XNPV
Updated: 07 February 2011
Note: This documentation is for the SQL2008 (and later) version of this XLeratorDB function, it is not compatible with SQL Server 2005.
Click here for the SQL2005 version of the XNPV function
Use the aggregate function XNPV to calculate the net present value of a series of irregular cash flows—cash flows of varying amounts occurring on various dates. All cash flows in a group are discounted to the earliest cash flow in the group using the same rate.
Given a set of cash flows in ascending date order, the equation for XNPV is:
Where
N = Number of cashflows
ci = Cashflow amount
di = Date of the cash flow
r = 1 + discount rate
Syntax
SELECT [westclintech].[wct].[XNPV] (
<@Rate, float,>
,<@CF_Amt, float,>
,<@CF_Date, datetime,>)
Arguments
@Rate
the rate to be used for discounting the cash flows in calculating the net present value. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@CF_Amt
the cash flow amounts. @CF_Amt is an expression of type float or of a type that can be implicitly converted to float.
@CF_Date
the date on which the cash flow occurred. @CF_Date is an expression of type datetime or of a type that can be implicitly converted to datetime.
Return Type
float
Remarks
· The XNPV aggregate function requires a series of cash flows (@CF_Amt) and the dates on which those cash flows occurred (@CF_Date) as input. As a result, the order of the cash flows is not important.
· There can be multiple cash flows with the same date.
· The discount rate (@Rate) must remain constant for the GROUP of the aggregate.
· If the discount rate (@Rate) is equal to -1, a NULL will be returned.
· @Rate is the annual rate
· Funds that are paid should be represented with negative numbers. Funds that are received should be represented as positive numbers.
Examples
In this example we have cash flows occuring in sporadically from 30-Nov-2011 through to 06-Feb-2014. The result reflects the discounting of the cash flows, using a rate of 6%, to 30-Nov-2011.
SELECT wct.XNPV(.06, cf_amt, cf_date) as NPV
FROM (VALUES
(-100000, '11/30/2011'),
(-50000, '3/15/2012'),
(-2500, '7/18/2012'),
(12500, '11/30/2012'),
(37500, '1/23/2013'),
(75000, '4/30/2013'),
(90000, '2/6/2014')
) n(cf_amt, cf_date)
This produces the following result.
NPV
----------------------
43568.8517245775
(1 row(s) affected)
In this example, we will use the same cash flows as the previous example, but instead of discounting the cash flows to the 30th of November, 2011, we will discount them to the 31st of January, 2011. Since XNPV is insensitive to order, we can just add another row at the end of the derived table.
SELECT wct.XNPV(.06, cf_amt, cf_date) as NPV
FROM (VALUES
(-100000, '11/30/2011'),
(-50000, '3/15/2012'),
(-2500, '7/18/2012'),
(12500, '11/30/2012'),
(37500, '1/23/2013'),
(75000, '4/30/2013'),
(90000, '2/6/2014'),
(0, '01/31/2011')
) n(cf_amt, cf_date)
This produces the following result.
NPV
----------------------
41511.5337068439
(1 row(s) affected)
We could have achieved the same result with a variety of different syntaxes. Here’s another way to arrive at the same result.
SELECT wct.XNPV(.06, cf_amt, cf_date) as NPV
FROM (
SELECT 0 as cf_amt
,'01/31/2011' as cf_date
UNION
SELECT *
FROM (VALUES
(-100000, '11/30/2011'),
(-50000, '3/15/2012'),
(-2500, '7/18/2012'),
(12500, '11/30/2012'),
(37500, '1/23/2013'),
(75000, '4/30/2013'),
(90000, '2/6/2014')
) n(cf_amt, cf_date)
) m
This produces the following result.
NPV
----------------------
41511.5337068439
(1 row(s) affected)
In this example, we will add another column to the derived table from the previous example, which will allow for a different rate for each period. This will return an error message, as the function requires that the rate value be the same for all cash flows.
SELECT wct.XNPV(rate, cf_amt, cf_date)
FROM (VALUES
(-100000, '11/30/2010', .0060),
(-50000, '3/15/2011', .0090),
(-2500, '7/18/2011', .0110),
(12500, '11/30/2011', .0140),
(37500, '1/23/2012', .0160),
(75000, '4/30/2012', .0220),
(90000, '2/6/2013', .0240),
(0, '01/31/2011', .0005)
) n(cf_amt, cf_date, rate)
This produces the following message and will not return a result.
