MIRR Calculator (for BA II Plus Users)
A tool to calculate the Modified Internal Rate of Return, simulating the cash flow entry process of the TI BA II Plus financial calculator.
The rate at which positive cash flows are reinvested. Often the company’s cost of capital.
The interest rate paid on money used for negative cash flows (the cost of borrowing).
Cash Flows (CF)
Enter the initial investment as a negative value (CF₀). Subsequent cash flows can be positive (inflows) or negative (outflows).
Visual Cash Flow Analysis
| Period (n) | Cash Flow |
|---|
What is the Modified Internal Rate of Return (MIRR)?
The Modified Internal Rate of Return (MIRR) is a financial metric used to evaluate the attractiveness of an investment. It is an advancement on the standard Internal Rate of Return (IRR) because it resolves some of IRR’s main theoretical problems. Specifically, MIRR provides a more realistic measure of profitability by explicitly assuming that positive cash flows are reinvested at a different rate—typically the firm’s cost of capital—and that the initial project costs are financed at the firm’s financing cost.
This calculator helps you calculate MIRR using a BA II Plus-style workflow, where you input a series of cash flows, a reinvestment rate, and a financing rate. The standard IRR calculation assumes that all interim cash flows are reinvested at the IRR itself, which can be an unrealistic and overly optimistic assumption. MIRR provides a more conservative and achievable rate of return.
The MIRR Formula and Explanation
The formula to calculate MIRR brings all negative cash flows to their present value (at the start of the project) and all positive cash flows to their future value (at the end of the project). The rate that connects these two values is the MIRR. The formula is:
MIRR = ( (FVpositive cash flows / PVnegative cash flows)(1/n) ) – 1
Where:
- FVpositive cash flows is the Future Value of all positive cash flows, compounded at the reinvestment rate.
- PVnegative cash flows is the Present Value of all negative cash flows, discounted at the financing rate. This is treated as a positive value in the formula.
- n is the number of periods for the investment.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Cash Flows (CF) | The series of cash inflows (+) and outflows (-) from the project. | Currency ($) | Varies by project scale. |
| Reinvestment Rate | The rate used to compound positive cash flows to the end of the project. | Percentage (%) | 5% – 15% (often Cost of Capital) |
| Financing Rate | The rate used to discount negative cash flows to the beginning of the project. | Percentage (%) | 4% – 12% (often Cost of Debt) |
| n (Periods) | The total number of periods over which the investment occurs. | Years, Quarters | 1 – 30 |
Practical Examples of MIRR Calculation
Example 1: Standard Project
Imagine a project with an initial cost of $50,000. It is expected to generate cash flows of $15,000, $20,000, and $25,000 over the next three years. The company’s financing rate is 6%, and it can reinvest positive cash flows at 9%.
- Inputs: CF₀: -50000, CF₁: 15000, CF₂: 20000, CF₃: 25000
- Rates: Financing Rate: 6%, Reinvestment Rate: 9%
- Result: Using the MIRR formula, the project’s MIRR would be approximately 13.78%, indicating a healthy return over the cost of capital.
Example 2: Project with Mid-term Outflow
Consider a different project with an initial investment of $100,000. It returns $60,000 in Year 1, requires an additional outflow of $20,000 in Year 2 for an upgrade, and then returns $80,000 in Year 3. The financing rate is 7% and the reinvestment rate is 10%.
- Inputs: CF₀: -100000, CF₁: 60000, CF₂: -20000, CF₃: 80000
- Rates: Financing Rate: 7%, Reinvestment Rate: 10%
- Result: The MIRR for this project calculates to approximately 14.51%. Knowing what is MIRR helps in correctly assessing such complex cash flow streams.
How to Use This MIRR Calculator
This tool is designed to mimic the cash flow register function on a financial calculator like the TI BA II Plus.
- Enter Rates: Input the Reinvestment Rate and Financing Rate in the top two fields.
- Enter Initial Investment (CF₀): In the first cash flow field, enter your initial outlay. This must be a negative number.
- Enter Subsequent Cash Flows: Input the cash flow for each period (C01, C02, etc.). Use the “Add Cash Flow” button if you have more periods than are shown by default. Outflows should be negative, inflows positive.
- Review the Results: The calculator automatically updates the MIRR and the intermediate values (Future Value of Inflows and Present Value of Outflows).
- Analyze Visuals: The bar chart and cash flow table will update in real-time to give you a clear picture of your project’s financial timeline. This is crucial for understanding the difference between IRR and MIRR.
Key Factors That Affect MIRR
Several factors can significantly influence the result of a MIRR calculation. Understanding them is key to a robust financial analysis.
- Reinvestment Rate: This is one of the most significant factors. A higher reinvestment rate will lead to a higher Future Value of inflows, thus increasing the MIRR.
- Financing Rate: A higher financing rate increases the Present Value of outflows, which in turn lowers the MIRR.
- Magnitude of Cash Flows: Larger positive cash flows will naturally increase the MIRR, while larger negative cash flows will decrease it.
- Timing of Cash Flows: Positive cash flows received earlier have more time to be reinvested, leading to a higher future value and a higher MIRR. The timing is a key differentiator when analyzing MIRR vs IRR.
- Project Length (n): A longer project gives more time for positive cash flows to compound, but it also means the final return is spread over more periods, which can have a complex effect on the final percentage.
- Initial Investment Size: A larger initial investment (the main component of PV of outflows) requires a much larger return to achieve the same MIRR percentage.
Frequently Asked Questions (FAQ)
The main difference is the reinvestment rate assumption. IRR assumes cash flows are reinvested at the IRR itself, which can be unrealistic. MIRR allows you to specify a more practical reinvestment rate, such as the company’s cost of capital, making it a more conservative and often more accurate measure of a project’s true return.
In cash flow analysis, a negative value represents a cash outflow (money being spent), and a positive value represents a cash inflow (money being received). The initial investment is an outflow to start the project, so it is entered as a negative number.
The financing rate should reflect your cost of borrowing money (e.g., the interest rate on a loan). The reinvestment rate should reflect the return you can realistically expect to earn on the project’s positive cash flows. Many firms use their Weighted Average Cost of Capital (WACC) as the reinvestment rate.
Yes. A negative MIRR indicates that the project is expected to lose money, even after accounting for the reinvestment of positive cash flows. It means the future value of your inflows is not enough to overcome the present value of your outflows.
While the BA II Plus doesn’t have a dedicated MIRR button, you calculate it in a multi-step process: first, you find the future value of all inflows at the reinvestment rate. Second, you find the present value of all outflows at the financing rate. Finally, you use these values as FV and PV in a standard Time Value of Money (TVM) calculation to solve for the interest rate (I/Y), which is the MIRR. This calculator automates that exact process.
A conventional cash flow stream has one initial outflow followed by a series of inflows. A non-conventional stream has more than one sign change (e.g., outflow, inflow, outflow, inflow). IRR can produce multiple results for such streams, but MIRR always produces a single, unambiguous result, which is a major advantage.
Generally, when comparing mutually exclusive projects, the one with the higher MIRR is considered more attractive, assuming it is above the cost of capital. However, it shouldn’t be the only metric used. You should also consider NPV, payback period, and the scale of the investment.
The main limitation is that it requires the user to estimate a reinvestment rate, which can be subjective. While it’s more realistic than IRR’s assumption, the accuracy of the MIRR is dependent on the accuracy of this estimated rate.