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 wombat319!!

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

NPV = PV of Cash Flows - Investment

The cash flows constitutes a constant growth perpetuity, so their PV is:

PV = CF1 / (r - g)

Where:
CF1 = first period's cash flow
r = discount rate
g = constant growth rate

So we have that:
PV = $5,000 / (0.10 - 0.05)
   = $5,000/0.05
   = $100,000

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

The NPV of this project is $20,000 .



b. What is the project IRR?

IRR is the discount rate at which the NPV equals zero, in other
words it is the rate that satisfies:
NPV = PV - I = 0

Then IRR is the discount rate r at which:
PV = I

So we have to find at which rate (IRR) is:
PV = CF1 / (IRR - g) = I

Then, for this problem is:
IRR = CF1/I + g =
    = $5,000/$80,000 + 0.05 =
    = 0.0625 + 0.05 =
    = 0.1125

So the IRR for this project would be 11.25%.


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

Regards,
livioflores-ga

Thanks for the help & explanation! I get it now!