MIRR Calculator: Modified Internal Rate of Return with Reinvestment

MIRR Input Parameters

Project Cash Flows

Enter the cash flows for each period. The first period is usually the initial investment (negative), followed by subsequent positive or negative flows.

Calculation Results

Formula Used:
MIRR = [ ( FV of positive cash flows / PV of negative cash flows ) ^ (1 / Number of periods) ] – 1
Where FV and PV are calculated using the Reinvestment Rate and Financing Rate respectively.

Cash Flow Summary

Cash Flow Summary (Currency: USD)

Period	Cash Flow	Reinvested Value (End of Project)	Financed Value (Start of Project)

Understanding MIRR: The Reinvestment Approach

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

The Modified Internal Rate of Return (MIRR) is a financial metric used to evaluate the profitability of an investment or project. Unlike the traditional Internal Rate of Return (IRR), MIRR addresses a critical flaw by explicitly considering the reinvestment rate of positive cash flows and the financing rate of negative cash flows. This makes it a more realistic and often preferred measure for investment appraisal, especially when dealing with projects that have uneven cash flow patterns or when the assumptions about reinvesting intermediate profits are crucial.

MIRR is particularly valuable for project managers, financial analysts, and investors who need to compare mutually exclusive projects or make decisions about capital allocation. It provides a single, easily interpretable rate that represents the project’s overall return, taking into account the cost of capital and the assumed rate at which profits can be put back to work.

MIRR Formula and Explanation

The calculation of MIRR involves several steps. First, all positive cash flows are compounded forward to the end of the project’s life using the assumed Reinvestment Rate. Second, all negative cash flows (including the initial investment) are discounted back to the beginning of the project’s life using the assumed Financing Rate. Finally, MIRR is calculated as the rate that equates the present value of the negative cash flows to the future value of the positive cash flows.

The core formula is derived from equating the future value of inflows to the future value of outflows:

Future Value of Positive Cash Flows = Present Value of Negative Cash Flows * (1 + MIRR) ^ Number of Periods

Rearranging to solve for MIRR:

MIRR = [ ( FV of positive cash flows / PV of negative cash flows ) ^ (1 / Number of periods) ] - 1

Variables Explained:

MIRR Calculation Variables

Variable	Meaning	Unit	Typical Assumption
Initial Investment Cost	The total upfront capital outlay required to start the project.	Currency	A single, usually negative, value at Period 0.
Project Cash Flows	Net cash generated or consumed in each period of the project’s life.	Currency	Can be positive (inflows) or negative (outflows).
Reinvestment Rate	The rate at which positive net cash flows generated by the project are assumed to be reinvested. Often assumed to be the company’s cost of capital or a target rate.	Percentage (%)	e.g., 8%, 10%, 12%.
Financing Rate	The rate at which negative net cash flows (including the initial investment) are financed. Often assumed to be the company’s cost of borrowing or cost of capital.	Percentage (%)	e.g., 6%, 8%, 10%.
Number of Periods (n)	The total duration of the project, typically in years.	Years	Count of cash flow periods.
Future Value (FV) of Positive Cash Flows	The total value of all positive cash flows compounded to the end of the project at the reinvestment rate.	Currency	Calculated using compound interest formula.
Present Value (PV) of Negative Cash Flows	The total value of all negative cash flows discounted back to the beginning of the project at the financing rate.	Currency	Calculated using present value formula.
MIRR	The effective rate of return that equates the compounded positive cash flows to the discounted negative cash flows.	Percentage (%)	The primary output metric.

How to Use This MIRR Calculator

Using this MIRR calculator is straightforward:

1. Initial Investment Cost: Enter the total amount spent at the very beginning of the project (Period 0). This should be a positive number representing the cost.
2. Reinvestment Rate: Input the percentage rate at which you assume positive cash flows generated by the project can be reinvested.
3. Financing Rate: Enter the percentage rate at which you assume negative cash flows (including the initial investment) need to be financed.
4. Project Cash Flows:
   • Start by entering the cash flow for Period 0. This is typically the negative of your initial investment cost.
   • Click “Add Period” to add subsequent periods.
   • For each new period, enter the expected net cash flow (positive for inflows, negative for outflows).
5. Calculate MIRR: Click the “Calculate MIRR” button.
6. Interpret Results: The calculator will display the MIRR, the Future Value of positive cash flows, the Present Value of negative cash flows, the Number of Periods, Net Future Value, and Net Present Value (at the financing rate).
7. Reset: Click “Reset” to clear all fields and start over.
8. Copy Results: Use the “Copy Results” button to quickly save the calculated figures.

Ensure your Reinvestment Rate and Financing Rate reflect realistic assumptions based on your company’s cost of capital, hurdle rates, or borrowing costs.

Practical Examples

Let’s illustrate with two scenarios:

Example 1: A Simple Project with Positive Returns

• Initial Investment Cost: $100,000
• Reinvestment Rate: 10%
• Financing Rate: 8%
• Cash Flows:
  • Period 0: -$100,000
  • Period 1: $30,000
  • Period 2: $40,000
  • Period 3: $50,000

Calculation:

• FV of Positive Cash Flows: ($30,000 * (1.10)^2) + ($40,000 * (1.10)^1) + $50,000 = $36,300 + $44,000 + $50,000 = $130,300
• PV of Negative Cash Flows: ($100,000 / (1.08)^0) = $100,000
• Number of Periods (n): 3
• MIRR: [ ($130,300 / $100,000) ^ (1/3) ] – 1 = [1.303 ^ 0.3333] – 1 = 1.0925 – 1 = 0.0925 or 9.25%

Interpretation: This project is expected to yield a return of 9.25%, considering how its profits are reinvested and its costs are financed.

