Modified IRR (MIRR) in Engineering Projects: Reinvestment, Comparison, and IRR Limitations

Understand Modified IRR (MIRR) in engineering projects: differences from IRR, reinvestment rate, finance rate, multiple IRRs, NPV relationship, and CAPEX decisions.

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Modified IRR, or MIRR — Modified Internal Rate of Return — is an adaptation of the Internal Rate of Return designed to reduce some limitations of traditional IRR. Instead of implicitly assuming that intermediate positive cash flows are reinvested at the project’s own IRR, MIRR uses a reinvestment rate defined by the analyst and, in its more complete formulation, a finance rate for negative cash flows. In engineering projects, this makes the return rate more consistent with the cost of capital and realistic reinvestment conditions.

MIRR does not replace Net Present Value as the central criterion for value creation. It is a complementary indicator, useful when managers prefer to see returns expressed as a percentage and when IRR produces unintuitive results, multiple solutions, or reinvestment assumptions that are difficult to defend. The decision should remain connected to NPV, free cash flow, WACC, and the nature of the alternatives being compared.

In CAPEX, retrofit, expansion, and modernization projects, MIRR is particularly useful for converting intermediate cash flows into a more realistic annual compound return. Its main contribution is not to “produce a better rate,” but to make explicit assumptions that traditional IRR leaves implicit.

What Is Modified IRR

Modified IRR is a single rate that relates the present value of negative cash flows to the future value of positive cash flows, using explicitly defined financing and reinvestment rates.

ACCA describes MIRR as an alternative to IRR that retains the ease of communicating a percentage return while reducing problems associated with the implicit reinvestment of intermediate cash flows. Damodaran also presents Modified IRR as an approach that can replace the assumption of reinvestment at the project’s own IRR with a more plausible rate.

Conceptually, the calculation occurs in three steps:

1. discount negative cash flows to present value using the finance rate;
2. compound positive cash flows to the end of the horizon using the reinvestment rate;
3. find the compound rate that connects these two values over the project life.

Why Traditional IRR Can Be Problematic

IRR is the rate that makes NPV equal to zero.

It is intuitive because it produces a percentage, but that simplicity can hide limitations.

Reinvestment assumption

The traditional interpretation of IRR can be associated with the idea that intermediate positive cash flows are reinvested at the project’s own IRR.

If a project has an IRR of 35% per year, assuming that every cash flow received during the project will also find reinvestment opportunities at 35% may be unrealistic.

Multiple IRRs

Non-conventional cash flows with more than one sign change can produce multiple mathematical solutions.

Example:

• negative initial investment;
• positive cash flows during operations;
• a large negative decommissioning cost at the end.

In this case, the NPV equation may cross zero more than once.

No economically useful IRR

Some cash-flow patterns may not produce a positive IRR or may generate a result that does not help the decision.

Inconsistent ranking

In mutually exclusive projects, IRR and NPV may point to different choices because of differences in scale and timing.

The article on NPV, IRR, Payback, and ROI examines these limitations in greater depth.

How MIRR Addresses the Reinvestment Assumption

The key change is to separate the return generated by the project from the rate at which its intermediate cash flows can be reinvested.

If the organization has a WACC of 12% and there is no reason to believe that intermediate cash flows will be reinvested at 30%, MIRR can use a reinvestment rate closer to 12% or another reference consistent with financial policy.

Conceptual MIRR Formula

One formulation is:

MIRR = (FV of positive cash flows / |PV of negative cash flows|)^(1/n) − 1

where:

• positive cash flows are compounded at the reinvestment rate;
• negative cash flows are discounted at the finance rate;
• n represents the number of periods between the beginning and end of the project.

The MIRR function in financial spreadsheets follows this logic by requesting the series of values, a finance rate, and a reinvestment rate.

Simplified Example

Consider a project:

Year	Cash flow
0	-R$ 1.000.000
1	R$ 300.000
2	R$ 400.000
3	R$ 500.000
4	R$ 600.000

Assume a reinvestment rate of 15% per year.

