The IRR Before Tax for the entire holding period is 15.3%, and the NPV Before Tax @10.00% is $387,998.

In this case 15.3% IRR is greater than the 10.00% discount rate, and that means if the initial investment in the beginning is increased by the $387,998 the IRR will be very close to the 10.00% discount rate (both numbers are rounded). The IRR is the discount rate that makes the NPV zero hence, if the IRR is exactly the same as the discount rate, the NPV would be zero (rounding means it is usually very close to zero). The IRR and the NPV use the same cash flows and the same process. The IRR simply runs lots of NPV's seaching for the discount rate that returns a NPV that is close to zero.

The IRR can be compared to the redemption yield of a bond, or the APY on a bank account.

Before Tax Cash Flows for IRR and NPV

MM/DD/YY	Cash Flow
01/01/2008	($743,557)
01/15/2008	($766,272)
02/15/2008	$5,404
03/15/2008	$5,404
04/15/2008	$5,404
05/15/2008	$2,495
06/15/2008	$2,495
07/15/2008	$2,495
08/15/2008	$2,495
09/15/2008	$2,495
10/15/2008	$2,495
11/15/2008	($9,567)
12/15/2008	$2,805
01/15/2009	$27,297
02/15/2009	$6,223
03/15/2009	$6,223
04/15/2009	$6,223
05/15/2009	$6,223
06/15/2009	$6,223
07/15/2009	$6,223
08/15/2009	$6,223
09/15/2009	$6,223
10/15/2009	$6,223
11/15/2009	$6,305
12/15/2009	$6,305
01/15/2010	$74,998
02/15/2010	($6,246)
03/15/2010	($106,757)
04/15/2010	$5,541
05/15/2010	$5,541
06/15/2010	$5,541
07/15/2010	$5,541
08/15/2010	$5,708
09/15/2010	$5,708
10/15/2010	$5,708
11/15/2010	$5,792
12/15/2010	$5,792
01/15/2011	($56,255)
02/15/2011	$5,897
03/15/2011	$6,251
04/15/2011	$6,251
05/15/2011	$6,251
06/15/2011	$6,251
07/15/2011	$6,251
08/15/2011	$6,251
09/15/2011	$6,251
10/15/2011	$6,251
11/15/2011	$2,826
12/15/2011	$2,903
01/15/2012	$64,533
02/15/2012	$3,002
03/15/2012	$6,674
04/15/2012	$6,674
05/15/2012	$6,674
06/15/2012	$6,674
07/15/2012	$6,674
08/15/2012	$6,674
09/15/2012	$6,674
10/15/2012	$6,674
11/15/2012	$6,674
12/15/2012	$6,759
01/15/2013	$76,590
02/15/2013	($3,960)
03/15/2013	($3,585)
04/15/2013	($3,585)
05/15/2013	($3,585)
06/15/2013	($74,816)
07/15/2013	$9,001
08/15/2013	$7,345
09/15/2013	$7,387
10/15/2013	$9,120
11/15/2013	$9,120
12/15/2013	$9,208
01/15/2014	($29,143)
02/15/2014	$9,322
03/15/2014	$9,708
04/15/2014	$9,708
05/15/2014	$9,708
06/15/2014	$10,009
07/15/2014	$10,009
08/15/2014	$10,009
09/15/2014	$10,054
10/15/2014	$10,054
11/15/2014	$10,054
12/15/2014	$6,466
01/15/2015	$111,646
02/15/2015	$6,560
03/15/2015	($6,986)
04/15/2015	($120,169)
05/15/2015	$10,337
06/15/2015	$10,647
07/15/2015	$10,647
08/15/2015	$10,647
09/15/2015	$10,693
10/15/2015	$10,693
11/15/2015	$10,693
12/15/2015	$10,693
01/15/2016	($24,761)
02/15/2016	$10,813
03/15/2016	$10,907
04/15/2016	$11,317
05/15/2016	$11,317
06/15/2016	$11,637
07/15/2016	$11,637
08/15/2016	$11,637
09/15/2016	$9,747
10/15/2016	$9,789
11/15/2016	$11,688
12/15/2016	$11,688
01/15/2017	$133,960
02/15/2017	$11,811
03/15/2017	$11,908
04/15/2017	$12,331
05/15/2017	$12,331
06/15/2017	$12,660
07/15/2017	$12,660
08/15/2017	$12,660
09/15/2017	$12,660
10/15/2017	$12,709
11/15/2017	$12,709
12/15/2017	$12,709
01/01/2018	$2,252,733

All the IRR's and NPV's are computed on a monthly basis using the XIRR and XNPV process which is designed to handle irregular cash flows. To verify the IRR or NPV a spreadsheet program like Excel, Google Spreadsheets, Matlab, etc. will need to be used, because most financial calculators are not able to compute irregular dates and cash flows like the table shown.

Here are links to other descriptions of XIRR and XNPV:

• Excel XNPV Description
• Excel XIRR Description
• Google Spreadsheet XNPV Description
• Google Spreadsheet XIRR Description
• MATLAB XIRR (Internal rate of return for nonperiodic cash flow) Description

Directions for XIRR/XNPV Excel Verification

1. Open Excel and try to insert function/financial/XIRR or XNPV
2. If the XIRR or XNPV is not there, select Tools/Add-ins, and add the analysis toolpak.
3. Copy and paste the cash flows shown into excel. If the paste does not go into separate columns try a paste special as text.
4. Insert the function/financial/XIRR or XNPV and highlight the dates, and cash flows as directed by the function.

How is a monthly IRR or NPV different from a Yearly IRR or NPV?

A Yearly IRR assumes that there is one total Cash Flow amount each year. If you are using an End-of-Period Convention, that Cash Flow is assumed to occur at the end of the year. Using this method, for example, a 30 year 12% mortgage evaluates to a 12% IRR for the lender. Most bankers know this is false, and they will consider the fact that the payments are received each month rather than at the end of the year, and correctly calculate that their IRR (Lender's Yield) on the mortgage is 12.68%. It is easy to correct for this calculation deficiency (since the monthly payment is always the same) by using a "Mid-Year Convention" which assumes that the annual cash flow occurs at the mid-point of the year involved. Using this convention, the computed Yearly IRR for the 12% mortgage returns to the (correct) 12.68%.

For the Mid-Year Convention to be accurate in computing IRR and NPV, however, the monthly cash flows must all be equal. This is almost always false with real estate investments, and in some cases it is grossly false. Consider development or other capital spending items such as rehabilitation. Think of the cash flow effect of re-financing or monthly draws on a development loan. Consider that leases end --- and their renewals (or new tenants) may involve Vacant Periods, Free Rent, Tenant Improvements and Commissions, all of which do not occur in convenient annual time frames. These and other events combine to assure that the monthly cash flows for real estate investments are and will be unequal. In turn, Yearly IRR and NPV calculations are almost always inaccurate, and sometimes grossly inaccurate.

For these reasons, competent real estate analysis software must compute monthly cash flows and compute the IRR and NPV measures on a monthly basis if those measures are to be accurate. Since these measures are continuously used in practice to compare and decide between real estate (and other) investments, accuracy is mandatory if proper decisions are to be made. In recognition of this, Excel (for example) corrected it's previous (until 1996) Yearly IRR and NPV routines with new XIRR and NPV routines that expressly consider the date of a cash flow rather than assuming they occur a year apart. Other spreadsheet programs such as Google and MATLAB also now offer this capability.