Example 2: A Project with Mixed Cash Flows

• Initial Investment Cost: $200,000
• Reinvestment Rate: 12%
• Financing Rate: 9%
• Cash Flows:
  • Period 0: -$200,000
  • Period 1: $50,000
  • Period 2: -$30,000 (unexpected cost)
  • Period 3: $100,000
  • Period 4: $120,000

Calculation:

• FV of Positive Cash Flows: ($50,000 * (1.12)^3) + ($100,000 * (1.12)^1) + $120,000 = $70,240 + $112,000 + $120,000 = $302,240
• PV of Negative Cash Flows: ($200,000 / (1.09)^0) + ($30,000 / (1.09)^2) = $200,000 + ($30,000 / 1.1881) = $200,000 + $25,250.32 = $225,250.32
• Number of Periods (n): 4
• MIRR: [ ($302,240 / $225,250.32) ^ (1/4) ] – 1 = [1.3417 ^ 0.25] – 1 = 1.0765 – 1 = 0.0765 or 7.65%

Interpretation: Even though the project has large positive flows, the intermediate negative flow and the chosen rates lead to a MIRR of 7.65%. This might be acceptable or not, depending on the company’s hurdle rate.

Key Factors Affecting MIRR

1. Magnitude and Timing of Cash Flows: Larger and earlier positive cash flows, and smaller and later negative cash flows, will generally lead to a higher MIRR.
2. Reinvestment Rate Assumption: A higher reinvestment rate significantly boosts the future value of positive cash flows, thus increasing MIRR. This highlights the importance of realistic reinvestment opportunities.
3. Financing Rate Assumption: A lower financing rate reduces the present value of negative cash flows, thus increasing MIRR. This reflects the cost of capital or borrowing costs.
4. Project Duration (Number of Periods): Longer projects can have different impacts depending on the pattern of cash flows. A higher exponent (1/n) for a MIRR greater than 1 will decrease the MIRR, and vice-versa.
5. Initial Investment Size: While a larger initial investment can lead to larger absolute returns, it also increases the denominator in the PV of negative cash flows, potentially lowering the MIRR if other factors don’t compensate.
6. Project Scale vs. Rate of Return: MIRR provides a rate, but it doesn’t inherently indicate the scale of the project. A project with a high MIRR but small cash flows might be less desirable than a project with a slightly lower MIRR but substantially larger absolute returns (NPV).

Common Misconceptions and Why MIRR is Preferred Over IRR

The primary advantage of MIRR over IRR lies in its more realistic assumptions. The standard IRR calculation implicitly assumes that all intermediate positive cash flows are reinvested at the IRR itself. This can lead to unrealistic results, especially for projects with high IRRs, as reinvesting at such high rates might not be feasible.

MIRR overcomes this by allowing separate, explicit assumptions for reinvestment rates (for positive cash flows) and financing rates (for negative cash flows). This provides a more accurate picture of a project’s true profitability, especially in diverse economic conditions or when comparing projects with significantly different cash flow timings.

FAQ about MIRR Calculation

What is the difference between IRR and MIRR?

The main difference is how intermediate cash flows are treated. IRR implicitly assumes reinvestment at the IRR itself, which can be unrealistic. MIRR allows for explicit, separate rates for reinvesting positive cash flows (Reinvestment Rate) and financing negative cash flows (Financing Rate), making it more practical.

Can MIRR be higher than IRR?

Yes, it’s possible. If the reinvestment rate is set higher than the IRR, the FV of positive cash flows will be higher, potentially leading to a higher MIRR. Conversely, if the financing rate is lower than the IRR, the PV of negative cash flows will be lower, also potentially increasing MIRR.

What are typical values for the Reinvestment Rate and Financing Rate?

Commonly, these rates are set to the company’s Weighted Average Cost of Capital (WACC), its target hurdle rate, or its borrowing cost. The choice depends on the specific context and the assumptions management wants to make about reinvestment opportunities and funding costs.

Does MIRR handle multiple sign changes in cash flows?

Yes, MIRR is generally better equipped to handle projects with multiple sign changes in cash flows compared to IRR, which can sometimes yield multiple solutions or no solution in such cases.

What does a MIRR equal to the Financing Rate mean?

If the MIRR is equal to the Financing Rate, it implies that the project’s return is just enough to cover its financing costs. The NPV at the financing rate would likely be zero or very close to it.

What does a MIRR equal to the Reinvestment Rate mean?

If the MIRR equals the Reinvestment Rate, it suggests the project’s returns are aligning with the assumed rate at which its profits can be put back to work.

How is Net Present Value (NPV) related to MIRR?

While MIRR is a rate, NPV is a dollar value. A project is generally considered acceptable if its MIRR exceeds the financing rate (or cost of capital) and its NPV is positive. The NPV calculated at the financing rate provides a measure of the absolute value creation.

Can the Reinvestment Rate be different from the Financing Rate?

Absolutely, and this is a key strength of MIRR. A company might borrow money at 7% (Financing Rate) but have opportunities to reinvest surplus cash at 12% (Reinvestment Rate). MIRR allows you to model these distinct rates.

Related Financial Tools

• NPV Calculator
• IRR Calculator
• Payback Period Calculator
• Discounted Cash Flow (DCF) Analysis Guide
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