# Which is better: NPV or IRR?

Before we try to understand why Net Present Value (NPV) is better than Internal Rate of Return (IRR) or the relationship/difference between them, let us understand both the methods in short in surface.

## Net Present Value (NPV)

Net Present Value (NPV) is the net of present values of total cash-inflows and cash-outflows.

i.e. Net Present Value (NPV)  = Present Value of Total cash-inflow – Present Value of Total cash-outflow

When we calculate present value, we discount all the future cash-flows with certain interest rate, which is generally cost of capital.

## Internal Rate of Return (IRR)

Whereas, Internal Rate of Return (IRR) is that value of discount rate or interest rate, which makes net present value “zero” i.e. net of present value of total-cash-inflow and outflow is 0. That is the major relationship of IRR with NPV.

In capital budgeting, NPV method is considered more superior to IRR method. In fact, NPV is the most reliable technique to judge various project alternatives and select the most profitable one.

## Net Present Value (NPV) vs Internal Rate of Return (IRR)

The major differences between Net Present Value and Internal Rate of Return is discussed below:

• Internal Rate of Return (IRR) method assumes that cash flow are re-invested at IRR rate of the same project, whereas, Net Present Value (NPV) method assumes that cash flow are re-invested at cost of capital. Thus consideration of NPV method is more valid or realistic than that of IRR.
• The end value provided by NPV method is consistent with value maximization objective but that of IRR method may not be consistent.
• For same cash-flow, there can exist more than one discounting rate to make NPV = 0; i.e. there can exist multiple IRR for same cash-flow making it confusing which to choose as accurate value. Let us take a famous example for that:

For above cash-flow, discounting rate of both 25% and 400% makes Net Present Value (NPV) of the project “0”. Therefore for this project, both 25% and 400% can be taken as IRR as per the theory which is not reasonable. Under such circumstances, the decision is misleading.

• The result of NPV method is consistent with “value additive principle” but the result of IRR method is not. Let us suppose that there are two projects A and B with different cash-flows throughout the life of project. Then,
NPV(A) + NPV(B) = NPV(A+B)
IRR(A) + IRR(B) ≠ IRR(A+B)
• Calculation of IRR is very tedious and in some cases, it is near to impossible to solve it manually.

From above points and examples, it is quite clear why NPV is better (superior) than IRR and also the differences or relationship between them.