Why dividend increase the average weightage number of shares?

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Hi,

i have been studying CFA and i have no problems tackling the questions on solving the average weightage number of shares.

I realize i memorize how is it being calculate instead of understand the concept why is it calculate this way.

Lets say on Jan 1 there are 100,000 share outstanding.
Then on Mar 1, company issue the 10% dividend

Therefore it is calculate as 100,000 * 1.1 *12 mths outstanding
I find that using the Jan outstanding multiply by 1.1 increase the number of shares.
I thought dividends are given in cash unless i request in the proxy that i like to reinvest the dividends back to the company, that way they will issue me shares.

Any reason why we need to increase the number of shares when factoring in dividends?

Thanks: