In this article, we’re going to look at what the Profitability Index formula is, how it works, and why it works the way it does.
The Profitability Index formula is:
Where is the Profitability Index, is the Net Present Value, and reflects the initial investment. This is our recommended formula, too.
Importantly, there is an alternative expression for the Profitability Index formula.
We can also write it like this…
Here reflects the Present Value. So we’re looking at the Present Value relative to the initial investment, instead of the Net Present Value relative to the initial cost.
Both expressions are acceptable, even though they are not the same, strictly speaking.
To explore the Profitability Index formula in more detail, and to understand why it works the way it does, keep reading. Let’s start with the absolute basics first.
Note, it’s helpful / useful if you know what that Net Present Value is. If you don’t, it’s worth reading this article first.
What is the Profitability Index?
Firstly, what is the Profitability Index (PI)?
In a nutshell, it’s just an investment appraisal tool or technique.
Fundamentally, the Profitability Index shows us the amount of money we earn for every $1 / £1 invested.
Now, we define the amount of money we earn as either the or the .
And you’ll see that we can use either of the two to calculate the Profitability Index (PI).
Core Benefit of the Profitability Index
The main contribution / core benefit of the Profitability Index is that it solves the magnitude issue of the Net Present Value.
What is the magnitude issue of the Net Present Value?
Consider that we tell you there are two projects, which we’ll conveniently call Project A and Project B.
And we tell you that Project A has a NPV of £10,000; and Project B has an NPV of £100,000.
Which would you choose, Project A or Project B?
Clearly, you’re thinking Project B, right?
Because of course, it’s £100,000 instead of £10,000.
It’s a higher NPV, so “obviously”, we should go with that.
The problem is that this doesn’t factor in the magnitude of the investment requirement.
If I now told you that the investment required for Project A is £20,000 and the investment requirement for Project B is £2,000,000, you’re probably not thinking choosing Project B anymore.
And if you still are, well it’s almost certainly not as straightforward a decision / choice as you thought it was before.
With NPV of £10,000 and £100,000, and investments of £20,000 and £2 million, that means that the Present Value (PV) of Projects A and B equate to £30,000 and £2.1 million pounds.
This Article features a concept that is covered extensively in our course on Investment Appraisal Mastery.
If you’re interested in mastering the Profitability Index and other investment appraisal / capital budgeting techniques, then you should definitely check out the course.
The key takeaway here is that you can invest 1% of the requirement of Project B, by investing in Project A, and earn a higher Net Present Value per pound / dollar invested.
Yes, Project B is giving you more money in total.
But in terms of how much your money is working for you, so how good, or how hard your money is working for you…
Project A is better than Project B that way.
Because it earns you more, for a given amount of money invested.
And this issue is what the profitability index solves.
How to calculate Profitability Index
So how to calculate the profitability index?
One way, is to take the NPV and divide it by the initial investment:
As simple as that.
This shows you how much money you make for every one dollar or one pound you invest.
Alternatively, you could calculate it as the ratio of PV to I, so that the PV (Present Value) is divided by the investment.
And this is the same as…
So in this example, if you calculate using this approach, then what you’re saying is, for every one pound you invest, this is the present value that you’re earning.
This is the present value of the future cash flow that you’re earning, for every pound you’ve invested.
And this will make sense when we look at an example.
Profitability Index Calculation Example #1
Let’s stick with the same Projects A and B that we saw earlier in this article, with the NPV of £10,000 for Project A, and £100,000 for Project B.
If we calculated the profitability index using the NPV / I approach, then you take the £10,000 NPV for A and divide it by the initial investment in A which is £20,000. Thus we have…
And that gives us 50p (50 pence).
How do you interpret that? How do you read that 50p?
Well, it just means that for every £1 pound you invest in Project A, you earn 50p.
Whereas for Project B, for every £1 pound you invest, you earn £0.05 (five pence). Because…
Put differently, you earn a 10th (1/10) of what Project A is offering you on a per pound invested basis.
Alternatively, if you take the PV over I approach, then we have…
And for B we have…
Using the PV / I approach, we’d interpret these values as following…
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We’d say that for every £1 pound that you invest in A, you earn £1.50 in cash flow, in present value terms.
So for every pound you invest, you’re going to earn the present value of all future cash flows equal to £1.50
Preference of the PI Formula
Personally, we prefer the first one – NPV over I.
Because the NPV / I approach shows us exactly how much money we make for every pound we invest.
Some people prefer PV over I approach, however.
It depends on what you fancy, and how you want to see it, really.
But now that you’ve understood what the profitability index formula is, and how it works including the issue it solves, let’s look at another profitability index example.
Profitability Index Calculation Example #2
Consider Garch Ltd, which has $550,000 available to invest.
It’s evaluating three projects, Archer, Brochure, and Catcher with the following information on cash flows…
The projects require investments of $300,000; $200,000; and $600,000 for Archer, Brochure, and Catcher respectively.
Investing in Archer will allow Garch Ltd to earn $80,000 in for the next 5 years.
