# Profitability Index Calculation

The profitability index (PI) of a series of cash flows is found by calculating the present value of all the cash flows from a project (PV) and dividing the value by the initial investment (I). The profitability index is sometimes referred to as the value investment ratio.

As the net present value of a series of cash flows (NPV )is the difference between the present value of the future cash flows and the initial investment, the profitability index formula can be rearranged and presented as follows:

Profitability index = 1 – Net present value of cash flows / Initial investment = 1 + NPV / I

The profitability index formula is a useful tool for ranking investment projects, particularly in situations where the business is subject to capital rationing, as it shows the present value of the project per unit of investment, and the higher the profitability index the more acceptable the project.

As the profitability index is a ratio, the scale of the project in absolute monetary terms is ignored.

## Profitability Index and Break Even

An investment project breaks even when the present value of the future cash flows is the same as the initial investment, that is, when the net present value is equal to zero.

Using the profitability index formula, and setting the present value of future cash flows (PV) equal to the initial investment (I), we get the following.

```PI = PV / I
PV = I at break even
PI = I / I = 1
```

At break even the profitability index is equal to one.

## Profitability Index Formula Rules for Project Selection

Having established that the break even point for a project occurs when the profitability index is one, we can say that a PI less than one shows a loss making project which should not be accepted, and a PI greater than one shows a profitable project which should be accepted. In addition, as the PI increases, the profitability of the project increases, so the project should be ranked higher.

To summarize, the profitability index (PI) decision rule is as follows:

1. If PI < 1 then reject the project
2. If PI = 0 then the project is at break even
3. If PI > 1 then accept the project, and rank in order of highest profitability index first

## Profitability Index Formula Example

Consider as an example, the following cash flow diagram. At the start of year 1 (today) there is a cash out flow of 4,000 representing an investment in a project. For simplicity, with no further investment, the amount of 6,000 is returned in 3 years time at the end of year 3.

The business decides that the appropriate discount rate to use is 8%. The discount rate (value the business places on its money) is very important in the calculation. It will depend on a number of factors such as the risk involved and what other opportunities the business has for the funds. At the very least it should greater than the rate a business could earn at a bank (minimal risk), and is usually a lot higher.

Cash flow diagram
Period 1 2 3
Cash Flow ↓ 4,000 6,000 ↑

The present value of the future cash flows of this project is given by the lump sum present value formula as follows:

```PV = FV / (1 + i)n
PV = 6,000 / (1 + 8%)3
PV =  4,762.99
```

The PI formula can now be used to calculate the profitability index.

```PI = PV / I
PI = 4,762.99 / 4,000 = 1.19
```

The project PI is 1.19 which is greater than 1, and the project should be accepted and ranked against the PI of other projects.

## Profitability Index < 1 Example

Consider now a second project whose initial investment at the start of year one is 140,000 and which returns a cash flow of 140,000 in year 5.

Using the same method as above, the present value of the future cash flows is given as follows:

```PV = FV / (1 + i)n
PV = 140,000 / (1 + 8%)5
PV = 95,281.65
```

Again, the PI formula is used to calculate the profitability index.

```PI = PV / I
PI = 95,281.65 / 100,000 = 0.95
```

The project PI is 0.95, as this is less than 1, the project is loss making, and should be rejected.

The two projects are completely different in scale, is absolute terms they are not comparable, however, by using the profitability index method we have shown that the first smaller project gives a positive return for each unit of investment, whereas the larger project gives a PI which is below break even, and should be rejected.