Msg 6522, Level 16, State 2, Line 1
A .NET Framework error occurred during execution of user-defined routine or aggregate "XNPV":
XLeratorDB_financial2008.Core.Exceptions+Function_AggregateException:
[Product version 1.7 Build: 0126.208]
An error occurred in Aggregate Function. (Accumulate) - Invalid Rate - Rate parameter cannot vary
Function: XNPV
Passed Parameters:
'Disc_rate' = System.Data.SqlTypes.SqlDouble:0.009
'CF_Amt' = System.Data.SqlTypes.SqlDouble:-50000
'CF_Date' = System.Data.SqlTypes.SqlDateTime:3/15/2011 12:00:00 AM
Internal refs:
'd_rate' = System.Double:0.006
'disc_amt' = System.Double:-100000
'start_date' = System.Double:40512
*** Extra Information: Invalid Rate - Rate parameter cannot vary
XLeratorDB_financial2008.Core.Exceptions+Function_AggregateException:
at XLeratorDB_financial2008.XNPV.HandleException(String Method, String Ref, XNPV& Merge, FunctionParamsClass& Params, Exception& Ex)
at XLeratorDB_financial2008.XNPV.Accumulate(SqlDouble Disc_rate, SqlDouble CF_Amt, SqlDateTime CF_Date)
.
If you want to caclute the present value of future cash flows using different rate for different periods, you can use the SUM function in conjunction with the XNPV function.
In this example, we set the rate equal to -1.
SELECT wct.XNPV(-1.0, cf_amt, cf_date) as NPV
FROM (VALUES
(-100000, '11/30/2010'),
(-50000, '3/15/2011'),
(-2500, '7/18/2011'),
(12500, '11/30/2011'),
(37500, '1/23/2012'),
(75000, '4/30/2012'),
(90000, '2/6/2013'),
(0, '01/31/2011')
) n(cf_amt, cf_date)
This produces the following result.
NPV
----------------------
NULL
(1 row(s) affected)
XNPV is an AGGREGATE function and supports all the syntax available to any SQL Server AGGREGATE function. Here is an example, using a GROUP BY, where we want to discount quarterly cash flow projection by quarter for 2011 and 2012 as at the end of 2010. We will use the CALCDATE function to convert the quarters to datetime values.SELECT region
,cf as cf_amt
,wct.CALCDATE(yr, quar * 3 + 1, 1) - 1 as cf_date
INTO #t
FROM (
VALUES
('New England',2011,1,9589),
('New England',2011,2,5866),
('New England',2011,3,9530),
('New England',2011,4,6805),
('New England',2012,1,2567),
('New England',2012,2,9403),
('New England',2012,3,5607),
('New England',2012,4,2469),
('MidAtlantic',2011,1,4366),
('MidAtlantic',2011,2,5488),
('MidAtlantic',2011,3,5955),
('MidAtlantic',2011,4,5450),
('MidAtlantic',2012,1,7255),
('MidAtlantic',2012,2,2458),
('MidAtlantic',2012,3,1738),
('MidAtlantic',2012,4,3866),
('Southeast',2011,1,1671),
('Southeast',2011,2,4383),
('Southeast',2011,3,4913),
('Southeast',2011,4,8209),
('Southeast',2012,1,1476),
('Southeast',2012,2,3056),
('Southeast',2012,3,3931),
('Southeast',2012,4,5476)
) n(region, yr, quar, cf)
INSERT INTO #T
SELECT DISTINCT REGION, 0, '12/31/2010'
FROM #T
SELECT REGION, wct.XNPV(.06, cf_amt, cf_date) as NPV
FROM #T
GROUP BY REGION
This produces the following result.
REGION NPV
----------- ----------------------
MidAtlantic 34485.683450933
New England 48958.3186196824
Southeast 30948.5929130596
(3 row(s) affected)
In this example, we will have different rates for different regions and use the XPV function to discount to 31-Dec-2011.
;with mycte as (
SELECT *
FROM (
VALUES
('New England', .0600),
('MidAtlantic', .0575),
('Southeast', .0550)
) n(region, rate)
)
SELECT n.region
,wct.XPV(mycte.rate
,'2010-12-31'
,MIN(wct.CALCDATE(yr, quar * 3 + 1, 1) - 1)
,wct.XNPV(mycte.rate, N.cf, wct.CALCDATE(yr, quar * 3 + 1, 1) - 1)) AS XNPV
FROM (
VALUES
('New England',2011,1,9589),
('New England',2011,2,5866),
('New England',2011,3,9530),
('New England',2011,4,6805),
('New England',2012,1,2567),
('New England',2012,2,9403),
('New England',2012,3,5607),
('New England',2012,4,2469),
('MidAtlantic',2011,1,4366),
('MidAtlantic',2011,2,5488),
('MidAtlantic',2011,3,5955),
('MidAtlantic',2011,4,5450),
('MidAtlantic',2012,1,7255),
('MidAtlantic',2012,2,2458),
('MidAtlantic',2012,3,1738),
('MidAtlantic',2012,4,3866),
('Southeast',2011,1,1671),
('Southeast',2011,2,4383),
('Southeast',2011,3,4913),
('Southeast',2011,4,8209),
('Southeast',2012,1,1476),
('Southeast',2012,2,3056),
('Southeast',2012,3,3931),
('Southeast',2012,4,5476)
) n(region, yr, quar, cf), mycte
WHERE n.region = mycte.region
GROUP BY n.region
,mycte.rate
This produces the following result.
region XNPV
----------- ----------------------
MidAtlantic 34567.3912690366
New England 48958.3186196824
Southeast 31117.7864263186
(3 row(s) affected)
See Also