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## Internal Rate of Return (IRR) (Discounted Cash Flow Measure) article

### Internal Rate of Return (IRR) (Discounted Cash Flow Measure)Start a 7 Day Free Trial

 Video Title: Learn about the Internal Rate of Return (IRR) (Discounted Cash Flow Measure)Video Publication_Date: Sunday, September 23, 2018Video Duration: 6:30Video Description:Shows how the Internal Rate of Return (IRR) is calculated, what factors are important, and how to use planEASe Sensitivity Analysis to investigate which assumptions the Internal Rate of Return (IRR) is sensitive to.

 2010 2011 2012 2013 2014 2015 IRR Before Debt 1.5% 9.0% 9.9% 9.0% 9.5% 8.0% IRR Before Tax 9.2% 12.1% 9.5% 11.0% 7.0% IRR After Tax 6.5% 8.8% 6.6% 7.8% 4.6% NPV Before Debt @10.00% (\$246,299) (\$54,097) (\$8,769) (\$106,089) (\$66,107) (\$273,216) NPV Before Tax @10.00% (\$236,599) (\$16,136) \$56,761 (\$17,540) \$42,716 (\$146,603) NPV After Tax @10.00% (\$233,929) (\$68,875) (\$32,053) (\$121,655) (\$95,859) (\$265,158)
You may think of the IRR as the annual Interest Rate or Yield (compounded annually) that the investment is paying you over the Holding Period. Naturally, the higher the yield, the better the investment.
Monthly Calculations
Of course IRR's took forever before computers, and even took a very long time on those old computers with no mouse. These days the computers are so fast that monthly IRR's are done almost instantly. In the world of commercial real estate, cash flows occur monthly and the dollar amounts of the revenue and expense cash flows are almost always irregular. In the past there were mathematical games that were played to get the IRR to reflect the monthly irregular cash flow, and you might still hear some of the old ways spoken of today, like "beginning or end of period" or "mid year convention" (Monthly vs Yearly IRR Discounted Cash Flow Measure Comparison). These tricks were necessary in a world where you typed individual cash flows into a calculator or spreadsheet. However, in the modern computing world there is no need for these mathematical tricks, because computers are now fast enough to handle the present value discounting process on a monthly basis. The initial process for computing IRR in Excel and other spreadsheets made the assumption that the cash flows occurred annually and at the end of the year. With the new speed of computers, it became feasible to compute IRR more accurately by including the date of the cash flow as well as the amount. This new (and much more accurate) method of computation is known within Excel (and other spreadsheets) as the XIRR function. Here are links to descriptions of the XIRR process:
XIRR Verification
If you are interested how to verify the monthly NPV look to this page Verify Monthly IRR and NPV Using Excel or Google Spreadsheets XIRR and XNPV. Also there is an "IRR Verification Report" shown at the end of this article that has all the monthly information to use for the verification for the last IRR After Tax.
Internal Rate of Return (IRR) Considers:
• All assumptions entered such as: Scheduled Income, Purchase Price, Down Payment, Current Debt Payment, Vacancies, Expenses, Property Taxes, Lease terms, Revenue Growth, Rent Control, Expense Growth, Property Tax Growth, Deferred Maintenance, Debt Amount (Ratio), Interest Rate, Interest Rate Changes, Payment Changes, Points, Prepayment Penalties, Depreciation, Capital Expenditures, Income Taxes, \$25,000 Exemption, Passive Losses, Appreciation, Capital Gains Tax ... and all other entered assumptions.
Internal Rate of Return (IRR) Ignores:
• Only assumptions not entered
Why is Internal Rate of Return IRR useful?
The nature of the NPV is that it takes everything into account that made up the cash flow. The only weakness is that it is hard to calculate (not with planEASe of course), and that it uses all the assumption values (so, in turn, you are required to enter these assumptions, which means more work on your part).
The Internal Rate of Return IRR is shown in these planEASe reports:
IRR Verification Report
Retail - 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