -trying different values of rate in the Excel
spreadsheet's NPV formula until find the "no difference" rate. I did
that because we cannot post a graph that shows the intersection of
both NPV profile)

--------------------------------------------

b. What is the IRR of each project?

IRR is the discount rate R that makes the NPV equals to zero, that is
the rate R that satisfies:

PV = I

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 Spreadsheet, you can use that
document as reference to learn the use of MS Excel to solve problems
like this one:
http://merlin.alleg.edu/employee/d/dgoldste/econ427/CH07-03a.xls

------------------------------------------

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

Best regards.
livioflores-ga

---

Clarification of Answer by livioflores-ga on 31 Oct 2004 00:11 PDT

Hi!!

I just need to modify the 4.11% line of the table (there is a little
mistake in the calculations):

Rate	  NPVA	          NPVB
4.11%	$2,154.46 	$2,154.54   ("No difference" rate)


Thank you.

The response was not only an answer, but a terrific explanation of the
problem and the solution.  As a result of this guidance, I was able to
work through the problem and understand it.  Very prompt.  Very
detailed.  Thank you.