This simplistic answer may not be correct, but I'll take a stab at it.
 
In your sentence, it seems to me that "home" is a condensed substitute for a hypothetical/understood prepositional phrase, as in . . . a trip "to their home." Further, in the fuller hypothetical sentence, there might be something like "The poorest students can't afford [to take] a trip [to their] home[s]." As such, "home" might now be seen more as adverbial, as would the hypothetical prepositional phrase "[to their] home."
 
Just a possibility--don't know for sure if this is accurate.
 
I do like your comment about how grammar, no matter how it is formulated, is not an exact science--an important point to teach students.
 
 
Tim Hadley
Ph.D. candidate, Technical Communication and Rhetoric
Texas Tech University

________________________________

From: Assembly for the Teaching of English Grammar on behalf of Craig Hancock
Sent: Mon 11/1/2004 8:31 AM
To: [log in to unmask]
Subject: a puzzling predicate noun


   I inadvertently put a puzzling sentence on a test and now am stuck trying to explain it.  (I actually welcome a chance to show them that all grammar gets a little leaky in a storm.) 
   "The poorest students can't afford a trip home."  What do I do with "home"?  Trip seems like the head of the noun phrase direct object. In a compound noun, doesn't the head usually come last? Surely a trip home is not the same as a home trip. Is home an appositional narrowing (restrictive)?  (If so, wouldn't the poorest students can't afford home come closer to the mark?) It seems adverbial, but a modifier of trip rather than afford, which doesn't make sense either. (If I took a trip home, I could think of it as complex transitive, but is that true if I can't afford one?) 
   Am I missing something easy and obvious?

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