What Is MIRR (Modified Internal Rate of Return)? Formula and Example
By Markets & Investing DeskUpdated Nov 10, 2026
Definition
MIRR is a single annualized rate of project return that assumes inflows are reinvested at a chosen rate, usually the cost of capital, and outflows are funded at the firm's financing cost.
Key takeaways
- MIRR compounds inflows forward at the reinvestment rate and discounts outflows back at the finance rate.
- Unlike IRR, MIRR always produces exactly one answer, even when cash flows change sign more than once.
- In the article's example, a project with an 18.66% IRR has a MIRR of 16.91% at a 12% reinvestment rate.
- When both rates equal the hurdle rate, MIRR above the cost of capital matches a positive NPV.
The modified internal rate of return (MIRR) is a single annualized rate that measures a project’s profitability. It assumes that positive cash flows are reinvested at a rate you choose, usually the firm’s cost of capital, and that cash outflows are funded at the firm’s financing cost. The standard internal rate of return (IRR) implicitly assumes that every inflow earns the IRR itself. MIRR replaces that assumption with explicit rates, so it gives a more conservative and more realistic reading of a project’s return, and it produces exactly one answer for any set of cash flows.
How MIRR Works
The internal rate of return is the discount rate that sets a project’s net present value to zero. Solving for that rate is mathematically the same as assuming every interim cash inflow is reinvested at the IRR until the project ends. For a project with a 30% IRR, that means assuming the company keeps finding 30% opportunities for each dollar the project throws off. In practice, freed-up cash is more likely to earn something close to the firm’s cost of capital.
MIRR handles the timing of cash flows in two separate steps instead of solving one equation:
- Move all inflows to the end. Each positive cash flow is compounded forward to the final period at the reinvestment rate. The sum is the terminal value of the inflows.
- Move all outflows to the start. Each negative cash flow is discounted back to period zero at the finance rate. The sum is the present value of the outlays.
Once the project is reduced to one outflow today and one inflow at the end, there is only one compound growth rate that connects them. That rate is the MIRR.
Because the analyst sets the rates, the reinvestment rate can be the firm’s weighted average cost of capital (WACC), a specific expected rate for redeployed cash, or different rates for different stages of a project. The cost of capital is the common default, but the method does not require it.
MIRR Formula
The MIRR formula is:
MIRR = (FV of positive cash flows at the reinvestment rate ÷ PV of negative cash flows at the finance rate)^(1/n) − 1
where:
- FV of positive cash flows = the sum of each inflow compounded to the final period at the reinvestment rate, usually the cost of capital
- PV of negative cash flows = the sum of each outflow discounted to period zero at the finance rate (the firm’s financing cost), entered as a positive number
- n = the number of periods in the project
For a positive cash flow received in period t of an n-period project, its future value is CF × (1 + reinvestment rate)^(n − t). For an outflow in period t, its present value is CF ÷ (1 + finance rate)^t. An outflow at period zero needs no adjustment.
Calculating MIRR in Excel or on a Financial Calculator
Spreadsheets have a built-in function: in Excel and Google Sheets, =MIRR(values, finance_rate, reinvest_rate), where values is the range of cash flows in period order with outflows entered as negatives. The function needs at least one positive and one negative value.
On a financial calculator without a MIRR key, compute the future value of the inflows at the reinvestment rate and the present value of the outflows at the finance rate. Then enter PV as the negative present value of outflows, FV as the terminal value of inflows and N as the project life, and solve for the interest rate.
Example of MIRR
Hypothetical project. A two-year project requires an initial outlay of $195. It returns $121 at the end of year one and $131 at the end of year two. The firm’s cost of capital is 12%, and that rate is used for reinvestment.
IRR first. The IRR is the rate that makes NPV equal zero:
0 = −195 + 121 ÷ (1 + IRR) + 131 ÷ (1 + IRR)²
Solving gives an IRR of about 18.66%.
Now MIRR. Assume the year-one cash flow of $121 is reinvested at 12% for one year. The year-two cash flow arrives at the end and is not compounded.
- Terminal value of inflows: $121 × 1.12 + $131 = $135.52 + $131 = $266.52
- Present value of outflows: the only outflow is $195 at period zero, so it stays $195
- MIRR = ($266.52 ÷ $195)^(1/2) − 1 = (1.3668)^(0.5) − 1 = 1.1691 − 1 = 16.91%
The gap of about 1.75 percentage points comes entirely from the reinvestment assumption. The IRR of 18.66% implicitly lets the $121 earn 18.66% in year two. MIRR lets it earn the 12% the firm can actually expect. Both figures exceed the 12% cost of capital, so the accept decision is the same here, but the IRR paints a more optimistic picture of how profitable the project is.
Example With Multiple Sign Changes
Hypothetical project. A project costs $100 today, returns $230 in year one, then requires a $132 cleanup outlay in year two. The cost of capital is 12%, used as both the finance rate and the reinvestment rate.
