Alpha and Beta Calculator
Free alpha and beta calculator. Measure your portfolio's market sensitivity (beta) and excess risk-adjusted return (alpha) against a benchmark index.
Modified IRR (MIRR) Calculator
Calculate MIRR with separate finance and reinvestment rates. Compare against standard IRR, see NPV, cash flow schedule, and reinvestment rate sensitivity.
E.g., -200000,25000,35000,45000 (negatives = outflows)
Cost of borrowing / discount for outflows
Rate earned on reinvested inflows
MIRRโง
11.64%
Modified Internal Rate of Return
Standard IRRโง
16.33%
IRR overstates โ it assumes reinvestment at IRR
NPV (at Finance Rate)โง
$100,906.56
โ
Positive NPV
PV of Outflowsโง
$200,000.00
Discounted at finance rate
FV of Inflowsโง
$432,230.98
Compounded at reinvestment rate
Profit Multipleโง
1.98ร
$395,000.00 returned / $200,000.00 invested
IRR vs MIRR Comparison
MIRR
11.64%
Standard IRR
16.33%
Finance Rate
6.00%
Cash Flow Schedule
| Period | Cash Flow | Cumulative | PV | FV |
|---|---|---|---|---|
| 0 | -$200,000.00 | -$200,000.00 | -$200,000.00 | -$263,186.36 |
| 1 | $25,000.00 | -$175,000.00 | $23,584.91 | $31,632.98 |
| 2 | $35,000.00 | -$140,000.00 | $31,149.88 | $42,582.85 |
| 3 | $45,000.00 | -$95,000.00 | $37,782.87 | $52,643.64 |
| 4 | $55,000.00 | -$40,000.00 | $43,565.15 | $61,867.52 |
| 5 | $65,000.00 | $25,000.00 | $48,571.78 | $70,304.00 |
| 6 | $80,000.00 | $105,000.00 | $56,396.84 | $83,200.00 |
| 7 | $90,000.00 | $195,000.00 | $59,855.14 | $90,000.00 |
Reinvestment Rate Sensitivity
| Reinvestment Rate | MIRR |
|---|---|
| 0% | 10.21% |
| 2% | 10.92% |
| 4% | 11.64% |
| 6% | 12.37% |
| 8% | 13.11% |
| 10% | 13.87% |
Planning notes, formulas, and examples
About the Modified IRR (MIRR) Calculator
The Modified Internal Rate of Return (MIRR) solves the two biggest problems with standard IRR: the unrealistic reinvestment rate assumption and the possibility of multiple IRRs when cash flows change sign more than once.
Standard IRR assumes all positive cash flows are reinvested at the IRR itself โ a rate that's often unrealistically high. MIRR uses two realistic rates instead: a finance rate for discounting negative cash flows (your cost of capital) and a reinvestment rate for compounding positive cash flows (your actual reinvestment opportunity).
The formula computes: (1) PV of all negative cash flows discounted at the finance rate, (2) FV of all positive cash flows compounded at the reinvestment rate, then (3) MIRR = (FV/PV)^(1/n) โ 1. This always produces a single, unique answer. MIRR is typically lower than IRR for high-return projects, revealing how much of IRR's optimism came from the reinvestment assumption.
When This Page Helps
Use this when standard IRR gives an unrealistic reinvestment assumption or more than one solution. MIRR applies separate finance and reinvestment rates, making project comparisons cleaner and easier to defend.
How to Use the Inputs
- Enter cash flows separated by commas (negative for outflows, positive for inflows).
- Set the finance rate (your cost of capital or borrowing rate).
- Set the reinvestment rate (realistic return on reinvested cash).
- Compare MIRR against standard IRR to see the reinvestment assumption impact.
- Check the NPV and profit multiple for absolute value measures.
- Use the sensitivity table to see how reinvestment rate assumptions affect MIRR.
Formula used
PV_neg = |ฮฃ(negative CFs / (1 + finance_rate)^t)|
FV_pos = ฮฃ(positive CFs ร (1 + reinvest_rate)^(nโt))
MIRR = (FV_pos / PV_neg)^(1/n) โ 1Example Calculation
Result: MIRR = 8.92% vs IRR = 12.8%
The standard IRR of 12.8% assumes reinvestment at 12.8%. MIRR at 8.92% uses realistic rates: 6% finance and 4% reinvestment. The 3.9pp gap shows how much IRR overstated the true return.
Tips & Best Practices
- Always report MIRR alongside IRR to show the reinvestment assumption impact.
- For comparing projects of different durations, MIRR is more reliable than IRR.
- A negative MIRR means the project destroys value even with favorable reinvestment.
- Use sensitivity analysis to bound the MIRR range under different reinvestment assumptions.
- If MIRR exceeds the finance rate, the project creates value; if not, reject it.
How It Helps
MIRR separates the cost of funding negative cash flows from the return earned on positive cash flows. That makes it more realistic than standard IRR when project cash flows are irregular or when the reinvestment assumption matters.
What To Check
Choose a finance rate that matches your borrowing cost or hurdle rate, and a reinvestment rate that reflects where interim cash can actually be placed. The gap between MIRR and IRR usually widens when IRR is high or cash flows are uneven.
Usefully Interpreted
If MIRR is above the finance rate, the project adds value on those assumptions. If it is below, the cash flows do not compensate for the funding cost.
Sources & Methodology
Last updated:
Methodology
This calculator parses the entered comma-separated cash-flow stream, discounts every negative cash flow to present value at the finance rate, compounds every positive cash flow to the terminal period at the reinvestment rate, and then solves MIRR from the ratio of those two values. It also computes a standard IRR with a Newton-Raphson iteration, NPV at the finance rate, and a reinvestment-rate sensitivity table using the same cash-flow stream.
The result depends directly on the finance and reinvestment assumptions entered by the user. It is a return-comparison worksheet, not a forecast of what a project will actually earn, and nonstandard cash-flow timing within periods is not modeled.
Sources
- 16.3 Internal Rate of Return (IRR) Method (OpenStax Principles of Finance) โ Reference for the standard IRR framework that MIRR is designed to improve on.
- 16.4 Alternative Methods (OpenStax Principles of Finance) โ Reference for modified return measures and capital-budgeting alternatives to standard IRR.
Frequently Asked Questions
Because IRR assumes reinvestment at the (high) IRR, while MIRR uses a more conservative reinvestment rate. The gap widens as IRR gets higher.
When the reinvestment rate and finance rate both equal the IRR. This is the special (unrealistic) case that standard IRR assumes.
Your cost of capital: WACC for corporate projects, mortgage rate for real estate, or the rate you'd pay to fund the investment.
Use the return you can realistically earn on interim cash flows, not the headline target return of the project. A conservative reinvestment assumption is usually more informative than an optimistic one.
Yes. When cash flows change sign more than once, IRR may have multiple solutions. MIRR always produces a single, unique answer.
NPV is theoretically cleaner for ranking projects. MIRR is useful when stakeholders prefer a percentage return metric that doesn't have IRR's flaws.
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