quick question with time value of option.

I understand that for American options…the further the time to expiration of the option, the greater the time value of the option as more time means there is more “potential” for the option value to increase further. that being said, why would someone NOT exercise an american call option on non dividend paying stock early? I would think the “earlier” someone exercises the option, the “more value” they get because there is more time value? However, the book says one wouldn’t exercise it because the payoff value is less than minimum value? I dont think I’m understanding that statement.

2 reasons: 1) the earlier you exercise, the sooner you have to pay the exercise price which means lost interest on that cash 2) more importantly, what if you exercise today and tomorrow it comes out the CEO was cooking the books and the stock tanks? If you hadn’t exercised, you would only lose the premium. Now you’re losing a lot more. By not exercising early you’re only taking part of upward movements, but by exercising early you are exposing yourself to downward movements as well. Also you should never exercise when there is still premium left since this is money you are giving away for nothing. If the stock is at $12 and you have a call with a strike of $10 and the option is trading at $2.30, if you exercise you are effectively paying $12.30 for a stock that you can buy for $12