MIRR Calculator: Combination Approach

What is the Modified Internal Rate of Return (MIRR)?

The Modified Internal Rate of Return (MIRR) is a financial metric used to assess the profitability of an investment. It is an enhancement of the standard Internal Rate of Return (IRR) because it resolves two of the IRR’s main flaws: the assumption of reinvesting positive cash flows at the project’s own IRR and the potential for multiple IRR values for projects with non-conventional cash flows (i.e., multiple changes in sign).

MIRR provides a more realistic measure by assuming that positive cash flows are reinvested at a rate that is more representative of the company’s opportunities, such as the cost of capital. Similarly, it assumes that any financing required for negative cash flows is done at the firm’s financing rate. The combination approach to calculate the MIRR of the project is particularly robust, as it explicitly discounts all negative cash flows to the present and compounds all positive cash flows to the end of the project’s life.

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The MIRR Combination Approach Formula

The core idea of the combination approach is to consolidate all costs into a single present value and all returns into a single future value. The formula is then derived from these two values and the project’s lifespan.

MIRR = ( (FV_{Positive Cash Flows} / PV_{Negative Cash Flows})^(1/n) – 1 ) * 100

To use this formula, we first need to calculate the components:

• FV_{Positive Cash Flows}: The Future Value of all positive cash flows, compounded to the end of the project at the reinvestment rate.
• PV_{Negative Cash Flows}: The Present Value of all negative cash flows (including the initial investment), discounted to the beginning of the project at the financing rate.
• n: The total number of periods in the project.

For more details on alternative methods, you might want to read about IRR vs MIRR Explained.

Formula Variables

Variable	Meaning	Unit	Typical Range
FV	Future Value of Inflows	Currency ($)	Positive Value
PV	Present Value of Outflows	Currency ($)	Positive Value
n	Number of Periods	Years / Months	1 – 50+
Reinvestment Rate	Rate for compounding inflows	Percentage (%)	5% – 15%
Financing Rate	Rate for discounting outflows	Percentage (%)	5% – 15%

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Practical Examples

Example 1: Standard Project

Let’s consider a project with a clear initial cost and subsequent positive returns.

• Initial Investment: $50,000
• Cash Flows: $15,000 (Y1), $20,000 (Y2), $25,000 (Y3), $30,000 (Y4)
• Reinvestment Rate: 10%
• Financing Rate: 8%

Using our calculator, the PV of outflows is simply the initial $50,000. The FV of the positive flows is calculated by compounding each to Year 4. This results in a MIRR of 20.58%. Since this rate is likely higher than the company’s hurdle rate, the project is attractive.

Example 2: Project with Mid-Term Outflow

This example shows how the combination approach handles non-conventional cash flows.

• Initial Investment: $100,000
• Cash Flows: $60,000 (Y1), -$20,000 (Y2), $70,000 (Y3), $80,000 (Y4)
• Reinvestment Rate: 12%
• Financing Rate: 9%

Here, the PV of outflows includes both the initial $100,000 and the present value of the $20,000 outflow in Year 2, discounted at 9%. The FV of inflows includes the future values of the cash flows from Years 1, 3, and 4. The resulting MIRR is 17.91%, providing a single, unambiguous rate of return. For a deeper dive, consider our guide on the Net Present Value (NPV) Calculator.

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How to Use This MIRR Calculator

1. Enter Initial Investment: Input the project’s upfront cost at Year 0 as a positive number.
2. Provide Cash Flows: In the text area, list the cash flows for each subsequent period, separated by commas. Use a negative sign for outflows (e.g., `500, -100, 600`).
3. Set Reinvestment Rate: Enter the annual rate (%) at which you expect to reinvest positive cash flows. This is often the firm’s cost of capital.
4. Set Financing Rate: Enter the annual rate (%) that reflects your cost of borrowing to finance the initial investment and any other outflows.
5. Review the Results: The calculator will instantly display the MIRR, along with the intermediate values for the Future Value of positive flows, the Present Value of all outflows, and the number of periods.
6. Analyze the Chart: The bar chart provides a quick visual of your project’s cash flow stream, helping you spot inflows and outflows over time.

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Key Factors That Affect MIRR

• Reinvestment Rate: A higher reinvestment rate will increase the future value of positive cash flows, leading to a higher MIRR. This is a crucial assumption that makes MIRR more realistic than IRR.
• Financing Rate: A higher financing rate increases the present value of outflows, which in turn lowers the MIRR. This rate reflects the cost of capital or borrowing.
• Timing of Cash Flows: Positive cash flows received earlier in a project’s life have more time to be reinvested and compound, leading to a higher FV and a higher MIRR.
• Magnitude of Cash Flows: Larger positive cash flows and smaller negative cash flows will naturally result in a more favorable (higher) MIRR.
• Project Length (n): For a profitable project, a longer duration generally allows for more compounding of reinvested cash flows, though the `(1/n)` component in the formula moderates this effect.
• Presence of Negative Cash Flows: Intermediate negative cash flows (outflows after Year 0) increase the total PV of outflows, thereby decreasing the MIRR. Proper handling of these is a key strength of the combination approach. Explore this further with our Discounted Cash Flow (DCF) Analysis tool.

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Frequently Asked Questions (FAQ)

1. Why is MIRR better than IRR?

MIRR is generally considered superior because it uses a more realistic reinvestment rate for cash inflows and avoids the multiple-IRR problem that can occur with projects having non-conventional cash flows.

2. What is a “good” MIRR?

A “good” MIRR is one that exceeds the company’s cost of capital or hurdle rate. There is no single magic number; it depends on the industry, risk of the project, and the company’s financial goals.

3. What’s the difference between the financing and reinvestment rates?

The financing rate is the cost to borrow funds for the project’s outflows. The reinvestment rate is the return earned on the project’s positive cash flows when they are put back into the business or other investments. Using two different rates is more realistic.

4. What if my project has no negative cash flows after the initial investment?

That is a common scenario. In that case, the “Present Value of Outflows” will simply be your initial investment, and the calculation proceeds as normal.

5. Can MIRR be negative?

Yes. A negative MIRR indicates that the project is expected to lose money, meaning the future value of your inflows is not enough to overcome the present value of your outflows.

6. How does the combination approach differ from other MIRR methods?

The combination approach is the most thorough, as it separates all outflows and inflows, discounting the former and compounding the latter. Other methods might only discount negative cash flows or only reinvest positive ones, but this one does both simultaneously for a complete picture. For comparative analysis, check our page on Capital Asset Pricing Model (CAPM).

7. Why are units (e.g., currency) important in the explanation but not a setting in the calculator?

The MIRR calculation is a ratio, so the result is a percentage that is independent of the currency used (e.g., $, €, ¥). As long as you use the same currency for all inputs, the final rate of return will be correct.

8. Where can I learn more about project valuation?

A great next step is to understand the Weighted Average Cost of Capital (WACC), which is often used as the discount rate in these calculations.

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Related Tools and Internal Resources

Expand your financial analysis toolkit with these related resources:

• IRR vs MIRR Explained: A detailed comparison of the two profitability metrics.
• Net Present Value (NPV) Calculator: Calculate the absolute value a project adds to a company.
• Discounted Cash Flow (DCF) Analysis: A comprehensive tool for valuing a company or project.
• Capital Asset Pricing Model (CAPM): Determine the expected return on an asset based on its risk.
• Weighted Average Cost of Capital (WACC): Calculate a firm’s blended cost of capital.
• Payback Period Calculator: Determine how long it takes for a project to recoup its initial investment.