If a stock has a dividend of 1.25 per share and then splits (3 shares for every 1 share owned) does the dividend change (1.25 divided by 3) to .416 per share as well? If yes, does it always decrease or can the company leave it at 1.25?

It's up to the board of directors to decide what happens to the dividend each quarter, but in most cases the dividend paid our per share would be divided by 3 if there's a 3-for-1 stock split. This keeps the amount of dividends received by each investor constant. Otherwise the company would be laying out three times as much cash in dividends.

Thanks for your answer! The split was disbursed today and the next dividend payout is in February but online information on the stock shows the dividend hasn't changed. One would think they might put it a little above .416 to prevent a big sell off. I'm just wondering how long until they disclose the new dividend price.

Usually companies announce their dividend 4-6 weeks before they pay it out, so don't look for an update until January. Most online finance sites simply report the last dividend paid - they don't predict what next quarter's dividend will be. The company may indeed put it a bit above 0.416 if they are doing well (which presumably they are or they wouldn't have made the split), but maybe not. Why would you think it would cause a big sell-off if they made it 0.416? What's important to investors is the dividend yield (dividend divided by stock price) - after a 3:1 split the yield would remain constant if the dividend per share was cut in third given that the market value per share is also now 1/3 of the old shares.