How can a stock fall by more than 100%?
Please show me the mathematics.

Have never understood how stocks work after dividends are declared and my googling skills are letting me down. Is this what normally happens when companies declare dividends and pay them out?

1) dividend gets declared
2) price shoots up since whoever is selling is factoring in the dividends + current price (sometimes it shoots up past the `dividents+price` level, which could be a bubble?)
3) dividends get paid (anyone who bought shares after the dividends was declared will receive the dividends, even if they owned the shares for just one day? also about how long does it take for dividends to get paid out after they are declared)
4) price goes down ideally to the level it was before dividends were declared.

Now you know who Kengen Shareholders felt. Company was declaring billions in profits, spending hundreds of millions on CSR but giving shareholders scones and yoghurt at Kasarani.

The relevant dates are:
1. Announcement date- When the Directors announce results and/or payment of dividend;
2. Books closure date - The cutoff date for shareholders to be paid. If you are on register on books closure date, you receive a dividend. If your name is entered on the register subsequently, you dont receive.
3. Payment date - the date on which dividend cheques and EFT are made.

In view of the above, the price of shares should fall on the books closure date by amount of dividend payable. Other falls and rises are irrational. This assumes that market is efficient.