# What is the profitability index (PI)? Computes the profitability index (PI) of a project, the present value of its future cash flows divided by the initial investment, with its net present value. - Page: https://www.acalculator.org/finance/profitability-index-calculator - JSON spec: https://www.acalculator.org/finance/profitability-index-calculator.json - Version: 3752226fcbaf ## Default answer Example with the default inputs (Present value of the cash flows From cash flows, Initial investment (today) $16,000.00, Discount rate 9%, Cash flows at the end of each period [2,000, 4,000, 5,000, 5,000, 5,000, 5,000]): Investing $16,000.00 for cash flows worth $18,835.62 today gives a profitability index of 1.177. ## Inputs | Key | Label | Description | | --- | --- | --- | | from | Present value of the cash flows | Work out the present value from the cash flows and a discount rate, or type it. | | initial | Initial investment (today) | The amount paid out at the start (time 0). It is not discounted. | | rate | Discount rate | The rate per period used to discount the cash flows, such as the cost of capital. | | flows | Cash flows at the end of each period | The net cash flow at the end of period 1, 2, 3 and so on, separated by spaces or new lines. Negative for money paid out. | | pv | Present value of future cash flows | The cash flows after today, each discounted to today and added up. | ## Outputs | Key | Label | Description | | --- | --- | --- | | pi | Profitability index | Present value of the future cash flows ÷ initial investment, to 3 decimals. | | npv | Net present value (NPV) | Present value of the future cash flows − initial investment. | | presentValue | Present value of the cash flows | Each cash flow ÷ (1 + rate)^period, added up. | ## Method PI = PV ÷ C₀, where PV = Σ CFₜ ÷ (1 + r)ᵗ for t = 1 to n is the present value of the cash flows after today and C₀ the initial investment; NPV = PV − C₀, so PI = 1 + NPV ÷ C₀. ## Assumptions - Each cash flow happens at the end of its period; the initial investment is today and is not discounted. - The discount rate is per period and stays the same for every period. - Discounting uses floating-point powers; a typed present value is divided exactly. ## Worked examples 1. from = flows, initial = $16,000.00, rate = 9%, flows = 2,000 or 4,000 gives pi = 1.177226, npv = $2,835.62, presentValue = $18,835.62. Source: OpenStax, Principles of Finance, 16.4 Alternative Methods (PI = present value of the benefits ÷ present value of the costs; Sam’s Sporting Goods’ embroidery machine: $18,836 ÷ $16,000 = 1.18; accept when PI is above 1, reject when below 1). https://openstax.org/books/principles-finance/pages/16-4-alternative-methods; OpenStax, Principles of Finance, 16.2 Net Present Value (NPV) Method (the $16,000 machine returns $2,000, $4,000 and four years of $5,000; at a 9% cost of funds the NPV is $2,835.63). https://openstax.org/books/principles-finance/pages/16-2-net-present-value-npv-method (OpenStax rounds its factors: $2,835.63 and 1.18). 2. from = pv, initial = $16,000.00, pv = $18,836.00 gives pi = 1.17725, npv = $2,836.00. Source: OpenStax, Principles of Finance, 16.4 Alternative Methods (PI = present value of the benefits ÷ present value of the costs; Sam’s Sporting Goods’ embroidery machine: $18,836 ÷ $16,000 = 1.18; accept when PI is above 1, reject when below 1). https://openstax.org/books/principles-finance/pages/16-4-alternative-methods: $18,836 ÷ $16,000 = 1.18 (1.17725 before rounding). 3. from = flows, initial = $10,000.00, rate = 10%, flows = 3,000 or 3,000 gives pi = 0.746056, npv = -$2,539.44. Source: OpenStax, Principles of Finance, 16.4 Alternative Methods (PI = present value of the benefits ÷ present value of the costs; Sam’s Sporting Goods’ embroidery machine: $18,836 ÷ $16,000 = 1.18; accept when PI is above 1, reject when below 1). https://openstax.org/books/principles-finance/pages/16-4-alternative-methods. 4. from = flows, initial = $8,000.00, rate = 0%, flows = 2,500 or 2,500 gives pi = 1.25, npv = $2,000.00, presentValue = $10,000.00. Source: OpenStax, Principles of Finance, 16.4 Alternative Methods (PI = present value of the benefits ÷ present value of the costs; Sam’s Sporting Goods’ embroidery machine: $18,836 ÷ $16,000 = 1.18; accept when PI is above 1, reject when below 1). https://openstax.org/books/principles-finance/pages/16-4-alternative-methods. ## FAQ ### What is the profitability index? The profitability index (PI) is the present value of a project’s future cash flows divided by what it costs today. It uses the same inputs as the net present value, but gives a ratio: the value each dollar invested brings back, in today’s dollars. ### How do I calculate the profitability index? Discount each future cash flow to today at your discount rate, add them up, and divide by the initial investment. A $16,000 machine that brings back $2,000, $4,000 and four years of $5,000 is worth $18,835.62 today at 9%, so PI = 18,835.62 ÷ 16,000 = 1.18. ### What is a good profitability index? Accept a project when its PI is above 1 and reject it when the PI is below 1. A PI of exactly 1 means the project earns exactly the discount rate: it neither adds nor destroys value. ### How is the profitability index related to NPV? PI = 1 + NPV ÷ initial investment. So the PI is above 1 exactly when the NPV is above $0, and both methods accept or reject the same single project. ### When can PI and NPV rank projects differently? When projects differ in size. NPV gives the dollar gain; PI gives the gain per dollar invested. A small project can have a higher PI but a lower NPV than a large one. When your capital is limited, ranking by PI shows which projects return the most per dollar. ### Some books divide the NPV by the investment. Which is right? Both ratios appear. NPV ÷ investment is the PI minus 1, so its cut-off is 0 instead of 1. This page uses present value ÷ investment, the form with a cut-off of 1. ## Sources - OpenStax, Principles of Finance, 16.4 Alternative Methods: the profitability index uses the same inputs as the NPV and divides the present value of the benefits by the present value of the costs; Sam’s Sporting Goods’ embroidery machine has PI = $18,836 ÷ $16,000 = 1.18; accept a project if the PI is greater than 1 and reject it if the PI is less than 1. https://openstax.org/books/principles-finance/pages/16-4-alternative-methods (retrieved 2026-10-18) - OpenStax, Principles of Finance, 16.2 Net Present Value (NPV) Method: NPV = PV of cash inflows − PV of cash outflows; the $16,000 machine with inflows of $2,000, $4,000 and $5,000 a year for four years has an NPV of $2,835.63 at a 9% cost of funds. https://openstax.org/books/principles-finance/pages/16-2-net-present-value-npv-method (retrieved 2026-10-18)