MIRR vs. IRR
Executive Summary
Key Takeaways
- ✓ IRR implicitly assumes interim cash flows reinvest at the IRR itself, an assumption that is often unrealistic, particularly for high-IRR projects.
- ✓ MIRR replaces this implicit assumption with two explicit, separately specified rates — a finance rate for outflows and a reinvestment rate for inflows.
- ✓ MIRR always produces exactly one solution, eliminating the multiple-IRR (or no-real-IRR) problem that can arise for non-conventional cash flow series.
- ✓ MIRR requires an analyst to make an explicit, documented reinvestment rate assumption, which is itself a discipline IRR does not impose.
Definitions¶
Internal rate of return (IRR), as defined on the IRR glossary page, is the discount rate at which a project's NPV equals exactly zero, calculated directly from the project's cash flow series with no separate rate inputs required.
Modified internal rate of return (MIRR), as defined on the MIRR glossary page, replaces IRR's implicit, self-referential reinvestment assumption with two explicit, separately specified rates — a finance rate applied to outflows and a reinvestment rate applied to inflows — producing a single, more defensible percentage return.
Side-by-Side Comparison¶
| Dimension | IRR | MIRR |
|---|---|---|
| Reinvestment rate assumption | Implicit — assumed equal to the IRR itself | Explicit — separately specified by the analyst |
| Number of rate inputs required | None (the rate itself is the unknown being solved for) | Two (finance rate and reinvestment rate) |
| Non-conventional cash flows (multiple sign changes) | Can produce multiple real solutions, or none | Always produces exactly one solution |
| Realism of the underlying assumption | Often unrealistic, especially for high-IRR projects | More realistic, since the reinvestment rate is chosen to reflect actually achievable opportunities |
| Ease of calculation | Simple — cash flow range only | Slightly more involved — cash flow range plus two explicit rate inputs |
| Excel function | =IRR(cash_flow_range) |
=MIRR(cash_flow_range, finance_rate, reinvestment_rate) |
| Transparency of assumptions | Reinvestment assumption is hidden inside the single calculated rate | Reinvestment assumption is visible and must be explicitly documented |
Decision Framework¶
Use IRR for a quick, simple percentage-return read on a conventional cash flow project, where the reinvestment assumption is not expected to be a material driver of the conclusion, and where audience familiarity with the standard IRR figure matters.
Use MIRR whenever the project's IRR is high enough that its implicit reinvestment assumption is genuinely questionable, whenever the cash flow series is non-conventional (more than one sign change), or whenever a more defensible, assumption-transparent return figure is required for an investment committee or lender presentation.
Use both together, as is common in institutional practice, to show explicitly how much of a project's headline IRR depends on its optimistic embedded reinvestment assumption — a large gap between IRR and MIRR is itself informative.
Why the Reinvestment Assumption Matters¶
IRR's defining equation solves for the single discount rate at which the present value of all future cash inflows exactly equals the initial outflow. Embedded in that mathematics is an assumption that every interim cash inflow, once received, is reinvested at that same rate for the remainder of the project's life. For a modest IRR, this assumption is a reasonable simplification. For a high IRR — the kind that often makes a project look particularly attractive — the assumption becomes harder to sustain: finding a steady stream of reinvestment opportunities offering, say, 35% for every dollar of interim cash flow is rarely realistic. MIRR removes this hidden optimism by requiring the analyst to specify a reinvestment rate directly, typically set closer to the entity's actual cost of capital or a realistically achievable market rate.
The Multiple-IRR Problem¶
A non-conventional cash flow series — one with more than one change of sign, such as an initial outflow, a period of inflows, and a later outflow (for example, a major mid-life overhaul or a decommissioning cost) — can mathematically produce more than one discount rate at which NPV equals zero, or none at all, making IRR ambiguous or entirely undefined for that project. MIRR does not have this problem, because its calculation compounds all outflows to a single present value and all inflows to a single future value before solving for one rate, a construction that by design always produces exactly one solution regardless of how many times the cash flow series changes sign.
Advantages¶
IRR advantages: simpler to calculate, requiring only the cash flow series; widely understood and recognized across finance audiences; does not require the analyst to choose an additional rate input.
MIRR advantages: more realistic reinvestment assumption, explicitly specified rather than hidden; always produces exactly one solution, even for non-conventional cash flows; forces the analyst to document their reinvestment rate assumption explicitly.
Limitations¶
IRR limitations: embeds an often-unrealistic reinvestment-at-IRR assumption; can produce multiple or no real solutions for non-conventional cash flow series.
MIRR limitations: requires two additional rate inputs, both of which are themselves judgement calls that must be justified; less universally familiar to audiences accustomed to IRR as the standard metric; a poorly chosen reinvestment rate can distort MIRR just as an unexamined implicit assumption can distort IRR.