The positive cash flows are carried forward to year 4:

• year 1: 300.000 × 1,15³;
• year 2: 400.000 × 1,15²;
• year 3: 500.000 × 1,15;
• year 4: 600.000.

The aggregate future value is then compared with the initial investment to find the equivalent compound rate.

Damodaran presents a similar example in which traditional IRR is higher than MIRR because the reinvestment rate assumed by MIRR is lower and more realistic.

MIRR versus IRR

Criterion	IRR	MIRR
Result	percentage rate	percentage rate
Reinvestment	associated with the IRR itself	rate defined by the analyst
Non-conventional cash flows	may generate multiple IRRs	tends to produce a single rate
Financing	not explicitly separated	may use a specific finance rate
Executive communication	very simple	simple, but requires additional assumptions
Relationship with NPV	indirect	indirect

MIRR improves interpretation, but it does not eliminate every problem associated with relative metrics.

MIRR Does Not Replace NPV

NPV measures absolute value created in monetary terms.

MIRR measures an equivalent compound rate.

Two projects may present:

• Project A: MIRR of 22%, NPV of R$ 500 thousand;
• Project B: MIRR of 18%, NPV of R$ 8 million.

If the projects are mutually exclusive and the company can finance either one individually, choosing A only because of its higher rate may destroy an opportunity for greater absolute value creation.

Discounted Cash Flow in Engineering Projects should remain the basis of the decision.

Reinvestment Rate

The reinvestment rate represents the expected return on intermediate positive cash flows until the end of the horizon.

Possible references include:

• WACC;
• minimum acceptable rate of return;
• rate of return on comparable alternative investments;
• corporate cash investment rate;
• a specific rate defined by financial policy.

The choice should be documented.

Do not use the rate merely to “improve” MIRR

The rate should not be selected to produce a desired result.

It must represent a plausible reinvestment opportunity.

Finance Rate

The finance rate represents the cost associated with negative cash flows.

It may reflect:

• cost of debt;
• WACC;
• marginal financing rate;
• internal policy for committed capital.

The treatment depends on the cash-flow perspective.

If the model is FCFF and WACC already represents financing, care is required to avoid economic double counting when introducing specific rates without consistency.

MIRR and WACC

WACC in Engineering Projects can be used as a reference for reinvestment or comparison, but not automatically.

The rule must respect:

• FCFF or FCFE perspective;
• project risk;
• currency;
• inflation;
• capital structure;
• financial policy.

MIRR above WACC may indicate a return above the cost of capital, but NPV should still confirm value creation.

MIRR and the Minimum Acceptable Rate of Return

The minimum acceptable rate of return is the minimum rate required to accept the investment.

An executive rule can compare MIRR with the required rate:

• MIRR > required rate: percentage return exceeds the requirement;
• MIRR = required rate: the project is at the threshold;
• MIRR < required rate: the return rate is insufficient.

However, NPV calculated at the required rate remains the consistent monetary criterion.

MIRR and Free Cash Flow

MIRR quality depends on the cash flow used.

Free Cash Flow in Engineering Projects should organize:

• CAPEX;
• OPEX;
• taxes;
• working capital;
• replacements;
• residual value;
• incremental benefits.

If sunk costs, interest, or working capital are treated incorrectly, MIRR merely converts a flawed cash flow into an apparently sophisticated rate.

MIRR and the Time Value of Money

The Time Value of Money analysis explains the operations MIRR combines: discounting negative cash flows and compounding positive cash flows.

The final rate is an equivalent compound return between the beginning and end of the horizon.

Why MIRR Tends to Be Lower than IRR in High-IRR Projects

When traditional IRR is very high and the reinvestment rate used in MIRR is lower, intermediate cash flows grow less by the end of the horizon.

This reduces the equivalent compound return.

This difference can be useful because it removes the impression that all intermediate cash can replicate the extraordinary profitability of the original project.

