Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure) article
Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure)
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Video Title: Learn about the Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure)
Video Publication_Date: Tuesday, May 21, 2024
Video Duration: 4:15
Video Description:
The topic for this commercial real estate investment analysis video is Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure). Throughout the video planEASe Software is used to illustrate Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure). The video does not use the current Proforma Example, but all the factors that the Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure) are sensitive to are covered.
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How the Modified Internal Rate of Return MIRR is calculated?Definition
The Modified Internal Rate of Return (MIRR) is the Present Value Discount Rate that makes the Net Present Value of the investment equal to zero when all positive future cash flows have been reinvested until the end of the Holding Period at the Reinvestment Rate, and all negative future cash flows have been funded at the Acquisition Date at the Safe Rate. Other sources have defined the FMRR measure (variously the Financial Management Rate of Return or the Findley Messner Rate of Return) to be the same as the MIRR.
Example
This example is designed to make sure the effect of the reinvestment rate of the Modified Internal Rate of Return (MIRR) process is very clear and not just shown as a mathematical formula. The actual investment was not very good (in fact there is $0 profit and a 0% Internal Rate of Return (IRR)), but because of the reinvestment opportunity, which could be some outside investment or the same investment, the Future Value shows a gain of $22,116.60 and the Modified Internal Rate of Return (MIRR) which uses only the initial negative number and the last future value number is 4.0770%.
Date
|
Actual
Cash Flow
|
Modified
Cash Flow
|
Future Value Reinvested
at 10.0000%
|
MIRR is an IRR on these
two Cash Flows
|
| 1 Jan 2010 | ($100,000.00) | Not Modified | | ($100,000.00) |
| 1 Jan 2011 | 20,000.00 | Compounded forward 4 years by 10% | 29,289.65 | 0 |
| 1 Jan 2012 | 20,000.00 | Compounded forward 3 years by 10% | 26,626.95 | 0 |
| 1 Jan 2013 | 20,000.00 | Compounded forward 2 years by 10% | 24,200.00 | 0 |
| 1 Jan 2014 | 20,000.00 | Compounded forward 1 years by 10% | 22,000.00 | 0 |
| 1 Jan 2015 | 20,000.00 | Not modified, received at end of investment | 20,000.00 | $122,116.60 |
| TOTALS |
$0.00
(IRR = 0)
| The actual investment only returned the same amount invested over five years. The Future Value is the total of all the positive cash flows reinvested at the Reinvestment Rate. | $122,116.60 | MIRR = 4.0770% |
Based on this example, describing the Modified Internal Rate of Return (MIRR) as the IRR of the Future Value calculation is a quick way to describe how the Modified Internal Rate of Return (MIRR) is calculated. Please note, also, that the only reason this investment shows a positive MIRR is because of cash flows generated external to the investment. Considering this, the measure might better be named the Modified External Rate of Return.
Modified Internal Rate of Return (MIRR) Considers: - All assumptions entered, Reinvestment Rate, Safe Rate
Modified Internal Rate of Return (MIRR) Ignores:- Only things that were not entered
Why is Modified Internal Rate of Return MIRR useful?
Relatively recently, theoreticians have developed the Modified Internal Rate of Return (MIRR) in response a perceived need to measure the growth in net worth due to an investment. The IRR calculation does not consider what happens to positive cash flows thrown off during the life of an investment. In order to do that, you need to assume a 'Reinvestment Rate' at which these cash flows are reinvested and then measure the total amount of cash generated by both the investment and the reinvestment of the cash generated during the life of the investment. Similarly the MIRR calculation assumes that the cash necessary to fund any negative cash flows after the initial investment is invested at a 'Safe Rate' at the beginning of the investment so that the necessary funds will be available at the time of the negative cash flow. The 'Safe Rate' would represent the rate at which the investor could actually place the money in an account where it would be liquid at the appropriate time.
The methodology used to correct the IRR for these deficiencies requires that the investor specify his 'Reinvestment Rate' for positive cash flows during the life of the investment, and his 'Safe Rate' for funding the negative cash flows during that life. The Safe Rate is used to discount all negative cash flows to the present (the Acquisition Date in this case), yielding a Present Value of the invested amounts which represents the sum of the initial investment plus the amount necessary to fund the future negative cash flows, assuming that the funding amount is invested at the Safe Rate on the Acquisition Date. The Reinvestment Rate is used to compound all future positive cash flows to the end of the investment period. This yields a Future Value which represents the sum of the cash received from the sale of the investment plus the amount that would be available from the reinvested positive cash flows.
