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Modified Internal Rate of Return (MIRR) Calculator

Calculate MIRR for a 5-year project using separate reinvestment and finance rates. Correct IRR's reinvestment assumption flaw, resolve multiple-IRR ambiguity on non-conventional cash flows, and compare MIRR directly against your WACC hurdle rate.

Modified Internal Rate of Return (MIRR) Calculator

Standard IRR assumes you can reinvest all profits at the same high project return — a wildly optimistic assumption. MIRR fixes this by using separate, realistic rates: a finance rate (your cost of capital for outflows) and a reinvestment rate (what your positive cash flows can realistically earn when put back to work).

Scenario Presets
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Discount rate for any negative mid-project cash flows

Rate at which positive cash flows are reinvested

Year-by-Year Cash Flow Analysis
YearCash FlowFV ContributionPV of Outflow
0 (Outlay)−$100,000—−$100,000
1$20,000$29,282—
2$30,000$39,930—
3$40,000$48,400—
4$40,000$44,000—
5$50,000$50,000—
Total FV / PV$211,612−$100,000
FV = Σ CF(positive) × (1+10.000)^(N−t) = $211,612
|PV| = initial outlay + PV of negative cashflows = $100,000
MIRR = (FV/|PV|)^(1/5) − 1 = ($211,612/$100,000)^0.2 − 1 = 16.1738%
MIRR
16.17%
Strong Return
<0 Loss|0–10% Marginal|10–15% Acceptable|15–20% Strong|20%+ Outstanding

Practical Example

A manufacturing firm invests $100,000 in a process upgrade. Annual cash flows: $20k, $30k, $40k, $40k, $50k. Cost of capital: 8%. Reinvestment rate: 10%.

FV = 20k×1.1⁴ + 30k×1.1³ + 40k×1.1² + 40k×1.1 + 50k×1.0 = 29,282 + 39,930 + 48,400 + 44,000 + 50,000 = $211,612
MIRR = (211,612 / 100,000)^(1/5) − 1 = 2.11612^0.2 − 1 = ~16.16%.

Standard IRR for this project would compute approximately 21.4% — misleadingly high because it assumes every dollar of profit is reinvested at that same 21.4% rate. MIRR's realistic 10% reinvestment assumption brings that down to 16.16% — the actual expected return. If your hurdle rate is 12%, both IRR and MIRR say accept; but if MIRR came in at 11.5%, the project fails the hurdle rate and should be rejected despite a positive standard IRR.

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What is Capital Budgeting, Project Valuation, and Why MIRR Replaced IRR in Rigorous Finance?

Internal Rate of Return was for decades the dominant project evaluation metric. Its intuitive appeal — a single percentage return — made it easy to communicate to executives and boards. But IRR has two mathematical failures that MIRR fixes: the reinvestment assumption flaw (IRR assumes you can always reinvest at the same high rate) and the multiple IRR problem (non-conventional cash flows with multiple sign changes can produce multiple mathematically valid IRR solutions, making it useless as a ranking metric).

Mathematical Foundation

Modified Internal Rate of Return (MIRR)
FV=∑t=1nCFt+(1+r)n−tMIRR=(FV∣PV∣)1/n−1FV = \sum_{t=1}^{n} CF_t^{+}(1+r)^{n-t} \qquad MIRR = \left(\frac{FV}{|PV|}\right)^{1/n} - 1
FVFV= Future Value of all positive cash flows, compounded at the reinvestment rate r to the end of the project (year n). Each positive CF_t is grown at rate r for (n−t) years. This FV represents total terminal wealth assuming all profits are recycled at the realistic reinvestment opportunity rate — typically WACC or expected market return (8–12%), not the project's own high IRR.
∣PV∣|PV|= Present value of all negative cash flows (outflows) discounted at the finance rate f. For a standard project with a single upfront investment: |PV| = C₀. For projects with multiple negative cash flows mid-period (e.g., decommissioning in year 5), those outflows are discounted back to year 0 at the finance rate.
MIRRMIRR= Modified Internal Rate of Return — the geometric average annual return that equates terminal wealth (FV) with present cost (|PV|) over n periods. Compare MIRR directly to the hurdle rate (WACC): MIRR > hurdle = accept; MIRR < hurdle = reject. MIRR fixes IRR's two mathematical failures: (1) unrealistic reinvestment assumption, (2) multiple solutions for non-conventional cash flows.

