# MIRR Calculator

Why do some investors use a MIRR calculation rather than the more standard IRR calculation to evaluate the feasibility of a project?

There are problems with the IRR equation:

- It is possible for the equation to return two different results for the same cash flows.
- The equation also implicitly assumes a reinvestment rate equal to the IRR for the project's positive cash flows.

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## What is the MIRR?

The modified internal rate of return is an annualized return on investment calculation that takes into account the difference between the firm or investor's finance rate and the reinvestment rate earned on the project's or investment's positive cash flows.

Where as the IRR assumes a reinvestment rate for the positive cash flows equal to the IRR, the MIRR explicitly requires the user to provide the reinvestment rate they expect to earn on the positive cash flows.

## Using the MIRR Calculator

In addition to the projected cash flow, the user sets four values.

- Finance Rate (Discount Rate)
- Reinvestment Rate
- Initial Investment Date
- Compounding Frequency

The finance rate is the interest rate you expect to pay on your loans if or when you borrow money. This rate is used to discount the negative cash flows (investments). Additionally, the NPV calculation uses the finance rate to discount all cash flows - positive or negative.

The reinvestment rate is the rate of return you anticipate earning on the positive cash flows generated by the project or investment.

The initial investment date is the date you expect the project or investment to start.

The compounding frequency matches the cash flow frequency. The equation used for the MIRR calculation calculates a compounded rate of return, unlike the IRR equation which assumes no compounding. With the IRR calculation, cash flows can occur on any date. With the MIRR they must happen on a date compounding is due. The MIRR cash flow can be irregular, but only to the extent cash flows are skipped.

As an example, if the compounding is set to "Quarterly" and the "Initial Investment Date" is August 15th, then the only other valid cash flow dates are November 15th, February 15th, and May 15th. **This is why the user can't change the dates.** The calculator calculates valid days for the cash flow.

The Internal Rate of Return (IRR) Calculator permits cash flows to be on any date

See the Net Present Value (NVP) Calculator to learn about the NPV result.

## The MIRR Proof

Wikipedia defines the MIRR as:

"The formula adds up the negative cash flows after discounting them to time zero using the external cost of capital, adds up the positive cash flows including the proceeds of reinvestment at the external reinvestment rate to the final period, and then works out what rate of return would cause the magnitude of the discounted negative cash flows at time zero to be equivalent to the future value of the positive cash flows at the final time period."

The calculated result for "Proof" should be zero i.e. "discounted negative cash flows at time zero to be equivalent to the future value of the positive cash flows at the final time period." If it isn't, then the result is suspect.

## Bottom Line

As with the IRR calculation, the intended use for the MIRR is not to calculate a rate-of-return on a single investment, but rather it is to be used for comparing mutually exclusive investment opportunities.

Other things being equal, the investment with the higher MIRR is the better business decision.

## Comments, suggestions & questions welcomed...