There is often a misconception that a reason to use the MIRR is because if you use the IRR, then the IRR is choosing a Reinvestment Rate for you. This is completely untrue, as the IRR does not use a Reinvestment Rate at all. The IRR uses the same process as the NPV which only uses a Discount Rate, and looks to discount the cash flow each month. The MIRR uses the same process as Future Value to modify the cash flows, such that there will only be a number at the beginning and one at the end. This is probably why there is not a XMIRR in Excel or Google Spreadsheets. After all, why count monthly when there is only a beginning and end cash amount to consider?.
The Modified Internal Rate of Return (MIRR) can be shown in these planEASe reports:
IRR Verification ReportRetail - Office
These cash flows and dates are those on which the Rate of Return After Tax in the planEASe analysis of the Retail - Office are based.'
planEASe Software plans operating cash flows monthly, and assumes that cash flows occuring during the month all occur at the middle of the month.Calculators and Spreadsheets typically schedule these cash flows at the end of the year (year-end convention).Since cash flows do actually occur unevenly during the year, the mid-month convention is more accurate.
The Internal Rate of Return (IRR) is defined as the Present Value Discount Rate which makes the Net Present Value of the Cash Flows involved equal to zero. The Net Present Value of ($0.16) shown below demonstrates that the Net Present Value of these Cash Flows is very close to zero when discounted at 4.5752% and, in turn, the IRR of the Cash Flows is very close to 4.5752%.
Date
|
Years
|
Cash Flow
|
Present Value
Discount Factor
|
Present Value
at 4.5752%
|
| 1 Jan 2010 | 0.00 | ($1,023,344.00) | 1.0000000 | ($1,023,344.00) |
| 15 Jan 2010 | 0.04 | 1,691.00 | 0.9982856 | 1,688.10 |
| 15 Feb 2010 | 0.12 | 1,680.00 | 0.9944997 | 1,670.76 |
| 15 Mar 2010 | 0.20 | 1,669.00 | 0.9910926 | 1,654.13 |
| 15 Apr 2010 | 0.28 | 1,658.00 | 0.9873341 | 1,637.00 |
| 15 May 2010 | 0.37 | 1,647.00 | 0.9837104 | 1,620.17 |
| 15 Jun 2010 | 0.45 | 1,636.00 | 0.9799798 | 1,603.25 |
| 15 Jul 2010 | 0.53 | (11,578.00) | 0.9763831 | (11,304.56) |
| 15 Aug 2010 | 0.62 | 3,579.00 | 0.9726804 | 3,481.22 |
| 15 Sep 2010 | 0.70 | 3,568.00 | 0.9689916 | 3,457.36 |
| 15 Oct 2010 | 0.79 | 3,556.00 | 0.9654352 | 3,433.09 |
| 15 Nov 2010 | 0.87 | 3,545.00 | 0.9617740 | 3,409.49 |
| 15 Dec 2010 | 0.95 | 3,533.00 | 0.9582441 | 3,385.48 |
| 15 Jan 2011 | 1.04 | 3,796.00 | 0.9546101 | 3,623.70 |
| 15 Feb 2011 | 1.12 | 3,785.00 | 0.9509900 | 3,599.50 |
| 15 Mar 2011 | 1.20 | 3,773.00 | 0.9477319 | 3,575.79 |
| 15 Apr 2011 | 1.28 | 3,761.00 | 0.9441378 | 3,550.90 |
| 15 May 2011 | 1.37 | 3,749.00 | 0.9406726 | 3,526.58 |
| 15 Jun 2011 | 1.45 | 3,737.00 | 0.9371053 | 3,501.96 |
| 15 Jul 2011 | 1.53 | 3,772.00 | 0.9336659 | 3,521.79 |
| 15 Aug 2011 | 1.62 | 3,760.00 | 0.9301252 | 3,497.27 |
| 15 Sep 2011 | 1.70 | 3,748.00 | 0.9265978 | 3,472.89 |
| 15 Oct 2011 | 1.79 | 3,736.00 | 0.9231970 | 3,449.06 |
