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,

Sseziwa

On 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.

>