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 |