Any help with solving the following problem is welcomed -- web sites,
formulas, etc.

	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?			
			
NPV Profile			
Discount			
Rate	NPVA	NPVB	
0%	FORMULA	FORMULA	
2%	FORMULA	FORMULA	
4%	FORMULA	FORMULA	
6%	FORMULA	FORMULA	
8%	FORMULA	FORMULA	
10%	FORMULA	FORMULA	
12%	FORMULA	FORMULA	
14%	FORMULA	FORMULA	
16%	FORMULA	FORMULA	
18%	FORMULA	FORMULA	
20%	FORMULA	FORMULA	
			
	b. What is the IRR of each project?		
			
	Project A IRR	FORMULA	
	Project B IRR	FORMULA

---

Request for Question Clarification by livioflores-ga on 03 Jul 2003 09:41 PDT

Hi boobe!!

Some concepts:
NPV Decision Rule that says: 
-General Rule: Accept a project if NPV >= 0. 
-Mutually Exclusive Projects: Accept the one having the largest NPV >=
0.

Present Value: 
 
          CF1               CF2              CF3      
PV  = -----------   +   -----------   +  -----------   r = interest
rate.
       (1 + r)^1         (1 + r)^2        (1 + r)^3      


Net Present Value: 
NPV = PV - I         where I = Initial Investment, in this case
$20,000
 

To calculate the IRR you must find r from the PV = I equation. In
other words IRR is the discount rate at which the NPV equals zero.
Calculating the IRR: 
-Trial & Error techniques 
-Calculator 
-Computer 

To do this using an MS Excel spreadsheet for this problem: 
1) Input your total costs for the project in one column (lets say
column "A").
2) Input your income (derived savings etc...) for the project (lets
say column "B")
3) Set up a column that adds the total costs and the total savings per
year ("C1" = "A1" - "B1", "C2" = "A2" - B2", etc...).
4) Click on the cell where you want your IRR calculated 
5) Enter "=IRR(" (without the quotes) and then highlight the total
costs + total savings column (C column)and hit enter.

Please, let me know if this satisfy your requirements of an answer, if
not tell what more do you need and I will gladly do it.

I will wait for your response in order to post it as an answer adding
the things that you will request.

Best regards.
livioflores-ga

Hi boobee,

a. The net present value of a series of cash flows is calculated by
the formula NPV = -I + C(n)/(1 + r)^n where C(1) is the cash flow in
period n, I is the initial investment, and r is the interest-rate

Rate	NPV A	        NPV B	
0	4000	        5000	
2	3071.066	3558.058	
4	2200.728	2224.909	
6	1384.096	990.4821	
8	616.7759	-154.194	
10	-105.184	-1217.13	
12	-785.35	        -2205.49	
14	-1426.94	-3125.71	
16	-2032.88	-3983.56	
18	-2605.82	-4784.23	
20	-3148.15	-5532.41	

As you can see, the net present value of Project B is higher than that
of Project A for interest rates of 6% or less.  Project A is preferred
for interest rates of 8% or more, although Project A becomes
potentially unattractive for interest rates higher than 10%.

b.  The Internal Rate of Return is the value of r for which the Net
Present Value is zero.  In this case, it can be solved using simple
algebra.  The Internal Rate of Return for Project A is 9.7%, and the
Internal Rate of Return for Project B is 7.72%.  This makes sense
based on what we saw above where Project B had a slightly negative net
present value at 8% and Project A had a slightly negative net present
value at 10%.

Sincerely,

Wonko

---

Request for Answer Clarification by boobee-ga on 03 Jul 2003 14:16 PDT

Hi Wonko,

Just wanted to make sure that figures were correct

NPV Profile						
Discount						
Rate	NPVA	NPVB				
0%	$4,000 	$5,000 				
2%	$3,071 	$3,558 				
4%	$2,201 	$2,225 				
6%	$1,384 	$990 				
8%	$617 	($154)				
10%	($105)	($1,217)				
12%	($785)	($2,205)				
14%	($1,427)	($3,126)				
16%	($2,033)	($3,984)				
18%	($2,606)	($4,784)				
20%	($3,148)	($5,532)				
						
Project A is preferred to B at interest rates 0% through 4%.  At 6%
project B has a lower NPV than A, however
at 10% through 20% the NPV of Project B is again higher than Project
A.
						
b. What is the IRR of each project?						
						
Project A IRR	9.70%					
Project B IRR	7.72%

---

Clarification of Answer by wonko-ga on 03 Jul 2003 21:43 PDT

You have the values right.  However, there is a misunderstanding about
how to interpret them.  I also made typographical errors (the 6%
should have been 4%, and the 8% should have been 6%).  One project is
preferred over another if it's net present value is greater than that
of the other Project (it has a higher POSITIVE net present value or
has a lesser NEGATIVE net present value).  Since the net present value
of Project B is greater than the net present value of Project A, it is
preferred for discount rates of 0% to 4%.  For discount rates of 6% to
20%, Project A is preferred because it has a greater net present value
(it is less negative in those cases where both are negative) then does
Project B. However, in general, one tries to avoid projects with zero
or negative net present values.

I apologize for my mistakes in presenting the results.  I appreciate
you double checking my work and pointing it out to me.

Sincerely,

Wonko

Once again you have outdone yourself -- five gold stars!!!