MIRR Calculator: How to Find MIRR on a Financial Calculator

Modified Internal Rate of Return (MIRR) Calculator

Modified Internal Rate of Return (MIRR)

0.00%

Future Value of Inflows

$0

Present Value of Outflows

$0

Number of Periods

0

MIRR = ( (Future Value of Inflows / Present Value of Outflows)^(1/n) ) – 1

Period	Cash Flow	Future Value (at Reinvestment Rate)	Present Value (at Finance Rate)

Breakdown of cash flows and their respective future or present values.

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

The Modified Internal Rate of Return, or MIRR, is a financial metric used in capital budgeting and corporate finance to estimate the profitability of a potential investment. It is a modification of the standard Internal Rate of Return (IRR) and serves to resolve some of the main problems with the IRR. Knowing how to find MIRR on a financial calculator provides a more realistic measure of a project’s return by explicitly assuming that positive cash flows are reinvested at a firm’s cost of capital, and that the initial outlays are financed at the firm’s financing cost.

Who Should Use It?

Financial analysts, corporate planners, and investors should use MIRR to rank and select between mutually exclusive projects. If a project’s MIRR is greater than the established hurdle rate (often the weighted average cost of capital, WACC), the project is considered a good investment. When comparing projects, the one with the higher MIRR is generally more desirable. Learning how to find MIRR on a financial calculator is a vital skill for anyone making long-term investment decisions.

Common Misconceptions

A primary misconception is that MIRR and IRR are interchangeable. The IRR assumes that all future cash flows are reinvested at the IRR itself, which can be an unrealistically high rate, leading to an overly optimistic view of a project’s potential. MIRR corrects this by allowing for a more practical, and typically lower, reinvestment rate, thus providing a more conservative and achievable return figure. Another issue with IRR is that it can yield multiple solutions for projects with non-conventional cash flows (i.e., multiple changes in the sign of cash flows), a problem that MIRR resolves by providing a single, unambiguous result.

MIRR Formula and Mathematical Explanation

The process of how to find MIRR on a financial calculator or manually involves three main steps. First, calculate the present value of all negative cash flows (outflows) discounted at the financing rate. Second, calculate the future value of all positive cash flows (inflows) compounded at the reinvestment rate. Finally, use these values to find the rate of return that equates the future value of inflows with the present value of outflows.

The formula is expressed as:

MIRR = ( FV_inflows / PV_outflows )^(1/n) – 1

Step-by-Step Derivation:

1. Calculate PV of Outflows: Sum the present values of all negative cash flows. The initial investment (at period 0) is already at its present value. Subsequent negative flows are discounted using the finance rate: PV_outflows = Σ [ CF^–_t / (1 + FinanceRate)^t ] for t=0 to n.
2. Calculate FV of Inflows: Sum the future values of all positive cash flows. Each positive cash flow is compounded to the end of the project’s life using the reinvestment rate: FV_inflows = Σ [ CF⁺_t * (1 + ReinvestRate)^(n-t) ] for t=0 to n.
3. Calculate MIRR: With the total PV of outflows and FV of inflows, solve for the MIRR. The formula finds the rate that makes the present value of the terminal value equal to the present value of the initial investment.

Variables Table

Variable	Meaning	Unit	Typical Range
FVinflows	Future Value of all positive cash flows	Currency ($)	> 0
PVoutflows	Present Value of all negative cash flows	Currency ($)	> 0 (as an absolute value)
n	Total number of periods in the project’s life	Count (e.g., years)	1 – 50+
Finance Rate	The cost of borrowing funds	Percentage (%)	2% – 15%
Reinvestment Rate	The rate at which cash inflows are reinvested	Percentage (%)	5% – 20%

Practical Examples (Real-World Use Cases)

Example 1: New Manufacturing Plant

A company is considering building a new plant. The initial investment is $5 million. It expects cash inflows of $1.5M, $2M, $2.5M, $3M, and $3.5M over the next five years. The company’s finance rate is 6%, and it can reinvest profits at a rate of 9%.

• Inputs:
  • Cash Flows: -5000000, 1500000, 2000000, 2500000, 3000000, 3500000
  • Finance Rate: 6%
  • Reinvestment Rate: 9%
• Calculation:
  • The PV of outflows is simply the initial $5M.
  • The FV of inflows is calculated by compounding each positive cash flow to year 5 at 9%.
  • Using the MIRR formula, the resulting MIRR might be around 19.8%.
• Interpretation: If the company’s hurdle rate is 15%, a MIRR of 19.8% indicates this is a financially attractive project and should be accepted. It shows a realistic return after considering financing and reinvestment realities.

Example 2: Real Estate Development

A developer is looking at a project with an initial land purchase and construction cost of $2 million (Year 0). They expect further capital outlay of $500,000 in Year 1 for marketing. From Year 2, they expect net rental income of $400k, $500k, and finally sell the property at the end of Year 4 for $3 million (total inflow in Year 4 is $3.5M).

