What is the profitability index (PI)?
Enter what a project costs today and the cash it brings back at the end of each period, with your discount rate. Or type the present value of those cash flows if you already have it. The calculator divides the present value by the cost to give the profitability index (PI), and shows the net present value (NPV).
- Profitability index
- 1.177
Investing $16,000.00 for cash flows worth $18,835.62 today gives a profitability index of 1.177.
1 or more: the project earns at least the discount rate
- Below 1: the project loses value at this rate
- 1 or more: the project earns at least the discount rate
- Net present value (NPV)
- $2,835.62
- Present value of the cash flows
- $18,835.62
Profitability index: 1.177. Investing $16,000.00 for cash flows worth $18,835.62 today gives a profitability index of 1.177.
The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use
How to calculate
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.
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.
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.
- 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
Each example is checked against the calculator on every build.
- 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 gives Profitability index 1.177226, Net present value (NPV) $2,835.62, Present value of the cash flows $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)
- Present value of the cash flows I know it, Initial investment (today) $16,000.00, Present value of future cash flows $18,836.00 gives Profitability index 1.17725, Net present value (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)
- Present value of the cash flows From cash flows, Initial investment (today) $10,000.00, Discount rate 10%, Cash flows at the end of each period 3,000, 3,000, 3,000 gives Profitability index 0.746056, Net present value (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
- Present value of the cash flows From cash flows, Initial investment (today) $8,000.00, Discount rate 0%, Cash flows at the end of each period 2,500, 2,500, 2,500, 2,500 gives Profitability index 1.25, Net present value (NPV) $2,000.00, Present value of the cash flows $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
How it works
With the initial investment C₀ (paid today), the cash flows CF₁, CF₂, …, CFₙ at the end of periods 1 to n, and the discount rate r per period (a percent ÷ 100):
- Present value PV = CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ
- Profitability index PI = PV ÷ C₀
- Net present value NPV = PV − C₀, so PI = 1 + NPV ÷ C₀
With "I know it", you type PV directly and the page divides it by C₀.
Rules:
- The initial investment is more than $0, up to $1 quadrillion. A typed present value may be negative.
- Enter 1 to 100 cash flows; a negative cash flow is money paid out in that period and lowers the PV.
- The discount rate is from −99% to 1,000% per period.
- Cash flows so small that every discounted value rounds to 0 in 64-bit floating point (about 2.5 × 10⁻³²⁴ or less) give no answer rather than a present value of $0.
- A result too large for a 64-bit floating-point number gives no answer and a message. So does a PI, or an NPV from a typed present value, that is not 0 but too close to 0 for one (about 2.5 × 10⁻³²⁴ or less), so neither is ever a silent 0.
- Discounting uses floating-point powers. A typed present value is divided exactly. The PI shows to 3 decimals and money to the cent, with halves rounded up (away from 0).
Assumptions
- Each cash flow comes at the end of its period. The investment is made today and is not discounted.
- The discount rate stays the same for every period.
Worked examples by hand
Sam's Sporting Goods (OpenStax). The machine costs $16,000 and returns $2,000, $4,000, then $5,000 a year for four years. At 9%:
PV = 2,000 ÷ 1.09 + 4,000 ÷ 1.09² + 5,000 × (1 ÷ 1.09³ + 1 ÷ 1.09⁴ + 1 ÷ 1.09⁵ + 1 ÷ 1.09⁶) = $18,835.62
PI = 18,835.62 ÷ 16,000 = 1.177, and NPV = 18,835.62 − 16,000 = $2,835.62. OpenStax rounds its discount factors and shows $2,835.63 and a PI of 1.18. With its rounded PV of $18,836, the PI is 18,836 ÷ 16,000 = 1.177 (1.17725).
A project to reject. $10,000 today for $3,000 a year for 3 years at 10%: PV = 3,000 × (1 − 1.1⁻³) ÷ 0.1 = $7,460.56, so PI = 0.746 and NPV = −$2,539.44.
No discounting. $8,000 today for $2,500 a year for 4 years at 0%: PV = $10,000, PI = 10,000 ÷ 8,000 = 1.250 and NPV = $2,000.
Other questions people ask
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.