Because the company gives a $.10 dividend to anyone who was a holder of the shares yesterday, today is called the "ex dividend" date, which means the price today trades without that $.10 dividend. Thus it is subtracted from the price of the stock at the open. The stock closed yesterday at $4.66 and will open at $4.56. For someone who owned the stock yesterday, he still has $4.66 on the open today because he will receive the $.10 dividend and then has the $4.56 share of stock; thus no difference, so don't think that somehow the stock has gone down in value due to this drop in price at the open today.
Actually, according to my learning, if he had sold at 4.88 and bought back today at 4.56 that would be 0.32 the equivalent of three 0.10 dividends but would not also collect the 0.10 dividend. My guess, if you wait a few days before buying back, it may go down a few cents below 4.56 but it is just as likely to go up as well.