No one can accept the late because he worked for late hours in the previous day. It is the responsibility of the employee to complete his work on daily basic. So it is not correct to accept that reason. You can implement late coming policy for your company.
Sample policy : Late coming is permitted till--- AM, if employee is coming after--- AM, then it would be considered as late arrival, and ---- late arrivals in a month will be considered as a one half day personnel leave.
You can implement according to your management acceptance for the same.
From India, Secunderabad
The suggestion that Vani gave is widely used in most IT Companies. Is your company a start-up?
Another couple of them in-vogue are:
1] An employee can come late if he/she has prior permission from his/her boss for late-stay the previous day. Ensures that the boss is-(1) aware of it & (2) has some amount of control of the situation [since HR wouldn't be tracking the late-comings on a minute-to-minute basis.
2] Implement some sort of an incentive/award for those who have absolutely no late-coming record [something like we have in some schools]--to encourage latecomers to correct themselves.
And finally, if none of your actions [including any rebukes] work, maybe you need to move tough on him--at least to ensure he doesn't become a wrong example to others later.
From India, Hyderabad
From India, Mumbai