IRR Formula and the Reinvestment-Assumption Question: A Practitioner's Guide to IRR, MIRR, and XIRR

Key Takeaways

When Your IRR Is 23.5% and Cash Yields 4%

Many IRR explainers stop after writing out the NPV = 0 identity. This one starts there, and then asks the question every honest investment-committee memo eventually has to answer: when your underwritten IRR is 23.5% but the reinvestment rate is 4%, what return should you actually expect?

The gap between those two numbers is a practical question whenever cash earns a real return. As of October 6, 2026, the 3-month Treasury bill yields 4.21% and the 10-year Treasury yields 5.27% (Federal Reserve H.15 data via FRED, series DGS3MO andDGS10). The spread between IRR and MIRR (the modified IRR that explicitly assumes interim cash flows compound at a chosen reinvestment rate rather than at the project's IRR) can be large on distribution-heavy deals. On the worked example below, a 23.5% IRR with a 5% reinvestment rate produces a MIRR of 15.8%, a 7.7-point gap. Both numbers are correct. They answer different questions.

This article covers the IRR formula, the reinvestment-assumption controversy (including the modern academic position from Magni and Martin in The Engineering Economist), MIRR mechanics with a CRE worked example, how the spread behaves as reinvestment rates change, and when XIRR is the right call. The audience is institutional CRE practitioners building IC memos, not first-year MBA students, though the formula derivation is here for completeness.

The IRR Identity, From NPV

The IRR is defined as the discount rate that makes the net present value of a series of cash flows equal to zero. For cash flows CF₀, CF₁, ..., CF_n occurring at the end of periods 0 through n, the IRR is the value r that satisfies:

Notice what the formula does not say. It says nothing about what happens to CF₁ after it is received. It says nothing about whether the analyst plans to reinvest interim distributions. It is a mathematical identity about the relationship between a stream of cash flows and a discount rate, nothing more. The practitioner intuition that “IRR assumes reinvestment at the IRR” is a true statement about reconciling IRR to a multi-period compound annual growth rate (CAGR), but it is not a statement about the IRR formula itself. We return to this distinction below.

Why There's No General Closed-Form Solution

For cash flows extending more than four periods after the initial outlay, the IRR equation is a polynomial of degree five or higher in 1/(1+IRR), and the Abel-Ruffini theorem says there is no general solution in radicals. A deal with seven years of cash flows produces a seventh-degree polynomial. IRR must be solved numerically.

In practice, every IRR calculation (Excel's IRR() function, Google Sheets, financial calculators) uses iterative root-finding. According toMicrosoft's documentation, Excel starts from a guess (you can pass one as the second argument; the default is 0.1, or 10%), cycles through the calculation until the result is accurate within 0.00001 percent, and returns #NUM! if it cannot find a result after 20 tries. For most well-behaved CRE cash flows with one sign change (negative outflow at acquisition, positive inflows thereafter), the iteration converges in a handful of steps to a unique IRR.

Cash flows with multiple sign changes (a deal with a recap or major capex spend mid-hold that briefly turns cash flow negative again) can produce multiple IRRs. Mathematically, Descartes' rule of signs bounds the count: the number of positive real roots is at most the number of sign changes in the cash flows, and differs from it by an even integer. A four-sign-change cash flow therefore has four, two, or zero positive roots (in the variable 1/(1+r), where positive roots correspond to IRRs above −100%). If the cumulative cash flow changes sign only once, the IRR is unique. Excel's IRR() returns whichever root its iteration converges to and gives no warning. This is one of the practical arguments for MIRR, which resolves the multiple-root problem by construction, though MIRR's value depends on the rates you choose.

The Reinvestment-Assumption Controversy

Many IRR explainers repeat the same line: IRR assumes that interim cash flows are reinvested at the IRR itself. The Corporate Finance Institute'sMIRR tutorial, for example, calls “the assumption that the obtained positive cash flows are reinvested at the same rate at which they were generated” one of the main problems with the IRR. The claim is common enough that most analysts learn it as fact.

It is also, at best, imprecise. It requires an asterisk that many explainers leave out.

The Magni-Martin position

Carlo Alberto Magni and John D. Martin, in “The Two Sides of the Reinvestment Assumption Fallacy in IRR and NPV,”The Engineering Economist 70(3), 122–151 (2025), argue that neither NPV nor IRR requires any reinvestment assumption. They distinguish exogenous reinvestment assumptions (imposed after the cash flows have been projected) from endogenous reinvestment (modeled while projecting the cash flows, to determine distributions to capital providers). The IRR formula is an algebraic identity relating a stream of cash flows to a single discount rate. It makes no statement, explicit or implicit, about what happens to interim cash flows after they leave the project. Reinvestment is a separate question, answered by a separate model.

