The 'time value' of an option, or a warrant with an expiry date, or anything that gives you certain rights for some period of time, is based on 2 things:
(1) Regular time value of money:
If I have the right to buy a share of APPL for $114, {current market price is $114}, and I can wait a year before I exercise that right, then for the next year, I can take that same $114 I need to exercise it, and I could invest it in other things. Even just investing at a low-risk 1% interest earning account as an example, means I could earn an extra $1.14, so the total value of the option is increased by at least that risk-free earnings rate over the period up to expiry. This means if a warrant has an expiry date of only 1 day, it's value should be lower by at least that $1.14, because to exercise it you would need to put cash out today, and can't earn the extra risk free investment income.
(2) The value of risk-reduction gained by deferring your decision on whether to exercise:
Assume I can buy a share of AAPL for $114, or I can buy an option that gives me the right to buy it for $114 at some point over the next year. If I own the option, and the price goes up to $120, then perfect - I can exercise the option, pay $114, and get a share worth $120. If it goes down to $110, then no problem - I would choose to not exercise the option, and my loss is equal only to the price of buying the option in the first place.
The longer you can wait before exercising, the more you are able to defer making a decision, which means your risk goes down. If I have an option to buy AAPL for $120 that expires tomorrow, it is almost worthless - because it would be very rare for AAPL to increase above $120 in just 1 day. If I have an option to buy AAP for $120 that expires in a year, it would have good value - because a 5% increase in value in 1 year could be very possible.
