NPV and IRR explained with example.

Hello everyone,

One of the main confusion that pops is regarding the conceptual difference b/w the IRR(Internal Rate of Return ) and NPV(Net Present Value).

Now we can easily understand the underlying formulas and calculations but there is an idea that has to be understood and the best to to understand is by picking up an suitable example.

I would suggest this Wiki article for a warm up.

http://en.wikipedia.org/wiki/Internal_rate_of_return

http://en.wikipedia.org/wiki/Net_present_value 

Example:- We need two investments for which the net NPV should be 50.
Cost of Capital = .2 or 20%

Investment one:       -100                 180

Investment two:       -100000           120060

NPV one = -100 + 180(1 + .2) = 50
NPV two = -100000 + 120060(1 + .2) = 50

You cannot judge an investment based on NVP as both are same but consider the amount of money in investment two but this is just an simple case when the investments are complex its hard to judge so . So that's why we need IRR but IRR is also not the ultimate solution.

Now lets calculate IRR for the same . We need a value r' for which the NVP must be Zero.

IRR one :-  -100  + 180/(1 + r') = 0
                  Simplify we get r' = 0.80 

IRR two :-    -100000 + 120060(1+r'')= 0
                     here r'' = .2006

r < r'  Investment  accepted

  r > r ' Investment rejected

In our case r  = .20 and r'= .80 and r''(Second investment) = .20

So clearly investment one is favorable as compared to investment two although up to fourth decimal place it is also higher or up to second decimal place almost equal but as you read wiki page carefully you see these methods are for mutually exclusive investment selection and thus investment one gives us higher return and thus should be chosen.

Nitin Arya