It seems like you will be able to make the payments but the proportion of car payment to income doesn't make the most sense. If you purchase a new M3 at around $65K, and finance it doing BMW select with a $10k down payment, your monthly payment will be roughly $700-$750 and then after 60 months, you will still owe about $25k on the car. keep in mind the $65K car is over $70k after tax and gas guzzler
Did you consider purchasing a used M3 and put down a decent down payment? Your monthly payment will still be high but at least you won't have the lump payment at the end.
Current: 2014 Porsche Cayman S - 6MT. Sold: 2013 E92 M3 DCT