Common Misconceptions¶
"MIRR is always the more accurate number." MIRR is only as reliable as the finance and reinvestment rates chosen for it. An unrealistically high reinvestment rate can overstate MIRR just as IRR's implicit assumption can overstate IRR — MIRR shifts the assumption from implicit to explicit, which improves transparency but does not remove the need for a defensible rate choice.
"IRR and MIRR will always be very different numbers." For a project with a modest IRR, evaluated using a reinvestment rate reasonably close to that IRR, the two can be quite similar. The gap widens specifically as the IRR rises relative to realistically achievable reinvestment rates.
"MIRR replaces IRR entirely in institutional practice." Both remain in common use. IRR's simplicity and familiarity keep it in wide use for quick comparisons; MIRR is reserved for situations where the reinvestment assumption or non-conventional cash flow timing make it the more defensible choice.
References & Further Reading¶
- Brealey, R., Myers, S., and Allen, F., Principles of Corporate Finance, McGraw-Hill
- CFA Institute, CFA Program Curriculum — Corporate Finance and Capital Budgeting
Continue Reading¶
Prerequisites¶
Related Pillars¶
Related Glossary¶
Related Comparisons¶
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Frequently Asked Questions
What is the core difference between MIRR and IRR?
IRR implicitly assumes every interim cash inflow is reinvested at the IRR itself for the remainder of the project's life. MIRR replaces that implicit, self-referential assumption with two explicit, separately specified rates — a finance rate applied to outflows and a reinvestment rate applied to inflows.
Why is IRR's reinvestment assumption considered unrealistic?
Because it requires the entity to find reinvestment opportunities offering a return equal to the project's own IRR for every interim cash inflow, which becomes increasingly implausible the higher the IRR is — a project showing a 40% IRR is implicitly assumed to reinvest its cash inflows at 40% as well, which is rarely achievable in practice.
Does MIRR always produce a lower result than IRR?
For a high-IRR project with a reinvestment rate assumption set below that IRR (the typical case), MIRR is generally lower, since it no longer credits the project with reinvesting at its own high internal rate. This is usually viewed as a more realistic, conservative result rather than a shortcoming of MIRR.
When does the choice between MIRR and IRR matter most?
When the project's IRR is high relative to realistically achievable reinvestment rates (widening the gap between the two metrics), and when the cash flow series is non-conventional, with more than one change of sign, in which case IRR may not even produce a single usable answer while MIRR always does.
Is MIRR harder to calculate than IRR?
Not materially — Excel's MIRR function requires the same cash flow range as IRR, plus two additional rate arguments (finance rate and reinvestment rate). The added requirement is conceptual as much as computational — the analyst must explicitly decide and document what those two rates should be, rather than letting the calculation implicitly assume a reinvestment rate on their behalf.
Should MIRR replace IRR entirely?
Not necessarily — IRR remains simpler to calculate and widely understood, and for a single, standalone, conventional-cash-flow project evaluated for illustrative or preliminary purposes, the distinction may not be decision-relevant. MIRR is the more defensible choice specifically when the reinvestment assumption matters materially to the conclusion, or when the cash flow series is non-conventional.
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Investment Analysis and Capital Budgeting
Investment analysis and capital budgeting is the discipline of deciding whether a project or investment is expected to create value, using a toolkit of quantitative techniques — net present value, internal rate of return, modified internal rate of return, payback period, and the profitability index — each applied to the same underlying forecast cash flow series but answering a subtly different question. This page is the hub for the Knowledge Centre's investment analysis content: what each technique measures, how the techniques relate to and sometimes conflict with one another, how discount rates and hurdle rates are set, how risk is layered onto the analysis through sensitivity, scenario, and Monte Carlo methods, and — distinctively — how capital-budgeting failure modes map onto FMAE's existing structural audit rule taxonomy.
MIRR (Modified Internal Rate of Return)
Modified Internal Rate of Return (MIRR) is a capital budgeting metric that corrects two specific weaknesses of IRR — its implicit assumption that interim cash flows are reinvested at the IRR itself, which is often unrealistic, and its potential to produce multiple or no real solutions for a non-conventional cash flow series. MIRR resolves both by using an explicit finance rate for outflows and a separately specified reinvestment rate for inflows, producing a single, more defensible rate of return.
IRR (Internal Rate of Return)
Internal Rate of Return (IRR) is the discount rate at which the net present value of a series of cash flows equals zero. It is the generic form of a metric that appears in financial models in several more specific variants, most commonly Project IRR and Equity IRR, each defined on its own cash flow basis. This page defines the generic IRR concept and the Excel functions used to calculate it; for the project finance-specific variants, see Project IRR and Equity IRR.