# Profitability Index (PI): Definition, Components, and Formula

## What Is the Profitability Index (PI)?

The profitability index (PI), alternatively referred to as value investment ratio (VIR) or profit investment ratio (PIR), describes an index that represents the relationship between the costs and benefits of a proposed project.

The profitability index is calculated as the ratio between the present value of future expected cash flows and the initial amount invested in the project. A higher PI means that a project will be considered more attractive.

### Key Takeaways

• The profitability index (PI) is a measure of a project's or investment's attractiveness.
• The PI is calculated by dividing the present value of future expected cash flows by the initial investment amount in the project.
• A PI greater than 1.0 is deemed as a good investment, with higher values corresponding to more attractive projects.
• Under capital constraints and mutually exclusive projects, only those with the highest PIs should be undertaken.
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## Understanding the Profitability Index (PI)

The profitability index is helpful in ranking various projects because it lets investors quantify the value created per each investment unit. A profitability index of 1.0 is logically the lowest acceptable measure on the index, as any value lower than that number would indicate that the project's present value (PV) is less than the initial investment. As the value of the profitability index increases, so does the financial attractiveness of the proposed project.

The profitability index is an appraisal technique applied to potential capital outlays. The method divides the projected capital inflow by the projected capital outflow to determine the profitability of a project. As indicated by the aforementioned formula, the profitability index uses the present value of future cash flows and the initial investment to represent the aforementioned variables.

When using the profitability index to compare the desirability of projects, it's essential to consider how the technique disregards project size. Therefore, projects with larger cash inflows may result in lower profitability index calculations because their profit margins are not as high.

## Formula for the Profitability Index

The profitability index can be computed using the following ratio:

### PV of Future Cash Flows (Numerator)

The present value of future cash flows requires the implementation of time value of money calculations. Cash flows are discounted the appropriate number of periods to equate future cash flows to current monetary levels. Discounting accounts for the idea that the value of $1 today does not equal the value of$1 received in one year because money in the present offers more earning potential via interest-bearing savings accounts, than money yet unavailable. Cash flows received further in the future are therefore considered to have a lower present value than money received closer to the present.

### Investment Required (Denominator)

The discounted projected cash outflows represent the initial capital outlay of a project. The initial investment required is only the cash flow required at the start of the project. All other outlays may occur at any point in the project's life, and these are factored into the calculation through the use of discounting in the numerator. These additional capital outlays may factor in benefits relating to taxation or depreciation.

## Interpreting the Profitability Index

Because profitability index calculations cannot be negative, they consequently must be converted to positive figures before they are deemed useful. Calculations greater than 1.0 indicate the future anticipated discounted cash inflows of the project are greater than the anticipated discounted cash outflows. Calculations less than 1.0 indicate the deficit of the outflows is greater than the discounted inflows, and the project should not be accepted. Calculations that equal 1.0 bring about situations of indifference where any gains or losses from a project are minimal.

When using the profitability index exclusively, calculations greater than 1.0 are ranked based on the highest calculation. When limited capital is available, and projects are mutually exclusive, the project with the highest profitability index is to be accepted as it indicates the project with the most productive use of limited capital.

The profitability index is also called the benefit-cost ratio for this reason. Although some projects result in higher net present values, those projects may be passed over because they do not have the highest profitability index and do not represent the most beneficial usage of company assets.

## Example of the Profitability Index

Imagine that a company is considering two potential projects: building a new factory, or expanding an existing one. The factory expansion project is expected to cost $1 million and generate cash flows of$200,000 per year for the next 5 years, with a discount rate of 10%. The new factory project is expected to cost $2 million and generate cash flows of$300,000 per year for the next 5 years, also with a discount rate of 10%.

To calculate the profitability index for the factory expansion project, the present value of the future cash flows would be calculated using the following formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n

Where PV is the present value, CF is the cash flow in a given year, r is the discount rate, and n is the number of years.

