What Was Probably True
Modal Verbs of Probability - Past
Modal verbs of probability express an opinion based on what a speaker knows about a situation at the moment of speaking. The following forms are used to speak about past situations.
This must have been left here on receipt of the order.
I could have been rich if I had done a better job with managed liabilities.
David might have kept the expense receipt.
'Must' plus the perfect form (must have done) expresses the idea that you are almost 100% sure of your opinion about a given situation which took place in the past.
Subject + must + have + past participle + objects
He must have been aware the endorsement would reflect poorly on the candidate.
They must have been involved in securing the endorsement.
'Might' or 'could' plus the perfect form of the verb (could / might have done) expresses an opinion that you think was probably true at a past moment in time.
Subject + might / could + have + past participle + objects
The bank guarantee could have been available last week.
The bank guarantee might have been valid a year ago.
'Can't' plus the perfect form of the verb (can't have done) expresses the idea that you are almost 100% sure that something was not true at a past moment in time. Note that the form is 'can't have done' NOT 'couldn't have done'.
Subject + can't + have + past participle + objects
Those raw materials can't have been good enough for your project.
A commercial loan can't have been given to that builder.