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The '''Modified Internal Rate of Return''' (MIRR) is a financial metric used to measure the return of an [[investment]] over a period of time. It is an improved version of the Internal Rate of Return (IRR) metric and is more commonly used in capital budgeting decisions as it accounts for compounding of returns. 

MIRR is calculated by taking the present value of cash inflows and subtracting the present value of cash outflows. The resulting net present value (NPV) is then divided by the initial cash outflow and the resulting number is then raised to the power of 1 divided by the number of periods. 

In conclusion, the MIRR metric is a more accurate measurement of investment returns compared to the traditional Internal Rate of Return metric, as it accounts for the compounding of returns over time. It is widely used by corporate finance professionals in capital budgeting decisions.

==Example of Modified internal rate of return==
To demonstrate how the Modified Internal Rate of Return (MIRR) metric works, let us consider a [[project]] that requires an initial investment of $100,000 and provides cash flows of $20,000 per year for 10 years. The discount rate is 8%. 

Using the MIRR formula, the calculation would look like this: 

<math>MIRR = (\frac{PV_F}{PV_I})^\frac{1}{N} - 1</math>

Where PV_F = $128,941.57, PV_I = $100,000 and N = 10 

<math>MIRR = (\frac{128,941.57}{100,000})^\frac{1}{10} - 1</math>

MIRR = 0.08 or 8%

In this example, the MIRR of 8% indicates that the project is expected to yield an 8% return over the 10 year period, adjusted for the compounding of returns. 

In conclusion, this example demonstrates how the Modified Internal Rate of Return (MIRR) metric is used to calculate the rate of return of an investment over a period of time. By accounting for the compounding of returns, the MIRR metric provides a more accurate measure of return when compared to the traditional Internal Rate of Return metric.

==Formula of Modified internal rate of return==
The Modified Internal Rate of Return (MIRR) is a financial metric used to measure the return of an investment over a period of time. It is an improved version of the Internal Rate of Return (IRR) metric and is more commonly used in capital budgeting decisions as it accounts for compounding of returns. The formula for MIRR is expressed as follows:

<math>MIRR = (\frac{PV_F}{PV_I})^\frac{1}{N} - 1</math>

Where PV<subF</sub> is the present value of future cash flows, PV<sub>I</sub> is the present value of the initial cash outflow, and N is the number of periods. 

In conclusion, the MIRR metric is a more accurate measurement of investment returns compared to the traditional Internal Rate of Return metric, as it accounts for the compounding of returns over time. It is widely used by corporate finance professionals in capital budgeting decisions.

==When to use Modified internal rate of return==
MIRR is a useful metric to use when making capital budgeting decisions. It can be used to compare the return of an investment to the [[required rate of return]], or to compare the returns of two different [[investments]]. Additionally, it can be used to measure the potential return of a project or investment over a period of time.

The MIRR metric is especially useful when making decisions regarding long-term investments, as it accounts for the compounding of returns over time. It is also useful when evaluating investments with non-conventional cash flows, such as multiple cash flows of different sizes.

==Types of Modified internal rate of return==
There are two types of Modified Internal Rate of Return (MIRR):
* The first type of MIRR is the reinvestment rate MIRR, which assumes that all cash flows are reinvested at the MIRR rate. This type of MIRR is most commonly used for investments where the cash flows are reinvested at the same rate of return.
* The second type of MIRR is the [[cost]] of capital MIRR, which assumes that all cash flows are reinvested at the cost of capital. This type of MIRR is most commonly used for investments where the cash flows are reinvested at a rate of return that is different from the MIRR rate.

==Steps of Modified internal rate of return==
The steps of calculating the Modified Internal Rate of Return (MIRR) are as follows:
* '''Step 1''': Calculate the present value of all future cash inflows.
This is done by discounting each cash flow at the required rate of return for each period.
* '''Step 2''': Calculate the present value of all initial cash outflows.
This is done by discounting the initial outflow at the required rate of return for the period.
* '''Step 3''': Calculate the net present value (NPV) of the investment.
The NPV is calculated by subtracting the present value of the cash outflows from the present value of the cash inflows.
* '''Step 4''': Calculate the Modified Internal Rate of Return.
The MIRR is calculated by dividing the NPV by the initial cash outflow and raising the resulting number to the power of 1 divided by the number of periods.

==Advantages of Modified internal rate of return==
The Modified Internal Rate of Return (MIRR) has several advantages over the traditional Internal Rate of Return (IRR) metric. These advantages include: 
* The MIRR metric takes into account the compounding of returns, which is a more accurate representation of the true return of an investment. 
* MIRR is less affected by the size and sign of cash flows making it more reliable in analyzing investments with multiple cash flows. 
* MIRR provides a better estimate of investment profitability by utilizing a discount rate that is different from the return rate used in the IRR metric.

==Limitations of Modified internal rate of return==
Despite its advantages, the Modified Internal Rate of Return (MIRR) has some drawbacks that should be considered when analyzing a potential investment. These include: 
* The MIRR relies on the assumption that any cash flows that are reinvested earn the MIRR rate. If the actual rate earned is different than the assumed rate, then the MIRR calculation will be inaccurate. 
* The MIRR calculation does not take into account the timing of cash flows. Cash flows that occur at different points in time can have different values and a change in the timing of cash flows can have a significant impact on the MIRR calculation. 
* The MIRR calculation assumes that cash flows are reinvested at the same rate as the MIRR rate. This may not be realistic as the rate of return in the reinvestment may differ from the MIRR rate. 

==Other approaches related to Modified internal rate of return==
Other approaches related to the Modified Internal Rate of Return (MIRR) include the following:
* '''Payback Period''': This metric is used to measure the number of periods it takes for an investment to pay for itself. It is calculated by dividing the initial cash outflow by the sum of all cash inflows. 
* '''Net Present Value (NPV)''': This metric is used to measure the present value of an investment, taking into account all future cash flows. It is calculated by taking the present value of all cash inflows and subtracting the present value of all cash outflows.
* '''Return on Investment (ROI)''': This metric is used to measure the profitability of an investment. It is calculated by taking the [[net income]] and dividing it by the total investment cost.

In conclusion, there are several approaches that are related to the Modified Internal Rate of Return (MIRR) metric and are used by corporate finance professionals in capital budgeting decisions. These include the Payback Period, Net Present Value (NPV), and Return on Investment (ROI) metrics.

{{infobox5|list1={{i5link|a=[[Net present value (NPV)]]}} &mdash; {{i5link|a=[[Payback period]]}} &mdash; {{i5link|a=[[Profitability index]]}} &mdash; {{i5link|a=[[Annualized rate]]}} &mdash; {{i5link|a=[[Real rate of return]]}} &mdash; {{i5link|a=[[Net asset value per share]]}} &mdash; {{i5link|a=[[Average annual growth rate]]}} &mdash; {{i5link|a=[[Accounting rate of return]]}} &mdash; {{i5link|a=[[Return on investment]]}} }}

==References==
* Satyasai, K. J. S. (2009). ''[https://ageconsearch.umn.edu/record/57496/files/9-Satyasai.pdf Application of Modified Internal Rate of Return Method for Watershed Evaluation1]''. Agricultural [[Economics]] Research Review, 22(conf), 401-406.
[[Category:Statistics]]