economics · cashflow
Modified Internal Rate of Return (MIRR)
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Inputs
$
Paste one row per line — separate columns with a comma or tab: Net Cash Flow ($/yr)
⚠ Needs at least 2 valid rows to calculate — 0 so far.
fraction
fraction
Description
Computes the modified internal rate of return — resolving standard IRR's multiple-roots (or no-root) ambiguity for a non-conventional, sign-changing cash flow by discounting negative flows at a finance rate and compounding positive flows at a separate reinvestment rate, rather than assuming both happen at the single rate IRR itself. No level-annuity counterpart exists in this discipline: a level annuity is by construction a conventional cash flow (one outflow, then constant positive inflows), which irr already resolves to exactly one unambiguous rate — MIRR's entire value proposition doesn't apply there, so building one would add a second number without adding any new decision-relevant information.
Variables
| Symbol | Unit | Description |
|---|---|---|
| MIRR | fraction | Modified Internal Rate of Return |
| C0 | $ | Up-front capital cost incurred at time zero, before any cash flow begins — treated as a negative cash flow at t=0 alongside any negative rows in the cash-flow array below. |
| CFₜ | — | One row per year, in order starting at year 1: that year's own net cash flow, pre-tax. A row can be negative (e.g. a mid-life workover cost) — this is exactly the non-conventional, sign-changing case MIRR is built for; irr_variable's single bisected rate becomes ambiguous or undefined there, while MIRR always returns one well-defined answer. Paste at least 2 years. |
| r_f | fraction | Rate used to discount negative cash flows (capital outlays) back to time zero — typically the company's cost of borrowing/capital. |
| r_r | fraction | Rate assumed for reinvesting positive cash flows forward to the end of the project life — typically the company's actual reinvestment opportunity rate, not necessarily the same as the finance rate. |
Assumptions
- Positive cash flows are reinvested at the entered reinvestment rate from the year received until the end of the project life.
- Negative cash flows (the initial investment and any negative array row) are discounted at the entered finance rate.
- Cash flow is in nominal, pre-tax dollars, matching every other calc's convention in this discipline.
- Finance rate and reinvestment rate are each held constant across the project life — neither is allowed to vary year to year.
Limitations
- MIRR's result depends materially on the chosen finance and reinvestment rates — unlike IRR, which needs no external rate assumption at all, MIRR requires the user to supply two, and a poorly chosen reinvestment rate can make a marginal project look artificially attractive or unattractive.
- No income, severance, or ad valorem tax deduction is applied.
- For a genuinely conventional (single sign-change) cash flow, MIRR and IRR will generally disagree numerically (different reinvestment assumptions) even though both are well-defined — a MIRR/IRR mismatch on a conventional cash flow reflects that assumption difference, not an error in either calculation.
Use Cases
- → Non-conventional cash flow screening: Get a single, unambiguous rate-of-return figure for a project with a mid-life negative cash flow (e.g. a major workover or facility upgrade) where irr_variable's own bisection can be unreliable.
- → Realistic reinvestment assumption: Model a reinvestment rate that differs from the project's own IRR — useful when a company's actual opportunity rate for redeployed cash is known to be lower (or higher) than what IRR implicitly assumes.
Related Calculations
Region Notes
General
Finance and reinvestment rate assumptions are company- and market-specific; using the same value for both collapses MIRR toward a level-reinvestment-rate assumption similar in spirit to IRR's own, so the real value of MIRR comes from deliberately setting them differently when a company's actual borrowing and reinvestment rates diverge.
References
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