Why would you use the profitability index method in capital budgeting, when other tools
like return on investment and net present value already exist?
To answer that question, let’s see what return on investment (ROI) and net present
value (NPV) provide us.
ROI relates the payoff (the expected project benefits) to the investment (the initial cash
outlay or cost).
NPV consider the time value of money, and considers cash flows over the entire life
of the project.
The profitability index incorporates all three of these elements.
The profitability index is closely related to ROI and NPV.
Once you understand how to calculate ROI and NPV, it is very easy to calculate the profitability
index next.
Here’s a project that we will use as the basis for all calculations.
It has an upfront investment of $1000 (shown as a negative, an outflow), and four years
of nominal benefits of $400 each (shown as positives, inflows).
To calculate ROI, we take the annual benefits and divide them by the investment.
$400 divided by $1000 is 40%.
Now that we have calculated that ROI outcome, is this a good or a bad number?
You can look at this in absolute terms: maybe the company that is considering this project
has a minimum requirement of 30% ROI for projects, and the ROI on project A exceeds that minimum.
You could also look at this in relative terms: maybe there are many other project proposals
with ROIs that are 50% or higher, in that case project A might not be the most attractive
one, and other projects might get higher priority.
To calculate NPV, you start off with translating the future benefits to today’s equivalent,
these are called present values.
The present value of $400 one year from now, using a discount rate of 20%, is $333.
$400 divided by 1.2.
The present value of $400 two years from now is $278.
$400 divided by 1.2 times 1.2.
The present value of $400 three years from now is $231.
$400 divided by 1.2 times 1.2 times 1.2.
The present value of $400 four years from now is $193.
$400 divided by 1.2 times 1.2 times 1.2 times 1.2.
The longer we have to wait for those future benefits, the more we have to discount the
future benefits, the lower the present value equivalent.
To calculate NPV, we take the cash outflow (negative number) from the investment and
sum the present values of the future benefits.
Those five numbers summed (the investment plus the present values), get us to $35 of
net present value.
Now that we have calculated that NPV outcome, is this a good or a bad number?
You can look at this in absolute terms: NPVs that are bigger than zero create value for
the company.
You could also look at this in relative terms: maybe there are many other project proposals
with NPVs far higher than 35, in that case project A might not be the most attractive,
especially when the investment budget is tight and not every project with a positive NPV
might end up getting selected.
There is one important number from the NPV calculation that we will need as an input
for the calculation of the profitability index:
the sum of the present values of the future benefits.
In the case of project A, this is $1035.
Let’s calculate the profitability index for project A: put the sum of the present
values of the future benefits in the numerator, and divide by the amount of the initial investment
in the denominator.
Working with present value equivalents is how the profitability index resembles the
NPV method.
Dividing by the amount of the initial investment is how the profitability index resembles the
ROI method.
$1035 divided by $1000 gives us a profitability index of 1.035.
Now that we have calculated that profitability index outcome, is this a good or a bad number?
You can look at this in absolute terms: projects with a profitability index higher than one
create value for the company.
You could also look at this in relative terms: maybe there are many other project proposals
with a profitability index far higher than 1.035, in that case project A might not be
the most attractive, especially when the investment budget is tight and not every project with
a profitability index higher than one might end up getting selected.
There are several ways to write down the profitability index formula.
You could express it as the sum of the present values of the future benefits divided by the
amount of the investment.
You could also express it as the sum of NPV plus investment, divided by the investment.
Or as NPV divided by investment, plus 1.
When you plug in the numbers from our profitability index example, you see that these versions
of the profitability index formula are all equivalent.
$1035 divided by $1000 is 1.035.
The sum of $35 and $1000 is $1035.
Divide this by $1000, and you get 1.035.
$35 divided by $1000 is 0.035.
Add 1 to this, and you get 1.035.
Different ways of writing the profitability index formula, same outcome.