• Inputs:
  • Cash Flows: -2000000, -500000, 400000, 500000, 3500000
  • Finance Rate: 7% (cost of their construction loan)
  • Reinvestment Rate: 5% (rate they can get on other stable investments)
• Calculation:
  • PV of outflows = $2,000,000 + ($500,000 / 1.07^1) = $2,467,289.
  • FV of inflows = ($400,000 * 1.05^2) + ($500,000 * 1.05^1) + $3,500,000 = $441,000 + $525,000 + $3,500,000 = $4,466,000.
  • MIRR = (($4,466,000 / $2,467,289)^(1/4)) – 1 = 16.03%.
• Interpretation: A 16.03% MIRR is a strong return for a real estate project. This gives the developer confidence in the project’s profitability, especially when compared to other potential developments. Learning how to find MIRR on a financial calculator is essential for this type of analysis.

How to Use This MIRR Calculator

This calculator simplifies the process of how to find MIRR on a financial calculator. Follow these steps for an accurate result:

1. Enter Cash Flows: In the “Cash Flows” text area, input the sequence of cash flows for your project, separated by commas. The first number must be the initial investment and should be negative. For example: -100000, 25000, 30000, 35000, 40000.
2. Set the Finance Rate: Enter the interest rate your company pays on borrowed funds into the “Finance Rate” field. This is used to discount any negative cash flows that occur after the initial investment.
3. Set the Reinvestment Rate: In the “Reinvestment Rate” field, enter the rate at which you expect to reinvest the positive cash flows generated by the project. This is often the company’s cost of capital.
4. Read the Results: The calculator automatically updates. The main result, the MIRR, is displayed prominently. You can also view key intermediate values: the total Future Value of Inflows, the total Present Value of Outflows, and the Number of Periods.
5. Analyze the Chart and Table: Use the dynamic chart and cash flow table to visualize the project’s financial structure and understand how the final MIRR was derived.

Key Factors That Affect MIRR Results

The final MIRR figure is sensitive to several key inputs. Understanding these factors is a crucial part of knowing how to find MIRR on a financial calculator effectively.

• Reinvestment Rate: This is one of the most significant factors. A higher reinvestment rate will lead to a higher future value of inflows, directly increasing the MIRR. This rate should realistically reflect the opportunities available for reinvesting profits.
• Finance Rate: This rate affects the present value of any negative cash flows that occur after time zero. A higher finance rate will decrease the PV of these outflows, which can surprisingly increase the MIRR if there are significant negative flows in later years.
• Timing of Cash Flows: Positive cash flows received earlier in the project’s life have more time to be compounded at the reinvestment rate, leading to a higher FV of inflows and a higher MIRR. Conversely, later-arriving inflows have less impact.
• Magnitude of Cash Flows: Larger positive cash flows will naturally lead to a higher MIRR, all else being equal. The size of the initial investment is also critical; a smaller initial outlay for the same returns will yield a much higher MIRR.
• Project Duration (Number of Periods): A longer project gives more time for positive cash flows to be reinvested and grow. However, the MIRR formula takes the ‘nth’ root, where ‘n’ is the project duration, which means the annualized return can be lower for very long projects even if the total return is high.
• Presence of Non-Conventional Cash Flows: If a project has negative cash flows in later years (e.g., for decommissioning costs), the finance rate becomes very important. These outflows are discounted, and their impact on the total PV of outflows will directly affect the final MIRR. This is a key reason how to find MIRR on a financial calculator is superior to basic IRR.

Frequently Asked Questions (FAQ)

1. Why is MIRR better than IRR?

MIRR is generally considered superior to IRR for two main reasons: 1) It uses a more realistic reinvestment rate for cash inflows instead of assuming they are reinvested at the project’s IRR. 2) It avoids the problem of multiple IRRs for projects with non-conventional cash flows.

2. What is a good MIRR?

A “good” MIRR is one that exceeds the company’s cost of capital or a predetermined hurdle rate. There is no single number, as it depends on the industry, risk of the project, and economic conditions. However, if MIRR > Cost of Capital, the project is expected to create value.

3. Can MIRR be negative?

Yes, a MIRR can be negative. This indicates that the project is expected to lose money, even after accounting for the time value of money. A negative MIRR means the future value of the cash inflows is not enough to cover the present value of the cash outflows.

4. What should I use for the reinvestment rate?

The most common and theoretically sound choice for the reinvestment rate is the company’s Weighted Average Cost of Capital (WACC). This represents the average rate of return the company expects to earn on its investments.

5. And what about the finance rate?

The finance rate should be the company’s cost of borrowing. If the project is financed with debt, this would be the interest rate on the loan. If it’s financed with a mix of debt and equity, the WACC could also be used here for simplicity, though a specific borrowing cost is more accurate.

6. How does MIRR compare to Net Present Value (NPV)?

Both are sound capital budgeting techniques. NPV gives an absolute dollar value that a project is expected to add to the firm, while MIRR gives a percentage rate of return. NPV is often preferred for deciding between mutually exclusive projects of different scales, but MIRR is excellent for assessing the efficiency of an investment and is easier to interpret for many managers. Proficient analysts know how to find MIRR on a financial calculator and also how to calculate NPV.

7. What are the main limitations of MIRR?

The primary limitation is that it relies on estimates for the finance and reinvestment rates, which can be subjective. It also doesn’t quantify the absolute value a project adds (unlike NPV), which can be misleading when comparing projects of vastly different sizes.

8. What does it mean if my calculator gives an error?

An error in a MIRR calculation typically occurs if the present value of outflows is zero or negative (which is impossible if there’s an initial investment) or if the future value of inflows is zero or negative. This implies the project never generates a positive return. Ensure your cash flows are entered correctly, with the initial investment as a negative number.