Laws & Principles

  • IRR's Fatal Flaw — The Reinvestment Rate Assumption: Standard IRR finds the discount rate r* that makes NPV = 0. The mathematical consequence: IRR implicitly assumes every positive interim cash flow can be reinvested at exactly r* — the project's own return rate. For a project with IRR = 35%, this means reinvesting all intermediate cash flows at 35% per year, indefinitely. In practice, marginal investment opportunities earn the market rate (8–12%). MIRR corrects this by explicitly separating the reinvestment rate (r, typically 8–15%) from the project's required return, producing a far more realistic yield.
  • The Multiple IRR Problem — When Standard IRR Becomes Invalid: When a project's cash flows change sign more than once (e.g., oil wells with decommissioning costs, phased construction with negative years), the NPV polynomial has multiple real roots — multiple r* values that set NPV = 0. Using the standard formula can produce two IRRs, say 12% and 28%, with no mathematical basis to prefer one. MIRR always produces a single unique answer because FV/|PV| is always a single positive number, and its nth root is always unique and real.
  • MIRR vs. NPV — Which Should Drive Capital Allocation: NPV answers 'how much absolute value does this project create?' MIRR answers 'what return rate does this project generate?' NPV correctly captures value when comparing mutually exclusive projects of different sizes: a $10M project with NPV=$2M is better than a $1M project with NPV=$0.5M, even if the smaller project has higher MIRR. MIRR is more useful for capital rationing when you have a fixed budget and must rank many small projects by return efficiency.
  • Hurdle Rate Setting — The Critical Input: The hurdle rate should be the firm's WACC — the blended cost of equity and debt financing. If WACC = 9%, any project with MIRR > 9% creates shareholder value. A hurdle rate set too high causes rejection of value-creating projects. Set too low, the firm accepts value-destroying projects. The reinvestment rate should equal WACC for a neutral assumption, or lower if the firm expects capital allocation opportunities to worsen.

Step-by-Step Example Walkthrough

" A manufacturing firm evaluates a $100,000 process upgrade generating: Year 1: $20K, Year 2: $30K, Year 3: $40K, Year 4: $40K, Year 5: $50K. Finance rate 8%, reinvestment rate 10%. "

  1. FV Year 1: $20,000 × (1.10)⁴ = $29,282.
  2. FV Year 2: $30,000 × (1.10)³ = $39,930.
  3. FV Year 3: $40,000 × (1.10)² = $48,400.
  4. FV Year 4: $40,000 × (1.10)¹ = $44,000.
  5. FV Year 5: $50,000 × (1.10)⁰ = $50,000.
  6. Total FV = $211,612. |PV| = $100,000.
  7. MIRR = (211,612 / 100,000)^(1/5) − 1 = 16.16%.
Final Result: MIRR = 16.16% vs. standard IRR ≈ 21.4%. The 5.2% gap is IRR's reinvestment bias. Both exceed the 8% hurdle rate (accept decision is the same), but MIRR correctly sizes the expected return for performance measurement and compensation benchmarking.

Quick Answer: Why use MIRR instead of standard IRR?

Standard IRR contains a hidden assumption: every positive interim cash flow is reinvested at the project's own IRR — for a 35% IRR project, that means finding another 35% opportunity, indefinitely. That assumption is almost never achievable. MIRR fixes this by letting you specify a realistic reinvestment rate (typically WACC). The result: MIRR is always lower than IRR for high-return projects, but far more honest. If IRR = 28% and realistic reinvestment = 10%, MIRR might be 16% — that's the real expected return.

The MIRR Formula — 3 Steps

Step 1 — Terminal Value of Positive Flows (at Reinvestment Rate r)

FV = ∑ CFₜ⁺ × (1 + r)ⁿ⁻ᵗ

Step 2 — Present Value of Negative Flows (at Finance Rate f)

|PV| = ∑ |CFₜ⁻| ÷ (1 + f)ᵗ

Step 3 — MIRR

MIRR = (FV ÷ |PV|)^(1/n) − 1

MIRR vs. IRR Scenarios

✓ Standard Project: IRR Overstates Return

  1. Project: $100K investment, 5-year cash flows. Reinvestment 10%, finance 8%.
  2. Standard IRR: ≈ 21.4% — assumes all interim cash flows reinvested at 21.4%.
  3. MIRR: 16.16% — 5.2pp lower, reflecting realistic 10% reinvestment.
  4. Impact: Both exceed 8% hurdle — same accept decision. But MIRR correctly sizes the return for executive scorecarding and capital allocation ranking.

