# Net Present Value and Internal Rate of Return

Net Present Value (NPV)

It is defined as (Sum of present value of all cash inflows) – (sum of present value of all cash outflows)
Decision Rule:  Accept the project if NPV is >= 0: Accept the project OR project is financially feasible.

Internal Rate of Return(IRR):

It means the rate at which the Present Value of cash inflow (CIF) is equal to Present Value of cash outflow (COF) or npv=0.
Decision Rule:
Accept project whose IRR>=Discounting Factor
where,
Discounting Factor = 1/[(1+r)^n]
where,
r is the interest rate/discounting rate and n is the period

Note: We can also define it in terms of future values but in general future values are generally used for savings and present value is used for investments

There is possibility of having two IRR values for same project. How can IRR have two different value? Let’s see the below problem
Question: Initial investment of the project is 100 and cash inflows in first and second years are 40 and 60 respectively. Find if the project is feasible or not?

From the definition of IRR, equate PV of initial investment = PV of cash inflows

```100 = 40/(1+r) + 60/(1+r)^2
```

this would lead to function defined by a quadratic equation and hence with two roots, hence IRR could have more than one value.

In general use NPV for decision making and IRR for communication

Reasons NPV as positive value and IRR as negative could be:

• adding new project to the existing project
• if there are any additional cash outflows apart from the initial investment (initial cash outflow) because of which cash inflows are positive and outflows negative could lead to negative IRR.

How do you identify if IRR is negative? In IRR excel function put some positive and negative percentages, it the value remains same then we have only one IRR otherwise there is more than one value for IRR.

A project with positive NPV and negative IRR is generally considered inconsistent.