Investing in Brochure instead, will allow Garch Ltd to earn $60,000 per year, every year for the next 5 years.
And lastly, investing in Catcher will earn Garch Ltd $155,000 in for the next 5 years.
The projects are divisible, meaning Garch Ltd can invest in parts of a project instead of having to invest fully in a given project.
For example, Garch Ltd could invest in Catcher even though the initial investment required is $600,000 while the company only has $550,000 available to invest.
In other words, the company could buy up to $550,000 worth of Catcher.
Or it could buy, for instance, half of Catcher and then all of Brochure; the point is, it can “mix and match”.
Which project(s) should Garch Ltd choose to invest in if it maintains a cost of capital of 8.5%?
Setting up to solve
How do we go about solving for this?
Start by calculating Present Value, and then the Net Present Value.
Like we said at the start of this article, it’s helpful to know how to calculate the NPV, and we’re going to assume that you’re fairly comfortable with that.
If you’re not comfortable with it, please go back to the article on NPV where we look at how to calculate NPV in much more detail.
Okay, so when you run the numbers, you’ll find that the PV is equal to:
- $315,251.37 for Archer,
- $236,438.52 for Brochure, and
- $610,799.52 for Catcher
We’ve got these estimates by just estimating the Present Value of an Annuity, like this…
Where represents the specific annual expected cash flow for each project; reflects the discount rate (aka cost of capital, hurdle rate, opportunity cost of capital), in this case, 8.5%. And represents the time frame for each project, in this case, 5 years.
And given these PV estimates, it’s trivial to get the for each project as…
- $15,251.37 for Archer,
- $36,438.52 for Brochure, and
- $10,799.52 for Catcher
Note that the figures above are obtained by just subtracting the initial investment from the Present Value estimates (remember, ).
Now, we can clearly see that Brochure has the highest NPV, followed by Archer, with Catcher in “last place” with the lowest NPV.
Calculate the PI
In this particular instance, the Profitability Index and the NPV are going to give you exactly the same results as far as interpretations go.
The Profitability Index for each project (using the NPV / I approach) are…
- $0.05 for Archer,
- $0.18 for Brochure, and
- $0.02 for Catcher
What do we mean by these?
If we think about Brochure for instance, the 18 cents means that for every $1 we invest in brochure, we expect to earn 18 cents.
Similarly, for every dollar we invest in Archer, we expect to earn 5 cents. And lastly, similar story for Catcher; we expect to earn $0.02 for every $1 invested.
If you estimate the Profitability Index using the PV / I approach, then you’d have $1.05; $1.18; and $1.02 as the PI for Archer, Brochure, and Catcher respectively.
Regardless of which approach you take, it’s clear that the highest PI here is Brochure, which also happens to have the highest NPV.
In other words, in this particular example, the interpretations / results from the PI are consistent with the results from the NPV capital budgeting tool.
You can have situations where you get different interpretations, however.
This comes back to the example that we saw at the very start of this article…
When we looked at Project A and B earlier on, we saw Project B had the higher NPV and Project A had the lower NPV.
But when we looked at the Profitability Index, it was the other way around. Project A had a better / higher PI, at £0.50 and Project B had a worse / lower PI at £0.05
So although the NPV was higher for Project B, the PI was higher for Project A.
And between NPV and the Profitability Index, you’re probably better off applying the rule or investment appraisal criteria using profitability index rather than NPV.
Advising “Garch Ltd”
So coming back to our example with Garch Ltd…
What do we advise?
We’d say the Garch Ltd should invest in Brochure and Archer because they have the higher Profitability Index, at 18 cents and 5 cents respectively, compared to just 2 cents for Catcher.
And depending on the risk free rate (typically the yield on U.S. Government Bonds), Garch Ltd should either deposit the remaining $50,000 and earn the risk free rate.
Or invest it elsewhere, as long as the return is greater than what it could earn by investing in Catcher.
How did we get the $50,000?
If we turn back to the question, remember that Garch Ltd had $550,000 available to invest.
Archer requires an investment of $300,000 and Brochure requires $200,000. That’s $500,000 in total.
In other words, they’ve got $50,000 remaining / lying idle.
Thus, they should either put that in a risk free security and earn the risk free rate, or invest it elsewhere, as long as they earn more than what they could earn by investing in Catcher.
If for whatever reason, Garch Ltd can’t find anything else to invest in, and the risk free rate is lower than say, inflation, then they should probably go ahead and invest in catcher.
That’s because while Catcher has a low Profitability Index vis-a-vis Archer and Brochure, it still is a positive NPV project!
Alright, in summary…
You learnt that the Profitability Index formula overcomes the magnitude problem of the Net Present Value (NPV) by showing us how much we are in for every $1 invested (or £1 invested).
Furthermore, you learnt that there’s 2 ways to calculate the PI, including one where we take the ratio of NPV to I, and another, where we take it as the ratio of PV to I.
Hopefully all of this makes sense. If any part of the profitability index formula isn’t quite clear, please re-read this article.
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