✗ Non-Conventional Flows: IRR Fails, MIRR Solves

  1. Oil well: Year 0: −$500K, Years 1–4: +$200K, Year 5: −$300K decommissioning. Two sign changes.
  2. Standard IRR: Two valid solutions — 7.66% AND 33.5%. No basis to prefer either.
  3. MIRR: FV = $928,205, |PV| = $704,174 → MIRR = 5.7%.
  4. Decision: 5.7% < 8% hurdle → reject. Single, unambiguous answer where IRR produced none.

Capital Budgeting Metrics Comparison

Metric Best Use
NPVMutually exclusive projects; absolute value creation
MIRRReturn ranking; non-conventional cash flows; capital rationing
IRRQuick screening of simple, conventional projects
Payback PeriodLiquidity-constrained decisions; venture screening

Capital Budgeting Directives

Do This

  • ✓Set reinvestment rate equal to WACC as the baseline. WACC is the neutral, theoretically defensible assumption — it reflects the marginal opportunity cost of capital. If you have a specific reinvestment project already identified, use its expected IRR. If not, WACC prevents both over-optimism and false conservatism.
  • ✓Always use MIRR (not IRR) for non-conventional cash flows. Decommissioning costs, environmental remediation, phased construction — all produce multiple sign changes where IRR is mathematically unreliable. MIRR produces a single unambiguous result regardless of how many times cash flows switch sign.

Avoid This

  • ✗Never use MIRR alone to choose between mutually exclusive projects of different sizes. A $10M project at MIRR 18% and a $1M project at MIRR 22% are not comparable by return rate alone. The smaller project has higher efficiency but creates far less absolute value. For mutually exclusive selection, NPV is the tie-breaker.
  • ✗Don't set reinvestment rate above WACC without justification. Setting reinvestment = 15% when WACC = 9% inflates MIRR and makes marginal projects appear acceptable. MIRR's main advantage over IRR is realism — undermining that assumption recreates the same bias you were trying to eliminate.

Frequently Asked Questions

What is the main difference between IRR and MIRR?

IRR implicitly assumes all positive interim cash flows are reinvested at the project's own IRR — often 25–35% — which is almost never achievable in practice. MIRR corrects this by using a user-specified reinvestment rate (typically WACC, 8–12%) for positive cash flows and a finance rate for negative mid-period flows. MIRR also always produces a single, unique answer — IRR can give multiple valid answers when cash flows change sign more than once, making it mathematically invalid for those projects.

What reinvestment rate should I use for MIRR?

The most common and defensible choice is the firm's WACC — it reflects the marginal cost of capital and represents the average return expected from the firm's portfolio. If you have a specific reinvestment project identified, use its expected return. For conservative analysis, use a risk-free or near-risk-free rate. Always sensitivity-test MIRR across a range (e.g., 6%, 8%, 12%) to understand how dependent the accept/reject decision is on this assumption — if the decision flips within the plausible range, it signals a marginal project requiring deeper analysis.

Can MIRR be negative?

Yes — MIRR is negative when the terminal value of positive cash flows (FV) is less than the present value of investments (|PV|). This means the project destroys value even accounting for time value of money. Mathematically, if FV/|PV| < 1, then (FV/|PV|)^(1/n) < 1, and subtracting 1 produces a negative MIRR. A negative MIRR is an unambiguous reject signal — the project returns less in present value terms than it costs, regardless of the reinvestment assumption chosen.

When should I use NPV instead of MIRR?

Use NPV when: (1) choosing between mutually exclusive projects of different scales — a $10M project with NPV=$2M beats a $1M project with NPV=$500K even if MIRR favors the smaller one; (2) you need the absolute dollar value created; (3) you need additive metrics across a portfolio (NPVs add arithmetically; MIRRs do not). Use MIRR when: (1) ranking many small projects under a fixed capital budget; (2) communicating return expectations to stakeholders; (3) dealing with non-conventional cash flows where IRR fails. Best practice: compute both and confirm they agree on accept/reject before committing capital.

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