MIRR Calculator - Modified Internal Rate of Return
Use this MIRR Calculator to calculate the Modified Internal Rate of Return for an investment, project, business case, or cash-flow series. Enter cash flows in order, choose a finance rate for negative cash flows, and choose a reinvestment rate for positive cash flows. The calculator estimates MIRR, present value of costs, future value of inflows, net cash flow, and comparison with standard IRR.
Table of contents
Use the MIRR Calculator
Enter cash flows separated by commas, semicolons, or new lines. Use negative numbers for investments or costs and positive numbers for inflows. For example: -100000, 25000, 30000, 35000, 40000, 45000. The calculator discounts negative cash flows at the finance rate and compounds positive cash flows at the reinvestment rate.
The entered cash flows, finance rate of 8.0000%, and reinvestment rate of 10.0000% give an annualized MIRR of 13.3136%.
This calculator is educational. MIRR depends on the cash-flow timing, finance rate, reinvestment rate, and whether cash flows are entered in the correct order. It does not guarantee future returns or replace full investment due diligence.
Quick answer
MIRR, or Modified Internal Rate of Return, is a project return measure that improves on standard IRR by using separate assumptions for financing costs and reinvestment of positive cash flows. It is often more realistic than IRR because it does not assume that interim inflows are reinvested at the IRR itself.
Here, positive cash flows are compounded to the end at the reinvestment rate, negative cash flows are discounted to the beginning at the finance rate, and \( n \) is the number of periods.
What is MIRR?
MIRR stands for Modified Internal Rate of Return. It is a financial metric used to estimate the return of an investment project while making more realistic assumptions than the traditional internal rate of return. Standard IRR finds the discount rate that makes the net present value of a cash-flow stream equal to zero. MIRR modifies that idea by separating two important assumptions: the cost of financing negative cash flows and the rate at which positive cash flows can be reinvested.
The standard IRR method can be useful, but it has limitations. One of the biggest issues is the reinvestment assumption. Standard IRR effectively assumes that positive interim cash flows can be reinvested at the IRR itself. If a project has a very high IRR, that assumption may be unrealistic. MIRR solves this by allowing the analyst to choose a more realistic reinvestment rate, such as the company’s cost of capital, expected portfolio return, or another practical reinvestment rate.
MIRR also helps when projects have multiple negative and positive cash flows. Traditional IRR can produce multiple answers when cash flows change sign more than once. MIRR reduces this problem by discounting all negative cash flows to the present and compounding all positive cash flows to the end. This creates a cleaner comparison between the present value of costs and the future value of benefits.
For example, suppose a project requires an initial investment of \( AED\ 100{,}000 \), then produces cash inflows of \( AED\ 25{,}000 \), \( AED\ 30{,}000 \), \( AED\ 35{,}000 \), \( AED\ 40{,}000 \), and \( AED\ 45{,}000 \). If the finance rate is \( 8\% \) and the reinvestment rate is \( 10\% \), MIRR estimates the annual compound return that connects the present value of the project’s costs with the future value of the reinvested inflows.
MIRR is used in capital budgeting, project finance, business case analysis, investment comparison, private equity, real estate, corporate finance, and financial education. It is especially useful when a project has interim cash flows and the analyst wants a more conservative or realistic return estimate than standard IRR.
MIRR formula
The core Modified Internal Rate of Return formula is:
Where:
- \( MIRR \) = Modified Internal Rate of Return for one cash-flow period.
- \( FV_{\text{positive cash flows}} \) = future value of all positive cash flows compounded to the final period at the reinvestment rate.
- \( PV_{\text{negative cash flows}} \) = present value of all negative cash flows discounted to period \( 0 \) at the finance rate.
- \( n \) = number of periods from the first cash flow to the final cash flow.
The future value of positive cash flows is calculated as:
Where \( C_t^+ \) represents positive cash flows and \( r_e \) is the reinvestment rate. The present value of negative cash flows is calculated as:
Where \( C_t^- \) represents negative cash flows and \( r_f \) is the finance rate. The absolute value is used because \( PV_{\text{negative}} \) is treated as a positive cost amount in the MIRR formula.