Plugging in the values for this example, we get:

• PV = $200,000 / (1 + 0.10)^1 +$200,000 / (1 + 0.10)^2 + ... + $200,000 / (1 + 0.10)^5 • PV =$750,319

The profitability index for the factory expansion project is then calculated as:

• PI = PV / Initial Investment
• PI = $750,319 /$1,000,000
• PI = 0.75

To calculate the profitability index for the new factory project, the present value of the future cash flows would be calculated using the same formula:

• PV = $300,000 / (1 + 0.10)^1 +$300,000 / (1 + 0.10)^2 + ... + $300,000 / (1 + 0.10)^5 • PV =$1,125,479

The profitability index for the new factory project is then calculated as:

• PI = PV / Initial Investment
• PI = $1,125,479/$2,000,000
• PI = 0.56

In this example, the factory expansion project has a higher profitability index, meaning it is a more attractive investment. The company might decide to pursue this project instead of the new factory project because it is expected to generate more value per unit of investment.

However, since both PIs are less than 1.0, the company may end up forgoing either project in favor of a better opportunity elsewhere.

Here are some advantages of the profitability index:

1. It considers the time value of money: The profitability index takes into account the fact that money today is worth more than the same amount of money in the future, due to the potential for earning interest. This makes it a more accurate measure of investment attractiveness than simply looking at the total expected cash flows.
2. It allows for comparison of projects with different lifespans: The profitability index can be used to compare projects with different lifespans, because it takes into account the present value of future cash flows rather than just the total expected cash flows.
3. It helps with decision-making under capital constraints: When a company has limited resources and can't pursue all potential projects, the profitability index can be used to prioritize which projects to pursue first.

Here are some disadvantages of the profitability index:

1. It only considers the initial investment: The profitability index only looks at the initial investment required for a project and ignores ongoing or future investments that may be necessary. This can make it difficult to accurately compare projects with different investment requirements.
2. It doesn't consider the size of the project: The profitability index does not take into account the size of the project, so a large project with lower profit margins may have a lower profitability index than a smaller project with higher profit margins.
3. It relies on accurate forecasting: The profitability index relies on accurate forecasting of future cash flows and discount rates, which can be difficult to predict with certainty. If the assumptions used in the calculation are incorrect, the resulting profitability index may not accurately reflect the attractiveness of the project.

### Profitability Index Pros and Cons

Pros
• Accounts for the time value of money

• Allows comparisons across different projects

Cons
• Does not consider ongoing future costs

• Ignores project size

• Bad forecasts or assumptions can make the analysis unreliable

## How Is the Profitability Index Computed?

The profitability index is a calculation determined by dividing the present value of futures cash flows by the initial investment in the project. The present value of the future cash flows is calculated using the time value of money, which takes into account the fact that money today is worth more than the same amount of money in the future due to the potential for earning interest. The initial investment is the amount of capital required to start the project.

## What Is the Profitability Index Used for?

The profitability index is used for comparison and contrast when a company has several investments and projects it is considering undertaking. The PI is especially useful when a company has limited resources and can't pursue all potential projects, as it can be used to prioritize which projects to pursue first. The index can be used alongside other metrics to determine which is the best investment.

## What Is a Good Profitability Index?

Generally, the higher the PI the better. A profitability index greater than 1.0 is often considered to be a good investment, as it means that the expected return is higher than the initial investment. When making comparisons, the project with the highest PI may be the best option.

## What Are Other Names for the Profitability Index?

The profitability index is also called the profit investment ratio (PIR), cost-benefit ratio, or the value investment ratio (VIR).

## The Bottom Line

The profitability index (PI) is a measure of the attractiveness of a project or investment. It is calculated by dividing the present value of future expected cash flows by the initial investment amount in the project. A PI greater than 1.0 is considered to be a good investment, with higher values corresponding to more attractive projects. The PI is useful for ranking and comparing different projects, but it is important to consider how this technique disregards project size and only looks at the present value of future cash flows and the initial investment. Under capital constraints and when comparing mutually exclusive projects, only those with the highest PIs should be undertaken.

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