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
01/15/2012	$0
02/15/2012	$0
03/15/2012	($525,000)
04/15/2012	$0
05/15/2012	$0
06/15/2012	$0
07/15/2012	$0
08/15/2012	$98,700
09/15/2012	$14,805
10/15/2012	$14,805
11/15/2012	$80,605
12/15/2012	$59,455
01/15/2013	($261,518)
02/15/2013	$79,195
03/15/2013	($21,667)
04/15/2013	$59,455
05/15/2013	($4,888)
06/15/2013	$59,455
07/15/2013	($4,888)
08/15/2013	$59,455
09/15/2013	$60,718
10/15/2013	$195,014
11/15/2013	$65,800
12/15/2013	$100,580
01/15/2014	$714,029
02/15/2014	$100,580
03/15/2014	$65,800
04/15/2014	$34,780
05/15/2014	$0
06/15/2014	$0
07/15/2014	$0
08/15/2014	$0
09/15/2014	$0
10/15/2014	$0
11/15/2014	$0
12/15/2014	$0

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.