weighted average number of shares outstanding

CFA Level I FRA
#1

QUESTION :

Shares outstanding on 1 January 2009

1,000,000 Shares issued on 1 April 2009 200,000 Shares repurchased (treasury shares) on 1 October 2009 (100,000) Shares outstanding on 31 December 2009 1,100,000

SOLUTION :

1,000,000 × (3 months/12 months) = 250,000 **1,200,000 × (6 months/12 months) =**600,000 1,100,000 × (3 months/12 months) = 275,000 Weighted average number of shares outstanding 1,125,000

MY QUERY :

In this why the calculation of 1,200,000 weighted average shares outstanding is done by 6/12 instead of 9/12 as it is mentioned above that 2,00,000 shares were issued in April so the remaining full 9 months total of 1,200,000 shares would be outstanding .

So , calculating the weighted average of 1,200,000 shares O/S it should be 1,200,000 x (9 months / 12 months ) instead of 1,200,000 x (6 months / 12 months ) as mentioned above .

Need clarification if I am wrong .

#2

Since the company bought back 100,000 shares on 10/1 there were 1,200,000 shares out from 4/1 to 10/1 which is 6 months. After 10/1 there were only 1,100,000 shares out.

#3

Thanks @chad.sandstedt .

It is really helpful thanks again .

#4

Here’s what I think is a “cleaner” way to do it - weight each transaction by the period remaining in the year

1,000,000 x 12/12 +200,000 x 9/12 -100,000 x 3/12

or, to make it even easier, (1,000,000*12 +200,000*9 - 100,000*3)/12

It’s mathematically equivalent, and easier to keep track of.

#5

Personally, I think that a candidate should try both approaches – the one given in the official answer and well clarified by Chad, and the one explained by busprof – and choose the one that is clearer in their own mind. In my experience, some candidates find the former approach easier to understand and implement, and other candidates find the latter more accessible.

I wrote an article on WACSO that goes through a comprehensive example using both approaches: http://financialexamhelp123.com/weighted-average-common-shares-outstanding-wacso/. The cool thing about it is that it’s in color.

(Full disclosure: as of 4/25/16 there is a charge to view the articles on my website. You can get an idea of the quality from the free sample articles here: https://www.financialexamhelp123.com/sample-articles/.)

#6

Yes, you are right it is much easier to calculate .

Thanks! . :slight_smile: