MIRR Calculator: How to Find MIRR on a Financial Calculator
Enter the total cost of the investment as a positive number (e.g., 100000).
Enter comma-separated values for each period (e.g., 30000, 40000, 50000). Use negative for outflows.
The rate at which positive cash flows are reinvested. Often the firm’s cost of capital.
The interest rate paid on money borrowed to finance the project (for negative 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 an investment. As its name suggests, it is a modification of the more commonly known Internal Rate of Return (IRR) and is designed to resolve some of the main problems with IRR. Specifically, MIRR provides a more realistic measure by making explicit assumptions about the reinvestment rate for positive cash flows and the financing rate for negative cash flows.
Unlike IRR, which assumes that all cash flows generated by a project are reinvested at the IRR itself, MIRR allows for a more practical scenario where cash inflows are reinvested at a rate closer to the company’s cost of capital. This distinction makes knowing how to find MIRR on a financial calculator a crucial skill for analysts seeking a more accurate assessment of a project’s viability.
The MIRR Formula and Explanation
The calculation for MIRR involves three main steps: finding the present value of all negative cash flows (outflows), finding the future value of all positive cash flows (inflows), and then calculating the rate that equates the two. The formula is as follows:
MIRR = [ (FVinflows / PVoutflows)(1/n) ] – 1
This formula shows how to find the MIRR and is less complex than it appears. It represents the compound annual growth rate that the investment is expected to generate.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| FVinflows | The Future Value of all positive cash flows, compounded to the end of the project’s life at the reinvestment rate. | Currency ($) | Positive Value |
| PVoutflows | The Present Value (as an absolute value) of all negative cash flows, discounted to Year 0 at the financing rate. | Currency ($) | Positive Value |
| n | The total number of periods for the investment (typically years). | Integer | 1 – 50+ |
Practical Examples
Example 1: Standard Project
A company is considering a project with an initial outlay of $100,000. It is expected to generate cash flows of $30,000, $40,000, $50,000, and $20,000 over the next four years. The company’s financing rate is 6% and its reinvestment rate is 8%.
- Inputs:
- Initial Investment: $100,000
- Cash Flows: 30000, 40000, 50000, 20000
- Reinvestment Rate: 8%
- Financing Rate: 6%
- Result: Using the calculator, the MIRR is approximately 14.59%. Since this is likely higher than the company’s hurdle rate, the project would be considered attractive.
Example 2: Project with a Negative Flow
Consider a project with a $250,000 initial investment. The cash flows are $80,000 (Year 1), $100,000 (Year 2), $120,000 (Year 3), but requires an additional outflow of $30,000 in Year 4 for decommissioning, followed by a final inflow of $60,000 in Year 5. The finance rate is 7% and the reinvestment rate is 10%.
- Inputs:
- Initial Investment: $250,000
- Cash Flows: 80000, 100000, 120000, -30000, 60000
- Reinvestment Rate: 10%
- Financing Rate: 7%
- Result: The MIRR for this project is calculated to be 11.53%. This example shows how MIRR capably handles non-conventional cash flows, a major advantage over IRR.
How to Use This MIRR Calculator
Using this calculator to find the MIRR is straightforward. Follow these steps:
- Enter Initial Investment: Input the initial cost of the project at Year 0 as a positive number.
- Enter Cash Flows: Provide the series of expected cash flows, separated by commas. Use positive numbers for inflows (profits) and negative numbers for outflows (costs).
- Set Reinvestment Rate: Enter the rate at which you assume positive cash flows will be reinvested. This is often the company’s Weighted Average Cost of Capital (WACC).
- Set Financing Rate: Input the rate at which the company borrows funds. This is used to discount any negative cash flows.
- Interpret the Results: The calculator will instantly show the MIRR. A project is generally accepted if its MIRR is greater than the hurdle rate or WACC. The intermediate values (FV of Inflows, PV of Outflows) are also provided for transparency.
Key Factors That Affect MIRR
Several factors can influence a project’s MIRR. Understanding them is key to a robust financial analysis.
- Initial Investment Size: A larger initial outflow requires larger subsequent inflows to achieve the same MIRR.
- Timing of Cash Flows: Inflows received earlier are more valuable as they can be reinvested for a longer period, thus increasing the FV of inflows and boosting the MIRR.
- Magnitude of Cash Flows: Simply put, larger positive cash flows will lead to a higher MIRR, all else being equal.
- The Reinvestment Rate: This is a critical assumption. A higher reinvestment rate will increase the future value of positive cash flows, leading to a higher MIRR. This is a primary differentiator from IRR.
- The Financing Rate: A higher financing rate increases the present value of any future negative cash flows, which in turn lowers the MIRR.
- Project Length (Number of Periods): A longer project provides more time for compounding, but the impact depends on the balance and timing of the cash flows throughout its life.
Frequently Asked Questions (FAQ)
- 1. What is the main difference between IRR and MIRR?
- The primary difference is the reinvestment assumption. IRR assumes cash flows are reinvested at the IRR itself, which can be unrealistically high. MIRR allows you to specify a more realistic reinvestment rate, such as the firm’s cost of capital.
- 2. Why are the finance and reinvestment rates different?
- They represent different economic realities. The finance rate is the cost of borrowing money (a cost), while the reinvestment rate is the return earned on invested capital (a gain). It’s rare for these two rates to be the same for a company.
- 3. What is a good MIRR?
- A “good” MIRR is one that is higher than the company’s cost of capital or a predetermined “hurdle rate.” If MIRR > Cost of Capital, the project is expected to add value.
- 4. Can MIRR be negative?
- Yes. A negative MIRR indicates that the project is expected to lose money, meaning the present value of the costs outweighs the future value of the returns.
- 5. How do I input cash flows for the MIRR calculator?
- Enter each period’s net cash flow separated by a comma. For example, for a 3-year project, you might enter “50000, 75000, 90000”.
- 6. Does MIRR solve the multiple IRRs problem?
- Yes. Because of its structure, MIRR always produces a single, unambiguous result, resolving the issue where projects with non-conventional cash flows (multiple sign changes) can have multiple IRRs.
- 7. How do I find MIRR on a financial calculator like a Texas Instruments BA II Plus?
- Most financial calculators do not have a direct MIRR button. The process involves calculating the NPV of inflows, finding their future value (FV), and then calculating the rate (I/Y) that equates the initial investment (PV) with that FV over the project’s life (N).
- 8. When should I use MIRR instead of IRR?
- MIRR is almost always preferable to IRR for project evaluation because of its more realistic reinvestment rate assumption. It is especially useful when comparing mutually exclusive projects of different sizes or durations.