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Difference Between IRR and MIRR

Both the IRR and MIRR are used by business experts to determine if a project is financially feasible. Read our blog to find out more about them.

Izhar Ahmad26 Sept, 2023

The IRR and MIRR analyses are two methods for estimating a project's prospective profitability and return on investment. Understanding IRR and MIRR and their differences will help you perform a more accurate financial analysis to estimate a project's potential.

The firm must choose the strategy that produces the greatest results while also meeting the demands of the investors.

What is the Internal Rate of Return?

Internal Rate of Return is a financial measure used to estimate the potential profitability of an investment or project. The nominal interest rate tells you one thing; however, the Internal Rate of Return (IRR) is another value that provides an effective return by considering the initial investment and future cash flows you’ll receive. Essentially, IRR allows you to estimate the future performance of an investment based on how much capital you invest today, and how much cash you can recover from it over the long term. It’s a ruler for how attractive someone’s business is to invest in.

What is the Modified Internal Rate of Return?

Modified Internal Rate of Return (MIRR) is an investment and finance metric, which helps to determine the effectiveness of an investment or the project considering all costs of capital and reinvestment cash flow returns. It is more accurate in its representation of the performance of an investment compared to the classical Internal Rate of Return (IRR). Simply put, MIRR assists individuals and corporations in making more informed investment and business decisions by taking a balanced approach to what comes in (cash in) and goes out (cash out), as well as what comes in during its lifetime (cash flows).

IRR and MIRR Formula

Understanding the formulas for IRR and MIRR is essential for anyone involved in financial analysis and investment decision-making. We have provided below the formulas for IRR and MIRR:

IRR Formula:

The IRR formula calculates the internal rate of return, which is the annualized percentage rate at which an investment is expected to generate returns. It is particularly valuable when evaluating projects with irregular cash flow patterns. The formula for IRR can be represented as follows: IRR= C 0 ÷(1+r) 0 + C 1 ÷(1+r) 2 + C 1 ÷(1+r) 2 +…….+ C n ÷(1+r) n where,

IRR represents the internal rate of return
C 0 denotes the initial investment
C 1 , C 2 , ………, C n represents the cash flow received
r signifies the rate of return

The IRR is determined by finding the value of ‘r’ that makes the sum of the present values of all cash flows equal to zero. This means that it is the rate at which the net present value (NPV) of an investment becomes zero.

MIRR Formula:

While IRR is a valuable metric, it has some limitations, particularly regarding the assumption that all cash flows are reinvested at the IRR itself. MIRR addresses this issue by considering a specified reinvestment rate (often the cost of capital) and a financing rate (the rate at which funds are borrowed or earned). The formula for MIRR is as follows: MIRR= (FV/PV) 1/n -1 Where,

MIRR signifies the Modified Internal Rate of Return
FV is the future value of all positive cash flow compounded at the reinvestment rate.
PV is the present value of all negative cash flows discounted at the financing rate.
n signifies the total number of periods.

IRR and MIRR Differences

Below, we have presented a comparison of IRR and MIRR in a tabular format to help highlight their distinctions:

