Find Mirr Calculator

Calculate MIRR

Enter your initial investment, cash flows, finance rate, and reinvestment rate to find the Modified Internal Rate of Return (MIRR).

Period (t)	Cash Flow	PV of Outflows	FV of Inflows

Cash Flow Analysis Table

What is the MIRR (Modified Internal Rate of Return)?

The Modified Internal Rate of Return (MIRR) is a financial metric used in capital budgeting and investment appraisal to assess the profitability of an investment. Unlike the traditional Internal Rate of Return (IRR), the MIRR explicitly assumes that positive cash flows generated by a project are reinvested at a specific rate (the reinvestment rate), and initial outlays or negative cash flows are financed at the firm’s financing cost (the finance rate). This makes the MIRR a more realistic measure than the IRR, which assumes reinvestment at the IRR itself.

The MIRR calculator helps investors and analysts find this modified rate, providing a better picture of a project’s potential return by using more practical assumptions about the rates at which funds are borrowed and reinvested.

Who Should Use the MIRR Calculator?

The MIRR Calculator is valuable for:

• Financial Analysts: To evaluate the attractiveness of different investment projects.
• Project Managers: To justify capital expenditures and compare alternatives.
• Investors: To assess the potential returns of investments with irregular cash flows.
• Students of Finance: To understand a more nuanced approach to investment appraisal compared to the basic IRR.

Common Misconceptions

A common misconception is that MIRR is always superior to IRR. While MIRR addresses the reinvestment rate assumption flaw of IRR, it still relies on accurate forecasts of future cash flows, the finance rate, and the reinvestment rate, which can be uncertain. Also, like IRR, MIRR doesn’t consider the scale of the investment.

MIRR Formula and Mathematical Explanation

The formula for the Modified Internal Rate of Return (MIRR) is:

MIRR = [ (FV_inflows / PV_outflows)^(1/n) – 1 ] * 100%

Where:

• FV_inflows is the Future Value of all positive cash flows (inflows) compounded at the reinvestment rate to the end of the project’s life.
  
  FV_inflows = Σ [ CF_t * (1 + r_reinvest)^(n-t) ] for all CF_t > 0, from t=1 to n
• PV_outflows is the Present Value of all negative cash flows (outflows, including the initial investment) discounted at the finance rate to time 0.
  
  PV_outflows = |Initial Investment| + Σ [ |CF_t| / (1 + r_finance)^t ] for all CF_t < 0, from t=1 to n
• n is the number of periods (typically years) over which the cash flows occur after the initial investment.
• r_reinvest is the reinvestment rate (per period).
• r_finance is the finance rate (per period).
• CF_t is the cash flow at period t.

Variables Table

Variable	Meaning	Unit	Typical Range
Initial Investment	The initial cost or outflow at period 0	Currency	Positive value (representing cost)
CFt	Cash flow at period t	Currency	Positive or Negative
rreinvest	Reinvestment rate per period	% or decimal	0% – 20% (0.0 – 0.20)
rfinance	Finance rate per period	% or decimal	0% – 15% (0.0 – 0.15)
n	Number of periods after initial investment	Count	1 – 50+
PVoutflows	Present Value of all outflows	Currency	Positive
FVinflows	Future Value of all inflows	Currency	Positive
MIRR	Modified Internal Rate of Return	%	-100% to +∞%

Table explaining variables in the MIRR calculation.

Practical Examples (Real-World Use Cases)

Example 1: Evaluating a New Machine Purchase

A company is considering buying a machine for $50,000. It’s expected to generate cash inflows of $15,000, $20,000, $18,000, and $10,000 over the next four years. The company’s finance rate is 6%, and it can reinvest positive cash flows at 9%.

• Initial Investment: 50000
• Cash Flows: 15000, 20000, 18000, 10000
• Finance Rate: 6%
• Reinvestment Rate: 9%

Using the MIRR Calculator with these inputs:

FV of Inflows = 15000*(1.09)^3 + 20000*(1.09)^2 + 18000*(1.09)^1 + 10000*(1.09)^0 = 19425.43 + 23762 + 19620 + 10000 = 72807.43

PV of Outflows = 50000 (no other negative cash flows)

MIRR = ((72807.43 / 50000)^(1/4) – 1) * 100 = (1.4561486^0.25 – 1) * 100 = (1.0984 – 1) * 100 = 9.84%

The MIRR is approximately 9.84%, which can be compared against the company’s hurdle rate.

Example 2: Project with Mid-Term Costs

An investment of $100,000 is expected to yield $40,000 in year 1, require an additional $10,000 outlay in year 2, and then yield $50,000 in year 3 and $60,000 in year 4. Finance rate is 5%, reinvestment rate is 10%.

