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You should be able to view the spreadsheet, or download it from this link:

(You do not have to have a dropbox account to view or download it. You can change the start year, the asset allocation (100/0 or 60/40), etc. The spreadsheet also shows the figures for a 20 year period as well as for 31 years.)

Here are the figures for a few selected 31 year periods, for an initial amount of $100,000, AA of 100/0:
Total RMD withdrawals, ending IRA value.
(BOY = Beginning of Year. EOY = End of Year)

***Take RMD 1st of Jan*** *** Take RMD last of Dec***
Start Total RMD End Value Total RMD End Value
1950 $362,335 $64,491 $383,743 $71,840
1970 $261,558 $113,500 $291,612 $143,659
1986 $381,168 $81,050 $407,674 $92,410

Ending in 2008, which had a loss of -38.5%
***Take RMD 1st of Jan*** *** Take RMD last of Dec***
1978 $508,450 $75,167 568,589 $78,300

Starting in 1974, which had a loss of -29.7%
***Take RMD 1st of Jan*** *** Take RMD last of Dec***
1974 $355,308 $98,322 $397,109 $115,636

In all these cases, taking the RMD at the end of year is better than taking it at the begining of the year. The total of the withdrawals is higher, and the final value is higher.

The spreadsheet also shows some other data; the number of years with a gain/loss and the average gain of the gain years and average loss of the loss years, etc.

The reason that EOY is better is that the average annual gain is 10%. If you take out the RMD at BOY, then the gain is on a lower amount. Of course, in a year with a loss it is better to take the RMD at BOY, since the loss will be on a lower amount. But there are many more years with a gain than a loss, and the average gain is larger than the average loss.

However, consider the case where the RMD is used for living expenses. If the RMD isn't taken until EOY, what provided the living expenses for the first year? We should look at the case where the first year's living expense is removed from the initial IRA. Assuming that this amount is equal to the first RMD ($3,650) then the figures are:

***Take RMD 1st of Jan*** *** Take RMD last of Dec***
Start Total RMD End Value Total RMD End Value
1978 $508,450 $75,167 $547,838 $75,442

Even in this case, with a lower initial IRA value, it is better to take the RMD at the end of the year.
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