Metric	IRR (Internal Rate of Return)	MIRR (Modified Internal Rate of Return)
Full Form	Internal Rate of Return	Modified Internal Rate of Return
Calculation	Finds the rate at which the Net Present Value (NPV) of cash flows becomes zero.	Uses a specified reinvestment rate and a financing rate to determine profitability.
Cash Flow Assumption	Assumes that all cash flows are reinvested at the IRR itself.	Recognizes that cash flows are reinvested at a different rate (reinvestment rate) and financed at another rate (financing rate).
Realism	May not always reflect practical reinvestment scenarios.	Provides a more realistic assessment by considering actual reinvestment and financing conditions.
Sensitivity to Cash Flows	Sensitive to the timing and magnitude of cash flows, particularly when they change sign (from positive to negative or vice versa).	Less sensitive to changes in cash flow patterns due to its use of a specified reinvestment rate.
Decision Criteria	If IRR exceeds the required rate of return or cost of capital, the investment is deemed acceptable.	If MIRR is greater than the cost of capital, the project is considered viable.
Multiple IRRs	Can yield multiple IRRs in complex cash flow patterns, making interpretation challenging.	Avoids the problem of multiple IRRs, providing a single, more reliable rate of return.
Consistency	IRR may lead to conflicting investment decisions when comparing mutually exclusive projects with different cash flow patterns.	MIRR offers more consistent investment decisions when evaluating mutually exclusive projects.
Popular Use Cases	Commonly used for simple projects with relatively straightforward cash flows.	Preferred for projects with unconventional cash flow patterns and varying reinvestment opportunities.
Formula	Uses a trial-and-error approach to find the rate that satisfies the NPV equation.	Employs a direct formula based on future and present values of cash flows, reinvestment, and financing rates.

IRR and MIRR Examples and Calculation

For the better understanding, we have provided few examples to calculate IRR and MIRR:

Example 1: IRR Calculation

Imagine you're considering an investment in a project that requires an initial cost of ₹10,000. Over the next five years, the project generates the following cash inflows: Year 1: ₹3,000 Year 2: ₹2,500 Year 3: ₹2,000 Year 4: ₹1,800 Year 5: ₹1,500 To calculate the IRR, we'll use these cash flows and the IRR formula: IRR= C 0 ÷(1+r) 0 + C 1 ÷(1+r) 1 + C 2 ÷(1+r) 2 + C 2 ÷(1+r) 2 + C 3 ÷(1+r) 3 + C 4 ÷(1+r) 4 10000= 3000÷(1+r) 1 + 2500÷(1+r) 2 + 2000÷(1+r) 3 + 1800÷(1+r) + 1500÷(1+r) 5 Using a financial calculator you would find that the IRR for this investment is approximately 12.67%.

Example 2: MIRR Calculation

Now, let's calculate the MIRR for the same investment project. We'll assume a reinvestment rate of 8% and a financing rate of 10%. First, calculate the future value (FV) of all positive cash flows reinvested at 8%: FV= 3000*(1+0.08) 1 +2500*(1+0.08) 2 +2000*(1+0.08) 3 +1800*(1+0.08) 4 +1500*(1+0.08) 5 Next, calculate the present value (PV) of the initial cost and negative cash flows at a financing rate of 10%: PV= -10000= 3000÷(1+r) 1 + 2500÷(1+r) 2 + 2000÷(1+r) 3 + 1800÷(1+r) + 1500÷(1+r) 5 PV= -9455.76 Now, Calculate the MIRR using the formula: MIRR= (FV÷PV) 1/n -1 MIRR= (11407.52/-9455.76) 1/5 -1 MIRR=10.48

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IRR and MIRR FAQs

Q1: Can IRR and MIRR be negative? A1: Yes, both IRR and MIRR can be negative, indicating that the investment may not meet the required rate of return or cost of capital. Q2: Why does IRR sometimes result in multiple rates of return? A2: IRR can yield multiple rates when cash flows change sign, leading to conflicting investment decisions in complex scenarios. Q3: When is MIRR preferred over IRR? A3: MIRR is preferred for projects with unconventional cash flow patterns or when cash flows cannot be reinvested at the IRR, providing more accurate investment assessments. Q4: How do you calculate IRR and MIRR in Excel? A4: In Excel, use the "IRR" function to calculate IRR and the "MIRR" function to calculate MIRR. Enter cash flows and the appropriate rates as inputs. Q5: What is the significance of the MIRR reinvestment rate and financing rate? A5: The MIRR reinvestment rate represents the rate at which positive cash flows are reinvested, while the financing rate represents the cost of capital or financing cost for the investment.

Can IRR and MIRR be negative?

Yes, both IRR and MIRR can be negative, indicating that the investment may not meet the required rate of return or cost of capital.