• Initial Investment: 100000
• Cash Flows: 40000, -10000, 50000, 60000
• Finance Rate: 5%
• Reinvestment Rate: 10%

Using the MIRR Calculator:

FV of Inflows = 40000*(1.10)^3 + 50000*(1.10)^1 + 60000*(1.10)^0 = 53240 + 55000 + 60000 = 168240

PV of Outflows = 100000 + 10000/(1.05)^2 = 100000 + 9070.29 = 109070.29

MIRR = ((168240 / 109070.29)^(1/4) – 1) * 100 = (1.54249^0.25 – 1) * 100 = (1.1143 – 1) * 100 = 11.43%

The MIRR is about 11.43%. Comparing this with other Investment Appraisal Methods helps in decision making.

How to Use This MIRR Calculator

1. Enter Initial Investment: Input the initial outflow at period 0 as a positive number.
2. Enter Cash Flows: List the subsequent cash flows (from period 1 onwards) separated by commas. Use positive numbers for inflows and negative numbers for outflows.
3. Enter Finance Rate: Input the rate (%) at which the company finances its investments or borrows funds.
4. Enter Reinvestment Rate: Input the rate (%) at which the company expects to reinvest the positive cash flows generated by the project.
5. Calculate: The calculator automatically updates the MIRR, FV of inflows, PV of outflows, and the number of periods as you type or when you click “Calculate MIRR”.
6. Review Results: The primary result is the MIRR (%). You also see the intermediate FV and PV values and the period count.
7. Analyze Table and Chart: The table details the contribution of each cash flow to the PV of outflows and FV of inflows. The chart visualizes the cumulative values.

The calculated MIRR gives a percentage return. Compare this rate to your company’s hurdle rate or the cost of capital to decide if the investment is worthwhile. A MIRR higher than the hurdle rate generally indicates an acceptable project.

Key Factors That Affect MIRR Results

• Initial Investment Size: A larger initial outflow will lower the MIRR, all else being equal, as it increases the PV of outflows.
• Timing and Magnitude of Cash Flows: Larger and earlier positive cash flows increase the FV of inflows and thus the MIRR. Later or larger negative cash flows increase PV of outflows, reducing MIRR.
• Reinvestment Rate: A higher reinvestment rate increases the FV of positive cash flows, leading to a higher MIRR. This is a critical assumption. Using our DCF analysis tools can help.
• Finance Rate: A higher finance rate increases the PV of negative cash flows (after period 0), reducing the MIRR.
• Project Duration (Number of Periods): The length of the project affects the compounding and discounting periods, influencing both FV and PV, and thus the MIRR through the (1/n) exponent.
• Accuracy of Cash Flow Forecasts: The MIRR is highly sensitive to the projected cash flows. Overly optimistic or pessimistic forecasts will lead to misleading MIRR values.
• Risk Associated with Cash Flows: While not directly in the MIRR formula, the riskiness of cash flows influences the appropriate finance and reinvestment rates chosen. Higher risk might warrant higher rates being used as benchmarks.

Frequently Asked Questions (FAQ)

Q1: What’s the main difference between MIRR and IRR?

A1: The main difference is the reinvestment rate assumption. IRR assumes cash flows are reinvested at the IRR itself, which is often unrealistic. MIRR allows you to specify a more practical reinvestment rate (and a finance rate for negative flows).

Q2: Is a higher MIRR always better?

A2: Generally, yes. When comparing mutually exclusive projects of similar scale and risk, the one with the higher MIRR is usually preferred, provided it’s above the hurdle rate. However, also consider Net Present Value (NPV).

Q3: What if all my cash flows after the initial investment are negative?

A3: If there are no positive cash flows after the initial investment, the FV of inflows will be zero, and the MIRR calculation will likely result in -100% or be undefined, indicating a loss-making project.

Q4: What should I use for the reinvestment and finance rates?

A4: The finance rate is typically the company’s cost of borrowing or weighted average cost of capital (WACC). The reinvestment rate should reflect the rate at which the company can realistically reinvest funds from the project – often the WACC or the return on average investments.

Q5: Can the MIRR calculator handle multiple negative cash flows after the initial investment?

A5: Yes, the calculator correctly accounts for negative cash flows after period 0 by discounting them at the finance rate to find the PV of outflows.

Q6: What does it mean if the MIRR is lower than the finance rate?

A6: It suggests the project’s return, even with reinvestment, is less than the cost of financing it, making it likely an unattractive investment.

Q7: How does the MIRR calculator handle the number of periods?

A7: The number of periods (n) is determined by the number of cash flow entries you provide after the initial investment.

Q8: Can MIRR be used for projects of different sizes?

A8: While MIRR gives a percentage return, it doesn’t directly account for the scale of the investment. For projects of different sizes, NPV is often a more reliable comparison metric. Our Capital Budgeting Guide discusses this.