Date: Jul 1, 2013 5:41 AM
Author: Dana DeLouis
Subject: Cashflow and TimeValue Question

Hello.   When doing Net-Present value types of problems, I seem to 
occasionaly get slightly different answers when compared to a very
popular spreadsheet program. The Spreadsheet program uses a standard
365 day year, yet I don't see anything in the Mathematica documentation
on this.
I've reduced the issue down to these two simple examples.

1. 3 simple daily cash flows in a row.
cf[[1,1,1]] is returning the start date, or time 0.
The days per year is a fraction, so I use Rationalize to return
the values used for easy viewing.

cf=Cashflow[{
{{2009,12,29},a},
{{2009,12,30},b},
{{2009,12,31},c}
}];

Rationalize[TimeValue[cf,r,cf[[1,1,1]]],0]

a + b/(r+1)^(1/365) + c/(r+1)^(2/365)

It appears the program uses 365 days/year also. This example would most
likely match.
We just note that the year 2009 is not a leap year.

2. However, If I change the year to 2007, which is also not a leap
year, it appears that the program is using a 366 day year. These types
of problems are giving slightly different answers then spreadsheets that
use a constant 365 day year.


cf=Cashflow[{
{{2007,12,29},a},
{{2007,12,30},b},
{{2007,12,31},c}
}];

Rationalize[TimeValue[cf,r,cf[[1,1,1]]],0]

a + b/(r+1)^(1/366) + c/(r+1)^(1/183)

Note: it's using 366 day year...
{1,2}/366
{1/366,1/183}

Does anyone have any insight? I'm not sure what the standard convention is.
I just note that both years are non leap years, yet different methods of calculations.
It appears to me that the random use of 366 is causing the slightly different answers.


Thanks in advance. :>)
Mac, and Mathematical v 9.