38. NPV/IRR. Growth Enterprises believes its latest project, which
will cost $80,000 to install, will generate a perpetual growing stream
of cash flows. Cash flow at the end of this year will be $5,000, and
cash flows in future years are expected to grow indefinitely at an
annual rate of 5 percent.
a. If the discount rate for this project is 10 percent, what is the project NPV?
b. What is the project IRR?

Hi again spockspock!!


Here we have a growing perpetuity case!!
For references see:
"Perpetuities":
http://www.netmba.com/finance/time-value/perpetuity/


a. If the discount rate for this project is 10 percent, what is the project NPV?

For a growing perpetuity the Present Value is:

            Initial Cash Flow 
PV = --------------------------------- = CF_0 / (r - g)
       (Discount rate - Growth rate) 

   = 5,000 / (0.10 - 0.05) =
   = 100,000


NPV = PV - I          where I is the initial investment.

Then:
NPV = 100,000 - 80,000 = 20,000

NPV = $20,000

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

b. What is the project IRR?

We must find R that satisfies the equation PV = I  .

PV = CF_0 / (R - g) = I

Then:
R = CF_0/I + g =
  = 5,000/80,000 + 0.05 =
  = 0.0625 + 0.05 =
  = 0.1125

Then IRR = 11.25% .

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

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

Best regards.
livioflores-ga

livioflores is so complete in his/her answers.  Definitely worth the
price.  Very detailed and explains concepts extremely well.  Wish this
person was teaching the class I am taking.