• MIRR is a capital-budgeting metric that measures the annualized return of an investment while making more realistic reinvestment and financing assumptions than the traditional IRR. Specifically, MIRR:
• Assumes positive cash flows are reinvested at a specified reinvestment rate (typically the firm’s cost of capital or WACC).
• Assumes cash outflows (financing) are financed at a specified finance rate (borrowing or financing cost).
– MIRR removes the multiple-solution problem of IRR and usually gives a more conservative, realistic profitability figure.
Key takeaways
– MIRR fixes two main IRR problems: (1) multiple IRRs when cash flows change sign more than once, and (2) the unrealistic IRR reinvestment-rate assumption.
– Use MIRR when you want one clear project return that reflects realistic reinvestment and financing rates.
– For mutually exclusive projects or capital-rationing decisions, NPV is usually the theoretically superior decision rule; use MIRR as a complementary metric.
MIRR formula (conceptual)
Let:
– FVpos = future value at the reinvestment rate of all positive cash flows compounded to the project’s end.
– PVneg = present value at the finance rate of all negative cash flows (usually initial outlays) discounted to time zero.
– n = total number of periods.
MIRR = (FVpos / PVneg)^(1/n) − 1
How MIRR works (intuitive)
1. Compound all positive cash inflows forward to the end of the project at the reinvestment rate (e.g., the firm’s cost of capital). This gives the future value of inflows (FVpos).
2. Discount all negative cash flows back to time 0 at the finance rate. This gives the present value of outflows (PVneg).
3. Find the single rate that turns PVneg into FVpos over n periods — that is the MIRR.
Step-by-step calculation (manual)
1. Choose the finance rate (r_f): the rate at which cash outflows are financed (borrowing cost).
2. Choose the reinvestment rate (r_r): the rate at which positive cash flows are assumed to be reinvested (often WACC).
3. For each positive cash flow CF_t at time t, compute its future value at the reinvestment rate: CF_t × (1 + r_r)^(n − t). Sum these → FVpos.
4. For each negative cash flow (including the initial outlay) at time t, compute its present value at the finance rate: CF_t / (1 + r_f)^t. Sum negative PVs → PVneg (take absolute value for the formula).
5. Compute MIRR = (FVpos / PVneg)^(1/n) − 1.
Excel / financial calculator
– Excel built-in: =MIRR(values, finance_rate, reinvest_rate)
• values: range of cash flows including initial negative outlay and subsequent cash flows.
• finance_rate: financing rate (borrow rate).
• reinvest_rate: reinvestment rate (WACC or expected reinvestment return).
– Financial calculators: Many have an MIRR function; otherwise compute FVpos and PVneg then solve with the formula above.
Worked numeric example
Assumptions (from a standard two-year example)
– Initial outlay (t=0): −$195
– Year 1 cash flow (t=1): +$121
– Year 2 cash flow (t=2): +$131
– Finance rate = reinvestment rate = cost of capital = 12%
– n = 2
1. Compound positive cash flows to end (t=2) at 12%:
• CF1 at t=1 → 121 × (1.12)^(2−1) = 121 × 1.12 = 135.52
• CF2 at t=2 → 131 × (1.12)^(2−2) = 131 × 1 = 131
• FVpos = 135.52 + 131 = 266.52
2. PV of negative cash flows at t=0 (finance rate 12%):
• PVneg = 195 (initial outlay at t=0)
3. MIRR = (266.52 / 195)^(1/2) − 1 = (1.36676)^(0.5) − 1 ≈ 0.1691 = 16.91%
Compare: IRR (calculated by solving NPV=0) = 18.66% for the same cash flows. MIRR (16.91%) is lower because it assumes reinvestment at 12% rather than at IRR.
MIRR vs IRR — main differences
– Reinvestment assumption: IRR assumes inflows can be reinvested at the IRR itself. MIRR assumes reinvestment at a specified reinvestment rate (more realistic).
– Uniqueness: IRR can produce multiple values when cash flows change sign multiple times; MIRR yields a unique rate.
– Interpretation: MIRR is often seen as a better measure of a project’s “true” yield under practical reinvestment/financing conditions.
MIRR vs FMRR
– FMRR (Financial Management Rate of Return) is most used in real-estate/REIT contexts. It specifies:
• A safe rate for funds earmarked to meet negative cash flows (highly liquid, low-risk).
• A reinvestment rate for positive cash flows (reflecting realistic reinvestment risk and return).
– MIRR is more generic: two rates (finance and reinvestment) but doesn’t always explicitly separate “safe” and “reinvestment” the way FMRR defines them.
When to use MIRR
– When you want a single, realistic return figure that reflects realistic reinvestment and financing rates.
– When projects have nonconventional cash flows (multiple sign changes) and IRR may be ambiguous.
– When comparing projects where reinvestment at IRR would be unrealistic.
When not to rely solely on MIRR
– For mutually exclusive projects and capital rationing decisions, NPV is the preferred theoretical decision rule because it measures value added directly.
– MIRR does not account for scale — a small project can have a higher MIRR but create less absolute value than a larger project with lower MIRR but higher NPV.
– MIRR requires you to pick finance and reinvestment rates, which are estimates that can be subjective.
Limitations and caveats
– Requires selecting reinvestment and finance rates — results are sensitive to these choices.
– Can lead to suboptimal choices when comparing mutually exclusive projects (use NPV in parallel).
– May hide timing differences: two projects with same MIRR can have very different cash-flow patterns and NPVs.
– Academics debate whether MIRR is a complete theoretical improvement over IRR; it is best used together with NPV and other metrics.
Practical decision steps (recommended workflow)
1. Compute NPV using an appropriate discount rate (WACC). Use NPV as primary decision metric for value creation.
2. Compute MIRR using realistic finance and reinvestment rates (often finance rate = borrowing rate, reinvestment rate = WACC).
3. Compute IRR as a reference, but do not assume reinvestment at IRR when making cash-management decisions.
4. Compare projects by NPV first; use MIRR and IRR to gauge return characteristics and robustness to reinvestment assumptions.
5. Sensitivity: test MIRR with alternative reinvestment and finance rates to see how much conclusions change.
6. Consider capital constraints and project scale explicitly — rank by NPV/NPV per capital unit if constrained.
Summary
– MIRR provides a single, generally more realistic annualized rate of return by incorporating explicit finance and reinvestment rates.
– It corrects two major IRR problems (multiple IRRs and unrealistic reinvestment assumptions) but still requires judgment in choosing rates and does not replace NPV for value-maximization decisions.
– Use MIRR alongside NPV and IRR, and always be explicit about the rates used in the calculation.
Source
– Investopedia, “Modified Internal Rate of Return (MIRR)” by Julie Bang.
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.