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.)

The sentence structures are very common and both appear in the passive voice. I’m also sure Phil’s advice on studying the perfect infinitive is the way of understanding the way both sentences are written. Notice in both sentences „it’s believed“ and „the company is believed“ fails to identify who believes this. That’s passive voice, and it’s written this way either because the writer doesn’t know exactly who believes this or chooses to leave the actor(s) unidentified for some reason. So, keep that in mind and study the perfect infinitive as Phil suggested and I’m sure you’ll gain a better understanding of the structure of the sentences. However, they both indeed carry the same meaning.

Sezme has given you an excellent answer. For more information, Patryk, the search term would be “perfect infinitive”.

Hey Patryk! “Have lost” in this sentence is referring to a time in the past which was prior to the belief, which is now also in the past. We can use both forms that you have given us in American English. Please feel free to book a trial class with me so we can go over this in further detail. Hope this helps!