Calculate MIRR Using HP 10bII
Professional Modified Internal Rate of Return Analysis & Guide
Formula: MIRR = [ (FV of Inflows / PV of Outflows)^(1/n) ] – 1
$18,315.30
$10,000.00
1.83x
Cash Flow Visualization
Figure 1: Comparison of the Initial Investment vs. Reinvested Terminal Value.
Detailed Cash Flow Schedule
| Year | Cash Flow | Reinvested Value at Terminal Year |
|---|
Table 1: Step-by-step reinvestment calculation for each period.
What is Calculate MIRR Using HP 10bII?
To calculate mirr using hp 10bii is to determine the Modified Internal Rate of Return, a financial metric that addresses the primary flaws of the standard Internal Rate of Return (IRR). While the HP 10bII is one of the most popular financial calculators in the world, it does not have a single “MIRR” button. Instead, professionals must use a specific sequence involving the Time Value of Money (TVM) keys or the cash flow (CFj) functions.
Investors and corporate finance managers should use this calculation when comparing projects with different scales or when the reinvestment rate assumption of the standard IRR (which assumes inflows are reinvested at the project’s own IRR) is unrealistic. A common misconception is that the HP 10bII cannot perform this calculation; in reality, it is a simple three-step process once you understand the underlying math.
Calculate MIRR Using HP 10bII Formula and Mathematical Explanation
The MIRR calculation involves three distinct steps: finding the present value of outflows, the future value of inflows, and finally the geometric return between the two. The formula used to calculate mirr using hp 10bii manually is:
MIRR = [(FV of Inflows @ Reinvestment Rate / PV of Outflows @ Finance Rate) ^ (1/n)] – 1
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| PV of Outflows | Present value of all negative cash flows discounted at the finance rate. | Currency ($) | Project Cost |
| FV of Inflows | Future value of all positive cash flows compounded at the reinvestment rate. | Currency ($) | Cumulative Gains |
| n | Number of periods (years/months). | Integer | 1 – 30 years |
| Reinvestment Rate | The rate at which intermediate cash flows are invested. | Percentage (%) | 5% – 15% |
Practical Examples (Real-World Use Cases)
Example 1: Equipment Purchase
Suppose a company buys a machine for $50,000. It generates $15,000 per year for 5 years. The cost of capital is 8%, but the company can only reinvest proceeds at 6%. To calculate mirr using hp 10bii, you would find the FV of the $15,000 payments at 6% over 5 years ($84,556) and then find the rate that turns $50,000 into $84,556 over 5 years. Result: 11.08%.
Example 2: Real Estate Flip
An investor puts $200,000 into a property. In year 1, they receive $20,000, and in year 2, they sell for $250,000. Using a reinvestment rate of 4%, the terminal value is $20,000(1.04) + $250,000 = $270,800. The MIRR is the rate that grows $200,000 to $270,800 in 2 years, which is 16.36%.
How to Use This Calculate MIRR Using HP 10bII Calculator
- Enter Initial Investment: Input the total cost of the project in the Year 0 field.
- Define Cash Flows: Input the expected annual income generated by the project.
- Set Duration: Input how many years the project will last.
- Rates: Input your Finance Rate (what you pay for debt) and Reinvestment Rate (what you earn on cash).
- Read Results: The calculator updates instantly. Compare the “Calculated MIRR” against your hurdle rate.
Key Factors That Affect MIRR Results
- Reinvestment Rate: This is the most sensitive variable. A higher reinvestment rate directly increases the MIRR.
- Finance Rate: If you have multiple outflows (e.g., maintenance in year 3), the finance rate determines their present cost.
- Timing of Cash Flows: Earlier cash flows have more time to compound, leading to a higher MIRR than later flows of the same size.
- Project Life (n): Long-term projects are more sensitive to compounding errors if the reinvestment rate is incorrect.
- Initial Outlay: Larger upfront costs require significantly higher terminal values to maintain a viable MIRR.
- Inflation: High inflation usually raises both the finance and reinvestment rates, which can distort real (inflation-adjusted) MIRR.
Frequently Asked Questions (FAQ)
IRR assumes you reinvest cash flows at the IRR itself, which is often unrealistically high. MIRR allows you to set a more realistic reinvestment rate.
No, it does not have a dedicated button. You must calculate the FV of inflows, the PV of outflows, and then solve for the interest rate using the TVM keys.
Not always. If your reinvestment rate is higher than the project’s IRR, MIRR will be higher. However, in most conservative corporate finance, MIRR is lower.
Yes. MIRR is specifically designed to handle “non-normal” cash flows where money flows out of the project in later years.
A “good” MIRR is any rate that exceeds the company’s Weighted Average Cost of Capital (WACC) or hurdle rate.
To calculate mirr using hp 10bii for months, ensure your rates are monthly (annual rate / 12) and “n” is the total number of months.
The MIRR will change if there are negative cash flows after Year 0, as their present value is determined by the Finance Rate.
Yes, if you treat dividends as cash inflows that are reinvested at a specific rate (like a savings account rate).
Related Tools and Internal Resources
- Full HP 10bII Manual – Comprehensive guide to all financial functions.
- Internal Rate of Return vs MIRR – Understanding the theoretical differences.
- Net Present Value Calculation – Solve for NPV using custom discount rates.
- Cost of Capital Guide – How to determine your finance rate for MIRR.
- Cash Flow Analysis – Advanced techniques for projecting inflows.
- Financial Calculator Guide – Comparisons of TI BA II Plus vs HP 10bII.