Free MIRR Calculator - Modified Internal Rate of Return

What is the Modified Internal Rate of Return?

The Modified Internal Rate of Return (MIRR) is a financial metric that addresses a key limitation of the conventional Internal Rate of Return (IRR). While the standard IRR assumes that all positive cash flows generated by a project are reinvested at the project's own IRR (a rate that can be unrealistically high), MIRR allows you to specify a separate, realistic reinvestment rate and a distinct finance rate for borrowing costs. This makes MIRR a more reliable tool for evaluating and comparing investment opportunities, especially when comparing projects of different sizes or timelines.

The MIRR calculator presented here lets you input a series of cash flows, a finance rate (the cost of financing negative flows), and a reinvestment rate (the rate at which positive flows are assumed to be reinvested). By applying the MIRR formula, the calculator provides an annualized return percentage that can be used alongside other metrics to assess profitability.

MIRR vs IRR: Core Differences

Both IRR and MIRR consider the time value of money by discounting future cash flows. However, their treatment of intermediate cash inflows differs fundamentally:

• IRR inherently assumes that every positive cash flow is reinvested at the project's own IRR, which may not be achievable in practice.
• MIRR lets you override that assumption by specifying a conservative reinvestment rate (e.g., the company's cost of capital or a typical money-market rate). The finance rate for negative flows is also set explicitly.

Because of this flexibility, MIRR often yields a lower (and more realistic) rate than IRR, and it produces a unique value for a given set of assumptions, avoiding the multiple-IRR problem that can occur with unconventional cash flow patterns.

The MIRR Formula

The MIRR is calculated using the following relationship:

$$\text{MIRR} = \left( \frac{FV_{\text{positive}}}{PV_{\text{negative}}} \right)^{\frac{1}{n}} - 1$$

where:

• $n$ – number of periods (typically years) until the project ends.
• $FV_{\text{positive}}$ – future value of all positive cash flows, compounded to the end of the project at the reinvestment rate $RR$.
• $PV_{\text{negative}}$ – present value of all negative cash flows, discounted back to time zero at the finance rate $FR$.

The individual components are expressed as:

$$FV_{\text{positive}} = \sum_{i=0}^{n} C_i^+ \cdot (1 + RR)^{n-i}$$ $$PV_{\text{negative}} = \sum_{i=0}^{n} \frac{C_i^-}{(1 + FR)^i}$$

Here:

• $C_i^+$ – positive cash flows (inflows) occurring in period $i$.
• $C_i^-$ – negative cash flows (outflows) occurring in period $i$.
• $RR$ – reinvestment rate (a percentage).
• $FR$ – finance rate (a percentage).

Only the inflows are included when calculating $FV_{\text{positive}}$, and only the outflows are used for $PV_{\text{negative}}$.

Worked Example

Consider the following investment project (amounts are in dollars):

Period	Cash Flow
0	-10,000
1	6,000
2	-4,000
3	8,000
4	3,000
5	7,000

Suppose the finance rate is 10% and the reinvestment rate is 12%. The project lasts 5 years.

Step 1: Compute $FV_{\text{positive}}$.
Positive cash flows occur in years 1, 3, 4, and 5. Compound each forward to year 5:

• Year 1: $6,000 ×$ (1.12)^{4} $=$6,000 × 1.5735 = $9,441
• Year 3: $8,000 ×$ (1.12)^{2} $=$8,000 × 1.2544 = $10,035
• Year 4: $3,000 ×$ (1.12)^{1} $=$3,000 × 1.12 = $3,360
• Year 5: $7,000 (no compounding) =$7,000

Total FV_{\text{positive}} \approx \29,836$.

Step 2: Compute $PV_{\text{negative}}$.
Negative cash flows occur at year 0 (-$10,000) and year 2 (-$4,000). Discount each to the present:

• Year 0: $10,000 /$ (1.10)^{0} $=$10,000
• Year 2: $4,000 /$ (1.10)^{2} $=$4,000 / 1.21 ≈ $3,306

Total PV_{\text{negative}} \approx \13,306$.

Step 3: Apply the MIRR formula.

$$\text{MIRR} = \left( \frac{29,836}{13,306} \right)^{\frac{1}{5}} - 1 = \left( 2.242 \right)^{0.2} - 1 \approx 0.1753 = 17.53\%$$

For comparison, the conventional IRR for this set of cash flows works out to 24.38%. The substantial gap illustrates why MIRR and IRR are not interchangeable: MIRR provides a more conservative, often more realistic picture when reinvestment rates differ from the project's IRR.

Key Takeaways

• MIRR corrects the unrealistic reinvestment assumption inherent in IRR, giving you a clearer view of a project's profitability.
• By requiring both a finance rate and a reinvestment rate, MIRR adapts to real-world conditions where borrowed money has a cost and surplus cash can be reinvested only at achievable rates.
• Always use MIRR alongside other financial metrics (NPV, payback period) for a complete assessment of an investment.

Whether you are analyzing a capital budgeting proposal, comparing mutual funds, or evaluating a real estate deal, the Modified Internal Rate of Return Calculator can help you understand the true potential return under practical financing and reinvestment constraints.