# Modified Internal Rate of Return (MIRR) Calculator

LAST UPDATE: October 15th, 2019

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

MIRR is a capital budgeting tool used to compare the different investments. It is a variation of the Internal Rate of Return (IRR) tool.
IRR assumes that funds from the project reinvest at the project’s rate of return. MIRR assumes that funds from the project reinvest at the firm’s cost of capital (which is often different from the rate of return of a proposed project).

### How is MIRR calculated?

MIRR is calculated using a time value calculation. $\text{MIRR} = \sqrt[\text{Number of Periods}]{\frac{\text{Future Value of Positive Cash Flows at Reinvestment Rate}}{-(\text{Present Value of Negative Cash Flows at Finance Rate})}} - 1$

Where:

• ‘Number of Periods’ is the number of periods
• ‘Future Value of Positive Cash Flows at Reinvestment Rate’ is the future value of each cash flow at the reinvestment rate.
• ‘Present Value of Negative Cash Flows at the Finance Rate’ is present value of each cash flow at the finance rate.

### Example

Using a finance rate of 3% and a reinvestment rate of 2%, find the MIRR of: Period 0: 2,000, Period 1: -50,000, Period 2: -35,000, Period 3: 10,000, Period 4: 100,000, Period 5: -5,000.

Step 1 – Future Value of Positive Cash Flows at Reinvestment Rate: $\text{Future Value} = \text{Present Value} \times (1 + \text{Rate})^{Periods}$ $\text{Future Value - Period 0} = 2,000 \times (1 + 0.02)^5 = 2,208.16$ $\text{Future Value - Period 3} = 10,000 \times (1 + 0.02)^2 = 10,404$ $\text{Future Value - Period 4} = 100,000 \times (1 + 0.02)^1 = 102,000$ $\text{Future Value - Total of all Positive Cash Flows} = 114,612.16$

Step 2 – Present Value of Negative Cash Flows at Finance Rate: $\text{Present Value} = \frac{\text{Future Value}}{(1 + {Rate}^{Number of Periods}}$ $\text{Present Value - Period 1} = \frac{-50,000}{(1 + {0.03}^1} = -48,543.69$ $\text{Present Value - Period 2} = \frac{-35,000}{(1 + {0.03}^2} = -32,990.86$ $\text{Present Value - Period 5} = \frac{-5,000}{(1 + {0.03}^5} = -4,313.04$ $\text{Present Value - Total of all Negative Cash Flows} = -85,847.59$

Step 3 – MIRR Calculation $\text{MIRR} = \sqrt[\text{Number of Periods}]{\frac{\text{Future Value of Positive Cash Flows at Reinvestment Rate}}{-(\text{Present Value of Negative Cash Flows at Finance Rate})}} - 1$ $\text{MIRR} = \sqrt{\frac{114,612.16}{-(-85,847.59)}} - 1$ $\text{MIRR} = \sqrt{\frac{114,612.16}{85,847.59}} - 1$ $\text{MIRR} = \sqrt{1.33506555047} - 1$ $\text{MIRR} = 1.0594989- 1$ $\text{MIRR} = 0.0594989$ $\text{MIRR} = 5.950\%$

### What is the difference between internal rate of return (IRR) and modified internal rate of return (mirr)?

MIRR is easier to calculate (IRR is only found through trial and error). MIRR also has other benefits such as factoring in the cost of capital.

IRR is difficult to calculate and can include situations where multiple rates of return can be generated. It also has a few drawbacks and problems compared with other rate calculation methods.