Question on treasury shares & retired shares

Hi,

I would like to ask a couple of questions below.

1) Are treasury shares included in market capitalization and EV calculations? Generally/in textbooks it should not be included. However, some analyst reports include while others don’t. Further, treasury shares should be excluded from the EPS calculations? Is this always the case, or does it depend on country? I know Japanese listed companies exclude treasury shares in their EPS calculations - would like to check for other countries.

2) Does it cost the company anything when it retires its treasury shares? Looking at journal entries, retiring shares shouldn’t impact cash but may impact retained earnings - would like to check if there is any substantial impact to the company during retirement of shares.

3) What is the incentive for a company to use retired shares for funding instead of issuing new shares? (ie. what incentive does the company have to hold treasury shares instead of just canceling them). Understand that treasury shares are generally considered less expensive than issuing new shares as this involves engaging investment banks and additional filings. Please provide more details/other reasons if you know.