```Date: Jul 2, 2013 12:31 AM
Author: Sseziwa Mukasa
Subject: Re: Cashflow and TimeValue Question

This will happen whenever the next period occurs in a leap year:(Debug) In[2]:= cf = Cashflow[{{{2003, 12, 29}, a}, {{2003, 12, 30}, b}, {{2003, 12, 31},     c}}];(Debug) In[3]:= Rationalize[TimeValue[cf, r, cf[[1, 1, 1]]], 0](Debug) Out[3]= a + c/(1 + r)^(1/183) + b/(1 + r)^(1/366)This is of course correct if you want to compute the time value at {2004,12,31} of this cash flow whereas using 365 is not correct.  So the real question is what happens for the defined cash flow in 2005?(Debug) In[15]:= Rationalize[TimeValue[cf, r, {2005, 12, 31}], 0](Debug) Out[15]= c (1 + r)^2 + b (1 + r)^(731/365) + a (1 + r)^(732/365)I suspect this will disagree with a simple spreadsheet's answer but is more correct, assuming daily compounding.Regards,SseziwaOn Jul 1, 2013, at 5:47 AM, Dana DeLouis <dana01@icloud.com> wrote:> 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.>
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