Here are the cash flows for two mutually exclusive projects:
Project A
Co= -$20,000  C1= $8000  C2= $8,000  C3= $8,000
Project B
Co= -$20,000  C1= 0  C2= 0  C3= 25,000

a. At what interest rate would you prefer Project A or B?
b. What is the IRR for each project?

***Please show work****

Decgirl --

We'll assume here that C0, C1, etc. represent cash flows for each
year.  If it were assumed that they represented quarterly returns, the
numbers would be dramatically higher.

The first task is to work out IRRs for each project.  IRR is defined as:
(NPV)/(1 + IRR)^t = Initial outlay, where t = number of years and IRR
is the IRR expressed as a decimal (9% would be .09).  What this
question is asking is: at what IRR does a 3-year return of $24,000
paid in equal annual installments equal a lump-sum of $25,000 paid in
year 3?

There are several ways to work this out:  one way would be to discount
cash flows for years 1, 2, 3 to get your NPV or net present value. 
Then you could find the interest rate that makes them equal.

I've done it a little differently in the spreadsheet you'll find
posted here.  This link will take you there directly but note that the
file name IS case-sensitive on this server:
TwinIRRs (Aug. 30, 2004)
http://www.mooneyevents.com/twinIRRs.xls

If you calculate the IRRs, you'll find that it's more attractive to
get $8,000 each year rather than wait 3 years to get the lump sum. 
Project A has an IRR of 9.70%; Project B = 7.72%.

What happens if we split the difference in IRRs, which some might
think makes sense?  You'll make the wait for Project B's cash flow
worse -- actually turning the project negative in NPV.  What needs be
done is to find a LOWER interest rate which makes Project B shine.  An
interest rate of 0% would make Project B dominant -- that's where
$25,000 paid in 3 years outstrips $24,000 paid annually.  But what
rate should be chosen in between 0% and 7.72%?

I first tried 6% -- you can try it or any other percentage by:
*  first saving the spreadsheet
*  then modifying the percentages in the Excel spreadsheet's formulas.  

Project A still has a higher NPV @6% -- so I then tried 4%.  At 4%,
Project B had a slightly higher NPV.  It turns out that the number
that will equalize the two is 4.11%

Anything higher than 4.11% will favor Project A; anything lower will
favor Project B.

Best regards,

Omnivorous-GA