The Profitability Index (PI), also known as the Profit Investment Ratio (PIR) or Value Investment Ratio (VIR), is a measure used to evaluate the attractiveness of a capital investment project. It is calculated by dividing the present value of future cash flows by the initial investment.
Understanding the Profitability Index
The Profitability Index helps businesses determine the value created per unit of investment. A PI greater than 1 indicates that the project is expected to be profitable, a PI equal to 1 suggests the project is expected to break even, and a PI less than 1 implies the project is likely to result in a loss.
Calculating the Profitability Index
There are two primary formulas for calculating the Profitability Index, both of which are referenced:
- PI = Present Value (PV) of Future Cash Flows ÷ Initial Investment
- PI = (Net Present Value + Initial Investment) ÷ Initial Investment
Let's break down these formulas and their components.
Method 1: Using the Present Value of Future Cash Flows
This method directly compares the total present value of expected future cash inflows to the initial cost of the investment.
- Present Value (PV) of Future Cash Flows: This is the discounted value of all cash inflows expected from the project over its lifespan, brought back to today's value using a specific discount rate (often representing the company's required rate of return or cost of capital).
- Initial Investment: This is the initial cash outflow required to start the project.
Formula:
$$ \text{Profitability Index (PI)} = \frac{\text{Present Value (PV) of Future Cash Flows}}{\text{Initial Investment}} $$
Method 2: Using Net Present Value (NPV)
This method utilizes the Net Present Value (NPV), which is the difference between the present value of future cash flows and the initial investment.
- Net Present Value (NPV): The sum of the present values of all cash flows, both incoming and outgoing, over the life of the investment.
- Initial Investment: The initial cash outflow.
Formula:
$$ \text{Profitability Index (PI)} = \frac{\text{Net Present Value (NPV) + Initial Investment}}{\text{Initial Investment}} $$
Notice that because NPV = (Present Value of Future Cash Flows) - (Initial Investment), adding the Initial Investment back to NPV results in the Present Value of Future Cash Flows. Thus, the second formula is mathematically equivalent to the first.
Calculating Net Present Value (NPV)
To use the second formula, you first need to calculate the Net Present Value. NPV calculation involves discounting all future cash flows back to their present value and summing them, then subtracting the initial investment.
Using spreadsheet software, the referenced method for calculating NPV is demonstrated with a discount rate:
=NPV (10% Discount Rate, Range of Net Cash Inflows/Outflows)
This function typically calculates the present value of a series of future cash flows at a specified discount rate. You would then subtract the initial investment (which is usually an outflow at time zero) to get the final NPV.
Example of NPV Calculation:
Suppose a project requires an initial investment of $10,000 and is expected to generate cash flows of $4,000 per year for 3 years. The discount rate is 10%.
| Year | Cash Flow | Discount Factor (10%) | Present Value |
|---|---|---|---|
| 0 | -$10,000 | 1.000 | -$10,000 |
| 1 | +$4,000 | 0.909 | +$3,636 |
| 2 | +$4,000 | 0.826 | +$3,304 |
| 3 | +$4,000 | 0.751 | +$3,004 |
| Total | NPV = $ -600 |
In this simple example, the NPV is -$600.
Example Calculation of Profitability Index
Let's use the example above to calculate the PI using both methods.
Assumptions:
- Initial Investment: $10,000
- PV of Future Cash Flows: $3,636 + $3,304 + $3,004 = $9,944
- NPV: -$600
Method 1:
$$ \text{PI} = \frac{\text{Present Value of Future Cash Flows}}{\text{Initial Investment}} = \frac{\$9,944}{\$10,000} = 0.9944 $$
Method 2:
$$ \text{PI} = \frac{\text{Net Present Value + Initial Investment}}{\text{Initial Investment}} = \frac{-\$600 + \$10,000}{\$10,000} = \frac{\$9,400}{\$10,000} = 0.94 $$
Note: There seems to be a slight calculation inconsistency in the example NPV ($9944 - 10000 = -56$). Let's correct the NPV based on the PV of Future Cash Flows calculated:
PV of Future Cash Flows = $9,944
Initial Investment = $10,000
NPV = $9,944 - $10,000 = -$56
Let's recalculate using the corrected NPV:
Method 2 (Corrected):
$$ \text{PI} = \frac{\text{Net Present Value + Initial Investment}}{\text{Initial Investment}} = \frac{-\$56 + \$10,000}{\$10,000} = \frac{\$9,944}{\$10,000} = 0.9944 $$
Both methods yield the same result, as expected.
Interpreting the Profitability Index
- PI > 1: The project is expected to generate a return greater than the required rate of return. This indicates that the project adds value and should be considered.
- PI = 1: The project is expected to generate a return exactly equal to the required rate of return. It is expected to break even in terms of adding value above the cost of capital.
- PI < 1: The project is expected to generate a return less than the required rate of return. This indicates that the project destroys value and should typically be rejected.
When choosing among multiple projects, a higher PI is generally preferred, as it suggests greater value creation per dollar invested. However, it's important to consider other factors like project scale and risk.