When MIRR Can Be Higher than IRR

It is also possible for the reinvestment rate or the cash-flow structure to produce MIRR above traditional IRR.

The result depends on the dates, signs, and rates adopted.

Therefore, there is no rule that MIRR will always be lower.

Non-Conventional Cash Flows

Engineering projects frequently include material costs at closeout:

• decommissioning;
• environmental remediation;
• dismantling;
• site restoration;
• replacement of a critical component;
• major overhaul.

These late negative cash flows can produce multiple IRRs.

MIRR tends to avoid this ambiguity by separating positive and negative cash flows and producing a single compound rate.

Decommissioning Example

Consider:

Year	Cash flow
0	-R$ 5 mi
1	R$ 2 mi
2	R$ 3 mi
3	R$ 3 mi
4	-R$ 2 mi

There are two sign changes: negative, positive, and negative again.

IRR may produce multiple mathematical roots.

MIRR treats positive and negative cash flows separately according to the defined rates, reducing ambiguity.

MIRR in Long-Life Projects

The longer the horizon, the greater the impact of the reinvestment assumption.

Projects lasting 15, 20, or 30 years accumulate intermediate cash flows for a long time. The difference between reinvesting at 12% and at 25% can be enormous.

Therefore, MIRR is especially relevant in:

• energy;
• infrastructure;
• industrial plants;
• concessions;
• data centers;
• utility assets;
• projects with long operating cycles.

MIRR in Retrofit Projects

Retrofits commonly have initial CAPEX followed by annual savings.

If IRR is very high because the investment is relatively small, MIRR can provide a more realistic view of compound profitability when annual savings are reinvested at a plausible corporate rate.

MIRR in Energy Efficiency

Efficiency projects can present high percentage returns.

MIRR helps answer:

• what compound return exists if the savings are reinvested at WACC?
• how should projects of different scales be compared?
• what rate remains after removing the assumption of reinvestment at the project’s own IRR?

It should be used together with NPV and the Profitability Index when capital is constrained.

MIRR in Reliability Projects

Reliability projects may generate irregular benefits by reducing expected losses.

MIRR can be calculated as long as the economic cash flows are defined, but the main uncertainty may lie in monetizing avoided losses.

In these cases, sensitivity and scenario analysis may be more important than the difference between IRR and MIRR.

MIRR and Mutually Exclusive Projects

MIRR reduces some IRR problems, but it is still a relative rate.

If two projects have different scales, a higher MIRR does not guarantee greater absolute value.

The priority should be:

1. verify the NPV of each alternative;
2. perform incremental analysis;
3. use MIRR as a complementary indicator;
4. consider risk and constraints.

Incremental Analysis with MIRR

MIRR can be calculated on the incremental cash flow between two alternatives.

This answers the question: what is the compound return on the additional capital required to move from alternative A to B?

If incremental MIRR exceeds the required rate and incremental NPV is positive, the higher-investment alternative can be economically defended.

MIRR and the Profitability Index

MIRR measures compound percentage return. PI measures value created per unit of capital.

Under capital rationing, PI may be more directly useful for prioritizing the use of budget. MIRR can complement the ranking by showing annualized return.

Neither replaces optimization of the portfolio’s total NPV.

MIRR and Payback

Payback measures the speed of capital recovery.

MIRR measures compound return over the full horizon.

A project may have fast payback and moderate MIRR if benefits after recovery are small.

Another may have slower payback and higher MIRR because it generates robust cash flows for many years.

MIRR and ROI

ROI may be based on accounting results or simple relationships between gain and investment.

MIRR is built on cash flow and the time value of money.

For long projects, the methodological difference is significant.

MIRR and Residual Value

Residual Value in Engineering Projects enters as a positive or negative terminal cash flow, depending on the case.

Because it occurs at the end of the horizon, it can materially affect MIRR when significant.

The assumption needs to be technically defensible.

