acalculator

What is the MIRR?

Enter the cash flows of an investment, starting with what you pay today, and the rates for borrowing and reinvesting. The calculator gives the modified internal rate of return (MIRR) and, when there is just one, the ordinary IRR to compare.

Your numbers

Read as: -16,000; 2,000; 4,000; 5,000; 5,000; 5,000; 5,000Start with the investment as a negative number, for example −16000 2000 4000.
MIRR
12%

At a 9% finance rate and a 9% reinvestment rate, these cash flows have a MIRR of 12%.

Future value of inflows
$31,589.22
Present value of outflows
$16,000.00
Periods
6
IRR
14.09%

MIRR: 12%. At a 9% finance rate and a 9% reinvestment rate, these cash flows have a MIRR of 12%.

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 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.

Example with the default inputs (Cash flows, starting today [-16,000, 2,000, 4,000, 5,000, 5,000, 5,000, 5,000], Finance rate 9%, Reinvestment rate 9%): At a 9% finance rate and a 9% reinvestment rate, these cash flows have a MIRR of 12%.

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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Cash flows, starting today -16,000, 2,000, 4,000, 5,000, 5,000, 5,000, 5,000, Finance rate 9%, Reinvestment rate 9% gives MIRR 12.004761%, Future value of inflows $31,589.22, Present value of outflows $16,000.00.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)
  2. Cash flows, starting today -120,000, 39,000, 30,000, 21,000, 37,000, 46,000, Finance rate 10%, Reinvestment rate 12% gives MIRR 12.609413%, Future value of inflows $217,297.50.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%
  3. Cash flows, starting today -120,000, 39,000, 30,000, 21,000, Finance rate 10%, Reinvestment rate 12% gives MIRR -4.804466%.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
  4. Cash flows, starting today -120,000, 39,000, 30,000, 21,000, 37,000, 46,000, Finance rate 10%, Reinvestment rate 14% gives MIRR 13.475911%.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
  5. Cash flows, starting today -1,000, -500, 800, 900, Finance rate 8%, Reinvestment rate 10% gives MIRR 6.756802%, Present value of outflows $1,462.96, Future value of inflows $1,780.00.

How it works

Enter the cash flows CF₀, CF₁, …, CFₙ: CF₀ is today, and CFₖ is at the end of period k. With the finance rate f and the reinvestment rate r (percents ÷ 100):

  • Present value of outflows PV = the sum of −CFₖ ÷ (1 + f)ᵏ over every negative CFₖ
  • Future value of inflows FV = the sum of CFₖ × (1 + r)ⁿ⁻ᵏ over every positive CFₖ
  • MIRR = (FV ÷ PV)^(1 ÷ n) − 1

The page also shows the IRR: the rate that makes CF₀ + CF₁ ÷ (1 + IRR) + … + CFₙ ÷ (1 + IRR)ⁿ = 0, when exactly one rate does.

Rules:

  • Enter 2 to 51 cash flows (1 to 50 periods), with at least one negative and one positive.
  • Each rate is from −99% to 1,000% per period.
  • The sums, powers and root are worked in floating point. The MIRR and the IRR show to 2 decimals and money to the cent, with halves rounded up (away from 0).

Assumptions

  • The rates are per period (per year for yearly cash flows) and stay the same throughout.
  • Zero cash flows count as neither outflows nor inflows, but still count as periods.

Worked examples by hand

The OpenStax project at 9%. Cash flows −16,000, 2,000, 4,000, 5,000, 5,000, 5,000, 5,000. PV of outflows = $16,000. FV of inflows = 2,000 × 1.09⁵ + 4,000 × 1.09⁴ + 5,000 × (1.09³ + 1.09² + 1.09 + 1) = $31,589.22. MIRR = (31,589.22 ÷ 16,000)^(1 ÷ 6) − 1 = 12.00%. OpenStax rounds its factors and shows $31,595.22, also 12%.

Excel’s example. −120,000, then 39,000, 30,000, 21,000, 37,000, 46,000, at a 10% finance rate and a 12% reinvestment rate. FV of inflows = 39,000 × 1.12⁴ + 30,000 × 1.12³ + 21,000 × 1.12² + 37,000 × 1.12 + 46,000 = $217,297.50. MIRR = (217,297.50 ÷ 120,000)^(1 ÷ 5) − 1 = 12.61% (Excel shows 13%). After three years only: −4.80% (Excel: −5%). At a 14% reinvestment rate: 13.48% (Excel: 13%).

Two outflows. −1,000, −500, 800, 900 at 8% and 10%. PV of outflows = 1,000 + 500 ÷ 1.08 = $1,462.96. FV of inflows = 800 × 1.1 + 900 = $1,780. MIRR = (1,780 ÷ 1,462.96)^(1 ÷ 3) − 1 = 6.76%.

Other questions people ask

What is MIRR?

MIRR, the modified internal rate of return, is the yearly return of a project when its outflows are financed at one rate and its inflows are reinvested at another. It fixes two problems of the IRR: the IRR assumes cash is reinvested at the IRR itself, and it can have more than one answer.

How do I calculate MIRR?

Discount every outflow to today at the finance rate and add them up. Grow every inflow to the last period at the reinvestment rate and add them up. MIRR = (future value of inflows ÷ present value of outflows)^(1 ÷ n) − 1, where n is the number of periods.

What is the difference between MIRR and IRR?

IRR is the rate that makes the net present value zero, and it assumes every inflow is reinvested at that same rate. MIRR uses a reinvestment rate you choose, usually the cost of capital. When the IRR is high, the MIRR is usually lower and more realistic.

What finance and reinvestment rates should I use?

A common choice is the company’s cost of capital (WACC) for both. Use a different finance rate when the outflows are paid with a loan at a known rate, and a reinvestment rate equal to what you can really earn on the cash.

Why does MIRR need a negative and a positive cash flow?

MIRR compares the cost of the outflows with the value of the inflows. With no outflows there is nothing to earn a return on, and with no inflows there is nothing earned, so there is no rate.

Is the MIRR the same as Excel’s MIRR function?

Yes. Like Excel, this calculator treats the first value as today and each later value as the end of a period. Excel’s example of −120,000 followed by five years of returns, at 10% and 12%, gives 13%; this page shows 12.61% before rounding.