When practitioners say “IRR assumes reinvestment at the IRR,” the most charitable reading is something more specific: if you want to reconcile the IRR to a multi-period CAGR computed against only the original equity outlay and the final disposition value, you have to assume the interim cash flows compounded at the IRR for the arithmetic to work out. That statement is true. But it is a statement about a particular reconciliation exercise, not about the IRR formula itself. The reinvestment assumption is imposed exogenously by the analyst who wants the CAGR reconciliation to hold; the formula does not require it.

Resolving the practitioner intuition

Why does the practitioner intuition persist if it is imprecise as stated? Because the reconciliation exercise is common enough that the assumption feels load-bearing. An investment-committee member who looks at a deal with a quoted IRR of 17% and asks “so if I invest $10M, I'll have $10M × 1.17⁵ = $21.9M at exit, right?” is implicitly assuming the interim distributions reinvested at the IRR. If they didn't (if the distributions sat in cash at 4%) the investor will have less than $21.9M at exit, and the realized multi-period CAGR on the original $10M outlay will be lower than 17%.

Both statements are correct. The IRR formula does not require a reinvestment assumption. The reconciliation of IRR to a CAGR on the original capital does. The practitioner intuition is a true statement about the second exercise misattributed to the first. Once you separate the two, the controversy collapses.

MIRR: The Formula

MIRR, the modified internal rate of return, reframes the question. Instead of asking “what discount rate zeros NPV,” MIRR asks: if interim cash inflows compound at one rate (the reinvestment rate) and the initial outflow is financed at another (the finance rate), what single annualized return reconciles the initial investment to the future value of all the proceeds?

Two practical choices determine MIRR: the reinvestment rate and the finance rate. The reinvestment rate is the yield the analyst can realistically earn on distributed cash, typically the risk-free rate (10-year Treasury or money-market yields), the LP's stated opportunity cost, or a weighted average of the two. The finance rate is the cost of capital for the negative cash flows, usually the project's debt cost or the firm's WACC. For most CRE deals with a single negative cash flow at acquisition, the finance rate distinction is academic: the initial outlay is already at time zero, so no PV discounting is needed and the finance rate doesn't change the answer.

By construction, MIRR resolves the multiple-IRR problem. There is only one MIRR for any cash flow stream because the formula collapses all positive cash flows into a single future value and all negative cash flows into a single present value before taking the geometric average. The polynomial that might have multiple roots in IRR has exactly one solution in MIRR. The answer still depends on the reinvestment and finance rates you choose, so document them.

Worked Example: A 7.7-Point Spread on a Distribution-Heavy Multifamily Deal

Consider a stylized, distribution-heavy multifamily acquisition: $10M of equity at close, $2M/year of distributions during a seven-year hold (a 20% cash yield on equity every year), a $3M refi event in year 3 that returns capital to LPs, and an $8M equity disposition in year 7. Most value-add deals return the bulk of their proceeds at sale, so this profile is deliberately extreme: it is chosen to make the reinvestment effect visible. The cash flow stream:

The IRR, the discount rate that zeros the NPV of the seven-year stream, is approximately 23.5%. The MIRR with a 5% reinvestment rate (an assumed rate between the 4.21% 3-month and 5.27% 10-year Treasury yields on October 6, 2026) is approximately 15.8%. The 7.7-point spread is the practical consequence of the reinvestment-assumption distinction: the $25M of total inflows grows to about $27.9M by year 7 when reinvested at 5%, versus about $43.7M if every inflow compounded at the 23.5% IRR, and MIRR makes that gap explicit.

The spread also depends on the reinvestment rate you pick, and it moves the opposite way from what many readers expect. On these same cash flows, the MIRR is 14.0% if distributions earn 0%, 14.3% at 1%, 15.5% at 4.21%, and 15.8% at 5%. A higher reinvestment rate raises the MIRR and therefore narrows the spread, from roughly 9.5 points at a 0% reinvestment rate to 7.7 points at 5%.

In an IC presentation, this deal should be quoted with both numbers. The IRR communicates the project's intrinsic return as a discount rate. The MIRR communicates the annualized return the LP should expect if interim distributions are reinvested at 5%, a reasonable base case for an LP who will not find another 23.5% deal for each distribution.

XIRR for Irregular Timing

A short sidebar before continuing: the standard IRR formula assumes cash flows occur at equal intervals (end of each period). Many CRE models work in monthly cash flows, and many include irregular events: refi closings, mid-quarter capex, sale proceeds on a non-standard date. XIRR, Excel's extended IRR function, takes a date for each cash flow and computes the annualized return using the actual number of days between flows. In many institutional models, “IRR” effectively means XIRR.

XIRR does not change the reinvestment-assumption discussion. It changes the discounting precision. The choice between IRR and XIRR is a choice about cash-flow timing granularity; the choice between IRR and MIRR is a choice about how to handle interim distributions. They are independent decisions.

