I asked the exact same question a while back: http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91348230
To answer your question:
A stock dividend does not (as you already pointed out) involve any cash payments. Instead, the amount of stocks is increased (say 10%) and after the increase in the amount of shares, all shares decrease in value (10% decrease in value). So the total market vale of shares does not change. However, the contributed capital in equity contains the stocks at par value (not market value). Thus, when you increase the amount of shares, it would look suddenly as if you had more contributed capital. We then have to adjust retained earnings in order to balance out this effect.
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