This pattern (negative, positive, negative) has two IRRs. Both 10% and 20% make the NPV equal zero, so the IRR alone cannot say whether the project beats a 12% hurdle.
MIRR resolves it:
- Terminal value of inflows: $230 × 1.12 = $257.60
- Present value of outflows: $100 + $132 ÷ 1.12² = $100 + $105.23 = $205.23
- MIRR = ($257.60 ÷ $205.23)^(1/2) − 1 = (1.2552)^(0.5) − 1 ≈ 12.03%
The MIRR sits just above 12%, and the project’s NPV at 12% is a small positive figure (about $0.13). The two measures agree.
Interpreting MIRR
The decision rule mirrors IRR: compare the MIRR with the required return, typically the cost of capital (often written k).
- MIRR > k: the project is expected to earn more than its cost of funds. When both the finance and reinvestment rates equal k, this is equivalent to a positive NPV.
- MIRR < k: the project earns less than the cost of capital and, on that basis, would be rejected. With both rates set to k, this corresponds to a negative NPV.
- MIRR = k: the project breaks even in present value terms.
The link to NPV follows from the formula. Discounting the terminal value of inflows back at k gives the present value of the inflows, and subtracting the present value of outflows gives NPV. MIRR exceeds k exactly when that difference is positive. If the finance rate or reinvestment rate differs from the hurdle rate, this equivalence no longer holds exactly, and the two measures can occasionally point in different directions near the margin.
MIRR is usually lower than IRR for attractive projects, because realistic reinvestment rates are below a high IRR. It is not automatically lower: if the chosen reinvestment rate is higher than the project’s IRR, MIRR will come out above IRR. If the reinvestment rate is set equal to the IRR and the finance rate is irrelevant (a single upfront outlay), MIRR and IRR are identical.
MIRR vs. IRR
| IRR | MIRR | |
|---|---|---|
| Reinvestment assumption | Interim inflows earn the IRR itself | Inflows earn a rate the analyst sets, usually the cost of capital |
| Financing of outflows | Implicitly at the IRR | Discounted at a stated finance rate |
| Number of solutions | Can have several when cash flows change sign more than once, or none | Always one |
| Bias | Tends to overstate profitability for high-return projects | More conservative for high-return projects |
| Consistency with NPV | Accept/reject usually agrees for conventional cash flows | Agrees in sign when both rates equal the hurdle rate |
MIRR vs. FMRR
The financial management rate of return (FMRR) is a related measure used mainly in real estate investment analysis, including for REITs. It goes a step beyond MIRR by splitting the treatment of cash into two explicitly defined rates:
- Safe rate: the return on funds set aside to cover future negative cash flows. These funds sit in liquid, low-risk holdings, so the rate is modest.
- Reinvestment rate: the return when positive cash flows go into another intermediate or long-term investment of comparable risk. Because that money is tied up and more exposed to risk, this rate is higher than the safe rate.
Where MIRR applies a finance rate to outflows, FMRR frames the outflow side as a liquid reserve earning a safe return. That fits property owners who must hold cash for future capital calls or negative operating periods.
When to Use MIRR
MIRR is a capital budgeting tool for judging whether a project clears its cost of capital and for comparing competing proposals. It is most useful when:
- Cash flows vary over time and the reinvestment assumption materially changes the result. Projects with large early inflows are where IRR’s optimism is strongest.
- Cash flows change sign more than once, as with projects that need mid-life overhauls or end with decommissioning or cleanup costs.
- A percentage figure is needed for communication. Managers and investment committees often prefer a rate of return to a dollar NPV, and MIRR supplies one without IRR’s main distortions.
Limitations of MIRR
It depends on a cost of capital estimate. MIRR cannot be calculated without a reinvestment rate and a finance rate, and estimating the cost of capital involves judgment about capital structure, the cost of equity and risk. Two analysts with different assumptions will get different MIRRs for the same project.
It can mis-rank mutually exclusive projects. MIRR is a percentage, so it says nothing about the dollar value a project creates. A small project with a high MIRR can rank above a much larger project with a lower MIRR that adds more total value. When projects are mutually exclusive and differ in scale or life, NPV provides a sounder basis for choosing among them.
It may fail under capital rationing. When a firm has a fixed budget and must select a combination of projects, ranking by MIRR does not guarantee the combination that maximizes total value.
Its theoretical basis is debated. Academics disagree on whether the IRR reinvestment critique is valid at all and on how MIRR should be interpreted, so some treat it as a practical adjustment rather than a fully grounded measure.
FAQs
Is MIRR the same as the rate of return an investor actually earns?
No. MIRR is a projection built from forecast cash flows and assumed reinvestment and financing rates. The return actually realized depends on what the cash flows turn out to be and what rates the reinvested cash really earns.
The Bottom Line
MIRR matters to analysts and managers who judge capital projects and want a percentage return without IRR's optimistic reinvestment assumption. It works well for projects with uneven or sign-changing cash flows. Because it depends on cost of capital estimates and ignores project scale, NPV remains the sounder basis for choosing among mutually exclusive projects or allocating a fixed budget.
