{
  "id": "profitability-index",
  "version": "3752226fcbaf",
  "status": "published",
  "name": "Profitability Index Calculator",
  "question": "What is the profitability index (PI)?",
  "summary": "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.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/profitability-index-calculator",
  "markdown": "https://www.acalculator.org/finance/profitability-index-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Present value of the cash flows",
        "description": "Work out the present value from the cash flows and a discount rate, or type it.",
        "type": "string",
        "enum": [
          "flows",
          "pv"
        ]
      },
      "initial": {
        "title": "Initial investment (today)",
        "description": "The amount paid out at the start (time 0). It is not discounted.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000000
      },
      "rate": {
        "title": "Discount rate",
        "description": "The rate per period used to discount the cash flows, such as the cost of capital.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -99,
        "maximum": 1000
      },
      "flows": {
        "title": "Cash flows at the end of each period",
        "description": "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.",
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "pv": {
        "title": "Present value of future cash flows",
        "description": "The cash flows after today, each discounted to today and added up.",
        "type": "number",
        "x-unit": "USD",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "pi": {
      "label": "Profitability index",
      "description": "Present value of the future cash flows ÷ initial investment, to 3 decimals.",
      "format": "number"
    },
    "npv": {
      "label": "Net present value (NPV)",
      "description": "Present value of the future cash flows − initial investment.",
      "format": "money"
    },
    "presentValue": {
      "label": "Present value of the cash flows",
      "description": "Each cash flow ÷ (1 + rate)^period, added up.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "flows",
      "initial": 16000,
      "rate": 9,
      "flows": "2000 4000 5000 5000 5000 5000",
      "pv": 18836
    },
    "outputs": {
      "pi": 1.1772262112441534,
      "npv": 2835.619379906453,
      "presentValue": 18835.619379906453
    },
    "text": "Investing $16,000.00 for cash flows worth $18,835.62 today gives a profitability index of 1.177."
  },
  "examples": [
    {
      "given": {
        "from": "flows",
        "initial": 16000,
        "rate": 9,
        "flows": [
          2000,
          4000,
          5000,
          5000,
          5000,
          5000
        ]
      },
      "expect": {
        "pi": 1.1772262112441534,
        "npv": 2835.619379906453,
        "presentValue": 18835.619379906453
      },
      "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); Python 3 with exact fractions: 18,835.62 ÷ 16,000 = 1.1772"
    },
    {
      "given": {
        "from": "pv",
        "initial": 16000,
        "pv": 18836
      },
      "expect": {
        "pi": 1.17725,
        "npv": 2836
      },
      "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)"
    },
    {
      "given": {
        "from": "flows",
        "initial": 10000,
        "rate": 10,
        "flows": [
          3000,
          3000,
          3000
        ]
      },
      "expect": {
        "pi": 0.7460555972952667,
        "npv": -2539.444027047333
      },
      "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; hand calculation in content.mdx: 3,000 × (1 − 1.1⁻³) ÷ 0.1 = 7,460.56; 7,460.56 ÷ 10,000 = 0.746"
    },
    {
      "given": {
        "from": "flows",
        "initial": 8000,
        "rate": 0,
        "flows": [
          2500,
          2500,
          2500,
          2500
        ]
      },
      "expect": {
        "pi": 1.25,
        "npv": 2000,
        "presentValue": 10000
      },
      "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; hand calculation in content.mdx: 10,000 ÷ 8,000 = 1.25"
    }
  ],
  "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)"
  ],
  "related": [
    "npv",
    "irr",
    "mirr",
    "payback-period",
    "wacc"
  ],
  "changelog": []
}