| 15 Nov 2011 | 1.87 | 2,001.00 | 0.9196960 | 1,840.31 |
| 15 Dec 2011 | 1.95 | 779.00 | 0.9163205 | 713.81 |
| 15 Jan 2012 | 2.04 | (3,586.00) | 0.9128455 | (3,273.46) |
| 15 Feb 2012 | 2.12 | (108,832.00) | 0.9093837 | (98,970.05) |
| 15 Mar 2012 | 2.20 | 3,454.00 | 0.9061572 | 3,129.87 |
| 15 Apr 2012 | 2.29 | 3,441.00 | 0.9027207 | 3,106.26 |
| 15 May 2012 | 2.37 | 3,428.00 | 0.8994076 | 3,083.17 |
| 15 Jun 2012 | 2.45 | 3,415.00 | 0.8959967 | 3,059.83 |
| 15 Jul 2012 | 2.54 | 3,548.00 | 0.8927082 | 3,167.33 |
| 15 Aug 2012 | 2.62 | 3,535.00 | 0.8893228 | 3,143.76 |
| 15 Sep 2012 | 2.71 | 3,522.00 | 0.8859502 | 3,120.32 |
| 15 Oct 2012 | 2.79 | 3,508.00 | 0.8826986 | 3,096.51 |
| 15 Nov 2012 | 2.87 | 3,495.00 | 0.8793511 | 3,073.33 |
| 15 Dec 2012 | 2.96 | 3,528.00 | 0.8761237 | 3,090.96 |
| 15 Jan 2013 | 3.04 | 3,670.00 | 0.8728012 | 3,203.18 |
| 15 Feb 2013 | 3.13 | 3,863.00 | 0.8694912 | 3,358.84 |
| 15 Mar 2013 | 3.20 | 3,850.00 | 0.8665124 | 3,336.07 |
| 15 Apr 2013 | 3.29 | 3,836.00 | 0.8632263 | 3,311.34 |
| 15 May 2013 | 3.37 | 3,822.00 | 0.8600581 | 3,287.14 |
| 15 Jun 2013 | 3.45 | 3,808.00 | 0.8567965 | 3,262.68 |
| 15 Jul 2013 | 3.54 | 763.00 | 0.8536519 | 651.34 |
| 15 Aug 2013 | 3.62 | (1,168.00) | 0.8504145 | (993.28) |
| 15 Sep 2013 | 3.71 | 3,720.00 | 0.8471895 | 3,151.54 |
| 15 Oct 2013 | 3.79 | 3,706.00 | 0.8440801 | 3,128.16 |
| 15 Nov 2013 | 3.87 | 3,691.00 | 0.8408791 | 3,103.68 |
| 15 Dec 2013 | 3.96 | 3,725.00 | 0.8377929 | 3,120.78 |
| 15 Jan 2014 | 4.04 | 3,724.00 | 0.8346157 | 3,108.11 |
| 15 Feb 2014 | 4.13 | 3,922.00 | 0.8314506 | 3,260.95 |
| 15 Mar 2014 | 4.20 | 3,907.00 | 0.8286021 | 3,237.35 |
| 15 Apr 2014 | 4.29 | 3,892.00 | 0.8254598 | 3,212.69 |
| 15 May 2014 | 4.37 | 3,877.00 | 0.8224302 | 3,188.56 |
| 15 Jun 2014 | 4.45 | 3,862.00 | 0.8193113 | 3,164.18 |
| 15 Jul 2014 | 4.54 | 3,846.00 | 0.8163042 | 3,139.51 |
| 15 Aug 2014 | 4.62 | 3,905.00 | 0.8132085 | 3,175.58 |
| 15 Sep 2014 | 4.71 | 3,889.00 | 0.8101246 | 3,150.57 |
| 15 Oct 2014 | 4.79 | 3,874.00 | 0.8071513 | 3,126.90 |
| 15 Nov 2014 | 4.87 | 3,858.00 | 0.8040903 | 3,102.18 |
| 15 Dec 2014 | 4.96 | 1,833.00 | 0.8011391 | 1,468.49 |
| 15 Jan 2015 | 5.04 | (6,170.00) | 0.7981009 | (4,924.28) |
| 15 Feb 2015 | 5.13 | (2,559.00) | 0.7950743 | (2,034.60) |
| 15 Mar 2015 | 5.20 | (2,575.00) | 0.7923504 | (2,040.30) |
| 15 Apr 2015 | 5.29 | (2,592.00) | 0.7893456 | (2,045.98) |
| 15 May 2015 | 5.37 | (78,787.00) | 0.7864485 | (61,961.92) |
| 15 Jun 2015 | 5.45 | 5,014.00 | 0.7834660 | 3,928.30 |
| 15 Jul 2015 | 5.54 | 4,998.00 | 0.7805906 | 3,901.39 |
| 15 Aug 2015 | 5.62 | 5,057.00 | 0.7776303 | 3,932.48 |
| 15 Sep 2015 | 5.71 | 5,041.00 | 0.7746813 | 3,905.17 |
| 15 Oct 2015 | 5.79 | 5,024.00 | 0.7718381 | 3,877.71 |
| 15 Nov 2015 | 5.87 | 5,007.00 | 0.7689110 | 3,849.94 |
| 15 Dec 2015 | 5.96 | 4,989.00 | 0.7660889 | 3,822.02 |
| 31 Dec 2015 | 6.00 | 1,332,012.00 | 0.7645881 | 1,018,440.49 |
| TOTALS | | $311,827.00 | | ($0.16) |
Written by
Michael Feakins, CCIM
of planEASe Software