Definition – 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).
Modified Internal Rate of Return Calculator
Formula – How is MIRR calculated?
MIRR is calculated using a time value calculation.
MIRR = Number of Periods√((Future Value of Positive Cash Flows at Reinvestment Rate) ÷ (- 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:
Future Value = Present Value x (1 + Rate)Number of Periods
Future Value – Period 0 = 2000 x (1 + 0.02)5 = 2,208.16
Future Value – Period 3 = 10000 x (1 + 0.02)5 = 10,404
Future Value – Period 4 = 100000 x (1 + 0.02)1 = 102,000
Future Value – Total of all Positive Cash Flows = $114,612.16
Step 2 – Present Value of Negative Cash Flows at Finance Rate:
Present Value = Future Value ÷ (1 + Rate)Number of Periods
Present Value – Period 1= -50000 ÷ (1 + 0.03)2 = -48,543.69
Present Value – Period 2 = -35000 ÷ (1 + 0.03)2 = -32,990.86
Present Value – Period 5 = -5000 ÷ (1 + 0.03)5 = -4,313.04
Present Value – Total of all Negative Cash Flows = -85,847.59
Step 3 – MIRR Calculation
MIRR = Number of Periods√((Future Value of Positive Cash Flows at Reinvestment Rate) ÷ (-Present Value of Negative Cash Flows at Finance Rate)) – 1
MIRR = 5√(114,612.16 ÷ -85,847.59) – 1
MIRR = 5√1.33506555047 – 1
MIRR = 1.0594989 – 1
MIRR = 0.0594989 or 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 compared with other rate calculation methods.
Sources and External Resources
- Wikipedia – Modified Internal Rate of Return – Wikipedia’s entry on modified internal rate of return, including the formulas and a calculation example.
- Xplaind – Modified Internal Rate of Return – Some different methods for calculating MIRR, including a spreadsheet.