2.1. The point, at which the discount factor shows the NPV as zero, is nothing but
IRR. In other words IRR exists at the point where NPV = 0 or the PV of
benefits is equal to PV of costs.
2.2. If PV of benefits is more than the PV of cost, (NPV > 0) NPV is positive. If
PV of benefits is less than the PV of costs, (NPV < 0) NPV is negative. If
PV of benefits is equal to the PV of costs, (NPV = 0) NPV is neutral. IRR
exists at the discount factor at which NPV = 0.
- How is IRR calculated? An Example:
3.1. A person wanted take up project ‘X’ with an initial investment of Rs.10, 000.
This project involves purchasing of machinery etc., The project is estimated
to have life span of 5 years. The estimated Salvage Value of the ‘left overs’
at the end of the fifth year is Rs.500. The other relevant estimations
pertaining to the project are as follows :-
Year Earning Cost Net Cash flow
1 3,000 1,000 2,000
2 3,500 1,000 2,500
3 4,000 1,000 3,000
4 5,000 2,000 3,000
5 5,000 2,000 3,000*
*includes Rs.500 as salvage value of the project.
3.2. Here, the earnings mean cash inflow in the form of returns. Cost means
‘Operation and Maintenance expenses’. The objective of the IRR calculation
is to ascertain discount factor (cost of capital) at which the investor recovers
the initial investment of Rs.10, 000 in terms of present value.
3.3. Solution: The reader may note that IRR can be determined only by trial and
error. A discount factor where NPV = 0 cannot be determined all of a
sudden. Therefore two different factors must be arbitrarily selected: one
yielding positive figure (NPV > 0) and another yielding negative figure
(NPV < 0). Next by using the interpolation formula between these two, IRR
can be determined at which NPV = 0. In arriving at the following solution by
trial and error, one discount factor worked at 10% and the other discount
factor worked at 12%.