Why does IRR sometimes result in multiple rates of return?

IRR can yield multiple rates when cash flows change sign, leading to conflicting investment decisions in complex scenarios.

When is MIRR preferred over IRR?

MIRR is preferred for projects with unconventional cash flow patterns or when cash flows cannot be reinvested at the IRR, providing more accurate investment assessments.

How do you calculate IRR and MIRR in Excel?

In Excel, use the "IRR" function to calculate IRR and the "MIRR" function to calculate MIRR. Enter cash flows and the appropriate rates as inputs.

What is the significance of the MIRR reinvestment rate and financing rate?

The MIRR reinvestment rate represents the rate at which positive cash flows are reinvested, while the financing rate represents the cost of capital or financing cost for the investment.

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The firm must choose the strategy that produces the greatest results while also meeting the demands of the investors.

What is the Internal Rate of Return?

What is the Modified Internal Rate of Return?

IRR and MIRR Formula

Understanding the formulas for IRR and MIRR is essential for anyone involved in financial analysis and investment decision-making. We have provided below the formulas for IRR and MIRR:

IRR Formula:

IRR represents the internal rate of return
C 0 denotes the initial investment
C 1 , C 2 , ………, C n represents the cash flow received
r signifies the rate of return

MIRR Formula:

MIRR signifies the Modified Internal Rate of Return
FV is the future value of all positive cash flow compounded at the reinvestment rate.
PV is the present value of all negative cash flows discounted at the financing rate.
n signifies the total number of periods.

IRR and MIRR Differences

Below, we have presented a comparison of IRR and MIRR in a tabular format to help highlight their distinctions:

Metric	IRR (Internal Rate of Return)	MIRR (Modified Internal Rate of Return)
Full Form	Internal Rate of Return	Modified Internal Rate of Return
Calculation	Finds the rate at which the Net Present Value (NPV) of cash flows becomes zero.	Uses a specified reinvestment rate and a financing rate to determine profitability.
Cash Flow Assumption	Assumes that all cash flows are reinvested at the IRR itself.	Recognizes that cash flows are reinvested at a different rate (reinvestment rate) and financed at another rate (financing rate).
Realism	May not always reflect practical reinvestment scenarios.	Provides a more realistic assessment by considering actual reinvestment and financing conditions.
Sensitivity to Cash Flows	Sensitive to the timing and magnitude of cash flows, particularly when they change sign (from positive to negative or vice versa).	Less sensitive to changes in cash flow patterns due to its use of a specified reinvestment rate.
Decision Criteria	If IRR exceeds the required rate of return or cost of capital, the investment is deemed acceptable.	If MIRR is greater than the cost of capital, the project is considered viable.
Multiple IRRs	Can yield multiple IRRs in complex cash flow patterns, making interpretation challenging.	Avoids the problem of multiple IRRs, providing a single, more reliable rate of return.
Consistency	IRR may lead to conflicting investment decisions when comparing mutually exclusive projects with different cash flow patterns.	MIRR offers more consistent investment decisions when evaluating mutually exclusive projects.
Popular Use Cases	Commonly used for simple projects with relatively straightforward cash flows.	Preferred for projects with unconventional cash flow patterns and varying reinvestment opportunities.
Formula	Uses a trial-and-error approach to find the rate that satisfies the NPV equation.	Employs a direct formula based on future and present values of cash flows, reinvestment, and financing rates.

IRR and MIRR Examples and Calculation

For the better understanding, we have provided few examples to calculate IRR and MIRR:

Example 1: IRR Calculation

Example 2: MIRR Calculation

Read Related Topics
Difference Between Dealer and Distributor	Difference Between Branding and Packaging	Difference Between Cardinal and ordinal Utility	Difference Between Cost Accounting and Management Accounting
Balance Sheet Vs Consolidated balance Sheet	Capital Expenditure and Revenue Expenditure	Types of Budget	Balance Sheet Vs Profit Loss Account