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 inept-ga,

Net present value can be described by the following equation:

NPV = (PV of Cash Inflows) - (PV of Cash Outflows)

Our cash inflow here is a perpetuity that is growing at a constant
annual rate. We calculate a perpetuity as described at the following
link:

http://www.netmba.com/finance/time-value/perpetuity/

So, in our case the formula is:

PV of growing perpertuity = C / (i - g)

Where:
C = income at the end of the first period
i = the current discount rate
g = the growth rate per period

PV of growing perpertuity = 5000 / (.1 - 0.05)
= 5000/0.05
= $100000

Now we can calculate NPV, since we know there is only one outflow
which occurs immediately:

NPV = (PV of Cash Inflows) - (PV of Cash Outflows)
= $100,000 - $80,000
= $20,000

So the NPV of this project is $20,000

To calculate the IRR, we need to find the discount rate which would
yield an NPV of 0. We can get the proper calculation using the above
NPV calculations:

5000 / (i - 0.05) = 80,000

Now we just need to solve for i:

80000/5000 = i - 0.05

0.0625 = i - 0.05
i = 0.1125

So the IRR for this project would be 11.25%. This is the point at
which the project would break even. Any rate above this would cause a
negative NPV, and any rate below it would cause a positive NPV (as we
saw with the original NPV calculation).

Hope that helps you understand NPV and IRR - please post a
clarification if anything above is unclear.

Cheers!

answerguru-ga

It appears to me that the formula is incorrect.  You say
80000/5000=i-.05.  I think it should be 5000/80000=i-.05.

Also, I'm confused.  It seems to me that the "point at which the
project would break even" is 10% - the discount rate.  Furthermore,
any rate above this would cause a positive NPV, not a negative one as
you assert.  What am I missing?