
Agreed. Understandable but not natural as they are, imho. Some more alternatives below. I have a slight preference for a somewhat option "that" to be included.
OR:
This is the first time that I've managed a company.
OR (for some of them, if they are happening now):
This is the first time that I am managing a company.
OR:
This is the first time that I am managing a company.
OR even, if it's about to start:
This is the first time that I will manage a company.

I like wwwkudu's pattern:
"This is the first time that I am managing a company."
This is the closest in meaning to the Amazigh (Berber) sentence.
I'll try to modify all the other sentences according to this pattern.
CK: Please confirm.
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added by Amastan, July 10, 2012
linked by Amastan, July 10, 2012
edited by Amastan, December 8, 2012
edited by Amastan, December 8, 2012