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.
Example:
David might have kept the expense receipt.
He can't have been able to know that the value of the company common stock price would fall so much.
A commercial loan can't have been given to that builder.
'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
Example:
They must have been involved in securing the endorsement.
This must have been left here on receipt of the order.
'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
Example:
The bank guarantee could have been available last week.
He could have had overdraft protection with the account.
'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
Example:
Those raw materials can't have been good enough for your project.
A commercial loan can't have been given to that builder.