MIRR Calculator (for HP 10bii Users)
Calculate the Modified Internal Rate of Return for complex cash flows.
The initial cost of the project. Enter as a positive number.
The rate at which positive cash flows are reinvested (e.g., WACC).
The interest rate paid on money used for negative cash flows (cost of borrowing).
Investment vs. Returns
This chart visualizes the comparison between the Present Value of all costs and the Future Value of all positive cash flows.
What is the Modified Internal Rate of Return (MIRR)?
The Modified Internal Rate of Return (MIRR) is a financial metric used in capital budgeting to measure the profitability of a potential investment. It’s considered a more realistic measure than the standard Internal Rate of Return (IRR) because it addresses two of IRR’s main flaws: the assumption that interim cash flows are reinvested at the project’s own IRR, and the potential for multiple IRR values for projects with non-conventional cash flows (i.e., multiple sign changes).
MIRR provides a single, unambiguous answer by explicitly assuming that positive cash flows are reinvested at a different rate (typically the company’s cost of capital or reinvestment rate), and that any negative cash flows are financed at the company’s financing rate. This makes it an essential tool for finance professionals, including those who frequently calculate MIRR using an HP 10bii or similar financial calculator, to compare projects of different sizes and durations more accurately.
The MIRR Formula and Explanation
The formula for MIRR might look complex, but it’s based on a straightforward concept: find the rate of return that equates the present value of all costs with the future value of all returns. The general formula is:
MIRR = ( FV(Positive Cash Flows) / PV(Negative Cash Flows) )(1/n) – 1
The calculation process involves three key steps:
- Calculate the Present Value (PV) of all negative cash flows. This includes the initial investment (at period 0) and any subsequent outflows. These are discounted back to time 0 using the Finance Rate.
- Calculate the Future Value (FV) of all positive cash flows. These cash inflows are compounded forward to the end of the project’s life using the Reinvestment Rate.
- Solve for the MIRR. The rate that makes the future value of the inflows equal to the present value of the outflows over ‘n’ periods is the MIRR. Our NPV calculator can provide further context on discounting.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| PV(Negative Cash Flows) | Present Value of all investment costs, discounted at the finance rate. | Currency ($) | Positive Value (representing total cost) |
| FV(Positive Cash Flows) | Future Value (Terminal Value) of all income, compounded at the reinvestment rate. | Currency ($) | Positive Value |
| n | Total number of periods for the investment. | Time (Years, Months) | 1 – 50+ |
| Finance Rate | The cost of borrowing funds for the investment. | Percentage (%) | 2% – 15% |
| Reinvestment Rate | The rate of return for reinvesting positive cash flows. Often the WACC. | Percentage (%) | 5% – 20% |
Practical Examples
Example 1: Manufacturing Plant Expansion
A company is considering a project with a high initial cost and steady returns. The financial details are as follows:
- Inputs:
- Initial Investment: $250,000
- Cash Flow Year 1: $60,000
- Cash Flow Year 2: $75,000
- Cash Flow Year 3: $80,000
- Cash Flow Year 4: $85,000
- Cash Flow Year 5: $90,000
- Reinvestment Rate: 10%
- Finance Rate: 6%
- Results:
- Using this calculator, you’d find the MIRR is approximately 15.65%. Since this is likely higher than the company’s hurdle rate, the project is attractive. This calculation is a key part of any solid guide to capital budgeting.
Example 2: Project with Mid-term Investment
Some projects require additional investment during their lifecycle. An HP 10bii calculator handles this by inputting a negative cash flow. Our calculator does the same.
- Inputs:
- Initial Investment: $50,000
- Cash Flow Year 1: $30,000
- Cash Flow Year 2: -$10,000 (an additional required investment)
- Cash Flow Year 3: $40,000
- Reinvestment Rate: 12%
- Finance Rate: 7%
- Results:
- The PV of outflows includes the initial $50,000 and the discounted value of the $10,000 outflow. The FV of inflows compounds the positive flows. The resulting MIRR is approximately 13.91%. This demonstrates a more complex scenario where standard IRR could be misleading. You can explore similar concepts with our IRR calculator.