MIRR and Sunk Costs

Sunk Cost should not be reintroduced in a continuation decision.

If the organization recalculates MIRR at a gate, the cash flow should start from the new base date and include only relevant future costs and benefits.

MIRR and Opportunity Cost

Reinvestment and finance rates represent real alternative uses of capital.

Opportunity Cost in Engineering Projects provides the economic logic for these references.

Using an arbitrary rate breaks that connection.

MIRR and Inflation

The reinvestment rate and cash flows need to be on the same basis.

Nominal cash flows require nominal rates. Real cash flows require real rates.

Mixing bases changes both compounded values and the resulting rate.

MIRR and Currency

The same rule applies to currency.

Cash flows in dollars should use rates consistent with dollars; cash flows in Brazilian reais should use rates consistent with reais.

Projects with revenues and costs in different currencies need to model exchange rates before calculating the final MIRR.

MIRR and Periodicity

If cash flows are monthly, MIRR calculated over monthly periods must be annualized correctly for comparison with annual rates.

The compound relationship is:

annual MIRR = (1 + monthly MIRR)^12 − 1

Multiplying the monthly rate by 12 is only a nominal approximation.

MIRR in Spreadsheets

Spreadsheets such as Microsoft Excel and Google Sheets provide a MIRR function.

The typical structure uses:

• cash-flow range;
• finance_rate;
• reinvest_rate.

Before using the function, verify:

• uniform periodicity;
• correct signs;
• rates on the same basis as the periods;
• at least one positive and one negative cash flow;
• consistency of the financial perspective.

The convenience of the function does not replace the economic definition of the rates.

Excel Example

If annual cash flows are in B2:B7, the function can be structured conceptually as:

=MIRR(B2:B7; finance_rate; reinvestment_rate)

The result will be a rate per period of the series.

If the series is annual, the result is annual. If it is monthly, it must be interpreted as monthly.

MIRR and Irregular Dates

The traditional MIRR function assumes regular periods.

Real projects may have irregular disbursement and receipt dates.

In that case, it may be necessary to build the calculation explicitly by date, using present and future values for each cash flow rather than relying directly on the standard function.

IRR versus MIRR Comparison Example

Consider:

Year	Cash flow
0	-R$ 1,0 mi
1	R$ 300 mil
2	R$ 400 mil
3	R$ 500 mil
4	R$ 600 mil

The IRR of this cash flow is high because returns are strong relative to the initial investment.

If the reinvestment rate is 10%, MIRR will be lower than IRR because cash flows from years 1 through 3 are not compounded at the project’s own high internal rate.

This does not mean the project became worse. It only changes the assumption about what happens to intermediate cash.

Example with Different Financing

Project A requires disbursements concentrated at the beginning.

Project B requires additional payments in year 3.

If late negative cash flows are financed at a different rate, MIRR can incorporate them explicitly.

Traditional IRR treats all cash flows within the same equation without separating this assumption.

MIRR and Capital Constraints

Damodaran notes that Modified IRR can be useful when capital constraints exist and the IRR reinvestment assumption is inadequate.

Even so, when the objective is to select a combination of projects under a limited budget, the Profitability Index and optimization of total NPV can be more direct.

MIRR and Project Portfolio

Project Portfolio Management can use MIRR as one return dimension, together with:

• NPV;
• PI;
• risk;
• strategic alignment;
• mandatory status;
• maturity;
• execution capacity;
• dependencies.

The rate should not become an isolated ranking.

MIRR and Stage-Gate

MIRR should be recalculated when cash flows change between gates.

Examples of changes:

• revised CAPEX;
• schedule delay;
• lower ramp-up;
• higher OPEX;
• shorter useful life;
• revised benefit;
• changed residual value.

Stage-Gate in Engineering Projects makes it possible to update the economic case before a new commitment.

MIRR and FEL

During FEL — Front-End Loading, cash-flow and rate assumptions mature.

