Modified Internal Rate of Return (MIRR)

What is MIRR?

The Modified Internal Rate of Return (MIRR) is a financial metric that measures a project’s profitability while using more realistic assumptions than the traditional IRR. MIRR assumes:
– Positive cash flows are reinvested at the firm’s cost of capital (or another specified reinvestment rate).
– Negative cash flows (initial outlays) are financed at the firm’s financing cost.

MIRR removes the IRR’s unrealistic reinvestment assumption (that cash flows are reinvested at the IRR itself) and eliminates the possibility of multiple IRR solutions.

MIRR formula

MIRR is calculated as:

MIRR = (FV_positive / PV_negative)^(1/n) − 1

where:
– FV_positive = future value of all positive cash flows compounded at the reinvestment rate to the end of period n
– PV_negative = present value of all negative cash flows discounted at the finance/borrowing rate to time 0
– n = number of periods

If the same rate is used for reinvestment and financing, the formula simplifies to the geometric average growth rate between the initial outlay and the future value of inflows.

How to calculate MIRR (step-by-step)

1. Choose:
2. Reinvestment rate for positive cash flows (commonly the firm’s cost of capital).
3. Financing rate for negative cash flows (borrowing cost).
4. Compound each positive cash flow forward to the end of the project using the reinvestment rate; sum these to get FV_positive.
5. Discount each negative cash flow back to time 0 using the financing rate; sum these to get PV_negative (usually the absolute value of initial outlays).
6. Apply the MIRR formula above.

Example

Project: 2-year project
– Initial outlay: −$195 at t=0
– Cash flows: $121 at t=1 and $131 at t=2
– Reinvestment rate (cost of capital): 12%

1. Compound positive cash flows to t=2:
2. FV = $121 × 1.12 + $131 = $266.52
3. PV of negative cash flows = $195
4. n = 2

MIRR = (266.52 / 195)^(1/2) − 1 = 0.1691 → 16.91%

For comparison, the IRR for this cash-flow stream is about 18.66%. MIRR (16.91%) gives a more conservative and typically more realistic estimate because it assumes reinvestment at the cost of capital rather than at the IRR.

MIRR vs. IRR

• Reinvestment assumption: IRR assumes reinvestment at the IRR; MIRR assumes reinvestment at a specified, typically lower, rate (cost of capital).
• Multiple solutions: IRR can produce multiple values when cash flows change sign multiple times; MIRR provides a single value.
• Practicality: MIRR usually gives a more realistic view of a project’s return and avoids overstatement of profitability.

MIRR vs. FMRR

• FMRR (Financial Management Rate of Return) is commonly used in real estate/REIT contexts.
• FMRR uses two explicit rates:
• A “safe rate” to roll negative cash flows (very liquid, low-risk).
• A “reinvestment rate” for positive cash flows (less liquid, market-based).
• MIRR typically uses a financing rate and a reinvestment rate but does not formalize a “safe rate” vs. “reinvestment rate” distinction as FMRR does.

Limitations of MIRR

• Requires choosing reinvestment and financing rates, which introduces subjectivity.
• May not identify the value-maximizing project when comparing mutually exclusive options — NPV is often a better decision rule for that purpose.
• Can be misunderstood by non-financial users.
• Theoretical debates exist about its foundations; results depend on the chosen rates and timing assumptions.

When to use MIRR

• When you want a single, realistic rate of return that reflects a practical reinvestment assumption.
• For projects with irregular cash flows or when IRR yields multiple solutions.
• As a complement to, not a replacement for, NPV analyses when ranking projects or evaluating capital budgeting choices.

Key takeaways

• MIRR refines IRR by using separate reinvestment and financing rates, producing a single, more realistic return measure.
• It is useful for ranking projects, handling alternating cash flows, and avoiding IRR’s optimistic reinvestment assumption.
• Still rely on NPV for absolute value comparisons and for choosing between mutually exclusive projects.