Describe the relationship of PI (Profitability Index) with NPV in an investment appraisal ?

NPV versus Profitability Index

The net present value (NPV) and profitability (PI) yield same accept or reject rules, because profitability index (PI) can be grater than one only when the project’s net present value is positive. In case of marginal projects, net present value (NPV) will be zero and profitability index (PI) will be equal to one. But a conflict may arise between the methods if a choice between mutually exclusive projects has to be made.

Consider the following illustration where the two methods give different ranking to the projects.

Project X Present value of cash inflows200000 $ Initial cash out flow100000 $ NPV100000 $ Profitability index2 Project Y Present value of cash inflows100000 $ Initial cash out flow40000 $ NPV60000 $ Profitability index2.5

Project X should be accepted if we use the NPV method, but project Y is preferable according to the profitability index (PI).

Which method is better?

The net present value (NPV) method should be preferred, except under capital rationing, because the NPV reflects the net increase in the firm’s wealth.

In our illustration, project X contributes all that project Y contributes plus additional NPV of40000$ (100000$ -60000$) at an incremental cost of100000$ (200000$ -100000$). As the NPV of project X’s incremental outlay is positive, it should be accepted.

Project X will also be acceptable if we calculate the incremental profitability index. This is shown as follows: Because the incremental investment has a positive NPV,40000$ and a profitability index (PI) grater than one, project X should be accepted. If we consider a different situation where two mutually exclusive projects return200000$ each in terms of NPV and one project costs twice as much as another, the profitability index (PI) will obviously give a logical answer. The net present value method will indicate that both are equally desirable in absolute terms. However, the profitability index (PI) will evaluate these two projects relatively and will give correct answer. Between two mutually exclusive projects will same NPV, the one with lower initial cost or higher PI will be selected.

Agree with MR. VENKITARAMAN he explained it very well in the following para:

"The net present value (NPV) and profitability (PI) yield same accept or reject rules, because profitability index (PI) can be grater than one only when the project’s net present value is positive. In case of marginal projects, net present value (NPV) will be zero and profitability index (PI) will be equal to one. But a conflict may arise between the methods if a choice between mutually exclusive projects has to be made".

To add further

PI method is used when there is capital rationing situation and funds are limited. In order to decide which Positive NPV projects to undertake and in what sequence. 

suppose your capital constraints, means limited funds for investments. so, PI index can be used to rank different npv projects. the projects with highest rank will be selected as it is the best source for utilization funds.

PI=PV/Initial Investment

Profitability Index relates to PV and Initial Investment. PI shows the feasibility of a project. if PI is less than the zero, the project is not feasible. and if it is equal to1 or greater than, we may consider that the project will be successful. 

so profitability index is a tool to determine the feasibility of a project.