Initially, the indicator may be based on benchmarks. With greater definition, it should incorporate:

• more accurate budget;
• schedule;
• quotations;
• expected performance;
• risks;
• useful life;
• contracting strategy.

MIRR should not remain frozen while the project changes.

MIRR and Sensitivity Analysis

Sensitivity and Scenario Analysis in Engineering Projects should test:

• CAPEX;
• benefits;
• delay;
• reinvestment rate;
• finance rate;
• useful life;
• residual value;
• OPEX.

If a small change in the reinvestment rate materially changes the conclusion, the project depends on a critical financial assumption.

MIRR and Monte Carlo

MIRR can be calculated in each iteration of a Monte Carlo simulation.

This produces a distribution of returns instead of a single value.

However, probabilistic NPV often remains more informative for measuring value creation under uncertainty.

Monte Carlo Simulation in Engineering Projects should be used when the distributions of the drivers are defensible.

When to Use MIRR

MIRR is especially useful when:

• managers require a percentage indicator;
• IRR is very high and the reinvestment assumption appears unrealistic;
• late negative cash flows exist;
• the project has multiple sign changes;
• the comparison requires a more realistic compound rate;
• there is a clear reinvestment and financing policy.

When MIRR Adds Little Value

It may add little value when:

• NPV already answers the decision clearly;
• cash flows are simple and IRR is moderate;
• the reinvestment rate is arbitrary;
• projects are mutually exclusive and the main issue is scale;
• cash flow is still immature;
• technical risk dominates much more than the difference between IRR and MIRR.

There is no need to add indicators merely to increase the number of figures in the Business Case.

Common Errors

Using MIRR as a substitute for NPV

A percentage rate does not measure absolute value created.

Choosing a convenient reinvestment rate

The rate needs an economic rationale.

Using a finance rate incompatible with the cash flow

This can create double counting with WACC or financing already modeled.

Mixing periodicities

Annual rates applied to monthly cash flows generate incorrect results.

Ignoring irregular dates

Standard functions generally assume uniform periods.

Recalculating MIRR with sunk costs

At gates, use only relevant future cash flows.

Comparing MIRRs of projects with incomparable risks

A higher rate may simply reflect a different risk profile.

Using MIRR to mask a negative NPV

If NPV at the required rate is negative, the economic decision needs to be explained clearly.

Not disclosing the rates used

Without the finance rate and reinvestment rate, the indicator is not reproducible.

How to Document MIRR in the Business Case

Record:

• cash flow used;
• FCFF or FCFE;
• periodicity;
• base date;
• finance rate;
• source of the finance rate;
• reinvestment rate;
• source of the reinvestment rate;
• horizon;
• resulting MIRR;
• corresponding NPV;
• traditional IRR;
• sensitivity;
• inflation and currency assumptions;
• person responsible for validation.

The objective is to allow the indicator to be reproduced and audited.

How to Present MIRR to an Investment Committee

An executive presentation can show:

Indicator	Result	Interpretation
NPV	R$ 4,2 mi	value created
IRR	28%	traditional internal return
MIRR	18%	compound return with realistic reinvestment
WACC	12%	cost of capital
Discounted payback	5,2 years	time to recovery

This prevents MIRR from being presented in isolation.

When Engineering Consulting Adds Value

MIRR mathematics is simple. The technical value lies in qualifying the cash flow that feeds it.

Engineering Technical Consulting can contribute with:

• CAPEX;
• schedule;
• OPEX;
• ramp-up;
• useful life;
• replacements;
• decommissioning;
• residual value;
• execution risks;
• engineering alternatives.

The Technical and Economic Feasibility Study integrates these assumptions with rates and DCF.

Final Considerations

Modified IRR is a useful evolution of traditional IRR when the assumption of reinvestment at the project’s own internal rate is difficult to defend or when the cash flow has non-conventional signs. By separating reinvestment and financing rates, MIRR makes part of the financial assumptions more explicit and produces a compound rate that is often more realistic.

