Should it read "The contractor shall provide details of the companies ability with regard to resources" or "The contractor shall provide details of the companys ability with regard to resources"? Is there a need for an apostrophe here?
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If there is one company, use company's ability. If there are many companies, use companies' ability.
The fact that the sentence contains of is irrelevant; of is merely a preposition that governs the noun phrase [the company's ability with regard to resources]. Strip away the modifying phrase [with regard to resources] and you're left with [the company's ability].
In this case, it should be clear that this is a straightforward singular possessive, hence company's rather than any other alternative.