{
  "id": "mirr",
  "version": "1bc55eeaf050",
  "status": "published",
  "name": "MIRR Calculator",
  "question": "What is the MIRR?",
  "summary": "Computes the modified internal rate of return (MIRR) of a series of cash flows from a finance rate and a reinvestment rate, with the IRR to compare.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/mirr-calculator",
  "markdown": "https://www.acalculator.org/finance/mirr-calculator.md",
  "kind": "function",
  "method": "MIRR = (FV of inflows at the reinvestment rate ÷ PV of outflows at the finance rate)^(1 ÷ n) − 1, where n is the number of periods after today.",
  "assumptions": [
    "The first cash flow is today (period 0); each later one is at the end of its period.",
    "The rates are per period and stay the same for every period.",
    "The IRR shows only when exactly one rate makes the net present value zero."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "flows": {
        "title": "Cash flows, starting today",
        "description": "The net cash flow now (period 0), then at the end of period 1, 2 and so on, separated by spaces or new lines. Negative for money paid out.",
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "finance": {
        "title": "Finance rate",
        "description": "The rate per period paid on money borrowed for the outflows.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -99,
        "maximum": 1000
      },
      "reinvest": {
        "title": "Reinvestment rate",
        "description": "The rate per period earned on the inflows when reinvested.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -99,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "mirr": {
      "label": "MIRR",
      "description": "The modified internal rate of return, per period.",
      "format": "percent"
    },
    "terminal": {
      "label": "Future value of inflows",
      "description": "Every inflow compounded to the last period at the reinvestment rate.",
      "format": "money"
    },
    "outflows": {
      "label": "Present value of outflows",
      "description": "Every outflow discounted to today at the finance rate.",
      "format": "money"
    },
    "periods": {
      "label": "Periods",
      "description": "The number of periods after today.",
      "format": "number"
    },
    "irr": {
      "label": "IRR",
      "description": "The internal rate of return, when exactly one rate makes the NPV zero.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "flows": "-16000 2000 4000 5000 5000 5000 5000",
      "finance": 9,
      "reinvest": 9
    },
    "outputs": {
      "mirr": 12.004761379617847,
      "terminal": 31589.219349799998,
      "outflows": 16000,
      "periods": 6,
      "irr": 14.085455304251383
    },
    "text": "At a 9% finance rate and a 9% reinvestment rate, these cash flows have a MIRR of 12%."
  },
  "examples": [
    {
      "given": {
        "flows": [
          -16000,
          2000,
          4000,
          5000,
          5000,
          5000,
          5000
        ],
        "finance": 9,
        "reinvest": 9
      },
      "expect": {
        "mirr": 12.004761379617856,
        "terminal": 31589.2193498,
        "outflows": 16000
      },
      "source": "OpenStax, Principles of Finance, 16.4 Alternative Methods (MIRR: outflows discounted to time 0 and inflows compounded to the end at the cost of capital; the $16,000 project at 9% has a MIRR of 12%). https://openstax.org/books/principles-finance/pages/16-4-alternative-methods (OpenStax rounds its factors and shows a terminal value of $31,595.22); Python 3 with exact fractions: 31,589.22 ÷ 16,000, to the power 1 ÷ 6, minus 1 = 12.0048%"
    },
    {
      "given": {
        "flows": [
          -120000,
          39000,
          30000,
          21000,
          37000,
          46000
        ],
        "finance": 10,
        "reinvest": 12
      },
      "expect": {
        "mirr": 12.60941303659051,
        "terminal": 217297.49504
      },
      "source": "Microsoft Support, MIRR function (−120,000 then 39,000, 30,000, 21,000, 37,000, 46,000; finance rate 10%, reinvest rate 12%: 13% after five years, −5% after three; 13% at a 14% reinvest rate). https://support.microsoft.com/en-us/office/mirr-function-b020f038-7492-4fb4-93c1-35c345b53524: 13% (Python 3: 12.609%)"
    },
    {
      "given": {
        "flows": [
          -120000,
          39000,
          30000,
          21000
        ],
        "finance": 10,
        "reinvest": 12
      },
      "expect": {
        "mirr": -4.804465524998081
      },
      "source": "Microsoft Support, MIRR function (−120,000 then 39,000, 30,000, 21,000, 37,000, 46,000; finance rate 10%, reinvest rate 12%: 13% after five years, −5% after three; 13% at a 14% reinvest rate). https://support.microsoft.com/en-us/office/mirr-function-b020f038-7492-4fb4-93c1-35c345b53524: −5% after three years (Python 3: −4.804%)"
    },
    {
      "given": {
        "flows": [
          -120000,
          39000,
          30000,
          21000,
          37000,
          46000
        ],
        "finance": 10,
        "reinvest": 14
      },
      "expect": {
        "mirr": 13.475911082831482
      },
      "source": "Microsoft Support, MIRR function (−120,000 then 39,000, 30,000, 21,000, 37,000, 46,000; finance rate 10%, reinvest rate 12%: 13% after five years, −5% after three; 13% at a 14% reinvest rate). https://support.microsoft.com/en-us/office/mirr-function-b020f038-7492-4fb4-93c1-35c345b53524: 13% at a 14% reinvest rate (Python 3: 13.476%)"
    },
    {
      "given": {
        "flows": [
          -1000,
          -500,
          800,
          900
        ],
        "finance": 8,
        "reinvest": 10
      },
      "expect": {
        "mirr": 6.756802328119016,
        "outflows": 1462.962962962963,
        "terminal": 1780
      },
      "source": "hand calculation in content.mdx: 1,000 + 500 ÷ 1.08 = 1,462.96; 800 × 1.1 + 900 = 1,780; (1,780 ÷ 1,462.96)^(1 ÷ 3) − 1 = 6.757%"
    }
  ],
  "sources": [
    "OpenStax, Principles of Finance, 16.4 Alternative Methods: MIRR with outflows discounted to time 0 and inflows compounded to the end at the cost of capital; the $16,000 project at 9% has a MIRR of 12%. https://openstax.org/books/principles-finance/pages/16-4-alternative-methods (retrieved 2026-10-05)",
    "Microsoft Support, MIRR function: the formula and an example (−120,000; 39,000, 30,000, 21,000, 37,000, 46,000; finance rate 10%, reinvest rate 12%). https://support.microsoft.com/en-us/office/mirr-function-b020f038-7492-4fb4-93c1-35c345b53524 (retrieved 2026-10-05)"
  ],
  "related": [
    "irr",
    "npv",
    "payback-period",
    "wacc"
  ],
  "changelog": []
}