The Complete Return-Metric Stack

No single return metric tells the whole story of a deal. Underwriting practice typically quotes a stack of metrics, each answering a different question. A reasonable default for a CRE acquisition:

The right IC-memo lead depends on the LP. In our experience, open-end core funds underwrite on income (cash-on-cash and stabilized yield) with IRR as the disposition cross-check. Value-add and opportunistic funds lead with IRR and often cite MIRR alongside. Family offices and direct investors tend to care more about equity multiple than time-value-weighted IRR because their hold periods are flexible. Fund-level LPs care about TVPI and DPI more than deal-level IRR. Knowing which metric to put first is part of the job.

How Interest Rates Affect the IRR-MIRR Spread

Cash now earns a meaningful return. As of October 6, 2026, the 3-month Treasury bill yields 4.21% and the 10-year Treasury yields 5.27% (Federal Reserve H.15 data viaFRED DGS3MO andDGS10). A MIRR calculated at a cash-like reinvestment rate is a more achievable benchmark when short-term rates are well above zero than when they sit near it, and the opportunity cost of distributed cash is real.

Higher rates do not widen the IRR-MIRR spread. They shrink it, modestly. The spread is set by how far the IRR sits above the reinvestment rate and by how much of the return arrives as interim distributions before exit. In the worked example above, the spread is about 9.5 points if distributions earn 0% and 7.7 points if they earn 5%. For a more typical profile, where most proceeds arrive at sale, the spread is much smaller: a 7-year deal with a 15% IRR that pays 6% of equity per year has a MIRR of 13.5% when cash earns 1% and 13.8% when it earns 4.21%, a gap of about 1.5 points at the lower rate and 1.2 points at the higher one. These figures are illustrative, computed from stylized cash flows; your deal will differ.

What a higher rate changes is how useful the MIRR question is. When cash yields 4–5%, “what did the distributions actually earn?” has a concrete answer, and an IRR far above that rate says less about terminal wealth than the MIRR does. Realized outcomes can also differ from underwritten IRRs for reasons unrelated to reinvestment, such as longer holds, slower rent growth, or refinancing delays. The reinvestment effect is one component: distributions that sit in cash do not compound at the project IRR, so the multi-period CAGR on the original equity outlay is below the IRR.

Some LPs may ask for MIRR alongside IRR in offering documents and quarterly reporting. Presenting both numbers up front answers that question before it is asked.

Five Mistakes Practitioners Make

• Quoting IRR alone when distributions are a large share of the return. When cash earns 4–5% and the IRR sits far above it, IRR alone overstates the realized annualized return on the original capital, most of all on distribution-heavy deals. Quote MIRR alongside.

• Using IRR() on a cash flow with multiple sign changes. Recap events, major capex spends, and refi-to-loss events can produce multi-sign cash flows. Excel returns whichever root its iteration converges to, with no warning. Use MIRR for these deals, or solve the polynomial graphically to see all the roots.

• Choosing a reinvestment rate that's not achievable. Setting MIRR's reinvestment rate equal to the IRR makes MIRR equal to IRR for a cash flow with a single initial outflow, so the calculation adds nothing. Use the actual achievable reinvestment rate: the risk-free yield, the LP's stated opportunity cost, or a documented blended rate. Don't pick a number that flatters the deal.

• Treating IRR as a forecast of terminal wealth. IRR is a discount rate, not a compound growth rate on the original equity. If you tell an LP “a 17% IRR on your $10M means $21.9M in five years,” you are implicitly assuming reinvestment at 17%. That is not what IRR says. Compute the realized CAGR separately if that's the question being asked.

• Using IRR on monthly cash flows without converting to XIRR. Excel's IRR() on monthly periods returns a monthly rate that has to be annualized. It is easy to forget to annualize or to annualize incorrectly ((1+r)¹²−1 vs 12r). XIRR with actual dates removes the ambiguity. Default to XIRR.

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Related Articles

The IRR methodology pillar links into the broader returns-analysis cluster:

• IRR Calculator and Formula for Real Estate: the calculator pillar with an interactive widget for running IRR on your own cash flows.
• Equity Multiple and MOIC: When the Multiple Matters More Than IRR: the time-blind complement to IRR.
• Cash-on-Cash Return: Levered vs. Unlevered: the current-yield metric.
• IRR Sensitivity Analysis and Stress Testing: how to test IRR under downside scenarios.
• TVPI, DPI, and RVPI: Fund-Level Return Metrics for LPs: the fund-level analog of IRR and equity multiple.
• Cap Rate Calculator and Formula: the entry-yield metric every IRR conversation eventually references.
• Preferred Return: Simple vs Compounding vs Accruing: how IRR interacts with promote structures.

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