If the cash-flow period is not yearly, the calculator annualizes the MIRR. If \( q \) is the number of cash-flow periods per year, then:
For example, if the cash flows are monthly and the MIRR per month is \( 1\% \), the annualized MIRR is \( (1.01)^{12} - 1 \), not simply \( 12\% \).
How to calculate MIRR
To calculate MIRR, first list all cash flows in chronological order. Negative cash flows represent investments, costs, or additional funding needs. Positive cash flows represent inflows, distributions, operating cash receipts, sale proceeds, or exit values. Then apply the finance rate to negative cash flows and the reinvestment rate to positive cash flows.
- Enter all cash flows in order. Start with \( C_0 \), then add \( C_1 \), \( C_2 \), and so on.
- Use negative signs for costs. Initial investment and future outflows should be entered as negative values.
- Use positive signs for inflows. Income, project returns, sale proceeds, or distributions should be entered as positive values.
- Choose a finance rate. This rate is used to discount negative cash flows to the beginning.
- Choose a reinvestment rate. This rate is used to compound positive cash flows to the final period.
- Calculate \( PV_{\text{negative}} \). Discount all negative cash flows to period \( 0 \).
- Calculate \( FV_{\text{positive}} \). Compound all positive cash flows to the final period.
- Apply the MIRR formula. Use \( MIRR = \left(\frac{FV_{\text{positive}}}{PV_{\text{negative}}}\right)^{1/n} - 1 \).
The number of periods \( n \) is usually the distance from the first cash flow to the final cash flow. If you enter six cash flows from \( C_0 \) through \( C_5 \), then \( n = 5 \). This is a common point of confusion. The number of periods is not always equal to the number of cash-flow entries.
Worked examples
Example 1: Basic MIRR calculation
Suppose an investment has the following yearly cash flows:
The finance rate is \( 8\% \), and the reinvestment rate is \( 10\% \). The initial investment occurs at \( t = 0 \), and the final cash flow occurs at \( t = 5 \), so \( n = 5 \).
Since the only negative cash flow is at period \( 0 \), the present value of negative cash flows is:
The positive cash flows are compounded to period \( 5 \):
Then MIRR is:
The result is the annual modified internal rate of return based on a realistic reinvestment rate of \( 10\% \), rather than assuming each inflow is reinvested at the project’s own IRR.
Example 2: MIRR with a later negative cash flow
Suppose a project has cash flows:
The negative cash flow in period \( 3 \) might represent a repair cost, reinvestment need, or additional capital requirement. MIRR handles this by discounting that negative cash flow back to period \( 0 \) using the finance rate:
The positive cash flows are compounded to the final period using the reinvestment rate:
This is one of MIRR’s strengths. It can handle projects with later outflows more cleanly than standard IRR, which may produce multiple rates when signs change more than once.
Example 3: Annualizing monthly MIRR
If monthly cash flows produce a MIRR of \( 1.1\% \) per month, the annualized MIRR is:
The annualized result is higher than \( 13.2\% \) because compounding is included. This is why the calculator shows both period MIRR and annualized MIRR.
MIRR vs IRR
MIRR and IRR both try to summarize a project’s cash-flow return as a percentage rate, but they use different assumptions. IRR finds the rate that makes net present value equal to zero. MIRR compares the future value of positive cash flows with the present value of negative cash flows while using separate finance and reinvestment rates.
| Measure | Main formula idea | Reinvestment assumption | Best use |
|---|---|---|---|
| IRR | \( 0 = \sum_{t=0}^{n}\frac{C_t}{(1+IRR)^t} \) | Implicitly assumes reinvestment at the IRR. | Simple projects with normal cash flows and one sign change. |
| MIRR | \( MIRR = \left(\frac{FV_+}{PV_-}\right)^{1/n} - 1 \) | Uses an explicit reinvestment rate chosen by the analyst. | Projects with interim cash flows, non-normal cash flows, or more realistic reinvestment assumptions. |
MIRR is often considered more conservative and more realistic when the IRR is very high. If a project has an IRR of \( 35\% \), it may be unrealistic to assume that every interim cash inflow can also be reinvested at \( 35\% \). MIRR lets you use a reinvestment rate such as \( 8\% \), \( 10\% \), or the company’s weighted average cost of capital.
