# Weighted average shares outstanding 30.4 kaplan

Hi!

Can someone please explain why I can’t just take the arithmethic average here which is 10 000 + 14 000 + 11 000=11 666,66?

The three numbers of shares were not outstanding for equal amounts of time.

• 11,000 (not 10,000) shares were outstanding for three months (January, February, March)
• 15,400 (not 14,000) shares were outstanding for five months (April, May, June, July, August)
• 11,400 (not 11,000) shares were outstanding for four months (September, October, November, December)

Okay thanks but I don’t get why we get 11 000 shares instead of 10k? Like the dividend actually happens 1 July and not 1 January.

I like to think of a stock dividend (or a stock split, or a reverse stock split) as replacing shares of one color with shares of another color.

On 1 January, they had, say, 10,000 red shares outstanding. On 1 April they issued 4,000 new red shares. On 1 July, they had a 10% stock dividend, which means that they replaced all 14,000 old, tattered red shares with 15,400 bright, shiny, new green shares, which are the color that will last till the end of the year (and the color that we’ll use for the EPS calculation). Thus, the 10,000 red shares on 1 January were replaced with 11,000 green shares, and the 4,000 red shares issued on 1 April were replaced with 4,400 green shares, and on 1 September, they repurchased 3,000 green shares.

The numbers I gave you were green share numbers. Red shares no longer exist, so they no longer matter.

Sorry but I don’t think I understand still. Why do we say the 11k shares comes at the start?
This is how I have noted it down so far.

Because the 10,000 old red shares that you had at the start are equivalent to 11,000 new green shares, and the EPS calculation will be based on green shares.

Stock splits, reverse stock splits, and stock dividends apply retroactively to all shares on or before the date of the split/reverse split/dividend.

Hmm I still think we can’t account for that since the dividend is paid in JULY and not in January. If they had said we will pay a dividend in January I would agree but now it is paid in July so I can’t follow the logic here. Can you please elaborate on this?

Do you understand what I write, above:

“Stock splits, reverse stock splits, and stock dividends apply retroactively to all shares on or before the date of the split/reverse split/dividend.”

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Alright, thanks. Just to really pick your brain, can you explain why it is retroactively? It just sounds strange to me in nature.

Once more, thanks again for your replies. Really helpful on my journey.

Think of it as you would making change: you received a \$5 bill on 1 January and have been carrying it around ever since. Today, you give it to me in exchange for five \$1 bills. The amount of money is the same, but now you have five times as many pieces of paper, and, for all intents and purposes, you might as well have had the five ones since 1 January.

Suppose, instead, that you own 2,000 shares of stock valued at \$100 per share, which you have had since 1 January. They’re blue. There’s a 4:1 stock split, so you trade in your 2,000 (old, blue) shares for 8,000 (new, red) shares valued at \$25 per share. There are no more blue shares, only red shares. At the end of the year, they’re going to calculate earnings per red share. For all intents and purposes, you have owned (the equivalent of) 8,000 red shares for the entire year

Now I finally got it after you wrote the stock example. So we actually hand in all our shares when there is a stock split to have them converted. I didn’t know that. Thanks for the clarification. Been thinking about this the whole week. Good job explaining it!

I’m glad that I finally hit on the right explanation.

You’re quite welcome.

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The arithmetic average isn’t appropriate here because it doesn’t account for compounding effects or different time periods. Instead, use the geometric mean for a more accurate measure of average growth rates over time.