Basic and diluted EPS - weighted average of shares outstanding

[archived_user]

In Kaplan Schweser (book 3, pg 66 ed 2014. Example: Effect on stock dividends)
In the book they say:
Jan 1st issued shares outstanding = 10.000 (12 month outstanding)
April 1st issued shares = 4.000 (9month outstanding)
July 1st 10% stock dividend (6 month til end of year)
Sep 1 shares repurchased = 3.000 (4 month til end of year)
When they calculate WA days outstanding:
January stock (10.000*12)+(10% stock dividend is 1.000*12) = 132.000 +
April stock (4.000*9)+(10% stock dividend is 400*9) = 39.600 -
Sep stock repurchase (-3.000*4) = -12.000
____________________________________________
Total days = (132.000+39.600-12.000)/12 = 159.600 /12 = 13.300
My question is….if stock dividend is on July 1st and not on Jan 1st or Apr 1st….
I have January = (10.000*12)+(10% stock dividend of 1.000 * 6) = 126.000
April = ( 4.000*9)+(10% stock dividend 400 * 6) = 38.400
Sep stock repurchase (-3000*4) = -12.000
____________________________________
Total would be: (126.000 + 38.400 -12.000)/12= 12.700
Can somebody explain why we take the whole period since issuance if stock dividend happened later? Thank you very much

 

[archived_user]

Stock dividend or Stock split changes must be applied retroactively to the beginning of the period, this is because it changes the entire number of shares outstanding and not just those issued after the stock dividend/split.
Assume that 100 shares outstanding for 6 months and then 1 share gets split in 2 on 1 July, then the calculation will be
100*2*12
and not,
100*6 + 200*6