Even so, it remains a relative indicator. Projects of different scales may have different MIRRs without the higher rate corresponding to the greater value created. Therefore, NPV should remain the reference for absolute value creation, while MIRR, PI, payback, and other indicators provide complementary perspectives.

In engineering, the most important result is not the isolated rate. It is the consistency among technical cash flow, schedule, CAPEX, OPEX, risk, useful life, residual value, and cost of capital. MIRR improves the analysis when it makes that consistency more transparent — not when it merely adds another percentage to the dashboard.

Technical references

[1] ACCA. Modified internal rate of return. Advanced Financial Management. London: Association of Chartered Certified Accountants. Available at: https://www.accaglobal.com/gb/en/student/exam-support-resources/professional-exams-study-resources/p4/technical-articles/Modified-internal-rate-return.html

[2] DAMODARAN, Aswath. Applied Corporate Finance. 4th ed. Hoboken: Wiley. Capital budgeting, profitability index and modified IRR. Available at: https://pages.stern.nyu.edu/~adamodar/pdfiles/acf4E/acf4Ebook.pdf

[3] DAMODARAN, Aswath. Capital Budgeting under Certainty. New York: NYU Stern. Available at: https://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/cbcert.html

[4] DAMODARAN, Aswath. Applied Corporate Finance — NPV, IRR or Modified IRR. New York: NYU Stern. Available at: https://pages.stern.nyu.edu/~adamodar/New_Home_Page/AppldCF/derivn/ch5deriv.html

[5] PROJECT MANAGEMENT INSTITUTE. The Standard for Project Management and A Guide to the Project Management Body of Knowledge (PMBOK® Guide). 8th ed. Newtown Square: PMI, 2025. Available at: https://www.pmi.org/standards/pmbok

Frequently asked questions

What is Modified IRR or MIRR?

It is a return rate that compounds positive cash flows at a defined reinvestment rate and discounts negative cash flows at a finance rate, producing an equivalent compound rate for the project.

What is the difference between IRR and MIRR?

Traditional IRR can be interpreted with reinvestment at the IRR itself. MIRR allows an explicit reinvestment rate and, in many formulations, a finance rate to be defined.

Is MIRR better than IRR?

It solves or reduces some IRR limitations, especially reinvestment and multiple rates, but it does not replace NPV as a measure of absolute value creation.

What rate should be used as the reinvestment rate?

It may be WACC, a minimum required rate, or another plausible opportunity rate, provided there is economic justification and consistency with the cash-flow currency and periodicity.

What rate should be used as the finance rate?

It depends on the cash-flow perspective and financial policy. It may reflect the marginal cost of financing or another consistent rate while avoiding double counting with WACC.

Can MIRR be higher than IRR?

Yes. The result depends on the cash-flow pattern and the rates adopted. There is no rule that MIRR must always be lower.

Does MIRR resolve multiple IRRs?

In general, the MIRR structure tends to produce a single rate by separating positive and negative cash flows, reducing ambiguity in non-conventional cash flows.

Should MIRR be used alone to approve projects?

No. It should be presented together with NPV and, as applicable, WACC, PI, payback, risk, and strategic criteria.

Supplementary technical materials

Related solutions

• Project, Program, and Portfolio Governance
• Engineering Indicators, Dashboards, and Executive Reports
• Process, Workflow, and Technical Approval Management

Related services

• Technical and Economic Feasibility Study
• FEL — Front-End Loading
• Engineering Technical Consulting
• Project Management

Core content on the topic

• NPV, IRR, Payback, and ROI in Engineering Projects
• Discounted Cash Flow in Engineering Projects
• WACC in Engineering Projects
• Free Cash Flow in Engineering Projects

Related technical content

• Time Value of Money in Engineering Projects
• Profitability Index in Engineering Projects
• Opportunity Cost in Engineering Projects
• Residual Value in Engineering Projects
• Sensitivity and Scenario Analysis in Engineering Projects