how much would it cost to travel to birmingham from cardiff by train or coach or taxi i have to be there by 7a

i have a flight booked to new york

I assume that you have to be at the airport by 7am. The last train from Cardiff is 21.25, arriving Birmingham New Street at 23.43* with a change at Bristol Parkway. There are none later in the night or very early in the morning.

*Change there with a wait until 00.10 for a train arriving at Birmingham International at 00.21.

Your last bus (National Express) is 15.20, arr Birmingham Coach Station at 18.05.

Check www.thetrainline.com for train fares and www.nationalexpress.com for coach fares.

You will have to ask a taxi firm for taxi fares. Those aren't available on the web.