# How to Use the Profitability Index?

In a perfect world, the company would accept all the positive NPV projects that come its way but in reality, we have things called constraints. For example, you might have a limited budget, and your manager says "look you can't go beyond this budget of a million dollars or two million dollars in terms of investing in projects". So even though you might have a bunch of positive NPV projects that would be optimal for the firm to invest in, you just don't have the budget to do that. Then the constraint could be something else, it could be the number of engineers or scientists that you have at your firm or so forth. So these constraints can actually make it where you can't accept all the positive NPV projects and you have to make a decision about which ones you're going to accept and which ones you're going to reject. To make that decision it's a little bit easier when you calculate something called the profitability index. I'm going to talk about how to calculate that in this article and let's jump into an example,

### Example:

Let's say that you have a budget of \$800 and you're trying to decide between the following three investments. So you've got three different project opportunities and we have the NPV for each one and then the upfront investment for each one. We need to know those things in order to calculate the profitability index.

Basically, with the profitability index, we're just taking the NPV divided by the amount of the upfront investment. You can think of it as NPV per unit of resource that is constrained. So the resource that is constrained here is funding, the budget, or the money.

So all we do is we make these calculations and it's going to be 1.17 for project A, and I'm doing some rounding here so it might be a little different from what you get. 1.04 for project B and then for project C we're going to get 1.12.

### Decision Making:

Now let's look at the bang for our buck here, this profitability index column and we'll go with the highest number that we have there. Because that's the project that's giving us the most NPV per dollar of the upfront investment. So project A is giving us the highest amount, so we would choose project A. We would accept project A and then we would reject the other two projects.

### Assumptions:

#1. Two things have to be true for this profitability index approach to be worthwhile and one is that the set of projects that we're choosing between has to completely exhaust the resource.

Let me give you an example to see where this assumption might be violated, well we're not completely exhausting the resource what am I doing here is, let's say we have project D. Then project D has an NPV of 51 and an upfront investment of 50. Now that would give it a profitability index of 1.0. Now, this would rank it last if we look at all the profitability indexes from the different projects.

However, we would actually be doing ourselves a disservice if we did not choose project D, and here's why. We said that project a is the best because it has this 1.17 but think about it, if we're choosing project A we still have \$50 left in our budget. So what does that mean? That would leave us this additional 50 here for project D we could combine and do project A, and project D and have higher NPV.

#2. another really important thing before you just run out and start using calculating profitability indexes make sure that there's just a single resource constraint.

Because in reality, it's not always we've got this budget issue and we have to choose among the projects. Like I said before it could be that you need more researchers or a scientist on each project or you have some kind of constraint of people. So if you have more than one constraint if it's not just a budget or if it's multiple things going on then you're actually going to have to use linear programming in order to solve it.