This is a very interesting question because you have two sentences which mean the same thing, but one uses "have" and the other does not.
My explanation is that in the second sentence, "the company is believed to...", the clause following "believed" is an infinitive form (to [verb]), and yet it is important that we place the action in the past. The only way to do so is by using the verb "have".
If we said, "The company is believed to lose a lot of money" it sounds like we're talking about the habitual present, and it doesn't match with "last year". And we can't say "to lost" because that is absolutely incorrect.
So we make the infinitive "to have" and we can follow it with the participle "lost" and now we are expressing the correct tense of the action of losing.
It is a common structure. Compare these two sentences:
"David Robertson is thought to go to the cafe every morning." (We are talking about Mr. Robertson's daily habit)
"David Robertson is thought to have gone to the cafe on Thursday." (We are talking about where he was on Thursday.)