How to Use This MIRR Calculator
This calculator is designed to be as intuitive as using an HP 10bii financial calculator for cash flow analysis. Follow these steps to get your MIRR:
- Enter Initial Investment: Input the total upfront cost of the project as a positive number in the “Initial Investment (CF0)” field.
- Set the Rates: Enter the “Reinvestment Rate” (the return you expect on reinvested profits) and the “Finance Rate” (the cost of borrowing) as percentages.
- Input Cash Flows: Enter the periodic cash flows. The calculator starts with four fields. Use the “Add Cash Flow” button to add more periods or “Remove Last” to shorten the project timeline. Enter negative cash flows with a minus sign (e.g., -5000).
- Review the Results: The MIRR is automatically calculated and displayed at the top. You’ll also see key intermediate values: the future value of all inflows, the present value of all outflows, and the total number of periods.
- Interpret the Chart: The bar chart provides a quick visual comparison of the total cost versus the total compounded return, giving you an at-a-glance view of the project’s scale.
Key Factors That Affect MIRR
The MIRR is sensitive to several inputs, which is why it’s a powerful analysis tool. Understanding these factors is crucial for anyone looking to calculate MIRR using an HP 10bii or this web tool.
- Reinvestment Rate: This is the most significant departure from IRR. A higher reinvestment rate will lead to a higher MIRR, as it assumes positive cash flows are put to better use.
- Finance Rate: A higher finance rate increases the present value of any negative cash flows after the initial investment, thus lowering the MIRR.
- Timing of Cash Flows: Early positive cash flows have more time to be reinvested, so they contribute more to the future value and increase the MIRR. This is a core concept in time value of money, further explained in our HP 10bii tutorial.
- Magnitude of Cash Flows: Larger positive cash flows will naturally increase the MIRR, assuming all other factors are constant.
- Project Length (n): A longer project gives more time for cash flows to be reinvested, but the `(1/n)` exponent in the formula means the effect can be complex. Typically, sustained positive cash flows over a longer period yield a more stable return.
- Presence of Negative Cash Flows: Additional investments (negative cash flows) during the project’s life increase the total present value of outflows, which will decrease the MIRR. This is a critical factor that makes MIRR superior to IRR, which can struggle with multiple negative flows. A payback period calculator can offer another perspective on risk.
Frequently Asked Questions (FAQ)
1. Why is MIRR better than IRR?
MIRR is generally considered superior to the Internal Rate of Return (IRR) because it makes more realistic assumptions. IRR assumes cash flows are reinvested at the project’s own (often high) IRR, while MIRR allows you to specify a more practical reinvestment rate, like the company’s cost of capital. MIRR also guarantees a single solution, avoiding the multiple-IRR problem. This is a key reason for its inclusion in advanced financial analysis, like that taught in our what is reinvestment risk guide.
2. What should I use for the reinvestment rate?
A common and conservative 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 assets. Using WACC provides a realistic view of how the project’s proceeds would likely be used elsewhere in the business.
3. What is the finance rate?
The finance rate is the interest rate the company pays on borrowed funds. It’s used to discount any negative cash flows that occur after the initial investment, reflecting the cost of financing those specific outlays.
4. How does this calculator compare to an HP 10bii?
This calculator automates the same underlying process you would use to calculate MIRR using an HP 10bii. On an HP 10bii, you would typically calculate the NPV of inflows, find their FV, and then solve for the rate that equates that FV to the initial investment. This tool performs those steps instantly in the background.
5. What does a negative MIRR mean?
A negative MIRR means that the project is expected to lose money. The total costs (present value of outflows) are greater than the expected returns (future value of inflows), even after accounting for reinvestment. These projects should generally be rejected.
6. Can I use this for uneven cash flow periods?
This calculator assumes that cash flows occur at regular, periodic intervals (e.g., annually). It is not designed for irregularly timed cash flows, which would require a more complex discounting/compounding formula based on specific dates.
7. What is the ‘Terminal Value of Inflows’?
This is another name for the Future Value (FV) of all positive cash flows. It represents the single lump sum value that all your project’s earnings would grow to by the end of the project’s life, assuming they are reinvested at the specified reinvestment rate.
8. What if my project has no positive cash flows?
If there are no positive cash flows, the MIRR cannot be calculated, as the Future Value of inflows would be zero. The calculator will show an error or a nonsensical result, as a return cannot be generated from a project that only costs money.