IRR can also create multiple answers when cash flows change signs more than once. MIRR usually avoids this multiple-IRR problem by converting all negative cash flows into one present value and all positive cash flows into one future value.
How to interpret MIRR
MIRR is interpreted as a modified compound return for the project or investment. If the MIRR is higher than the required return, hurdle rate, or cost of capital, the project may be attractive. If the MIRR is lower than the required return, the project may not meet the investor’s return target.
| MIRR result | General interpretation | What to check next |
|---|---|---|
| \( MIRR < \text{required return} \) | The project may not meet the required return. | Check NPV, risk, cash-flow reliability, and strategic value. |
| \( MIRR = \text{required return} \) | The project approximately meets the return target. | Check whether the project risk justifies acceptance. |
| \( MIRR > \text{required return} \) | The project may be attractive under the MIRR rule. | Check project size, NPV, liquidity, and downside scenarios. |
| Very high MIRR | The project appears to create strong modified returns. | Check assumptions, cash-flow timing, reinvestment rate, and whether inputs are realistic. |
MIRR should not be used alone. A smaller project may have a high MIRR but create little total value. A larger project may have a lower MIRR but a much higher NPV. If capital is limited, MIRR can help rank projects. If the goal is total value creation, NPV remains extremely important.
Finance rate vs reinvestment rate
The finance rate and reinvestment rate are the two inputs that make MIRR different from IRR. The finance rate represents the cost of funds used to cover negative cash flows. It may be the borrowing rate, cost of capital, project financing cost, or another relevant discount rate for outflows.
The reinvestment rate represents the return that can reasonably be earned on positive cash flows after they are received. This rate is usually lower than a very high IRR because reinvesting every interim inflow at the same high project return may not be realistic.
Choosing realistic rates matters. If the reinvestment rate is set too high, MIRR may overstate the project’s return. If the finance rate is set too low, later negative cash flows may be understated. The rates should match the project context, company policy, and investment opportunity set.
Common mistakes
- Entering cash flows in the wrong order. MIRR depends on timing. The first value is period \( 0 \), the second is period \( 1 \), and so on.
- Forgetting negative signs. Investments and costs should be entered as negative cash flows.
- Using the same rate for finance and reinvestment without thinking. Sometimes the same rate is reasonable, but MIRR is most useful when these assumptions are chosen deliberately.
- Comparing monthly MIRR with annual hurdle rates. Annualize period MIRR before comparing with annual required returns.
- Using MIRR instead of NPV for project size decisions. MIRR gives a rate, while NPV gives value in currency terms.
- Ignoring risk differences. A higher MIRR project may still be riskier or less reliable.
- Assuming MIRR is guaranteed. MIRR is calculated from assumed or historical cash flows; actual future results can differ.
A good habit is to document the finance rate, reinvestment rate, cash-flow frequency, and reason for each assumption. This makes the MIRR calculation easier to defend and compare.
Related calculators and guides
Use these related Num8ers tools to continue working with project returns, cash-flow analysis, and investment decision-making:
FAQs
What is a MIRR Calculator?
A MIRR Calculator estimates Modified Internal Rate of Return by discounting negative cash flows at a finance rate and compounding positive cash flows at a reinvestment rate.
What is the MIRR formula?
The formula is \( MIRR = \left(\frac{FV_{\text{positive cash flows}}}{PV_{\text{negative cash flows}}}\right)^{\frac{1}{n}} - 1 \), where \( n \) is the number of periods.
What is the difference between MIRR and IRR?
IRR finds the rate that makes NPV equal to zero, while MIRR uses separate finance and reinvestment rates. MIRR is often more realistic for projects with interim cash flows.
What is the finance rate in MIRR?
The finance rate is used to discount negative cash flows to the present. It may represent borrowing cost, cost of capital, or the cost of funding project outflows.
What is the reinvestment rate in MIRR?
The reinvestment rate is used to compound positive cash flows to the final period. It represents the rate at which interim inflows can realistically be reinvested.
Is MIRR better than IRR?
MIRR is often better when reinvestment assumptions matter or when cash flows change signs more than once. IRR can still be useful for simple projects with normal cash-flow patterns.
Can MIRR be negative?
Yes. MIRR can be negative when the future value of positive cash flows is less than the present value of negative cash flows over the project period.